Acoustic Wave Sensors: Theory, Design

Chapter 1 Why Acoustic Sensors? Precise measurement tools are necessary parts of most successful scientific and engine...

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Chapter 1

Why Acoustic Sensors?

Precise measurement tools are necessary parts of most successful scientific and engineering enterprises. The sensing devices that we consider in this volume are such tools, capable of measuring physical, chemical, and biological quantifies. What they have in common is that they all employ acoustic waves in their operation. The purpose of this introductory chapter is to provide an overview of these devices, and to answer the question: why use acoustic sensors?

1.1

What Is a Sensor?

The sensors we consider here produce an output signal in response to some input quantity, as indicated schematically in Figure 1.1(top). The output signal is usually electrical m an analog voltage or current, a stream of digital voltage pulses, or possibly an oscillatory voltage whose frequency represents the value of the input quantity. The range of input quantities covered in this book is large, including physical quantities such as the mechanical properties of thin films, and chemical and biological quantities such as the concentrations and identities of unknownspecies in air or liquid media. Inside the typical sensor of Figure 1.1(top), a process of transduction takes place, converting the input event into an electrical signal. The sensor may also contain circuitry that converts the often feeble electrical signal from the transduction process into a more robust form suitable for use outside the sensor itself. The output signal may be stored in a computer memory for later examination. Possible applications would have the signal activating an alarm to warn of the 1 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-077460-7

2

1.

Why Acousac Sensors? SENSOR i

i lll

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i

i

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Figure 1.1 Sensor principles. (Top) Schematic diagram of a sensor that produces an electrical output in response to the presence of an input quantity. (Bottom) Biosensor comprising the generic device shown at top with a molecular recognition layer that has a highly selective response.

presence of a toxic vapor, or combining with other signals to provide a physician with information on which to base a medical decision. Sensors are characterized in many different ways. Their sensitivity is a measure of the magnitude of the output signal produced in response to an input quantity of given magnitude; their resolution is a measure of the minimum change of input quantity to which they can respond; and their selectivity characterizes the degree to which they can distinguish one input quantity from another. However, with chemical sensors for vapors or gases, high selectivity is usually desired but often hard to achieve. A telling example is the commercial Taguchi gas sensor for natural gas or propane, which employs a fairly nonselective solid-state process

1.2 The Microsensor Revolution and the Role of Acoustics

3

that takes place at the surface of its heated sensing resistor. When a gas molecule reaches the sensor surface, it can strongly affect the electrical resistance of the element and thus trigger an alarm circuit. According to the manufacturer's instructions, however, the user achieves selectivity by mounting the device high on the wall if natural gas is to be detected, or near the floor if propane sensing is desired---propane being more dense than natural gas! In contrast, with certain biosensors selectivity can be very high. The biosensor may include as a "front end" a biorecognition element which responds to only one biological substance. As illustrated in Figure 1.1 (bottom), the molecular recognition element may contain particular molecules that react with only one other type of molecule. The example in the figure suggests using particular antibodies (the dark cloven objects) that bind to only one type of antigen (the triangularly shaped one). Exploiting this bioselectivity can permit detection of very low concentrations of substances in a very dense background of other molecules.

1.2

The Microsensor Revolution and the Role of Acoustics

The development of integrated circuits reduced the cost of computing, storing, and transmitting information from one location to another. It also made possible very sophisticated yet economical systems to deal with signals from sensors. But until recently, the sensors themselves had not evolved much, and were still fairy large and expensive devices. As an example, a standard device for determining the concentration and identity of unknown vapors was still a heavy, half-meterlong infrared spectrophotometer costing around ten thousand dollars. Sensor development lagged behind that of integrated circuits, and so increasing attention was directed toward the development of inexpensive microsensors. The success of this effort has resulted in the availability of a growing number of microsensors that are now moving from the research laboratories into development, commercialization, and use [1]. The effort worldwide engages many workers, and resulted in more than three thousand references to "chemical sensors" alone in the period from 1985 through 1989. One thread of this work has been the miniaturization of familiar potentiometric and amperometric chemical sensors [2]. Another is the use of optical sensors in which changes in optical index of refraction, amount of absorbance, or intensity of photoluminescence provide chemical or biological information. Yet another part of the effort has been based on acoustics, or more explicitly, the use of elastic waves at frequencies well above the audible range propagating in specially designed solid sensing structures.

4

1. Why Acoustic Sensors?

The first of the acoustic sensors was the so-called quartz crystal microbalance (Fig. 1.2a). The "QCM," as it has been known by chemists, employed a slightly modified quartz crystal made initially to stabilize the frequencies of radio transmitters. The modification that permitted it to be used for chemical sensing was the addition of a sorptive film on the crystal. This device was analyzed and improved by a succession of workers starting in the 1950s [3; 4]. Another advance was made in the late 1970s when Wohltjen and Dessy [5] realized that chemical vapor sensing could be accomplished with a device designed originally for processing purely electrical signals, the surface-acoustic-wave delay line (Figure 1.2b). In this device, acoustic waves are generated and detected with the comblike conducting structures shown at each end of the device; a piezoelectric material in the device substrate converts energy between electrical and mechanical forms at the comblike structures. More recently, two other sensors were introduced that employ similar principles but exploit different modes of elastic wave propagation- the acoustic-plate-mode device (Figure 1.2c) and the flexuralplate-wave device (Figure 1.2d). These devices are conveniently small, relatively inexpensive, quite sensitive, and inherently capable of measuring a wide variety of different input quantities. It is because of these far-reaching characteristics that we have written this book in order to bring a diverse audience of readers an understanding of acoustic sensor principles.

1.3

Where They Fit and How They Are Used

The four types of sensors that we discuss in this book operate over a frequency range of three orders of magnitude - - from less than one to more than one-thousand megahertz. In fact, the frequency spectrum of acoustic waves actually extends to more than eighteen orders of magnitude, as indicated by Figure 1.3 (page 6). This range is nearly as large as that commonly shown in charts of the electromagnetic wave spectrum. Incidentally, Figure 1.3 shows that there are many other types of acoustic sensors designed for purposes ranging from imaging the human heart to detecting cracks in airplane parts [6]. All of the sensors of Figure 1.2 "sense" by producing a change in the characteristics of the path over which the acoustic waves travel; the nature of these changes will be discussed in detail in later chapters. As suggested in Figure 1.4 (page 7), there are several ways of detecting such changes. One is the "active" approach in which one makes the sensor a part of an electronic oscillator circuit

1.3 Where They Fit and How They Are Used Cell with Liquid

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Output Transducer

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Piezoelectric Substrate

_..._~.~~ ~

P =__.._

5

Output

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Piezoelectric Quartz Substrate

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.

(d)

Output

Membrane Sorptive Layer Silicon Substrate Figure 1.2

Schematic sketches of the four types of acoustic sensors discussed in detail in this book: (a) Resonant quartz crystal like that used in electronic communications systems (after Lu [6]); (b) Surface-acoustic-wave delay line with selective absorptive coating (after Wohltjen and Dessy [5]); (c) Acoustic-plate-mode delay line made from quartz crystal (after Ricco and Martin [7]); (d) Thin-membrane flexural-plate-wave delay line made by microfabrication techniques from a silicon wafer.

so that a change in the characteristics of the acoustic path cause a change in the frequency of the oscillator. This approach is a natural one for the quartz crystal resonator (Figure 1.2a), as the resonator was originally made for use in electronic oscillators. In a typical vapor-sensing application, the sorption of vapor molecules in a polymeric coating applied to one surface of the crystal increases the crystal's mass and lowers its resonant frequency and that of the circuit in which it is installed. The active approach is also illustrated with the surface-acousticwave and the flexural-plate-wave devices in Figures 1.2b and 1.2d, where electronic amplifiers are shown connected between input and output transducers of the devices. The alternative approach for getting information from these acoustic sensors is to measure the sensor characteristics passively; that is, to supply an external

6

1. Why Acoustic Sensors?

FREQUENCY

(Hz) 1013 10 I z

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Figure 1.3 Acoustic-wave spectrum. Almost as broad as the familiar electromagneticwave spectrum, the spectrum of acoustic waves that have been excited or detected covers frequencies that range over roughly eighteen orders of magnitude. The four sensors on which we concentrate, indicated by bold lines, range in operation from below 1 MHz to slightly above 1000 MHz.

electrical test signal and determine the response of the sensor to that signal. For example, as shown in later chapters, by measuring the attenuation of the test signal we can determine the viscosity of a fluid that contacts one of these sensors. In the following chapters we discuss these measurement options thoroughly. The most commercially developed of the acoustic sensors we will discuss is the quartz-crystal microbalance. This device is often used in vacuum deposition systems where it measures the thickness of deposited coatings. The commercial sensor shown in Figure 1.5 (page 8) includes a vacuum-tight water cooling system and a microprocessor-based controller that can be set for measuring and indicating the deposition rate and total thickness of films having different densities and sound speeds. Incidentally, hereafter we will refer to this device by the

1.4 About the Authors and the Rest of the Book ,

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more generic name "thickness-shear-mode" (TSM) sensor, since that name emphasizes the mode of propagation instead of the material from which the device is made. The surface-acoustic-wave sensor is also commercially available, either as a single sensor or as a part of an entire sensing system. The authors hope that informing potential users about acoustic sensors may stimulate the wider use of all the sensors that we discuss.

1.4

About the Authors and the Rest of the Book

It will be clear upon skimming through this book that we are dealing with a multidisciplinary subject. The disciplines involved include acoustics, electrical circuits, chemistry, some biology, and a lot of materials science and engineering. In view of this diversity, we have tried to provide plenty of supportive background material. The same multidisciplinary mix characterizes the authors: some are chemists (Ballantine, Ricco, Wohltjen, and Zellers); one is an electrical engineer (Martin);

8

1. Why Acoustic Sensors?

Figure 1.5 Commercial deposition thickness monitor (courtesy Sloan, Inc.) employing AT-cut, 5-MHz quartz crystal in the sensor head at left. Digital control and readout equipment is shown at right. one a chemical engineer (Frye); one an applied physicist working in an electrical engineering department (White); and one works in environmental and occupational health (Zellers, again). Three are academics (Ballantine, White, and Zellers); three work for the U. S. Government (Frye, Martin, and Ricco); and one started and runs his own sensor systems business (Wohltjen). We hope that this diversity is enriching. The remaining chapters have the following functions and contents: Chapter 2 introduces the acoustic principles common to all the devices; Chapter 3 describes the devices in detail and shows how specific input quantities affect the characteristics of the propagation path; Chapter 4 examines the ways these sensors can be used to determine materials properties; Chapter 5 looks at the chemical and biological applications of these sensors; and Chapter 6 deals with practical sensor systems.

References

9

References 1. Muller, R. S.; Howe, R. T.; Senturia, S. D.; Smith, R. L.; White, R. M. Eds., Microsensors; IEEE Press: New York (1990). 2. Madou, M. and Morrison, S. R. Chemical Sensing with Solid-State Devices; Academic Press, New York (1989). 3. Sauerbrey, G. Z. Phys., 155, 206 (1959). 4. King, Jr., W. H. Anal. Chem., 36, 1735 (1964). 5. Wohltjen, H. and Dessy, R. Anal. Chem., 51, 1458 (1979). 6. Lu, C.-S. J. Vac. Sci. Technol., 12, 578 (1975). 7. Ricco, A. J. and Martin, S. J. Appl. Phys. Letters, 50, 1474 (1987).

Chapter 2

Fundamentals of Acoustic Waves

This chapter explores the properties of elastic waves, as well as their electrical excitation and detection in piezoelectric materials. The types of elastic waves we consider, together with the velocities with which they travel, are shown in Figure 2.1. The bulk waves exist in a hypothetical medium which has no boundaries whatsoever. Introducing a single plane boundary that forms a semi-infinite solid permits surface elastic waves to propagate along that single boundary. Adding a second boundary parallel to the first forms a plate, and permits the propagation of plate waves that also have sensor applications. In this chapter we consider elastic wave fundamentals, and then in Chapter 3 we show how each of these wave types can be used in sensors.

2.1

Wave Propagation in an Elastic Medium

An elastic medium behaves as a distributed mass-spring system in which displacement of a single element results in the propagation of a disturbance throughout the medium. A particle at a free surface is different from one interior to the solid, in that it is constrained by adjacent particles from only one side. Thus, disturbances at a surface can behave somewhat differently from those in the interior of a solid. In fact, such boundary considerations give rise to unique modes of propagation that can only exist at the free surface of a solid. Before considering such so-called surface waves, it is instructive to examine plane waves that propagate far from any perturbing boundaries. Just as a mass/spring system oscillates due to the interplay of an inertial force associated with the mass with a restoring force from the spring, an elastic wave 10 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All rights of reproduction in any form reserved. ISBN O-12-077460-7

2.1 Wave Propagation in an Elastic Medium

II

arises from the interplay of distributed elastic and inertial forces. While the mass/spring-system response is described by a differential equation involving mass, displacement and time, wave motion in the solid is somewhat more complex. Like the one-dimensional vibrating string, particle displacement in the solid is a function both of time and position, and the equation of motion must be a localized description. The waves that can propagate in a solid depend upon both the properties of the solid and its boundaries [1]. Figure 2.1 shows schematically the waves that can propagate in an unbounded solid, a semi-infinite solid having a single plane boundary, and in a solid plate that has two plane boundaries. The terminology, definitions and analyses that follow in this chapter are used to determine the nature of these wave motions and the phase velocities of the waves in particular solids.

Surface (Rayleigh) Wave

Bulk Longitudinal Wave

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(b)

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Vp

2 0 0 0 - 1 2 , 0 0 0 m/s Anti Symmetric

Vp = 1 0 0 - 4000 mls

Figure 2.1 Pictorial representations of elastic waves in solids. Motions of groups of atoms are depicted in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, vp, are shown below each sketch. (a) Bulk longitudinal (compressional) wave in unbounded solid. (b) Bulk transverse (shear) wave in unbounded solid. (c) Surface acoustic wave (SAW) in semi-infinite solid, where wave motion extends below the surface to a depth of about one wavelength. (d) Waves in thin solid plates.

12

2.1.1

2. F u n d a m e n t a l s of Acoustic W a v e s

DISPLACEMENT, STRESS, AND STRAIN

Application of force to a solid puts the solid under stress. Stress results in strain l within the solid: atoms or molecules of which the solid is composed are displaced from their unstressed locations. When a solid is deformed, the displacement of each particle from its original position is represented by a displacement vector u(x,y,z,t). In general, the displacement has components, which vary continuously from point to point in the solid, in the x, y, and z directions. A plane wave generates displacements that vary harmonically in the direction of wave propagation; if this is the x direction, for example, it may be represented as [ 1]:

u(x,y,z,t) = (ulx + ugy + u3z)e j(o't-kx),

(2.1)

in which u l, u2, and u3 represent particle displacements in the x, y, and z directions, respectively; x, y, and z are unit vectors in their respective directions; ~ is the angular frequency of the wave (to = 2wf, where f is frequency); j = X / - 1; and k is the wavenumber (k = 2or/A, where A is wavelength). As the name implies, the contours of constant displacement for a plane wave are planes perpendicular to the propagation direction. Figure 2.2 depicts a solid crystalline lattice perturbed by compressional and shear plane waves moving in the positive z direction. Because simple translation of the entire solid is not of interest, this class of motion is eliminated to give a parameter related only to local deformations of the solid; this parameter is the displacement gradient, Vu. The gradient of a vector field Vu is a second-rank tensor, specified by a 3 by 3 matrix. The elements of this displacement gradient matrix are given by (Vu)iy = Oui/Oxj, also denoted ui,j in which i denotes the ith displacement element and j denotes a derivative with respect to the jth spatial coordinate, 2 i.e. [ 1],

Vu =

OullOx OullOy au~laz OuJcgx OuJOy OuJOz ~ . Ou3/cgx Ou3/Oy Ou3/Oz/

(2.2)

The displacement gradient represents changes in interparticle distance as well as local rotations caused by the displacement. Just as the effect of simple translation was eliminated by taking the gradient of the displacement vector, the contributions due to rotations can be eliminated, resulting in a parameter that describes only the local stretching of the solid. This 1Stress is the force/unit area applied to the material, while strain is the dimensionless ratio of the length of the stressed material to its unstressed length. 2For the sake of simplicity in notation, xt, i = 1, 2, 3, will occasionally be used in place of x, y, and z, respectively.

2.1 Wave Propagation in an Elastic Medium

13

Figure 2.2 Plane waves propagating in a solid, showing (a) compressional and (b) shear waves. is accomplished by adding the displacement gradient to its transpose, the result being the strain matrix S, with elements given by [ 1] 1

su = -~(audOxj + Ouj/Ox~).

(2.3)

Strain is the change in length per (unstrained) unit length in the solid as a result of applied stress and can be calculated for any direction in the solid from the

14

2. Fundamentals of Acoustic Waves

strain tensor. For an infinitesimal element having direction cosines (ll, 12,/3), the strain is given by Siylily. Thus, the element Sll represents strain in the x direction, while $22 and $33 represent strains in the y and z directions, respectively. Thus, the diagonal strain terms (Sii) represent axial or compressional strains, while the off-diagonal elements (Sij with i ~:j ) are shear strains. The shear strains physically represent the angular change (in radians) between elements initially in the ith and jah directions. Example 2.1:

Suppose a bar of length L is rigidly fastened at one end at x = 0 and stretched in the x direction, as shown in Figure 2.3, being deformed according to u l --khx, u2 = u3 = O. Derive the elements of the strain matrix.

From Equation 2.2, ul,l = kh, while all the other elements of the displacement gradient are zero. As a result, the only non-zero strain element is S ll = kh. This represents a fractional change in length, in particular an elongation, in the x direction of magnitude kh.

Solution:

To represent completely the state of stress at each point in a solid requires use of a stress tensor, T. Each element of the stress tensor, Tij, represents the i th component of force per area acting on the j~h face of an infinitesimal volume element. T allows the determination of the stress in any direction on any plane

Figure 2.3

Bar under uniaxial strain.

2.1 Wave Propagation in an Elastic Medium

15

interior to the solid. The stress vector acting on a plane with a normal component as specified by the direction cosines (11,12,13) is given by Tijlj.

2.1.2

EQUATION OF MOTION

Definition of stress and strain permits derivation of the equation of motion for elastic deformations of a solid, in particular wave motion. Figure 2.4 shows an elemental volume of an elastic solid. The stresses that exert forces in the x direction of each face are indicated, with the assumption that stress has only changed a small amount ATi across the elemental lengths Ax, Ay, Az. The force exerted on each face is the product of the stress component indicated times the area over which the stress acts. The summation of all of the x-directed forces acting on the cube is thus F1 = [ ( T l l + ATt 1)A1 - Tl tA1] + [(T12 + AT12)A2- TI2A2] + [(TI3 + ATI3)A3- TI3A3].

(2.4)

The area of a face with a normal component in the xi direction is

Figure 2.4 Elemental volume of an elastic solid, showing forces exerted on each face.

16

2. Fundamentals of Acoustic Waves

Ai = Y.j.k ~YkAxJAxk( i , j , k) and its acceleration is i i i - 02ui/Ot2. Newton's law, F = m//, relates net force to acceleration in the x~ direction. The mass of the elemental volume is given by pAxAyAz, where p is the density (mass/volume) of the solid. From Equation 2.4 and Newton's law,

02Ul ATIIAyAz + ATIEAxAz + ATI3AxAy = pAxAyAz Ot2.

(2.5)

Dividing by the volume element AxAyAz and passing to the infinitesimal limit results in a one-dimensional partial differential equation, which can be generalized to all three coordinates:

3 OTij O2u~ Oxj = P " j= l Ot2

Equation of Motion (2.6)

This is the equation of motion for a solid (actually a set of three equations, corresponding to i = 1,2,3), relating inertial forces to the stress gradient. Completion of the characterization of a solid requires postulation of a relationship between stress and strain. It has been experimentally observed that for small deformations, the strain in a body is linearly proportional to the applied stress. In one dimension this is known as Hooke's law, relating the elongation of a spring or elastic material to the tensile force. A principle such as this, which relates stress to strain, is known as a constitutive relation, and can be generalized to three-dimensional, non-piezoelectric solids [ 1]: 3

Tij -" E

ciJkISkl'

Elastic Constitutive Relation (2.7)

k,l=l

in which the Ciykt, called elastic stiffness constants, serve as "microscopic spring constants" in describing what strain results from a given stress. The elastic constants completely characterize the elastic behavior of a solid in the smalldeformation limit. 3

2.1.3

REDUCED NOTATION (ENGINEERING NOTATION)

The four indices of the elastic stiffness constants, cokt, result in the possibility of as many as 34 = 81 elements in the stiffness tensor. Because the stress and strain 3A strain of 10-3 is a large strain, near the fracture strain for many substrate materials. Thus, one might consider that the linear behavior characterized by Hooke's law (or its three-dimensional analog, Equation 2.7) is limited to situations where the strain is 10-5 or less.

2.1 Wave Propagation in an Elastic Medium

17

tensors are symmetric, i.e., Tij = Tji and Sij = Sji, at most six of the nine elements of each tensor can be unique. For this reason, a system has been adopted for reducing the number of indices from two to one [ 1]. In reduced notation, the double index ij is replaced by a single index I as shown in Table 2.1. In equation form, the use of reduced index notation is signified by the use of capital subscripts, as St and/'!. The symmetry properties that allow reduction of the number of entries in the stress and strain tensors also allow reduction of the number of elastic stiffness constants cij~,i in the stiffness matrix. Replacing first the pair ij by a reduced index I from Table 2.1, then replacing kl by a reduced index J from Table 2.1, results in a stiffness matrix requiring only 36 entries in reduced notation: ctj, where I and J range from 1 to 6. Using reduced indicial (engineering) notation, Equation 2.7 is more succinctly expressed as [ 1] 6 T! = ~ cuSj.

Reduced Elastic Constitutive Relation

(2.8)

J = l

The stiffness matrix is also symmetric with respect to the interchange of reduced indices I and J so that for the most general solid, 21 distinct entries (6 diagonal and 15 triangular entries) are required to completely characterize the solid. Since the elastic properties reflect the symmetry of the material, as crystal symmetry increases the number of distinct elastic constants required to characterize the material decreases; for example, the number of independent constants is 6 for a trigonal material, 3 for a cubic material, and 2 for an isotropic material. The nonzero elastic constants for several materials are listed in Table 2.2. We note from Table 2.2 that isotropic materials, such as polyethylene and polycrystalline aluminum, are specified by only two independent elastic constants: c ll and c44. Alternatively, one may characterize the elastic properties of an isotropic medium by Young's modulus and Poisson's ratio, E and v respectively, or by the Lam6

Table 2.1

Reduced Index Notation i

Index ij

Reduced Index I

11

1

33 23or32 13or31

3 4 5

12 or 21

6

ill

|

Matrix Representation

/'6 T2 7'4 /'5 T4 T3

18

2. Fundamentals of Acoustic Waves Mechanical Properties of Selected Materials [1]

Table 2.2

Material Aluminum (polycrystalline) Lithium Niobate Polyethylene Quartz Zinc Oxide ii

ii

i

ii

i

ii

ii

Density

......

(kg/m 3)

Cll

Stiffness (10'~ newtonlmZ)

C33

2695

11.1

4700 900 2651 5680

20.3 0.34 8.674 20.97

i

i

i

ii

r

C12

.......

C13

C14

2.5

i

l

24.5

6.0 0.026 5.794 4.247

10.72 21.09 1

II

I

9

I

I

5.3

7.5

0.699 12.11

1.191 10.51

I

I

0.9

III

-1.791 I

I

II

constants, A and/x. See [2]. Anisotropic crystals, such as lithium niobate, quartz, and zinc oxide, require several more elastic constants.

Example 2.2: Calculate the stress distribution required to obtain the deformation specified in Example 2.1 in a cubic material. Solution: In Example 2.1 it was found that Sll = kh. In reduced notation, St = kh, while $2 through $6 are all zero. Using the reduced notation and the stiffness matrix for a cubic material [ 1]:

T1

Cll

7"2 T3 T4 T5 I'6

1r = |C12 /~ !

Cl2 C12 0 0 Cll Cl2 0 0 0 C12 Cll 0 0 0 0 0 C44 0 0 / 0 0 0 C44 0 0 0 0 0 C44

Sl 0 0 0 0 0

(2.9)

Performing the'matrix multiplication, Tl = cllSl = Cllkh, T 2 "- c12S1 = cl2kh, and/'3 = c 1 2 8 1 "- cl2kh, while all other entries are zero. The point is that in addition to the tensile stress Tl that caused the bar to stretch in the x direction, tensile stresses/'2 and/'3 acting in the y and z directions, respectively, are also necessary in order to obtain the simple strain field of Example 2.1. The reason is that a uniaxial strain typically results in contraction of the material in the transverse directions, causing non-zero strains in the y and z directions, rather than the simple strain field specified in Example 2.1. It is this tendency for a material to transmit strains in one dimension to strains in the other dimension that necessitates a tensorial stress-strain relation.

2.1.4

THE W A V E E Q U A T I O N

From the equation of motion (Equation 2.6) and the elastic constitutive equation (Equations 2.7, 2.8), it is a simple matter to derive the wave equation, which de-

2.1 Wave Propagation in an Elastic Medium

19

scribes the propagation of plane acoustic waves in a non-piezoelectric solid. The symmetry of the strain matrix means that Skl in Equation 2.7 is equivalent to Ouk/OXl. Differentiating Equation 2.7 with respect to xj gives 3

OT o

02uk

3

Z O X j - Z CijkltgxjOx, j= 1 j,k,l= 1

(2.10)

Equating the right-hand sides of Equations 2.10 and 2.6 results in the wave equation for non-piezoelectric, elastic solids [3]: 3

02u~.

02Ui = Z CijklOXJOXl P Ot2 j,k,l=l

Non-piezoelectricWave Equation (2.11)

It should be noted that Equation 2.11 represents a set of three wave equations (i = 1, 2, 3) in the particle displacements ul, u2, and u3, with summation over the indices j, k, and I. The polarization of a wave refers to the direction of particle displacement. In general, the solution to Equation 2.11 consists of three propagating wave types: a quasi-compressional wave, whose principal polarization lies along the direction of propagation, and two quasi-shear waves, each of whose principal polarizations is perpendicular to the propagation direction, as indicated in Figure 2.2. Equation 2.11 looks imposing, but in certain instances it reduces to a very simple set of equations, as illustrated in the next example. Example 2.3: Derive the set of wave equations corresponding to plane wave propagation along the x direction of a cubic crystal. The partial derivatives taken with respect to y and z are zero. Using the stiffness matrix corresponding to cubic symmetry in Equation 2.11 results in the following set of partial differential equations: Solution:

02ul 02Ul P Ot2 = Cll OX2 ,

02u2 p at 2

c92U3

(2.12)

02u2 =

c44 Ox 2 ,

(2.13)

02U3

P Ot2 = c 4 4 0 x 2.

(2.14)

Note that the equations for u; are decoupled in this case and may be solved independently. Equations 2.12-2.14 have three solutions representing acoustic waves having displacements along the x, y, and z directions, respectively. A solution to each of these equations is

20

2. Fundamentals of Acoustic Waves (2.15)

ui(x,t) = uioeJ(oJt-kx),

representing wave propagation in the + x direction: ui is the displacement in the ith direction and Uio is the amplitude. 4 Since Ul lies along the direction of propagation, the solution u i(x,t) represents a compressional wave propagating along the x axis, while u2 and u3 represent two shear waves propagating along +x, as indicated in Figure 2.2(b). Substituting Equation 2.15 into Equations 2.12-2.14 and noting that 02ui/Ox 2 = - k 2 u i and c92ui/c)t2 = -to2ui results in the dispersion relation for the compressional wave: poJ2 = Cl lk 2.

Dispersion Relation

(2.16)

A dispersion relation such as this allows one to calculate the phase velocity 5 of the waves, given by v = r For the compressional wave, Equation 2.16 implies that vl = "V'cll/p, while the dispersion relations for Equations 2.13 and 2.14 indicate that v2 = v3 = (c44/p) 1/2.

Example 2.4:

Calculate the compressional and shear wave velocities in aluminum

and polyethylene. Solution: Using values of c11, c44, and p from Table 2.2 in the equations given above for the compressional velocity (vi) and shear velocity (v2) yields the following:

,=,

Material

vl (m/s) compressional

v2 (m/s) shear

6420 1940

3050 540

Aluminum Polyethylene , .....

,

,

,

,

,

,

,

1,

,1,

,1,

In Example 2.2, Equation 2.11 reduced to equations for three uncoupled modes capable of propagating along the x axis of a cubic crystal. Under such conditions, the propagation direction is referred to as a p u r e - m o d e direction. In general, pure modes result when waves are propagating along a symmetry plane of a crystal and have polarization perpendicular to or parallel to this plane. Also, propaga4The quantity with physical significance is understood to be the real part of the expression for ui. The j in the exponent represents ( - 1)1/2.The exponential can be written in terms of sine and cosine functions using Euler's identity, ejx = cos(x) + jsin(x), from which the displacement is seen to be ui(x,t) = u~ocos(~- kx). A similar approach is used by electrical engineers to represent sinusoidally varying currents and voltages. 5The phase velocity is the speed at which one must travel to keep the phase of a sinusoidal wave at a constant value. The phase of the wave described by Equation 2.15 is the quantity ( ~ - kx).

2.1 Wave Propagation in an Elastic Medium

21

tion normal to or along a rotation axis of a crystal results in pure modes. When the propagation direction is in a direction with lower symmetry, quasi-modes are obtained whose longitudinal and shear components are coupled.

2.1.5

BULK-WAVE DAMPING

In the derivation of the acoustic wave equation (Equation 2.11), no consideration was given to energy loss mechanisms. In general, acoustic waves propagate with diminishing amplitude in a real crystal as a result of several loss mechanisms. Attenuation may arise from such mechanisms as phonon scattering, impurity (or Raman) scattering, and thermoelastic attenuation. Thermoelastic attenuation arises in compressional waves due to heat flow from compressed to expanded regions. The flow of heat is an irreversible process that increases entropy, which in turn can be related to attenuation. Thermoelastic attenuation is proportional to the thermal conductivity of the solid and, while important in metals, is not the dominant damping mechanism in insulators used in acoustic devices. In high-quality, insulating single crystals, the dominant damping mechanism is phonon scattering, which can be treated phenomenologically by introducing a viscous term into the elastic constitutive relation for the solid (Equation 2.8), 6

r~ = ~" (cu& + nuSs),

(2.17)

J=l

in which the viscosity tensor rltj has the same symmetry as the elastic stiffness tensor cu. The following example will serve to illustrate how attenuation may be predicted using this model. Example 2.5: Calculate the attenuation for a y-polarized shear wave propagating along the x axis of a cubic crystal, based on the elastic constitutive relation modified to include viscous damping, Equation 2.17.

In the case of harmonic motion, for which Sj = ja~Sj, Equation 2.17 implies that attenuation may be accounted for by representing the elastic constants cu by complex elastic constants cu + jo~u. (This is analogous to accounting for dielectric loss in electromagnetic and optical waveguides by the well-known method of postulating a complex dielectric constant or a complex index of refraction.) Equation 2.13, the lossless wave equation for this shear wave, becomes Solution:

02u2 p Ot: =

02u2 (c44 + jtor144) Ox2 9

(2.18)

22

2. Fundamentals of Acoustic Waves

The solution to this lossy wave equation is (2.19)

u2(x,t) = A + e j(~-~ri) e -ax,

in which a is the attenuation of the wave. Substituting Equation 2.19 into 2.18 results in the dispersion relation for shear wave propagation in the lossy material: --/90)2 = (C44 + jtor/44)(Ot + jk) 2.

(2.20)

Equating the real parts and then the imaginary parts of this equation yields --pr 2 "- C44(r 2 -- k2) - 2wakr/44

(real)

(2.21)

(imaginary)

(2.22)

and 0 = 2~kc44 + tor/44(ot2 -

k2).

The presence of the viscous damping term results in a second-order perturbation of the wave velocity and a first-order contribution to the attenuation. Since for most materials a ,~ k, Equatio n 2.22 enables solution for the attenuation coefficient a: to2'044 ot = 9 2pv 3 '

(2.23)

in which the viscous term 7144characterizes the damping of this y-polarized shear wave. The important point to note from this example is that the attenuation is proportional to the square of the frequency. This prediction has been borne out experimentally with both bulk and surface waves for a number of materials. Since the loss increases rapidly with frequency, it is important to use high-quality materials for acoustic sensors operating at high frequency.

2.2

Piezoelectricity

The coupling between strain and electrical polarization that occurs in many crystals provides a means for generating acoustic waves electrically. When the structure of a crystal lacks a center of inversion symmetry 6, the application of strain changes the distribution of charge on the atoms and bonds comprising the crystal in such a manner that a net, macroscopic, electrical polarization of the crys-

6A crystal structure with a center of inversion symmetryhas the property that a straight line drawn from any point in the lattice through the center of inversion will meet an equivalent point at an equal distance from that center.

2.2 Piezoelectricity

MECHANICALVARIABLES Strain ~ (2) ~

Stress I (2)

j

23

ELECTRICALVARIABLES ( Displacement

(Field k

(1)

Figure 2.5 Relations among mechanical and electrical variables for a crystal (after Nye [5]). The direct piezoelectric effect is the production of electric displacement by the application of a mechanical stress; the converse piezoelectric effect results in the production of a strain when an electric field is applied to a piezoelectric crystal. The relation between stress and strain, expressed by Equation 2.7, is indicated by the term "Elasticity." Numbers in square brackets show the ranks of the crystal property tensors: the piezoelectric coefficients are 3rd-rank tensors, and the elastic stiffnesses are 4th-rank tensors. Numbers in parentheses identify l st-rank tensors (vectors, such as electric field and electric displacement), and 2nd-rank tensors (stress and strain). Note that one could expand this representation to include thermal variables (see [5]) and magnetic variables.

tal results (see Figure 2.5). Crystals exhibiting this d i r e c t piezoelectric effect always exhibit the c o n v e r s e effect as well, whereby the crystal is strained by the application of an electric field. Of the 32 different crystallographic point groups to which crystalline materials belong, 21 are non-centrosymmetric (have no center of inversion); one of the 21, due to its high symmetry, has all zero piezo-

24

2. Fundamentals of Acoustic Waves

Table 2.3

Material

Symmetry Class

Gallium Arsenide Lithium Niobate Quartz Zinc Oxide

Trig. 3m Trig. 32 Hex. 6ram Cub. 43m

,

,

.,,

,

,

..

,

Piezoelectric Stress Constants

Piezoelectric Stress Constants (coulomb/m z) exl

ex4

exs

eyz

ea

ez3

3.7

2.5

0.2

1.3

-0.573

1.32

0.154 0.171

-.0436 -0.48

,

,

.

,=

i

ii

l

II

Ill

I

I II

I

electric stress constants 7. The remaining 20 piezoelectric point groups are spread among all seven of the crystallographic systems (cubic, hexagonal, etc.), making it impossible to generalize a priori about whether a given material will be piezoelectric unless its crystallographic point group is known. The coupling between electric field and strain can be accounted for by an appropriate modification to the elastic constitutive relation (Equation 2.8), as well as the electromagnetic constitutive relations,

TI = c~fl~ - etj Ey

(2.24)

Piezoelectric Constitutive Relations

and

Di = e~o.Ej + eijSj,

(2.25)

in which eli are the piezoelectric stress constants, having units of charge/(length) 2, Ei are the electric field components, Di are the electrical displacement components, and e0. are the permittivity constants. The above equations, known as the piezoelectric constitutive relations, completely describe the interplay of stress, strain, and electric field in a piezoelectric solid [6]. In these equations, summation over the repeated indices is assumed. The piezoelectric stress matrix (ety) is a third-rank tensor; reduced notation has been applied so that the subscript I (running from 1 to 6) replaces two lower-case subscripts. Thus, 18 piezoelectric constants are necessary to characterize a piezoelectric material in the most general case. The form of ety for various crystal classes is shown in Table 2.3. In general terms, as crystal symmetry increases, the number of unique piezoelectric constants decreases; as mentioned above, crystals possessing at least one center of inversion, including isotropic materials and many cubic crystals, are 7Other common forms of the constitutive relations for piezoelectric media, employing different piezoelectric coefficients, are [1]: E + a,jej s, = ~,jrj r~ = ~ s j - h,jOj o, = d,jTj + e~ej e, =-h,~sj + b~Oj The quantity stj is the compliance of the solid.

2.2 Piezoelectricity

25

non-piezoelectric and thus have piezoelectric constants equal to zero. The manner in which an electric field gives rise to strain in a crystal is best illustrated by an example.

Example 2.6:

Calculate the strain induced in a piezoelectric ZnO crystal by an electric field of I KV/cm applied along the z axis of the crystal, i.e., E = Ezz.

Solution: implies

If the crystal is unrestrained at its surfaces, then/'i = 0 and Equation 2.24 6

3

cuSj = ~ eljEj. y=l j=l

(2.26)

ZnO is a hexagonal material (symmetry class 6mm) with elastic constants as given in Table 2.2 and piezoelectric constants as given in Table 2.3. Applying the matrices appropriate to the crystal class results in the following equations: CllSl + C12S2 + c13S3 -"

el3Ez

cl2Sl + CllS2 + c13S3 = el3Ez c13S1 -I- c13S2 -I- c33S 3 "$4"- $5-

e33Ez

$6 = 0

Solving this set of equations by matrix inversion and using the appropriate elastic and piezoelectric constants for ZnO yields $1 = $2 = (-5.44 x 10 -12 m/V)Ez and $3 = (1.17 x 1O-II m/V)Ez. For the applied field Ez = 105 V/m, the corresponding strains are SI = $2 = - 5 . 4 4 • 10 -7 and $3 = 1.17 • 10 -6. Thus, an electric field along +z results in elongation of the crystal in the z direction and compression along the x and y axes, as indicated in Figure 2.6 (page 26). In fact, the lateral compression is such that the change in unit volume (known as the dilatation and equal to S l + $2 + $3) is nearly zero. These strains are reversed if the electric field direction is reversed. In general, the strains resulting from an applied field increase with the magnitude of the piezoelectric constants e 0 so that lithium niobate, for example, exhibits larger strains than does gallium arsenide for a given electric field. However, the particular strain pattern found depends on the form of the piezoelectric matrix (and hence, on the crystal class involved) as well as the electric field direction.

2.2.1

THE WAVE EQUATION FOR UNBOUNDED PIEZOELECTRIC MATERIALS

From the piezoelectric constitutive relations it is a simple matter to derive the wave equation for piezoelectric media. The piezoelectric wave equation is typi-

26

2. F u n d a m e n t a l s of Acoustic Waves

Figure 2.6

Strain induced in a ZnO crystal by an electric field applied along the z-axis.

cally written in terms of the displacements ui coupled with an electrical potential, if, rather than coupled with the electric field components Ei. Noting that Ek = -Otl~/Oxk, we can write Equation 2.24 as

3 Out 3 04, Tiy = ~ cijkt-~xk + ~1 e q , ~ . k,t= t

=

tgxk

(2.27)

Application of the equation of motion (Equation 2.6) to Equation 2.24 yields 3 y,k,t=;

Cqkl

d2Ui 3 02t~ t92Ui q- ~ eijk = p~. OXktgXj y,k= l OxkOxj tgt2

(2.28)

2.2 Piezoelectricity

27

If Equation 2.28 is compared with the wave equation in non-piezoelectric media (Equation 2.11), the presence of an additional term involving the electrical potential qb is apparent. This term may be considered as a source term responsible for the generation of an acoustic wave by an applied, time-varying electrical potential. 8 Conversely, the wave displacements generate an accompanying electrical potential through which the piezoelectric wave can be electrically detected. Equation 2.28 represents three equations in four unknowns: ul, u2, u3, and tk. A fourth equation may be obtained from Equation 2.26 by noting that in a region with no free charges, the electrical displacement is solenoidal (V 9 D = 0). This implies that OD~/Ox~ = 0 so that Equation 2.28 becomes 3

t92Rl

3

eikl i,k,l= 1 OXkOXi

02t~

~ 6.ik~ "- 0. i,k= 1 OXkOXi

(2.29)

The effect of coupling between displacement and potential in piezoelectric plane waves can best be illustrated by an example. Example 2.7:

Consider the

in a ZnO crystal. Write Solution:

propagation of a z-polarized, x-propagating shear electric field.

wave

the equation(s) describing the

Using the appropriate elastic and piezoelectric matrices, Equations 2.28 and

2.29 lead to

02u3

tgEt~

02u3

c 5 5 0 x 2 q- ex5 O--xT = p Ot2

(2.30)

and

t92U3

t92t~

ex5 0x 2 -- El l ~ x 2 -- 0.

(2.31)

Using the second equation, ~b is eliminated from the first, yielding C55 -t-

2

ex5) t92U3 Ell

t92U3

OX2 = p 0t2 '

(2.32)

while ul and u2 are zero. Note that Equation 2.32 is identical in form to Equation 2.11 with the following substitution for the term in parentheses:

c55 = c55 1 +

ex.__.___~5 = c55(1 + K2).

(2.33)

C55E11

8Note that the source term is non-zero only in regions where it varies spatially. This is an important consideration in the mechanism by which acoustic waves are launched in the thickness-shear mode resonators that we consider later.

28

2. Fundamentals of Acoustic Waves

The stiffness parameter c55 has, in effect, been increased by the factor (1 + K 2) - - - a n effect known as piezoelectric stiffening. The factor K 2 is the electromechanical coupling coefficient for the x-propagating, z-polarized plane wave: 2

ex5

(2.34)

K2 = ~ .

C551[11

Piezoelectric stiffening increases the wave velocity from that obtained in the non-piezoelectric case. Wave velocity is given by v = (c'55/p)It2. Since the factor K2 has' a value of 0.0717, which is much less than unity, the perturbation in wave velocity caused by piezoelectric stiffening can be approximated as: = [(1 -[- K2) 1/2 - 1] ~- K2~ ,

(2.35)

Z

V

leading to a 3.6% velocity increase for the wave considered in ZnO. The coupling factor K 2 is a measure of how strongly the electrical potential and mechanical displacements associated with a wave interact. From Equation 2.31, the electrical potential accompanying the shear displacement u3 is given by ex5 -- - - u ~'11

3.

(2.36)

Thus, the electrical potential is proportional to mechanical displacement, having a value of ~b = ( - 6 . 3 • 10 9 V/m)u3 for ZnO; a shear displacement of 10 A thus leads to a potential of - 6 . 3 volts. This potential has the same wave description as the displacement, = t~od(a't-~),

(2.37)

and is depicted in Figure 2.7. The electric field can be found by differentiating the potential: Ex = -O~/Ox = -jk~. This leads to an electric field described by E =

ik~exSu3x.

(2.38)

Ell

The electric field is along the direction of propagation and 90 ~ out of phase with the particle displacement, as shown in Figure 2.7.

2.2.2

ENERGY DENSITY AND POWER FLOW

Because passage of an elastic wave causes time-harmonic deformation of a crystal, each unit volume through which the wave passes has time-varying potential (strain) energy and kinetic energy. At any point in the crystal, the time-varying

2.2 Piezoelectricity

29

u(x,to)

Z

'~

X

r

X

l

E(x,to)

Z

9

~

9

~

,

-,~

~

--=~0.4.n=

"-

-=~o

4---

-

,~

~

~'

41--

9

-.~

-"

4-

9

~

~X .~

Figure 2.7 Electric field propagating along with mechanical wave in ZnO. potential energy is maximum when strain, or deformation, of the crystal at that point is maximum and the local particle velocity is zero; after one-quarter wave period has elapsed, local deformation of the crystal reaches zero and velocity (hence kinetic energy) reaches its maximum absolute value. Thus, there is an interchange of kinetic and strain energies, much as in a mass-spring oscillator. The instantaneous kinetic energy density (kinetic energy per volume) is given by 3

E

(2.39)

i=1

In this equation, the squares of the particle velocities are summed over the three directions (the subscript being repeated by squaring the quantity). The instantaneous strain energy density (energy per volume) is given by

6 Us =

~ l,J= 1

3 1

,

1 ijki' ~Oui ~ouk ,

ij,k,1 = I-~C

oxj ox,

(2.40)

30

2. Fundamentals of Acoustic Waves

where c' denotes the piezoelectrically stiffened elastic constants in piezoelectric materials. The similarity between this equation and the expression for the energy stored in a compressed spring, Us = -~kx 2, is apparent. In piezoelectric media, the strain energy is multiplied by the factor (1 + K 2) due to piezoelectric stiffening of the elastic constants. Thus, the strain energy includes electrical stored energy in this case. To calculate the magnitude of the electrical energy density Ue independent of the strain energy, the relation lie =

D" E _ 2

~

Di" Ei :~

- -=

(2.41)

is used. Example 2.8: Calculate the kinetic and strain energy densities for the shear wave examined in the Example 2.7. Solution: Since the shear wave is z-polarized and x-propagating, the only nonzero derivative in Equation 2.39 is Oua/Oxt = -jku3. Thus, the strain energy density is given by Us

=

1., { Ou3 ~2 \ Oxl]

=

1 c55k2u 3

(2.42)

and the kinetic energy density is ,2 UK = 1,,~t02 2v "3"

(2.43)

As mentioned previously, the energy stored in crystal deformation becomes kinetic energy one quarter of a cycle later. Thus, an energy conservation principle (known as the Rayleigh principle) applies to waves propagating in a lossless medium: peak strain energy density must equal peak kinetic energy density. One can apply this concept to calculate the wave velocity: an acoustic wave propagates at the velocity for which peak kinetic energy density exactly equals peak strain energy density. Setting Equation 2.42 equal to Equation 2.43 yields the phase velocity: v = to]k = (c'55/p) 1/2.

(2.44)

This agrees with the velocity found by solving the wave equation. It is instructive to calculate the electrical energy density for this problem. As found in Ex-

2.3 P e r t u r b a t i o n s in Acoustic W a v e P r o p a g a t i o n

31

ample 2.2, the only non-zero component of E is Ex. Thus, the peak electrical energy density is 1. E = Ue= - ~ - D

el l (jkexsu3 ]j 2 = /

- - -

2 \

r

k2e2u 2 x5

3

.

(2.45)

2r

Dividing the electrical energy density by the strain energy density yields UE

2 e x5

Us

c'55ell

K2

1 + K z"

(2.46)

The last term is approximately equal to K 2 when K 2 '~ 1. Thus, the electromechanical coupling coefficient (/(2) has a second interpretation: K 2 is approximately equal to the ratio of peak electrical energy density to peak strain energy density.

2.3

Perturbations in Acoustic Wave Propagation

In acoustic-wave sensor applications, one typically detects the change of wave velocity v and/or attenuation a that is induced as the device interacts with the environment. Consequently, it is important to understand how these interactions cause a sensor response. Changes in wave velocity and attenuation can be fundamentally related to changes in wave energy density and power dissipation, respectively. With regard to velocity changes, the power density P (power/area) carded by a wave can be related to the wave energy density U (energy/volume) stored in a lossless medium. Considering a unit cube (Figure 2.8, page 32) through which a wave is passing, the transit time for the wave across the cube is ~"= 1Iv. When the wave passes through the cube, the energy density in the cube increases by the incident power times the transit time: U = P~" = P/v. Thus,

P = Uv.

(2.47)

This relation can be used to relate changes in wave energy density to changes in wave velocity in a lossless medium, i.e., one in which P is constant. Implicitly differentiating Equation 2.47 yields Av V0

= --

AU U0

(2.48) '

where vo and Uo denote unperturbed propagation velocity and energy density,

32

2. Fundamentals of Acoustic Waves

Transit time --

x=l/v---

I -..,

Power --,

,-m

,,--

mm

Density mD

P

I ~

m

m

m

m

/

Stored Energy Density U Figure 2.8 Energy stored per unit volume is dependent upon incident power flow and propagation velocity.

respectively. Equation 2.48 represents a fundamental relation between wave velocity and energy density for a system excited at a given frequency: the fractional change in wave velocity is equal to the negative of the fractional change in wave energy density. This may seem reasonable if one considers that in a system excited at a given frequency, the wavelength adjusts so that the peak kinetic energy equals the peak potential energy of the wave. The result is that changes of the medium that affect the wave energy density will cause changes of the wave velocity. Example 2.9: If a plane wave propagates in a medium in which the mass density changes, how is wave velocity affected? Solution:

The peak kinetic energy density UK is 3 (2.49)

=

i=1

Implicit differentiation of the varying quantities leads to

AUK Ap = . UK Po

(2.50)

2.3 P e r t u r b a t i o n s in Acoustic W a v e P r o p a g a t i o n

33

Thus, from Equation 2.48, the fractional change in wave velocity is minus the fractional change in mass density of the medium: Av

Ap

= - --.

v0

(2.Sl)

190

The preceding analysis will be used extensively in Chapter 3 to derive relations between mass accumulation and wave velocity for acoustic modes other than plane waves. Next, the effect on wave propagation of power dissipation in a lossy medium is considered. From conservation of energy, the power dissipated by the wave Pd (power/volume) must be balanced by a reduction in power transmitted by the wave P. If the wave is propagating in the x direction, then

ed =

OP Ox

-- --'-.

(2.52)

Since energy density and power flow are proportional to the square of wave amplitude, in a lossy medium

P(x) = Po e-2ax,

(2.53)

OP - - 2t~P. ax

(2.54)

so that

Combining Equations 2.52 and 2.54 yields

ed a = 2P"

(2.55)

Equation 2.55 indicates the relationship between wave attenuation and power dissipation in the medium: attenuation is one-half the ratio of power dissipated to power transmitted by the wave. Note that in the derivations of this section, velocity and attenuation changes depend on ratios of energy and power, not on absolute levels. Consequently, in the small-signal limit, velocity and attenuation changes are independent of wave amplitude. It will be seen in Chapter 3 that many perturbations affect wave propagation. In general, perturbations change both energy storage and power dissipation and thus result in a combination of velocity and attenuation changes. The manner in which the propagation of the wave is described is therefore important and will be discussed here briefly.

34

2. F u n d a m e n t a l s of Acoustic W a v e s

The continuous propagation of a wave in the x direction is described generally as

u(x,y,z,t) = u(y,z)ey"-~x,

(2.56)

where y is a complex propagation factor representing both attenuation and wavenumber:

y = a + j k = a + j to

(2.57)

v

If frequency is constant, then changes in wave propagation can thus be represented by Ay = Aot

-

jko Av

(2.58)

v0

or, in normalized form, as [4] A7' =

A7 Aa Av - . , = ko k0 J v0

(2.59)

in which k0 is the unperturbed wavenumber. The latter makes clear that Aa/k and Av/vo are consistently normalized orthogonal components of changes in the complex propagation factor y caused by a generalized perturbation [4]. The dependencies of these quantities on a given perturbation therefore will be the subject of numerous theoretical calculations as well as experimental measurements to be discussed in later chapters. Since perturbations generally involve changes in both stored energy and dissipated power, it is useful to combine Equations 2.48 and 2.55 to define a complex power transfer Prfrom the wave, by the perturbation, that accounts for both power dissipation Pd and changes in stored energy AU:

PT = Pd + j2ooAU.

(2.60)

Using Equations 2.48, 2.55, and 2.59, changes in the complex propagation factor y are related to this complex power transfer [4], Aa ko

A v = Pr J v0 2koP'

(2.61)

giving a general relationship between power transferred from the wave Pr and the resulting changes in the wave propagation factors, Av/vo and Aa/k. It will be demonstrated in Chapter 3 that measuring (or calculating) both Aa/k and Av/vo and plotting these changes parametrically (i.e., one versus the other) often simplifies the representation of a wave perturbation. Since Aa/k and Avlvo

References

35

are orthogonal components of A3", parametric representation is a means of displaying the perturbation in the complex plane, a strategy that often yields a simpler and/or more distinctive form than is characteristic of individual plots of Av/vo or Aa/k.

References 1. Auld, B. A. In Acoustic Fields and Waves in Solids; Wiley: New York (1973). 2. Landau, L. D. and Lifshitz, E. M. Theory of Elasticity, 3rd ed.; Pergamon: New York, Ch. 1 (1986). 3. Brekhovskikh, L. and Goncharov, V. Mechanics of Continua and Wave Dynamics; Springer-Verlag: New York, (1982). 4. Martin, S. J.; Ricco, A. J.; Niemczyk, T. M.; Frye, G. C. Sensors and Actuators, 20, 253-268 (1989). 5. Nye, J. F. Physical Properties of Crystals; Clarendon Press: Oxford (1957). 6. IEEE Standard on Piezoelectricity 176-1987; IEEE Press: Piscataway, NJ (1986).

Chapter 3

Acoustic Wave Sensors and Responses

Devices based on piezoelectric crystals, which allow transduction between electrical and acoustic energies, have been constructed in a number of configurations for sensor applications and materials characterization. This chapter examines those devices most commonly utilized for sensing applications, including the thicknessshear mode (TSM) resonator, the surface acoustic wave (SAW) device, the acoustic plate mode (APM) device, and the flexural plate wave (FPW) device. Each of these devices, shown schematically in Figure 3.1, uses a unique acoustic mode. A distinction can be made between one-port acoustic devices, such as the TSM resonator, and two-port devices, including the SAW, APM, and FPW devices. In one-port acoustic devices, a single port serves as both the input and the output port. The input signal excites an acoustic mode which in turn generates charges on the input electrode. These signals combine to produce an impedance variation that constitutes the TSM resonator response. In two-port devices, one port is used as the input port and the other as an output port; these are typically interchangeable. The input signal generates an acoustic wave that propagates to a receiving transducer, which regenerates a signal on the output port. The relative signal levels and phase delay between input and output ports constitute two responses I.

IAs noted in Chapter 1, with all of these devices one has the option of using the device as part of an active c i r c u i t - one containing an energy source such as a battery m or in a passive manner where one measures the device characteristics by supplying a time-varying probe signal to the device. In the active device measurement mode, one monitors the oscillation frequency. In the passive measurement mode, one might monitor the resonant frequency and quality factor of the quartz crystal resonator of Figure 3.1a; correspondingly, one might measure the phase shift and the attenuation of the APM delay line of Figure 3.1 c.

36 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All rights of reproduction in any form reserved. ISBN O-12-077460-7

t~ O me t~ I= .r

t~ C

t~ "O O t~ r~

Figure 3.1 Schematic sketches of the four types of acoustic sensors. (a) Thickness-Shear Mode (TSM) resonator; (b) Surface-Acoustic-Wave (SAW) sensor; (c) Shear-Horizontal Acoustic-Plate-Mode (SH APM) sensor; and (d) Flexural-PlateWave (FPW) sensor.

38

3. Acoustic Wave Sensors and Responses

Acoustic wave devices are sensitive, to varying degrees, to perturbations of many different physical parameters, both intrinsic to the device and extrinsic. Chemical sensitivity is typically imparted by attaching a thin film to an acoustically active region (i.e., a region having significant acoustic amplitude) of the device surface. Acoustic sensing is possible only when the film (or adjacent medium) interacts with the acoustic modes' Thus, the film must serve as a chemical-to-physical t r a n s d u c e r - one or more of its physical properties must change in response to the presence (and, optimally to an extent proportional to the concentration) of the chemical species to be detected. Clearly, important sensor parameters such as sensitivity, selectivity, reversibility, and durability are critically dependent on this chemically sensitive film, as detailed in Chapter 5. Commonly, the increased mass density of the film, arising from species accumulation, is relied upon for a sensor response. Changes in other film parameters, including elastic and electrical properties, however, can also contribute to the response and must therefore be considered as well. All the acoustic wave devices examined for sensing applications will function in a gaseous or vacuum ambient, but only a subset of them operate effectively when they are in contact with liquids. Acoustic devices that generate primarily shear motion in a liquid, e.g., the TSM resonator and shear-horizontal SH-APM device, can operate without excessive damping. In contrast, devices with substantial surface-normal displacement components (e.g., the SAW device), which radiate compressional waves into the liquid, suffer excessive damping. An exception to this rule occurs for devices utilizing waves that propagate at a velocity lower than the sound velocity in the liquid, e.g., the FPW device. Regardless of the disposition of the displacement components, such modes do not radiate coherently and are thus relatively undamped by liquids. Those modes that do propagate in contact with liquids, while not excessively damped, are nevertheless influenced by liquid properties. The mechanisms whereby all these devices interact with their immediate e n v i r o n m e n t - be it a thin film, a liquid, or both --as well as the resulting response, will be described in this chapter.

3.1

Thickness-Shear Mode (TSM) Resonator

The thickness-shear mode (TSM) resonator, widely referred to as a quartz crystal microbalance (QCM) 2, typically consists of a thin disk of AT-cut quartz with circular electrodes patterned on both sides, as shown in Figure 3.2. Due to the piezoelectric properties and crystalline orientation of the quartz, the application of a voltage between these electrodes results in a shear deformation of the crystal. The crystal can be electrically excited in a number of resonant thickness-shear modes.

3.1 Thickness-Shear Mode Resonator

Figure 3.2

39

Schematic of a thickness-shear mode quartz resonator.

For each of these, displacement maxima occur at the crystal faces, making the device sensitive to surface perturbations. The perturbations to be considered in this section include surface loading by (1) an infinitesimally thick mass layer, (2) a contacting Newtonian fluid, and (3) a viscoelastic layer of finite thickness. The T S M resonator was originally used in v a c u o to measure metal deposition rates [ 1]. More recently, the T S M resonator has been shown to operate in contact with liquids [2,3], enabling its use as a solution-phase microbalance. The device is typically incorporated in an oscillator circuit, where the oscillation frequency tracks the crystal resonance and indicates mass accumulation on the device surface. This microbalance capability has facilitated a n u m b e r of gas- and liquid-phase sensor applications that will be discussed in Chapter 5. W h e n an alternating voltage is applied across the T S M resonator electrodes, shear waves having opposite polarities are generated at the electrodes on the two 2The term "quartz crystal microbalance" is an unfortunate name for this device for several reasons: (1) The word "crystal" is redundant when it follows "quartz," a crystalline material; (2) the devices do not invariably act exclusively as microbalances, being subject to a number of other physical perturbations as well; (3) the name could also correspond to a SAW, APM, or FPW device fabricated from quartz. The term thickness-shear mode (TSM) resonator follows the convention used for the SAW, SH-APM, and FPW notations in that it describes the nature of the acoustic mode upon which the device is based.

40

3. Acoustic Wave Sensors and Responses

faces of the crystal resonator. The waves are generated only at the electrodes because those are the only regions in the crystal where the piezoelectric source term eqkE varies spatially. The displacement Ux in the crystal is a superposition of these waves: Ux(y,t) = (Ae yky + Be-Y~Y)e j'~,

(3.1)

where A and B are constants, r is the angular excitation frequency (r = 2,trf), k is the wavenumber, t is time, and j = (-1)1/2. The resonant condition for the TSM resonator can be determined by tracing the path of one propagating shear wave, shown in Figure 3.3, which may be thought to originate at the top electrode. After transiting the crystal, this wave is reflected (with phase shift due to reflection qbr = r at the bottom crystal face, returns to the top electrode where it again reflects (with ok,.= r phase shift) and is once again propagating downward having experienced a total round-trip phase shift of (2khs + 2fir), where hs is the thickness of the crystal. When this total phase shift is an integer multiple of 2r constructive interference (i.e., coherence) between the incident and return waves leads to crystal resonance. Noting that k = 2r = r where A is acoustic wavelength and vs is the shear wave velocity, this criterion for resonance leads to the following resonance conditions:

and

Nvs fN = 2hs'

(3.2b)

where N is an integer. Equation 3.2a indicates that resonances occur when the crystal thickness hs is a multiple of half the acoustic wavelength A. The shear wave phase velocity vs in the substrate is given by vs =

(3.3)

where/zq and pq are the shear stiffness and mass density, respectively. Equation 3.2b indicates the frequencies at which the family of resonances can be excited, corresponding to various values of the mode index N. A more detailed analysis indicates that the surface electrodes can excite only the odd harmonics, i.e., N = 1, 3, 5 . . . . [4]. Example 3.1: Calculate the fundamental resonant frequency for an AT.cut quartz crystal with hs = 0.033 cm, /xq = 2.95 X 1011 dyne/cm 2, and pq = 2.65 g/cm 3.

3.1 Thickness-Shear Mode Resonator

41

Figure 3.3 Transit of a shear wave, illustrating the resonant condition.

Solution: From Equation 3.3,1:, = 3.34 • 10s cm/s; substituting this into Equation 3.2b gives fl = 5.06 MHz. Having derived the condition for crystal resonance allows the displacement profile at resonance to be calculated. When the crystal is operated in air or vacuum, the crystal faces experience no external restoring force and are considered to be stress-free boundaries; this implies that OUx/Oy = 0 at the upper and lower crystal faces. Applying this boundary condition to Equation 3.1 yields the shear displacement profile across the crystal:

Ux(y,t ) = Uxo cos(kNy) ejoJt,

(3.4)

where Uxo is the surface displacement amplitude and kN = Nrr/hs. Equation 3.4 represents a standing shear wave with maxima at the crystal surfaces. Since displacement varies only across the thickness of the crystal in this one-dimensional model, Equation 3.4 describes a family of thickness-shear modes, each having a unique standing shear-wave pattern across the crystal thickness. Figure 3.4 (page 42) illustrates the mode profiles for the fundamental (N = 1) and third-harmonic (N = 3) resonances. These modes are referred to as "thickness-shear" because the shear displacement varies across the thickness of the device. Note that these modes do not involve any change in the thickness of the substrate. For a typical crystal thickness of 0.33 mm, these modes are excited at approximately 5 and 15 MHz, respectively.

42

3. Acoustic Wave Sensors and Responses

Figure 3.4 Shear displacement profiles across the resonator thickness for the fundamental and the third-harmonic resonances. (Reprinted with permission. See Ref. [9]. 9 1991 American Chemical Society.)

3.1 Thickness-Shear Mode Resonator

3.1,1

43

TSM RESONATOR MASS SENSITIVITY

The presence of displacement maxima at the crystal surfaces makes the thickness-shear mode very sensitive to surface mass accumulation. Mass that is rigidly bound moves synchronously with the crystal surface, perturbing the TSM resonant frequency. The relation between surface mass accumulation and resonant frequency change can be derived from a simple variational principle proposed by Rayleigh [5]: resonance in a mechanical system occurs at frequencies at which the peak kinetic energy Uk exactly balances the peak potential energy Up. This principle is a consequence of the fact that energy is periodically exchanged between kinetic and potential forms at resonance. The accumulation of an ideal mass layer at the crystal surface, which is an anti-node or maximum of displacement, causes an increase in the kinetic energy with no change in potential energy This assumes that the mass layer is sufficiently thin and/or rigid and that displacement is uniform across its thickness, i.e., it acts as an acoustically thin layer. The Rayleigh hypothesis indicates that when mass accumulates on the surface, the resonant frequency must change to rebalance kinetic and potential energies. The peak kinetic energy density Uk (energy per surface area) in the TSM resonator occurs at the instant when particle velocities are maximum and displacements are zero. This energy is found using Equation 2.39 and summing the kinetic energies from infinitesimal slices taken across the crystal thickness, beginning with the infinitesimally thin surface mass layer (electrode mass is neglected): hs

Uk -- ---~

psUxo -t- pq

l Ux(y)

dy ,

(3.5)

where Ps is the areal mass density (mass/area) of the surface mass layer and pq is the volume mass density (mass/volume) of the quartz substrate. Substituting Equation 3.4 into 3.5 and integrating yields

Uk-

u:o( 2

- Ps 4- p q h s

)

.

(3.6)

2

The peak potential energy density Up in the TSM resonator occurs at an instant (depicted in Figure 3.4) when displacement is maximum in the crystal and velocity is zero. From Equation 2.40, this is given by

1. k2uZ fh~ 22 Up = ~l~q XOJo sin2(ky) dy = tzqk 4uxohs "

(3.7)

44

3. Acoustic W a v e Sensors and Responses

Invoking the Rayleigh hypothesis by balancing peak kinetic and potential energy densities (Equations 3.6 and 3.7) gives a relationship between resonant frequency to and surface mass density ps: = 1 +

h,pq

,

(3.8)

where a~o = (NTr/hs)(/Xq/pq) 1/2 is the unperturbed resonant frequency, i.e., that obtained when Ps = 0. For Ps "~. hspq, Equation 3.8 is approximated by a linear relationship:

af fo

=

h,pq

,

(3.9)

indicating that the fractional shift in resonant frequency is equal to the fractional change in mass contributed by the mass layer. This linear approximation to Equation 3.8 has been found to hold for mass fractions up to about 2% [6]. Combining Equations 3.2, 3.3, and 3.9 gives the Sauerbrey equation commonly used to relate changes in TSM resonant frequency to surface mass density Ps [1]:

2f ps Af =

-

([.Lqtoq) l/2 .

(3.10)

E x a m p l e 3.2: (a) If the sensitivity S is defined by S = dfldps, find the sensitivity of a 5 MHz TSM resonator having thickness hs = 0.033 cm and quartz density pq = 2.65 g/cm 3. (b) If the limit of mass resolution is defined as the mass density that gives a frequency shift three times larger than the oscillator fluctuation, and TSM resonator stability is O.1 Hz, calculate the limit of mass resolution.

Solution: (a) From the definition of sensitivity and Equation 3.9, S = dfldps = -fol(pqh) = -57 Hz-cm2/~g. This means that for each 1/zg/cm 2 of mass accumulation, the resonant frequency will decrease by 57 Hz. (b) The limit of mass resolution is the mass density that causes a frequency shift of 0.3 Hz: Rm = 3(AJ)/S = (0.3 Hz)/(57 Hzcm2//zg) = 5 ng/cm 2.

The high mass sensitivity calculated in the previous example justifies the term "microbalance" in describing the sensing capabilities of the quartz resonator. Equation 3.9 can be used to calculate frequency shifts for surface accumulations that behave as ideal mass layers. A real film behaves as an ideal mass layer if it is sufficiently thin and rigid so that it moves synchronously with the oscillating device surface. On a TSM resonator, this condition is realized if the acoustic phase shift ff across the film is small, i.e., ~b '~ ~'. The phase shift is

3.1 Thickness-Shear Mode Resonator

45

where p, G, and h are the film density, shear modulus (assumed real for now), and thickness, respectively. Under this condition, Equations 3.9 and 3.10 can be used to predict the change in frequency contributed by the film, using Ps = ph. Example 3.3:

Does a 1 ton film on a 5 MHz TSM resonator that has G = 101~ dyne/cm 2 and p = 1 g/cm 3 behave as an ideal mass layer? If so, what frequency shift does it cause?

Solution: Substituting film parameters and frequency into Equation 3.11 gives tk--0.03. Since this phase shift is small compared with w, the dominant contribution to the resonator response is due to the film mass and it may be considered an ideal mass layer. Using hq = 0.033 cm and pq = 2.65 g]cm3, Equation 3.9 indicates Af = -5.7 kHz. The previous example illustrates the calculation of frequency shifts caused by films that behave as an ideal mass layer. Section 3.1.9 will describe the treatment when films do not meet this criterion.

3.1.2

ELECTRICAL

CHARACTERISTICS

OF AN UNPERTURBED

TSM RESONATOR

In the previous section we considered the conditions under which mechanical resonances would occur in a TSM resonator. In considering only the mechanical properties of the crystal, however, we neglected consideration of how these resonances would actually be excited or detected. The device uses a piezoelectric substrate material in which the electric field generated between electrodes couples to mechanical displacement. This allows electrical excitation and detection of mechanical resonances. In constructing a practical sensor, changes in resonant frequency of the device are measured electrically. The electrical characteristics of the resonator can be described in terms of an equivalent-circuit model that describes the impedance (ratio of applied voltage to current) or admittance (reciprocal of impedance) over a range of frequencies near resonance. There are two general types of equivalent-circuit models that can be used to describe the resonator: the distributed (or transmission-line) model and the lumped-element model. The distributed model for the TSM resonator is shown in Figure 3.5a, page 46 [7]. This distributed model uses a transmission line to represent the propagation of acoustic energy across the device thickness. The acoustic variables, stress T and particle velocity v, are coupled, via a transformer, to an electrical port. The model thus has two acoustic ports and one electrical port. By terminating the acoustic ports in a mechanical impedance Zs, representing the surface "loading condition," the electrical response of the device is obtained from the model.

46

3. Acoustic Wave Sensors and Responses

(a)

v2

vI

!!';AZ ta,'iI"='-! ~;cJil!

/

-jAZ

sinll(d) T1

T2

-c o

V

(b)

L1

c~

c~ ~:: R 1

m m

Figure 3.5 Equivalent-circuit models to describe the near-resonant electrical characteristics of the resonator: (a) distributed model; (b) lumped-element model. (Reprinted with permission. See Refs. [7;14]. (a) 9 1994 American Institute of Physics and (b) 9 1993 AmericanChemical Society.)

3.1 T h i c k n e s s - S h e a r M o d e R e s o n a t o r

47

With an unperturbed device the surfaces may be considered stress-free boundaries (neglecting electrode mass): T1 = T2 = 0, so that Zs = 0. Thus, the unperturbed condition corresponds to short-circuiting the acoustic ports in the equivalent-circuit model of Figure 3.5a. The distributed (transmission-line) equivalent-circuit model of Figure 3.5a can be reduced to a simpler lumped-element model, shown in Figure 3.5b, to describe the near-resonant electrical characteristics [7]. This lumped-element model is called the "Butterworth-Van Dyke" equivalent circuit [8]. A static capacitance Co arises between the electrodes located on opposite sides of the insulating quartz. A capacitance Cp is included to account for parasitic capacitance that is found to arise in the test fixture: C ~ = Co + Cp. Since the quartz is also piezoelectric, electromechanical coupling gives rise to an additional motional contribution (L l, C1, R l), i.e., one that is associated with the motion of the resonating crystal in parallel with the static capacitance. The static capacitance dominates the electrical behavior away from resonance, while the motional contribution dominates near resonance. This model simulates the TSM resonator electrical characteristics over a range of frequencies near resonance. The elements of the circuit are given by [9]"

Co-

~2A hs ' 8K'2Co

C1-- (Nqr)2, L1 =

1

2

tosC1

,

(3.12a)

(3.12b) (3.12c)

r/q el

-

I&qC1

(3.12d)

where A and hs are electrode area and substrate thickness; tos = 2"n'fs, where fs is the series resonant frequency for the unperturbed TSM resonator; K 2, E2z,/Xq, pq, and r/q are the square of the quartz electromechanical coupling coefficient, dielectric permittivity, shear stiffness, mass density, and effective viscosity, respectively. TSM resonator electrical characteristics are typically described in terms of electrical admittance, defined as the ratio of current flow to applied voltage (the reciprocal of impedance). The total TSM resonator admittance can be determined from inspection of the equivalent circuit model:

Y(to) = jtoC o -~ Zm 1 '

(3.13)

48

3. Acoustic Wave Sensors and Responses

where the motional impedance for the unperturbed resonator is 1

Zm = R1 + jtoLI + -jas ----.

(3.14)

The series resonant frequency fs is defined as the frequency at which the motional reactance is zero, i.e., 1

jtosL~ + . . . . = 0. ja,,C~ Solving Equation 3.15 for tos, and noting that tos = 2r

(3.15) gives

1

fs = 2r

(3.16)

for the unperturbed device. When f > fs, Equations 3.14 and 3.15 indicate that the motional branch has a net inductance. This resonates with the parallel capacitance C o, causing a "parallel resonance." The parallel resonant frequencyfp is defined as the frequency at which the total reactance (motional plus static admittances) is zero:

,[1(,

_,

Figure 3.6 shows the admittance magnitude and phase angle measured near the fundamental resonance of a TSM resonator in air. The figure indicates the series (fs) and parallel (fp) resonances, where the admittance phase angle ( / Y ) is zero and device reactance is zero. The admittance magnitude Irl is near maximum at f~ and near minimum at fp. The solid lines in Figure 3.6 are the admittance magnitude and phase calculated from the equivalent-circuit model (Equations 3.12-3.14) using best-fit values of Co, Cp, fs, and Rl.

3.1.3

ELECTRICAL CHARACTERISTICS OF THE TSM RESONATOR WITH AN ARBITRARY SURFACE PERTURBATION

Piezoelectric coupling between mechanical displacement and electrical potential in the quartz causes the mechanical interactions of a surface perturbation with the TSM resonator to influence the electrical characteristics of the TSM resonator, i.e., the impedance or admittance. By using a continuum model that describes the coupled mechanical displacement and electrical potential, the electrical characteristics can be related to the properties of the perturbing mass or liquid layer [ 10]. The continuum model can be solved to obtain an equivalent circuit that ap-

Admittance Mag., IYI (mS)

Admittance Phase, LY (deg) I

I

I

0

0

0

0

0

0

O

0

r

o

~

~t'rl ! q

q

I

q q

=.

)i,

~'~

(1)

m--

t~

m.

~D ml mlt

~D

O

0

O

01

b

G.

O

4~ ~D

50

3. Acoustic Wave Sensors and Responses

proximates the electrical characteristics of the TSM resonator for excitation frequencies near resonance [9,11 ]. The equivalent circuits (Figure 3.5) can be used to describe the electrical response of the perturbed device. The lumped-element model, Figure 3.5b, is most convenient to use. When the resonator has a surface perturbation, the motional impedance increases, as represented by the equivalent-circuit model of Figure 3.7. This model contains the elements Co*, L1, Cl, and R1 corresponding to the unperturbed resonator. In addition, the surface perturbation causes an increase in the motional impedance Zm, as described by the complex electrical element Ze in Figure 3.7a. This element is given by [12] Ze --

Nrr ( Zs ~, 4K~wsCo \ZqJ

(3.19)

where Zq = (pqlZq)1/2 is the quartz shear-wave characteristic impedance and Zs is the shear mechanical impedance at the device surface [ 13]:

z~ = Txy [

~a.2o)

Vx lY=O

where Txy is the sinusoidal steady-state shear stress (force per area in the xdirection on a y-normal plane) imposed on the contacting medium by the resonator, and Vx is the resulting x-directed surface shear particle velocity. Zs is a complex quantity: the real part, Re(Zs), corresponds to the component of surface stress in phase with the surface particle velocity and represents mechanical power dissipation at the surface; the imaginary part, Im(Zs), corresponds to the stress component 90 ~ out-of-phase with particle velocity and represents mechanical energy storage at the surface. Letting Ze = R2 + jtoL2 allows the complex element Ze to be represented by a real motional resistance R2 and inductance L2, as indicated in Figure 3.7b. From Equation 3.19, the motional impedance elements L2 and R2 can be related to the components of the surface mechanical impedance as [ 14]

N'n" Re(Zs) R2 = 4K2tosCo Zq N~r Im(Zs) L2 = 4K2~2sCo ---:---. Zq

(3.21a)

(3.21b)

The electrical characteristics of the TSM resonator with a generalized surface perturbation can be described by the equivalent-circuit model of Figure 3.7b [ 14]

3.1 Thickness-Shear Mode Resonator

(a)

(b)

__L_k. 1

51

,,, T

ILl

/r

t

Co : =

C1

Co =

==C 1

R1

R1 L2 R2

J, Lumped-elementequivalent-circuit models for the perturbed resonator [ 14]" (a) with complex impedance element Ze, and (b) with motional inductance L2 and resistance R2. (Reprinted with permission. See Ref. [14]. 9 1993 American Chemical Society.) Figure 3.7

with L2 and R2 related to the mechanical impedance contributed by the surface perturbation through Equations 3.21. The electrical admittance of the loaded resonator is as given in Equation 3.13, but with the motional impedance given by: Zm :

(RI + R2) +

jm(L1 +

L2) 4-

1

jmCl

.

(3.22)

Since the series resonant frequency is defined as the point where motional inductance and capacitance resonate, the motional inductance L2 causes a shift in series resonant frequency (relative to the unperturbed case) given by" Afs = -

L2f~ 2(LI + L2)

~"

L2A 2LI

.

(3.23)

The formalism outlined above will be applied to determine equivalent-circuit models for a TSM resonator with (1) an ideal mass layer, (2) a contacting semiinfinite liquid, and (3) a viscoelastic film. By determining the mechanical impedance Z s associated with each perturbation, the equivalent-circuit model arising from each can be obtained. In cases where the perturbation cannot be easily modeled, the procedure can be reversed: the resonator response is used to determine Z s and thereby characterize the perturbation.

52

3.1.4

3. Acoustic Wave Sensors and Responses

E L E C T R I C A L C H A R A C T E R I S T I C S OF T S M R E S O N A T O R W I T H AN IDEAL MASS LAYER

An ideal mass layer is assumed to have an infinitesimal thickness, yet contribute a finite areal mass density to the device surface. In Section 3.1.1, we noted that this criterion holds as long as the acoustic phase shift across the film ff is small compared with ~r. The equivalent-circuit model for the mass-loaded resonator can be determined from the surface mechanical impedance Zs contributed by a surface perturbation. The surface stress required to sinusoidally accelerate a mass layer is [14] Txy = Ps Vxo = jtopsV~o

(3.24)

where Ps is the areal mass density (Ps = ph, where p and h are film density and thickness) contributed by the mass layer, and vxo is the surface particle velocity. From Equation 3.20, the surface mechanical impedance associated with the mass layer is [14]: Z mass layer =

Txy I = jtops. Vx [y=O

(3.25)

Combining Equations 3.19 and 3.25 gives the motional impedance elements arising from the ideal mass layer [9,14]' 2 tosL l ps

N zrps

L2 = NTrN/ t.~qpq = 4g2tosCoN/ ij,qpq R2 = 0.

(3.26a) (3.26b)

Equations 3.26 reflect

the fact that moving surface mass leads to energy storage (L2) but no power dissipation (R2 = 0). Energy stored in the inductance arises from the kinetic energy of the mass layer moving synchronously with the resonator surface. The ideal mass layer causes a shift in the series resonant frequency that can be determined from Equation 3.23 [9]: A.fs ~

L2fs

2

2f sPs = ---'--'--'2LI N~v/12,qpq

(3.27)

reproducing the Sauerbrey equation [ 1] derived in Section 3.1.1. When a mass layer is added to one side of the TSM resonator, the electrical characteristics are changed, as described by the element L2. Figure 3.8 shows the effect of mass loading on TSM resonator admittance near resonance. It is apparent that the major effect of the mass layer is to translate the admittance curves

3.1 Thickness-Shear Mode Resonator

~

53

A

C---t

3.0

L

I~]---- A

B

~. 2.5

B m

9 C m

E

9o

2.0

D 1.5

~.o 0.5

0 i

i

ii1|

i

i

i

t

t

i

I A

90 ~

-

=-;-

=

-

60

'

j

,,

~3o .~

a,,

' 0

B ~

I~

-3o

'

-90 !

i !

, '

4.98

I

'

4.99

I

'

5.00

Frequency

A

._.j-'

'

5.01

(MHz)

Figure 3.8 Electrical admittance vs frequency before and after deposition of a 124 nm Au layer: (A) in air, (B) in water; after Au deposition: (C) in air, (D) in water. (Reprinted with

permission.

See

Ref.

[9]. 9

1991

American

Chemical

Society.)

54

3. Acoustic Wave Sensors and Responses

toward lower frequency without affecting the admittance magnitude. The admittance of the TSM resonator under mass loading can be obtained from the unperturbed case by the addition of the inductance L2 to the motional arm of the equivalent circuit. This element represents the increased kinetic energy contributed by the mass layer moving synchronously with the TSM resonator surface. The solid lines in Figure 3.8 are admittances calculated from the equivalent-circuit model (Equations 3.12-3.14) after adding an inductance value L2 = 188/xH corresponding to the surface mass density of 225/xg/cm 2.

3.1.5 ELECTRICAL CHARACTERISTICS OF THE TSM RESONATOR CONTACTED BY LIQUID The TSM resonator can be operated in liquid to measure either (1) the accumulation of mass onto the surface from the liquid phase, or (2) properties of the contacting liquid itself. In this section we derive the equivalent-circuit model for the resonator contacted by a semi-infinite Newtonian fluid. A Newtonian fluid is one in which the shear stress and the gradient in fluid velocity are related by a constant, independent of amplitude or frequency [15]:

Ovx T x y = - r l Oy

(3.28)

where rl is the shear viscosity of the fluid. The velocity field, vx, generated in a contacting liquid by the in-plane oscillation of the TSM resonator surface is determined by solving the Navier-Stokes equation for one-dimensional plane-parallel flow [ 15,16]:

O2Vx

rl Oy2 = pVx,

(3.29)

where p and r/are the liquid density and shear viscosity, respectively, and ~x = Ovx/Ot. The solution to this equation with an oscillatory shear driving force at the solid-liquid boundary is [15]

Vx(y,t) = Vxoe-Y/S cos ( ~ -

o~t),

(3.30)

where y is the distance from the surface, Vxo is the surface particle velocity and 8 is the decay length for the envelope of the liquid velocity field. Equation 3.30 represents a critically damped shear wave radiated into the liquid by the oscillating TSM resonator surface (Figure 3.9).

too

,.q me t~ gr r gO m/

gh t~ O =

Figure 3.9

Cross-sectional view of a TSM resonator contacted on one side by a liquid. (Reprinted and adapted with permission.

O

See Ref. [14]. 9 1993 American Chemical Society.)

tall L~

56

3. Acoustic Wave Sensors and Responses

The decay length, 8, is [ 16] =

.

(3.31)

The shear stress imposed by the surface on the liquid to generate the velocity field of Equation 3.30 is [14]

OVx [

_ *lVxo (1 + j).

,=o

(3.32)

8

Application of Equation 3.20 and 3.31 to Equation 3.32 yields the surface mechanical impedance due to a semi-infinite liquid [ 14]:

Zs=

topt/)1/2 2

(3.33)

(1 +j).

The motional impedance elements arising from liquid loading are found from Equations 3.21 [9,14,17]:

L2 = ~ R2-

I~qpq

= 4K2tosCo

2tos/Xqpq

(3.34a)

tOsLl ( 2tosprl ) ,/2 Nzr ( p r l ) , / 2 N~r /Xqpq - 4K2Co 2tos/Xqpq

(3.34b)

where we note that R2 --- tosL2 for loading by a Newtonian fluid [ 14]. Equations 3.34 were derived for one-sided liquid contact; for two-sided, L2 and R2 are doubled. The motional inductance L2, representing the kinetic energy of the entrained liquid layer (with effective thickness 8/2), leads to a decrease in the series resonant frequency [14,17] from Equation 3.23 in agreement with the prediction of Kanazawa and Gordon [ 18]:

Af s _~

L zf s _ 2Ll

f 3/2 ( . . p rl .)'/2 N 7rld~qpq

(3.35)

The motional resistance, R2, represents power radiated into the contacting liquid by the oscillating device surface. It can be considered a shear-wave "radiation resistance." This motional resistance leads to resonance damping. Muramatsu et al. [19] and Beck et al. [20] have shown experimentally that the motional resis-

3.1 Thickness-Shear Mode Resonator

57

tance arising from liquid contact is proportional to (pr/) 1/2. Martin et al. have shown that Equation 3.34b accurately predicts the magnitude of the motional resistance for devices with sufficiently smooth surfaces [ 14]. Yang and Thompson [21] have noted that when a TSM resonator is operated in a liquid, fringing electric fields can enter the liquid, making C o sensitive to the dielectric properties of the liquid. This sensitivity, which can be considered to arise from changes in the parasitic capacitance Cp, is especially pronounced when both electrodes are immersed. Tiean et al. [22] have noted that under these circumstances, a parallel conductance must be added to the equivalent-circuit model to account for conduction through the liquid between electrodes. Example 3.4: Calculate the liquid decay length 8, motional resistance R2, and change in series resonant frequency Afs caused by placing water in contact with one face of a 5 MHz TSM resonator having Co = 5 pF. For quartz [231: K 2 = 7.74 • 10-3, pq = 2.65 g/cm 3,/.tq = 2.95 • 1011 dynelcm2; for water: p = 1 g/cm 3, and r / = 0.01 P. Solution: From Equation 3.31, the liquid decay length in water at 5 MHz is 8 = 0.25 ~m. From Equation 3.34b, the motional resistance is 290 ohms; From Equation 3.35, Afs = -713 Hz. The sensitivity of the TSM resonant frequency to liquid properties, illustrated in the previous example, necessitates close control of liquid properties when trying to measure mass accumulation from solution [24]. Liquid viscosity, in particular, varies exponentially with absolute temperature and must be closely controlled to avoid spurious TSM resonator responses. When liquid contacts one face of the TSM resonator, the electrical response of the TSM resonator changes, as described by the elements R2 and L2. Figure 3.10 (page 58) shows admittance-vs-frequency data (points) measured as the density-viscosity product (pr/) of a solution contacting the TSM resonator varies. With increasing pr/, the admittance magnitude plot shows both a translation of the series resonance peak toward lower frequency, and as a diminution and broadening of the peak. The solid lines in Figure 3.10 are admittances calculated from the equivalent-circuit model when best-fit L2 and R2 values are included. The model accurately produces the admittance-vs-frequency curves measured under liquid loading using parameters determined from the unloaded TSM resonator. The translation of the admittance curves arises from the inductance contribution L2; this element represents the kinetic energy of the entrained liquid layer. The broadening and diminution of the resonance peaks arises from the resistance contribution R2; this element represents power dissipated due to radiation of a damped shear wave into the liquid.

58

3. Acoustic Wave Sensors and Responses

3.0

i

A

A

E 2.5 "O .IBr elml

2.0

r

m

3i

1.5 C

C

rm 1.0 e.--.

i

I I I I i.~I I I I I I I !1

i

ii

i

Dry Device

E <

0.5

0.0 90 A

O~

"O

60

O U} .r

a.

30

r

Cl

r e a

E

qD

-30 A -60 4.965

4.970

4.975 Frequency (MHz)

4.980

Figure 3.10 Electrical admittance vs frequency near the fundamental resonance with glycerol (in water) solutions contacting one side of a TSM resonator: (A) 0% glycerol, (B) 40% glycerol, (C) 60% glycerol, (D) 70% glycerol. (Reprinted and adapted with permission. See Ref. [ 14]. @ 1993 American Chemical Society.)

3.1 Thickness-Shear Mode Resonator

3.1.6

59

EFFECT OF SURFACE ROUGHNESS ON TSM RESONATOR LIQUID LOADING

In Section 3.1.5 we noted that in-plane oscillatory motion by a smooth TSM resonator surface generates plane-parallel laminar flow in a contacting fluid. We describe this fluid that is dragged along by the oscillating surface as "viscously coupled." A textured surface, with either random roughness or lithographically defined features, exhibits an enhanced interaction with a contacting fluid. This is evidenced by an increase in motional resistance (R2) and inductance (L2) measured upon liquid contact. Schumacher [25] and Beck et al. [26] have identified one source of this increased solid-liquid interaction: vertical features on the surface constrain or "trap" a quantity of fluid (in excess of that viscously coupled), forcing it to move synchronously with the oscillating surface. This trapped fluid thus behaves as an ideal mass layer, as opposed to a viscously entrained liquid that would undergo a progressive phase lag with distance from the surface. The kinetic energy of trapped fluid leads to an increase in the motional inductance (L2) and frequency shift over that measured with a smooth device. Researchers have also shown that a textured device exhibits increased motional resistance (R2) over a smooth device [27,28]. This is believed to be due to the generation of compressional waves and surface-normal fluid motion by surface asperities that increase power dissipation in the liquid. The electrical response of a liquid-loaded TSM resonator can be related to the , shear mechanical impedance, Zs, at the device surface. This mechanical impedance serves as a quantitative measure of the strength of the interaction between the solid and a contacting liquid. The electrical characteristics of the TSM resonator with a generalized surface perturbation can be described by the equivalent-circuit model of Figure 3.7b. Measurements can be made on a dry TSM resonator to determine C o, LI, Cl, and R1. Fixing these parameters and fitting the equivalent-circuit model to data measured on an immersed device determines R2 and L2. Equations 3.21 can then be used to determine the components of Zs from L2 and R2. Figure 3.11 shows the components of the surface mechanical impedance measured vs the liquid parameter (pr/) 1/2 for several values of surface roughness [ 14]. The real part of Zs represents power dissipation in the liquid by the oscillating device surface; the imaginary part represents energy storage. The dashed line is the mechanical impedance calculated for an ideally smooth surface in contact with a Newtonian liquid (Equation 3.33). For the smooth surface, Re(Zs)= Im(Zs), indicating that peak energy storage is equal to power dissipation. For smooth devices, Equation 3.33 indicates that both real and imaginary parts

60

3. Acoustic Wave Sensors and Responses

of Zs are proportional to (pT/)1/2. This dependence arises from viscous coupling of liquid to the surface. The data in Figure 3.11 show that even for rough devices, these components continue to vary as (pr/) I/2, indicating that viscous coupling occurs even in the presence of surface roughness. For devices with roughness much less than the liquid decay length 8 (0.25 gm in water at 5 MHz), Zs is very close to that predicted for an ideally smooth surface (dashed line). As the roughness scale approaches 8, both real and imaginary parts of Z~ increase, indicating an enhanced solid-liquid interaction. The imaginary part, in particular, shows an offset that increases roughly proportionally with the average surface roughness 3. Since Im(Zs) is associated with energy storage, and this offset has been shown to be proportional to the density of trapped fluid, this effect is attributable to liquid trapping in surface features. Re(Zs) increases more erratically with surface roughness, indicating increased power dissipation by the rough surface. The origin of this increased dissipation is believed to be due to a conversion from plane-parallel liquid flow to surface-normal flow by surface asperities [14]. When the scale of surface roughness is small compared with the liquid decay length 8, roughness has a negligible effect on liquid coupling. In this case, the surface can be considered hydrodynamically smooth [29], contributing a negligible influence on device response. When the roughness scale approaches the liquid decay length & however, the additional response caused by roughness is quite significant. The frequency shift observed with water contact, for example, is more than doubled by an average surface roughness of 240 nm. The role of surface roughness in device response has been frequently overlooked. Several researchers have reported device responses that greatly exceeded that predicted for a smooth device. Rejakovic et al. [30] reported frequency shift enhancements of 1.8-2.6 for 5 MHz devices and 7.1-7.4 for 9 MHz devices. To account for this "excess" response, Thompson and coworkers [31-34] and Haardt [37] have postulated liquid ordering in a layer adjacent to the surface, giving rise to greatly enhanced liquid density and viscosity. Haardt claims viscosity enhancements near the surface of 4.2 times that of the bulk liquid. The results of Figure 3.11, however, indicate that for devices having hydrodynamically smooth surfaces, the measured responses agree well (in comparison with the discrepancies noted above) with those calculated for an ideally smooth surface using bulk values of density and viscosity. Within experimental uncertainties, there is no evidence for enhanced liquid properties near the surface. The changes in device response caused by surface texture can be used to advantage in constructing sensors to measure liquid properties. The response of a 3Average surface roughness was measured using a scanning optical interferometer. See [14].

3.1 Thickness-Shear Mode Resonator

'1 A

O

1

- ".

I

I

I

I

0"(ca~c.)

O <10 nm Z~ 197 nm v 525 nm

61

1

)< V

o"

N" n-

~A

3

O )< V

o"

.~ N E l

2

O

0.0

0.1

0.2

0.3

0.4

0.5

0.6

(p~)V2 (g cm-2 s-1/2) Normalized components of the surface (shear) mechanical impedance Zs (at 5 MHz) vs liquid properties for several surface roughnesses. (Reprinted and adapted with permission. See Ref. [14]. @ 1993 AmericanChemical Society.) Figure 3.11

62

3. Acoustic Wave Sensors and Responses

smooth device depends only on the liquid density-viscosity product (pr/), making it difficult to separately measure fluid density and viscosity with a smooth device. However, the presence of surface texture causes an additional response (due to trapping) proportional to density. By combining smooth- and texturedsurface devices in a single sensor, researchers have demonstrated the determination of both fluid density and viscosity [38]. 3.1.7

SOLID~LIQUID B O U N D A R Y C O N D I T I O N S A N D W E ~ I N G TEXTURED SURFACES

OF

In calculating liquid displacements generated by a resonator surface in contact with a liquid, a non-slip boundary is typically assumed at the interface. This relies on having sufficient interfacial force between the solid and liquid to ensure that the liquid layer adjacent to the solid moves with the solid and that continuity of displacement is maintained across the interface. Since the TSM resonator response is very sensitive to liquid loading, the device is particularly sensitive to the details of solid/liquid coupling. Recent results by Thompson and coworkers [31-34] have called into question whether the non-slip boundary condition rigorously holds under all conditions. They have shown that surface treatments can affect the response of the TSM resonator to liquid loading. In particular, coating the electrode surface with a monolayer of an alkane thiol resulted in significantly smaller frequency shifts due to water loading. The critical parameter, it was believed, was the decrease in the surface's affinity for water: liquid contact angles increased indicating increased hydrophobicity for the treated surface. To explain the change in response with surface treatment, they argue that with a hydrophilic surface, the solid-liquid interaction is sufficiently strong to ensure a non-slip boundary, while a hydrophobic surface gives a weak solid-liquid interaction so that interfacial slip occurs, i.e., a discontinuity in displacement arises at the solid/liquid interface. Interfacial slip would lead to a diminished liquid displacement, resulting in less device response, as observed. While this explanation is plausible, recent results suggest an alternate mechanism for this change in solid/liquid interaction with surface treatment. Martin et al. [14] measured the effect of surface treatments on the liquidloading response with devices having various surface roughnesses. With hydrodynamically smooth devices, the surface treatments used by Thompson et al. had no significant effect on device response. With devices having roughness on the order of the liquid decay length, however, the liquid-loading response was diminished by the hydrophobic surface treatment, consistent with the observations of Thompson et al. The fact that surface treatments only modified the liquid loading of rough devices indicates that the treatments are modifying a response con-

3.1 Thickness-Shear Mode Resonator

63

tributed by surface roughness. The response contributed by surface roughness to the frequency shift (from an increase in motional inductance L2) arises from liquid trapping. Thus, the liquid trapping process is apparently being modified by changes in the liquid contact angle. It is reasonable that liquid trapping by concave surface features should depend on the microscopic liquid contact angle. Capillary forces tend to draw a contacting liquid into concave surface features present in a rough surface, such as pits, crevices, or pores. These capillary forces are stronger for hydrophilic (low contact angle) surfaces than for hydrophobic (high contact angle) ones. Whether the volume fraction of these features that does not contain liquid is filled with air compressed by liquid entry (Figure 3.12a) or only the vapor of the liquid (if the surface is filled from a vacuum or by liquid displacement, Figure 3.12b), the result is qualitatively the same. The extent of liquid trapping is determined by a competition between forces, of which the capillary force is dependent on the microscopic liquid contact angle. Hence, liquid trapping in a rough surface is greater with a hydrophilic surface than with a hydrophobic one. To model the dependence of liquid trapping by a rough surface on the liquid contact angle, we consider a sinusoidally corrugated surface, approximating the surface texture actually produced by a polishing procedure. We further assume that the groove periodicity is equal to the crest-to-trough amplitude. When the surface is initially wet by a liquid, the rapid initial contact of the solid by the liquid can result in the liquid spanning small concave asperities and trapping air. To simplify the analysis, we assume that the entire volume of air below the crests is trapped in the initial wetting process. Upon bridging the crests, the trapped air is compressed by capillary forces, tending to draw liquid into the crevice. The shape of the trapped air bubble after compression is shown for several contact angles in Figure 3.12 (page 64) (dashed lines); liquid lies above the line while air is below. These shapes were determined by simultaneously satisfying the contact angle requirement and balancing the capillary pressure across the interface [39] (AP = y/r where y is the liquid surface tension and r is the radius of curvature of the liquid meniscus) with the pressure increase arising from isothermal compression of the trapped air (AP = Pamb (Vi/Vf- 1) where Pambis ambient pressure and Vi and Vf are the initial and final volumes of the trapped air). With high-energy surfaces (low contact angle), the capillary forces can result in substantial void pressures ~ 20 atm for 0 = 0 in Figure 3.12. It is clear from Figure 3.12 that the amount of liquid penetration depends strongly on the liquid contact angle. In addition, since capillary pressures vary inversely with asperity size, the amount of liquid penetration also depends on the size of the asperity. These trends are shown in Figure 3.13 (page 65) where the volume fraction of the pore filled by liquid is plotted vs the contact angle for

I a_. 120 I m m I m I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I O I I I I I T I I I I I I I I I I I I I I I I I I

\

I

i

tO8

9O

l l l w n w w w ~ I

Om

l l w w w w w w m w m w m m m

I ill

I

III

idl I I

II

0

II

III

#0

i IIi

~ i I

<108

i

iiiI

I i

i

I

ii

III i I

i

I

i

ii iii i i

i

iii

III

ii

III

III

.

iiiiiiii ii i

Illl

.

.

.

I

.

.

.

.

.

b

~

,

__ J. I _ _ - -- I-

~

lI?

I. . . . .

.J. __ - -- J - - - -- - - - - . 7 '

__/

Figure 3.12 Cross-section of a liquid meniscus formed as liquid penetrates into a sinusoidally-textured surface, illustrating contact angle-dependent trapping [14]: (a) with trapped air, and (b) without trapped air. The dashed lines indicate the initial (nonequilibrium) penetration of liquid for the indicated microscopic contact angle. The solid lines indicate the equilibrium penetration, becoming complete for 0 < 108 ~ (upper) or 0 < 117 ~ (lower). (Reprinted with permission. See Ref. [141. 9 1993 American Chemical Society.) 64

3.1 Thickness-Shear Mode Resonator I

1.0

_

~

--"

_

m'

"=

i

I

_

"="

,.

q=,

~

-i

iq=

q~

~

i

iI

i

I i

9

I

0

-I"

"-

i

I

""'

3000

I

-.

I:

3000

.,=4

i

- - 1 0 0 , 1000,

I!

- -

i

I

1000

0.8

i

_

~

100--1 .,,.4

i

65

-.,

0.6

I

%

I I

% I

%

I I

0.4

I %

0

I %

0.2

%%

I I U

0.0

..

. ... I ii

ii Iillll

, i

i

I. . . .

I

I

I

i

~,

,

i I

1.0 I.==4

I=..4 o,=.I

0.8 0

.,=4

0.6 3000 q~

0

100

0.4

0.2

0.0 0

30

60

90

120

150

180

Liquid Contact Angle (deg) Figure 3.13 Variation of liquid penetration into a sinusoidal surface feature (Figurc 3.12) with liquid contact angle [14]. Different curves are obtained for different groove dimensions: peak-to-peak amplitude is indicated in nanomctcrs next to each. (Reprintedwith permission. See Ref. [14]. 9 1993 American Chemical Society.)

66

3. Acoustic Wave Sensors and Responses

various sized asperities. The results demonstrate that, especially for small asperities, there is a critical contact angle where the volume fraction filled drops dramatically. 3.1.8

D Y N A M I C S OF A TSM R E S O N A T O R WITH A VISCOELASTIC F I L M

This section examines the dynamic behavior and the electrical response of a TSM resonator coated with a viscoelastic film. The elastic properties of viscoelastic materials must be described by a complex modulus. For example, the shear modulus is represented by G = G' + jG", where G' is the storage modulus and G" the loss modulus. Polymers are viscoelastic materials that are important for sensor applications. As described in Chapter 5, polymer films are commonly applied as sorbent layers in gas- and liquid-sensing applications. Thus, it is important to understand how polymer-coated TSM resonators respond. 9A film deposited on the TSM resonator surface is subjected to an oscillatory driving force at the TSM resonator/film interface. Typically, the film is bonded to the TSM resonator surface sufficiently well that the base of the film moves synchronously with the resonator surface. However, the upper portions of the film may lag behind the driven surface, as shown in Figure 3.14. The dynamic behavior of the film's shear displacement vs position across the film thickness hf can be predicted from a continuum electromechanical model described by Reed et al. [ 10]. Several distinct regimes of dynamic behavior can be identified [40], determined by the acoustic phase shift, q~, across the film. If the film is sufficiently thin and/or rigid so that ~b ,~ ~'/2, then the entire film tends to move synchronously with the resonator surface, as shown in Figure 3.15a (page 68). In this case, displacement ux is uniform across the film thickness and a negligible strain (proportional to the displacement gradient, Vux = OUx/Oy) occurs in the film. In this regime the device responds, as described in Section 3.1.1, only to the surface mass density ps (product of film thickness and density) contributed by the film. This is because the elastic energy stored in the film, proportional to G'lVUxl 2, and power dissipated, proportional to triG" I V//x [ 2, remain negligible when ~b ,~ 7r/2. This can be referred to as the microbalance regime of operation m where changes in resonant frequency can be monitored to unambiguously indicate the mass/area accumulated on the TSM resonator surface. If the film coating is compliant, resulting in an appreciable phase shift through the thickness of the film, the upper regions of the film tend to lag behind the driven resonator/film interface. Significant shear deformation is induced in the film causing elastic energy to be stored and dissipated. In this regime, film displacement is not synchronous with the driving resonator surface, but varies

3.1 Thickness-Shear Mode Resonator

67

Figure 3.14 Cross-sectional view of a thickness-shear mode resonator with a polymer film coating the upper surface [40]. Shear displacement profiles are shown at maximum excursion. (Reprinted with permission. See Ref. [40]. 9 1991 IEEE.) across the film thickness, as depicted in Figures 3.15b and 3.15c. In this case the resonator no longer functions as a simple microbalance, but resonant frequency and damping depend upon film thickness, density, and shear elastic properties. The sensitivity of the device to these parameters enables the device to be used to extract film properties in this regime [40]. For tk ~< ,r/2, displacement at the upper surface of the film exceeds that at the resonator surface (i.e., overshoot occurs), as shown in Figure 3.15b, but remains essentially in-phase with the driving surface displacement. In this case, the frequency is lower than for the uncoated resonator. For ~b near rr/2, film resonance occurs and the interaction between the resonator and film exhibits characteristics of coupled resonant systems [40]: displacement in the film/resonator system exhibits in-phase and out-of-phase modes, with a concurrent splitting of resonant frequency into two corresponding branches. For th -> ,r/2, the upper film surface is 180 ~ out of phase (Figure 3.15c) and frequency is higher than for the uncoated device. In addition, the system is highly damped in the vicinity of resonance, making sensor operation more difficult. Although it is difficult to directly observe the dynamic behavior of the film, which varies across the film thickness, its influence on the TSM resonator elec-

68

3. Acoustic Wave Sensors and Responses

b

a ,

I

c

|,

ii

p/ I I I I

I I I

/

I

I l l l I I l,

Figure 3.15 The dynamic film response generated by the oscillating resonator surface varies with the acoustic phase shift tk across the film [40]: (a) for ck < < ~'/2, synchronous motion occurs; (b) for tk ~ r overshoot of the upper film surface in-phase with the resonator surface occurs (film resonance occurs when ck = Ir/2); (c) for tk > ~'/2, the upper film surface is 180~ out-of-phase. The film is the thin region at the top; the crystal is below. (Reprinted with permission. See Ref. [40]. 9 1991 IEEE.)

trical characteristics can be more readily determined. By considering the mechanical coupling between the resonator and a film overlay, an equivalent circuit model can be derived that relates the near-resonant electrical characteristics to the film properties. This model allows prediction of how film properties influence the resonant frequency and damping. In addition, in the regime where the film is deformed, measurement of the electrical characteristics of a film-coated resonator can be interpreted to obtain the film's shear storage and loss moduli [40].

3.1.9

ELECTRICAL CHARACTERISTICS OF A TSM RESONATOR COATED WITH A VISCOELASTIC FILM

Chemically sorbent films are commonly coated on TSM resonators to construct gas or vapor sensors. The absorption of species by these films leads to a change in the areal mass density as well as plasticization or softening of the film. Corn-

3.1 Thickness-Shear Mode Resonator

69

monly, however, polymer films are either sufficiently soft to begin with, or become softened by temperature or vapor absorption, that the criterion for considering the film as an ideal mass layer, namely that tk "~ ~r/2, is not satisfied. Then, a more detailed model for the resonator-film interaction must be considered. The equivalent circuit model of Figure 3.7 can be used to describe the nearresonant electrical characteristics of the quartz resonator coated by a viscoelastic film. The surface film causes an increase in the motional impedance, denoted by the complex element Ze. From Equation 3.19, this element is proportional to the ratio of the surface mechanical impedance Zs contributed by the film to the characteristic shear wave impedance Zq of the quartz. The oscillating resonator surface may be considered as a source for shear waves that are radiated into the contacting film. The upper film surface reflects these radiated shear waves downward, so that the mechanical impedance seen at the quartz surface is dependent upon the phase shift and attenuation undergone by the wave in propagating across the film. When the film is rubbery, significant phase shift across the film occurs. Consequently, the coupling of acoustic energy into the film depends upon thin-film interference. The finite thickness of a film on the resonator surface makes the calculation of the mechanical impedance at the surface analogous to that of an appropriately terminated transmission line [41 ]. Noting the correspondence between stress and voltage and between particle velocity and current, the stress-free upper film surface is analogous to a short-circuited electrical transmission line. From this analogy, the input impedance seen at the resonator/film interface is [40]

Zs = Txy [

= Zo tanh ('yhf),

(3.36)

Vx [y=hq where Zo = (Gpf)112 and 3' = Jto(pf/G)ll2; G and pf are film shear modules and density; hq is quartz thickness. Equations 3.19 and 3.36 can be combined to find the change in (electrical) motional impedance that arises from a viscoelastic film on a thickness-shear mode resonator [40]:

Nzr

(Gpf)l/2

. . . . . Id, . qpq Ze . . 4K2tosCo

tanh (Thf).

(3.37)

For lossless films, G" = 0 and Ze is imaginary; in this case, Ze represents energy stored in the film, becoming infinite at film resonance when th = mTr12 (m odd). For lossy films, G" > 0, and Ze becomes complex, with the real part (R2) representing power dissipation in the film and the imaginary part (L2) representing energy storage. The dependence of Ze in Equation 3.37 on ~/hfmakes it difficult to resolve Ze into real elements R2 and L2, except in a few limiting cases.

70

3. Acoustic Wave Sensors and Responses

A condition of film resonance occurs when the acoustic phase shift ~ across the film reaches an odd multiple of 7r/2. This enhances the coupling of acoustic energy into the film, resulting in a greater extraction of electrical energy from the source. Consequently, dramatic changes in the motional impedance occur at film resonance (these arise from the complex Ze contribution (Equation 3.37)). These changes lead to changes in the resonant frequency, Af, and damping, R2, for the coated resonator that can be determined from Ze using Equations 3.21 and 3.23. Figure 3.16 shows the changes in resonant frequency, Af, and damping, R2, as a function of film phase shift tk and loss tangent (G"/G') calculated from Equations 3.21, 3.23, and 3.36. The behavior of Af and R2 with ~ is distinct in each of the regimes of dynamic film response outlined previously: (a) For ~b ,~ 7r/2, Af decreases linearly with ~b and damping is nearly fixed at the uncoated resonator value. (b) For ~b ~ zr/2, Af decreases more rapidly with ~b, while R2 increases from the uncoated resonator value. In this regime, dynamic calculations indicate overshoot of the upper film surface, leading to significant deformation in the film. (c) For ~b ~ 7r/2 (film resonance), Af increases rapidly, while R2 is maximum. The discontinuity that occurs in resonant frequency can be attributed to the abrupt change in mode shapes shown in Figure 3.15 (b and c). Energy dissipation in the film diminishes away from resonance. 3.2

Surface Acoustic Wave (SAW) Devices

The stress-free boundary imposed by the surface of a crystal gives rise to a unique acoustic mode whose propagation is confined to the surface and is therefore known as a sulface acoustic wave (SAW). In 1887 Lord Rayleigh discovered this mode of propagation in which acoustic energy is confined very near the surface of an isotropic solid [5]. This mode, now known as the Rayleigh wave [5], is of interest to seismologists because it is excited by earthquakes. The utility of Rayleigh waves in sensor applications is also due to the surface confinement of energy, allowing them to be excited by surface electrodes [42] in piezoelectric materials and also making the wave extremely sensitive to surface perturbations. In order to satisfy the stress-free boundary condition, coupled compressional and shear waves propagate together in a SAW such that surface traction forces are zero (i.e., T..~ = 0, where .~ is normal to the device surface). The generalized surface acoustic wave, propagating in the z-direction, has a displacement profile u(y) that varies with depth y into the crystal as u(x,y,z,t) = (ux(y)eJ4"l,~ + Uy(y)eJ4~2~+ Uz(y)eJ4J3~)eJ~t-Tz,

(3.38)

3.2 Surface Acoustic Wave (SAW) Devices

71

3500

3000 2500

C

A

A

2000

B

1500 1000 500 0 C

A

-20

N 3: _v

B -40

A -60

-80

-100

I . . . . . . . . . .

0

,

. . . . . . . .

'r

,

rJ2

,,

'3~4

~rdn) Figure 3.16 Variation in resonant frequency (Af) and damping (R2) vs the film phase shift ~b for various values of the film loss tangent (G"/G'): (A) 0.1; (B) 0.25; (C) 1.0. (Reprinted with permission. See Ref. [40]. 9 1991 IEEE.)

where to is the angular frequency (2,n'f); 3' is the complex propagation factor; Ux, Uy, and Uz represent displacement components in the x-, y-, and z-directions, re-

72

3. Acoustic Wave Sensors and Responses

spectively, and ~ the phases of the components with respect to Uz. The component Uy is perpendicular to the surface, Uz is in the direction of propagation, and Ux is transverse to the yz plane (i.e., the sagittal plane). The displacement components ui(y) vary approximately as e -2'ry/x, where )t is the SAW wavelength along the surface and y is distance into the substrate; amplitude thus decays rapidly with distance into the bulk of the crystal. A crosssectional view of the strain field generated by a surface wave propagating along the surface of a crystal is shown in Figure 3.17. The strain energy density, also shown in the figure, indicates that the majority of wave energy is contained well within one wavelength of the surface, which thus acts as a waveguide. At higher frequencies (i.e., shorter wavelengths), acoustic energy is confined more closely to the surface and wave sensitivity to surface perturbations increases. The sensitivity of SAW devices to surface perturbations is dependent upon the wave amplitude at the surface. The wave amplitude can be represented by the surface particle velocities Vxo, Vyo, and Vzo in the x-, y-, and z-directions, respectively. These are listed in Table 3.1 (page 74) for several different substrate materials. For propagation in an isotropic medium or along a pure-mode direction of a crystal (e.g., a plane of symmetry), Equation 3.38 reduces to a Rayleigh wave, characterized by having no transverse component: Ux = 0. Since Uy and Uz are 90 ~ out of phase, the particles move in an elliptical orbit in the sagittal plane; the surface motion resembles that of the ocean under the influence of a passing wave. The presence of the surface-normal displacement component makes the SAW poorly suited for liquid sensing applications. When the SAW medium is contacted by a liquid, this component generates compressional waves in the liquid; the power thus dissipated leads to excessive attenuation of the SAW. 3.2.1

S A W E X C I T A T I O N AND DETECTION

The discovery by R. M. White of the University of California at Berkeley that surface acoustic waves could be excited and detected by lithographically pattemed interdigital electrodes on the surface of piezoelectric crystals [42] has led to widespread use of SAW devices in a number of signal-processing applications. These include frequency filters, resonators, delay lines, convolvers, and correlators [43,44]. A surface acoustic wave (SAW) is most conveniently excited on a piezoelectric crystal using an interdigitated electrode pattern, or interdigital transducer (IDT), as shown in Figure 3.18 (page 75). Application of a voltage between alternately connected electrodes causes a periodic electric field to be imposed on the crystal. When an altemating voltage is applied, a periodic strain field is gen-

3.2 Surface Acoustic Wave (SAW) Devices Probed Film

I~,

"~

73

.._1

STRAIN ENERGY

== 13

Figure 3.17 Deformation field due to a SAW propagating to the right along a solid surface (top) and the associated distribution of potential energy (bottom).

74

3. Acoustic Wave Sensors and Responses Properties of Several SAW Substrate Materials

Table 3.1 9

,

,

,

,,

,

,

,

,,

,

,

,,

i

,,

,

==

,

,

,

,,

,,,

,

,

Substrate Cut

Propagation Direction Quartz ST X Lithium Niobate -y Z Gallium Arsenide Z X + 22.5 ~ ii

i ill

V~o

Vyo

V~o

Propagation Velocity

coP

coP

coP

4~

4Jz

3.158

0.13

1.34

0.88

90

90

0

3.488

0

0.83

0.56

--

90

0

2.763

0.16

1.22

0.91

0

90

0

( x l 0 s cmls)

( x l O-6 cml/Z gt/Z)

(degrees)

ill

erated in the piezoelectric crystal that produces a standing surface acoustic wave. This standing wave gives rise to propagating waves that are launched in both directions away from the transducer; the wavefronts are parallel to the transducer fingers. The transducer operates most efficiently when the SAW wavelength, A, matches the transducer periodicity, d. This occurs when the transducer is excited at the synchronous frequency, defined by fo = vo/d, where Vo is the SAW propagation velocity. As discussed in Section 2.2.1, propagation of a mechanical wave in a piezoelectric medium is accompanied by an associated wave potential, ~b. When the wave is incident on a receiving transducer, this potential induces a current flow in each transducer electrode; these currents combine to produce a current flow in the external detection circuit. The addition of current contributions in the receiving transducer is also optimized when the transducer periodicity matches the acoustic wavelength. Thus, a reciprocity relation holds, as it must for a passive linear device, between the wave and external signals.

3.2.2

INTERDIGITAL TRANSDUCER FREQUENCY RESPONSE

Each transducer finger may be considered to be a discrete source for the generation of surface waves in a piezoelectric medium because the piezoelectrically generated stress varies with position near each transducer finger. A simple trans-

3.2 Surface Acoustic Wave (SAW) Devices

75

fer function relates the continuous wave (CW) voltage V1 applied to a finger and the electrical potential associated with the waves radiated in each direction [43]"

d~+-

I,*sV],

=

(3.39)

where/Xs is a substrate-dependent constant, (h+ is associated with the rightward propagating SAW, while ~b- is a leftward propagating SAW. The parameter/Xs may be considered frequency independent: the frequency response of the transducer arises mainly from interference between finger contributions, and is relatively insensitive to the frequency response of the individual elements. This

r (a) . ,.. V" 9

--!

(b)

' i. x......

o

i

i

i

. . . .

V1

2

II

"3

ii

Transmitter

(c)

i

'

Receiver

,T,TTT

t-

T~~T,

Piezoelectric Substrate .

.

.

.

.

.

.

.

.

.

.

Ill

.

.

.

.

.

.

-!

Figure 3.18 Interdigital transducer, formed by patterning electrodes on the surface of a piezoelectric crystal, for exciting surface acoustic waves: (a) SAW electrical potential, (b) plan view, (c) side view.

76

3. Acoustic Wave Sensors and Responses

approximation is typically made in analyzing wave scattering from an array of elements: the "element factor" is typically considered frequency-independent compared with the "array factor." When an array of fingers is excited, as occurs with an interdigital transducer (IDT), the wave potential for a rightward propagating wave ~+ evaluated at position z is a vector sum of the contributions from each finger: Nf-I

dP+(z)=l~s E

VneJkCz-zn)'

(3.40)

n=O

where zn is the position of the nth finger excited with voltage Vn; Nf is the total number of fingers. Equation 3.40 has the form of a discrete Fourier transform [45] of the sequence Vn. Consequently, the frequency response of the device is proportional to the Fourier transform of the sequence of transducer finger contributions. Schemes have been devised to vary the individual finger contributions in order to achieve a desired frequency response. The interested reader is referred to excellent books on SAW filter design by Datta [43], Morgan [44], and Ristic [46]. If Nf identical fingers are spaced periodically with period d and excited with alternating voltages Vn = (-1)n Vo, Equation 3.40 becomes Nf-I

~b+(0) = IxsVo ~

( - 1)ne-jnkd/2.

(3.41)

n=O

The sum in Equation 3.41 is a geometric series whose elements become unity, and add constructively, when kd/2 = mTr, where m is an odd integer. This condition defines the relationship between SAW wavelength, A, and transducer periodicity, d, for coherent addition, as shown in Figure 3.19. The IDT excites odd harmonics at odd multiples of the synchronous frequency: fm= mfl. Moving away from the synchronous frequency, the addition of components from individual fingers becomes incoherent, giving rise to the frequency response [~+(f)[=

sin (X) X

(3.42)

in which X=

Np~(f - fo)

fo

0.43)

where fo is the transducer's synchronous frequency and Np is the number of IDT periods: Np = Nf/2. The wave potential as a function of the detuning parameter

3.2 Surface Acoustic Wave (SAW) Devices 4-

I-

--

4-

'i,,i i

,ii

--

I ........I I, , ""I, .i

i.~ +x

I

I

I

I

I

I

I

I

I

I

~lJ

I

\lJ

I I I Figure 3.19

+

I

I

77

"-

I

I I

I I

I I

I I

Relationship between transducer periodicity and coherently excited waves.

X, described by Equation 3.23, is shown in Figure 3.20 (page 78). Note that when X is a multiple of 11",th+ is zero ~ a result of complete cancellation between finger contributions. Consequently, the frequency interval B between the first nulls on either side of the synchronous frequency is B -

2

Np

.

(3.44)

Thus, the transducer bandwidth B is inversely proportional to the number of IDT fingers. As will be described in Chapter 4, a narrow bandwidth is desirable for oscillator applications in order to avoid spurious oscillations and to improve stability. The frequency response measured between a pair of transducers having Ao = 32/xm and Np = 50 finger pairs is shown in Figure 3.21 (page 79). The amplitude, shown on a log (decibel) scale, shows the characteristic sin(X)/X behavior. The delay line phase shift q0 is

2 ~rfL q~(f) = k L -

Vo

,

(3.45)

78

3. Acoustic Wave Sensors and Responses

10

X s

m,/I,

i

__._

X-Ir

f,i

--..

Figure 3.20

... L

X

v

The calculated transducer response, sin(X)/X, vs the "detuning parameter,"

X. (Reprinted with permission. See Ref. [46a].)

where L is the path length (center-to-center distance) between transducers. Differentiation of Equation 3.45 shows that the phase slope dq~/dfis proportional to L/A, the transducer separation in wavelengths.

3.2.3

SAW PERTURBATION MECHANISMS

When SAW devices are used for sensors or thin-film characterization, the measured responses arise from perturbations in wave propagation characteristics, specifically wave velocity and attenuation, resulting from interactions between the SAW and a surface layer. Because a SAW propagating in a piezoelectric medium generates both mechanical deformation and an electrical potential, both mechanical and electrical coupling between the SAW and surface film are possible. Consequently, a number of interactions between surface waves and a surface film have been found that give rise to velocity and attenuation responses. SAW-film interactions that arise from mechanical coupling between the wave and film include mass loading caused by the translation of surface mass by the SAW surface displacement, and elastic and viscoelastic effects caused by SAWinduced deformation of a surface film. SAW-film interactions that arise from electrical coupling between the wave and film include acoustoelectricinterac-

50i

--"

-r

"

"'

'~

.......~ . . . . . .

Calculated

' ............ " ........

Insertion

Measured

Insertion

~ ........

Loss

Loss ....... ; .........." ' ' | . . . . . .

80 ~

................

"

t

70

0 8O 0

B~

-r,=r .4..)

(D

r

90

0

,A

100bD--

1

II

,I

t I

4.'1

I

"l

m.

|

r%

gO

"- ,,,,"

110 90

95

100

105

Frequency (MHz) Figure 3.21 See Ref. [46a].)

The frequency response measured between a pair of interdigital transducers. (Reprintedwith

,~---"

#B m.

80

3. Acoustic Wave Sensors and Responses

tions between electric fields generated by the SAW and charge carders in a conductive film. This section examines the velocity and attenuation changes caused by several interactions between SAWs and surface layers. This survey is by no means exhaustive---new interactions are being discovered all the time. 3.2.4

SAW MASS LOADING

The simplest interaction, and the one most utilized for SAW sensor applications, is the response due to changes in the areal/mass density (mass/area) on the device surface. The harmonic motion of the crystal surface caused by the passing surface wave causes particles bound to the surface to be translated in an elliptical orbit in synchronism with the SAW surface displacement. The effect on wave velocity and attenuation of this interaction may be derived from energy considerations. Movement by the wave of a surface layer that is sufficiently thin or rigid that it moves synchronously with the wave causes an increase in the kinetic energy density, U,, of the wave without dissipating any wave energy. From the discussion in Section 2.3, this is expected to change the wave propagation velocity without affecting attenuation. The change in average kinetic energy per area of surface is AUk =

p,.V2

+ V2 yo +

V2zo),

(3.46)

where Vxo, Vyo, and Vzo are the SAW particle velocities at the surface and Ps is the surface mass density. Particle velocities are related to particle displacement u by vi = jtoui. This increase in kinetic energy density results in a decrease in wave velocity, according to Equation 2.48. Combining Equations 2.47, 2.48, and 3.46 yields an expression for the change in wave velocity arising from surface mass loading: ~_~V ~.

Vo

tO

ps

V xo +

v yo +

v zo

tOP

toP

toP

.

(3.47)

Due to the greater confinement of wave energy near the surface that occurs as operating frequency increases, surface particle velocities increase in proportion to (pto)l/2. Thus, the quantities in parentheses (Vio2/toP), being independent of wave amplitude and depending only on the substrate material, remain constant. Slobodnik et al. have tabulated these normalized surface particle velocities for a large number of substrates [47]; parameters for the most commonly used SAW substrates are listed in Table 3.1. Note that for propagation along a crystalline axis of lithium niobate (LiNbO3), two components of par-

3.2 Surface Acoustic Wave (SAW) Devices

81

ticle velocity are generated (in the y- and z-directions). X propagation in the ST cut of quartz (a rotated cut chosen for its desirable temperature characteristics), however, results in three components of particle velocity because of the lack of crystal symmetry. Grouping all the substrate-dependent constants together results in the expression for the mass-induced change in SAW propagation velocity" Av =

Vo

-Cmfop,,

(a.4a)

where the mass sensitivity factor Cm is

Cm=T

2 + .1)2o ~rrVo Vxo . . . . + .V. zo .. toe top toe

(3.49)

Note from Equation 3.48 the frequency dependence of the SAW mass sensitivity: the fractional velocity change Av/vo varies with operating frequency fo. Because the mass layer is assumed (in this case) to be lossless, Equation 2.55 implies that attenuation is unchanged by mass loading. Example 3.5: (a) Calculate the mass sensitivity factor CmfOr a IO0-MHz SAW device on ST-cut quartz. (b) If a SAW device is incorporated in an oscillator loop, so that fractional frequency changes track fractional velocity changes (i.e., Aflfo = Av/vo), calculate the sensitivity S = dfldps. (c) Calculate the limit of mass resolution for a typical SAW oscillator stability of 1 Hz.

(a) Using Equation 3.49 with normalized surface particle velocities (V2xo/oJP, etc.) obtained from Table 3.1, Cm = 1.29 • 10-6 cm2-s/g. (b) The sensitivity calculated for the 100-MHz SAW device is S = dAf/dps = -Cmf2o = - 13 Hz-cm2/ng. (c) The limit of mass resolution is Rm = 3AflS = 3 Hz/(13 Hz-cm2]ng) = 0.23 ng/cm2.

Solution:

The previous example illustrates the superior mass sensitivity of the SAW device in comparison with the TSM resonator: sensitivity is some 200 times larger for the 100-MHz SAW device than for the 5-MHz TSM resonator. Part (b) of the Solution also reveals that mass sensitivity, when expressed in the form df/dps, increases with f2. The velocity and attenuation changes resulting from depositing a mass layer on a 97-MHz SAW device using an ST-cut quartz substrate are shown in Figure 3.22 (page 82). Velocity decreases linearly in this thickness regime, yielding cm = 1.32 • 10 -6 cm2-s[g, in good agreement with the mass sensitivity factor calculated above for a 100-MHz SAW. As predicted from the model, the relative attenuation change (Aa[k, where a is the attenuation and k = 2~r/A is the wavenumber) due to mass loading is negligible in comparison with Av/vo (shown on the same scale).

100

.

.

.

.

=

'

=

.....

= '

i

"=

. . . . . .

~

800.

. . . . .

0

~

>0 "~

<1

700

-100

600

-200

500

-300

400

-400

3oo

-500

200

-600

100

-700

A

_

-1

_

A

&

A

A

A

A

A

t

J

0

1

A

,,

A

&

A

A

I

2

A

,

A

,

A

A

A

I

3

A

A

A

, ,

A

A

I

4

,,

A

A

A

A

0

A

,I,

5

,

,

6

Ps (/gg/cm2) Figure 3.22

Fractional change in SAW propagation velocity and attenuation vs thickness of an evaporated metal film.

(Reprinted with permission. See Ref. [48]. 9 1989 IEEE.)

3.2 Surface Acoustic Wave (SAW) Devices

3.2.5

83

SAW ACOUSTOELECTRIC RESPONSE

When a SAW propagates in a piezoelectric material, it generates a layer of bound charge at the surface that accompanies the mechanical wave. This bound charge is the source of the wave potential ~b discussed previously and also generates an evanescent electric field, shown in Figure 3.23. When a conductive film is deposited onto the SAW medium, charge carriers in the film redistribute to compensate for the layer of bound charge generated by the passing surface wave. The effect of wave/charge-carrier coupling on SAW propagation can be determined from a model that accounts for wave-generated conduction currents in the film and displacement currents in the adjacent dielectric media. The interaction can be visualized by reference to an equivalent-circuit model [48], shown in Figure 3.24. The time-varying surface charge generated by the wave is represented by an alternating-current source. The current generated per area of surface, Io, is

[48] 12 = 2K2 tok2( Eo + Es)P,

(a.5o)

where K 2 is the electromechanical coupling coefficient squared (see Table 3.1), and Eo and ~s are air and substrate dielectric permittivities, respectively; k and P

Figure 3.23 Evanescent electric field generated by a surface acoustic wave propagating along the surface of a piezoelectric crystal. (Reprinted with permission. See Ref. [54]. 9 1989 Elsevier Publishers.)

84

3. Acoustic Wave Sensors and Responses

|

i

ill

9 I1

k(o I F

I

_~l

i

A

'

11

'

'

'IF

io ej(ut AIR SOLID

kE1 i

......... II

........

13 Figure 3.24 Equivalent-circuit model to describe the acoustoelectric interaction between a SAW and charge-carriers in a film overlay. (Reprinted with permission. See Ref. [48]. 9 1989 IEEE.)

are the acoustic wavenumber and power density (power per beam width). Note that the current generated is proportional to K2 and P. Displacement currents generated in the substrate and air arise from capacitances (per area of surface) of k~s and k~, respectively, Conduction currents in the film overlay are accounted for by the shunt conductance k2o's, where ors is

3.2 Surface Acoustic Wave (SAW) Devices

85

the sheet conductivity of the film. The sheet conductivity, ors, of a film is related to the bulk conductivity, or, and film thickness, hf, by ors = orhf. It is simple to derive the changes in velocity and attenuation arising from SAW/thin-film acoustoelectric coupling using the formalism outlined in Section 2.3. In the absence of a conductive film, energy is stored in the evanescent electric field generated by the wave. The complex power flow in this case (into the capacitors k~s and k~o in Figure 3.24) is Parl =

2jo,k(Eo + E,)

9

(3.51)

With a conductive film on the surface, this power flow becomes e r 2 = 2[k2ors + jtok(Eo + Cs)]"

(3.52)

The difference in power flows is the acoustoelectric effect, which is measured as

film conductivity is changed: PT = P r 2 -

12 k2 ors Prl = - - - ~ jtokcs(k2ors + jtokcs) '

(3.53)

where cs = Go + r Substituting Equation 3.50 for Io2 into Equation 3.53 gives the complex power flow, Par. This may be substituted into Equation 2.61 to obtain the change in complex propagation factor, % Equating real and imaginary parts indicates the partitioning of this effect between AV/Vo and A a l k [48]: Av

Vo = Aa k -

2

K2

cr~

2

orzs + (VoCs)2

(3.54a)

K2 VoC~tr~ 2 or2$ + (VoCs)2.

(3.54b)

Equations 3.54 agree with those derived by Datta from field considerations [43]. These equations, plotted vs ors in Figure 3.25 (page 86), have the form of a relaxation response [48]: as ors varies from much less than vocs to much greater, SAW velocity decreases monotonically while attenuation goes through a peak. The magnitude of the acoustoelectric response is proportional to K 2, and is thus substrate dependent. Table 3.2 (page 87) shows that K 9 is much larger for LiNbO3 than for quartz. The peak in attenuation, as well as the maximum rate of velocity decrease, occurs at a critical sheet conductivity defined by orc - VoCs. Referring to the equivalent circuit of Figure 3.24, this behavior can be interpreted physically" the SAW can be regarded as a current source, with a reactive source impedance given by k(~ + Es). Regarding the "load" impedance as kEors, maxi-

1

",

,

'

,"

'

,

'

~'

'

,

9

,

i.

16 .,

14 0

12

r/l mt

-2

10

qp~ |

E

,e

o

0 =1

0 .m

8

ilmm

6

el :3

4

o -5 -6

-7 !,,

-9

-8

I --7

Log(sheet Figure

3.25

film overlay.

I -6

,

,

I "5

conductivity,

,,

I -4

ohm

......

1 "3

,,,

I -2

"1

"1 c m " 1 )

Calculated acoustoelectric velocity and attenuation changes vs the sheet conductivity of a

dk~

r

3.2 Surface Acoustic Wave (SAW) Devices

Table 3.2

87

Acoustoelectric Properties of Several SAW Substrate Materials

Substrate Cut Propagation Direction

Vo ( x l O s cm/s)

Kz (%)

cs (pF/cm)

3.158

0.11

0.5

3.488

4.8

4.6

2.763

0.022

1.2

Quartz ST X Lithium Niobate -Y Z Gallium Arsenide Z X + 22.5 ~

mum power dissipation occurs when the magnitude of the load impedance matches the magnitude of the source impedance, i.e., when ors = ore.

Example 3.6: Deposition of a 100 nm-thick Al film on a LiNb03 SAW device causes sheet conductivity vary from as "~. VoCs to ors ~> vocs. (a) What acoustoelectric velocity and attenuation changes arise from this film? (b) What is the maximum acoustoelectric attenuation (in dB) for a IO0-MHz LiNb03 device with a path length of 100 h?

Solution:

(a) From Figure 3.25 or Equation 3.54a, note that as ors varies from much less than VoCs to much greater, Av/vo decreases by K2/2 = 2.4% = 24,000 ppm. (b) The maximum acoustoelectric attenuation, occurring when ors = VoCs, is Aa/k = K214 = 0.012 or Ac~A = .0754. The attenuation per wavelength in dB is 20 log(e '~A) = 0.65 dB per wavelength. For a device with a 100A propagation path length, the acoustoelectric attenuation is 65 dB, a very substantial loss! The previous example illustrates that the acoustoelectric response can be very significant with SAW devices, particularly those using strongly piezoelectric substrates such as LiNbO3. In fact, the acoustoelectric response can be much greater than the mass loading response in certain instances. Shown in Figure 3.26 (page 88) are the SAW velocity and attenuation responses measured as a nickel film is deposited onto a quartz SAW device [48]. Deposition of the film causes both an acoustoelectric and a mass response. The mass response causes a linear decrease in velocity, with no attenuation change, over the entire thickness range; the acoustoelectric response causes a rapid drop in velocity and a peak in attenuation over the 10 to 3 0 / ~ thickness range.

i,i

tj

'1

'

I

"

|

I

I

'

'

I1'

'~ I

II

i

I I

3.0

&

0

o

2.5 E t:3.

t

~o

&

-200

o

&

&o o& AO&

2.0

f

-400

t~ tXl

l"

m

tt~

to

1.5

o =j

o t~

o r

t

-600

1.0

9

&

o

O m

t~ r~

&

C:T (I) LL

0.5

A &

C

&

<

-800

0

&A&&A&AA,tU~AAAA&AAA A A A J

.....

I

0

_

I

2

......

I

I

4

6

,L

I

8

|

II

10

12

9 I1,, ,,

14

I1

16

II

II

18

20

_~

Time, min Figure 3.26

"0 0

&

m

Measured changes in SAW velocity and attenuation vs metal film thickness, illustrating the acoustoelectric interaction.

(Reprinted with permission. See Ref. [48]. 9 1989 IEEE.)

3.2 Surface Acoustic Wave (SAW) Devices

3.2.6

89

PARAMETRIC REPRESENTATION OF THE SAW ACOUSTOELECTRIC RESPONSE

An interesting parametric relationship exists between Av/vo and At~/k arising from thin-film acoustoelectric perturbations. From Equations 3.29 (a and b) [48],

vo

4=

(3.55)

It is apparent from Equation 3.36 that the acoustoelectric interaction takes on a particularly simple form when At#k is plotted vs AV/Vo, with sheet conductivity as the variable parameter: as Ors increases from zero, a semicircle centered at (AV/Vo, Aa/k) = (-K2/4,0) and having radius K2/4 is traced out [48]. The angular position along the semicircle corresponding to ors is [48]

ors = VoCst a n ( 2 ),

(3.56)

where 0 is the angular displacement along the semicircle with respect to the ors = 0 point. The acoustoelectric response can be isolated from the data of Figure 3.26 by subtracting the mass contribution from the AV/Voresponse; this is accomplished by simultaneously measuring the mass accumulation using a quartz crystal microbalance (which, due to the relatively thick metal electrodes covering both its active surfaces, does not exhibit an acoustoelectric response). This acoustoelectric response, shown in the 7'(Aa/k vs Av/vo) plane in Figure 3.27 (page 90), takes the form of a semicircle as predicted by Equation 3.55. The radius R of the best-fit semicircle is 3.50 x 10 -4, indicating a K 2 value of 1.4 • 10-3, slightly higher than the literature value of 1.1 • 10 -3 for surface acoustic waves on ST-cut quartz [43].

3.2.7

ELASTIC AND VISCOELASTIC FILMS ON A SAW DEVICE

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (ph) contributed by the film the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAWinduced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment.

('3331 686I @ "[817]"J;~I ~ S -uo!ss!uu;xt ql!~ p~ugd=~) "osuods~).l 3.ul:);)[~)olsno;:)l~ oql j o

(todd) ~ 0

00;~-

00~-

uog~u;sozdaz ~.~oumred

V 009-

008-

i•-

== == "=

/.Z's a.m~;A

0

I 9 -.,.

i

1

~-

,-...

I L. 0 q,) r~

-

'

--

I I

-

'

I

I

-OOE

i

3 SO

-

'

00s

0 f,#

<

_.

I I

' 0",

"0 "O

OOl~

3.2 Surface Acoustic Wave (SAW) Devices

91

The mechanical properties of a linear, isotropic material can be specified by a bulk modulus, K, and a shear modulus, G. For an ideal elastic solid, these moduli are real-valued. For real solids undergoing sinusoidal deformation, these are best represented as complex quantities [49]: K = K' + jK" and G = G' + jG". The real parts of K and G represent the component of stress in-phase with strain, giving rise to energy storage in the film (consequently K' and G' are referred to as storage moduli); the imaginary parts represent the component of stress 90 ~ out of phase with strain, giving rise to power dissipation in the film (thus, K" and G" are called loss moduli). The wave energy stored and dissipated in the film depends upon the strain modes generated by the SAW. Two distinct regimes of film behavior can be identified. Films that are thin and rigid behave as acoustically thin: the entire film moves synchronously with the substrate surface, resulting in uniform displacement across the film thickness. Figure 3.28a (page 92) shows the deformation arising in an acoustically thin film. Displacements ui are constant across the film thickness, and only gradients 4 in the plane of the film arise. In Figure 3.28a, the gradient in Uz leads to regions of compression and tension in the film, while the gradient in uy lead to bending. Films that are thick or soft behave as acoustically thick: the upper film portions lag behind the film/substrate interface, causing non-uniform displacement across the film thickness. Figure 3.28b shows the deformation in an acoustically thick film. Displacement varies not only in the plane of the film but also across the film due to inertial lag of the upper film regions. The deformation in an acoustically thick film arises from a combination of both in-plane and cross-film gradients, with cross-film gradients dominating. As shown in Figure 3.28b, the gradient in Uz across the film leads to shear deformation of the film. The regimes in which in-plane and cross-film gradients dominate and the corresponding velocity and attenuation changes will be considered below. Since the strain modes generated in each regime are different and result in distinct device responses, it is essential to understand the regime of operation for any particular measurement. The regime of film operation can be determined from the ratio R of cross-film to in-plane gradients induced by the SAW [50]:

R = Afvoph

Icl

(3.57)

where p, h, and G are the film density, thickness, and shear modulus and A is a substrate-dependent parameter having a value of 1.9 for ST-cut quartz [50]. When the film coating is sufficiently thin (small h) and rigid (large I G I ) in compari4A gradient is defined as the magnitude and direction of the maximal spatial rate of change.

92

3. Acoustic Wave Sensors and Responses

Figure 3.28 Deformation generated by a SAW (a) in an acoustically thin (R < < 1) film, in which in-plane displacement gradients (due to sinusoidal wave variation) dominate, and (b) in an acoustically thick (R - l) film, where cross-film gradients (due to inertial film lag) also arise. (Reprinted with permission. See Ref. [50]. 9 1994 American Chemical Society.) son to the oscillation frequency, such that R ,~ 1, in-plane gradients dominate over surface-normal gradients and the film is acoustically thin. When film properties are such that R -> 1, inertial lag becomes significant so that surface-normal gradients are dominant (Figure 3.28b), and the film is acoustically thick. E x a m p l e 3.7: For a film on a IO0-MHz ST-quartz SAW device, what film thickness h marks the transition from acoustically thin to thick for (a) a glassy polymer film with G' = 10 l~ dyne/cm 2, and (b) a rubbery polymer film with G' = 107 dyne/cm2? Assume p = 1 g/cm 3, G" ~ G ', and A = 1.9.

3.2 Surface Acoustic Wave (SAW) Devices Table 3.3

93

Moduli Associated with the Strain Modes (Figure 3.29) Generated by a SAW in an Acoustically Thin Film (R ,~ 1) [50]. ,

,

,,

,

,

,

,,

,,,

1,

Modulus E~

Strain

Displacement Gradient

Modulus Definition

(in terms of ~, it)

(in terms K, G)

Transverse Shear Bending

OUx/OZ

E (l) = Tt3/(2Sl3)

t~

G

Ouy]Oz

E (2) = T23](2S23)

Longitudinal Compression

OUz/OZ

E (3)

Mode

=

T33]$33

~0

~0

4~(A + p) A + 2/x

4G(3K + G) 3K + 4G

Setting R = 1 in Equation 3.57 and solving for h gives the film thickness at the transition between the acoustically-thin and thick regimes: (a) For ] G I = 10l~ dyne/cm2, h = 1.7/zm; (b) for lG ] = 107 dyne/cm2, h = 1.7 nm.

Solution:

If the film is acoustically thin (R ,~ 1), then displacements are constant across the film thickness, and only gradients in the plane of the film arise. The SAWinduced film deformation can be decomposed into three translations (in the x-, y-, and z-directions) and three strain modes, as shown in Figure 3.29 (page 94). An important parameter in determining the contribution of each strain mode in perturbing SAW propagation is the modulus E (i) - - t h e ratio of stress to strain associated with each strain mode in Figure 3.29. These moduli are listed in Table 3.3 in terms of the intrinsic elastic properties of the film, represented in terms of the Lam6 constants (A,/z) and the bulk and shear moduli (K, G). These sets of moduli are interrelated [51 ].

3.2.8

SAW RESPONSE FROM ACOUSTICALLY THIN FILMS

Changes in SAW propagation velocity and attenuation are determined by the mechanical impedances at the substrate/film interface resulting from film translational and strain modes. The impedance associated with each film translation is floph, and with each strain mode is -joohE~i)/V2o, where E (i) are taken from Table 3.3. Thus, from a perturbation analysis, the change in SAW propagation arising from acoustically thin films is [50]: A T = Ao~ ko ko

Av =jcoh Ci p J Vo i=1

~

Vo

(3.58)

94

3. Acoustic Wave Sensors and Responses

Y a

. . . . . . . .

i

,

IU x

-Z

X

Y b

-Z

X

C

L

!

-Z

X

Figure 3.29 Strain modes generated in an acoustically thin (R < < 1) film due to sinusoidal variation in the direction of propagation of the three displacement components. (Reprinted with permission. See Ref. [50]. 9

American Chemical Society.)

3.2 Surface Acoustic Wave (SAW) Devices

95

where the SAW-film coupling parameter ci v z/(4koP): Vio denotes the surface particle velocity (related to surface displacement Uio by Vio = jtOUio) in each direction, and P is the SAW power density (power flow per beam width). The ci parameters, given in Table 3.4 for X-propagation in the ST-cut of quartz, are determined for SAW propagation in the uncoated substrate and are assumed to be unchanged by the film. Each displacement component contributes two terms to Equation 3.58: one, proportional to p, arises from the kinetic energy associated with film translation; another, proportional to E (i), arises from the potential energy associated with film strains (modes shown in Figure 3.29). The kinetic contribution causes a SAW velocity decrease in proportion to film mass per area ( p h ) ~ the mass loading contribution. Equating real and imaginary parts of Equation 3.58 yields velocity and attenuation changes resulting from the SAW/film interaction. With elastic films, the intrinsic elastic moduli are real, resulting in real Ea~ and imaginary A3,/ko, so that Aa/ko = 0. Substituting the E a) expressions written in terms of the Lam6 constants (A,/z) from Table 3.3 into Equation 3.58 yields the Tiersten formula [52] --"

Av •o

io

z)] oJh[ Cl( /9 ) _~Vo + c2p + c3( /9 _ 4/z2 AA++ /2/x 11o

(3.59)

that gives the SAW velocity change contributed by an acoustically thin (R ,~ 1), elastic (K" = G" = 0) film. While Equation 3.59 does not apply to viscoelastic films, the velocity and attenuation arising from acoustically thin, viscoelastic films can be determined from Equation 3.58 by inserting complex moduli (e.g., K and G) into the Er expressions.

Table 3.4 SAW-Film Coupling Parameter ci and Phase Angles ~i for SAW Propagation in the X-direction of ST-cut Quartz [47] , , . ,

,.

,

,

Displacement Component

,

ci (•

i,

.

,

,..,

i

VZol(4koP) -z cmZ-s/g)

Uz .

.

.

.

.

.

.

.

.

.

.

.

.

, ,

,,

. . . . .

~, (deg)

0.013 1.421 0.615

Ux Uy

.

90 90 0 ,

,

,

,,,

96 3.2.9

3. Acoustic Wave Sensors and Responses S A W R E S P O N S E F R O M A C O U S T I C A L L Y THICK F I L M S

Next, we focus on a portion of the film that is small in lateral extent compared with the SAW wavelength. As the wave passes a fixed point, the lower surface of the film oscillates in response to the sinusoidal SAW surface displacement. If the film is acoustically thick (R > 1), the upper portions of the film tend to lag behind the driven substrate/film interface, inducing strains across the thickness of the film. This inertial deformation of the film results in nonuniform displacement across the film. The perturbations of SAW velocity and attenuation caused by the film are related to the mechanical impedances experienced by the surface displacement components in deforming the film. In the acoustically thick regime, film displacement may be thought to arise from a superposition of waves generated at the substrate/film interface and radiated into the film (Figure 3.30). The upper film surface reflects the radiated waves downward so that the mechanical impedance seen at the substrate/film interface is dependent upon the phase shift and attenuation undergone by the waves in propagating across the film. Consequently, a distributed model is used for the film, in which the impedance at the lower film surface depends upon the nature of the interference between the waves generated at the lower film surface and those reflected from the upper (film/air) surface. From the aforementioned considerations, a perturbational formula can be derived for the SAW velocity and attenuation changes, applying to either acoustically thin or thick viscoelastic films [50]:

A'y_ A~

~V

~ ci[3iMi

. . . . . . = ~., ko ko J Vo i=1

where

to

tanh (jflih).

2 ( P- E(i)/Vo)l/2

fli = to "

Mi

(3.60a)

(3.60b)

with Ml = M3 = G, while M2 = K; qJi and Ea~ values are as given in Tables 3.3 and 3.4. Calculating the sum in Equation 3.60a and equating real and imaginary parts determines Aa/ko and AV/Vo. The fli factors in Equations 3.60 represent propagation constants for waves with polarization direction xi propagating across the film (Figure 3.30): fl~ and f13 are associated with shear waves generated by the in-plane surface displacements Uxo and uzo, respectively;/32 is associated with a compressional wave generated by the surface-normal displacement Uyo. The response given by Equation 3.60 is largely determined by the phase shifts 4~i = Re{ flih}, where Re{ } denotes the real part of the complex expression. For

3.2 Surface Acoustic Wave (SAW) Devices

97

Air h Film

131

13 3

~2

#

Uy all

m,m

m,m

IBm

UZ m,,,,

>z

Figure 3.30 Displacement in the film is a superposition of waves generated at the substrate/film interface by the surface displacements Uio and radiated across the film. The surface-normal component Uyo generates compressional waves, while the in-plane components (Uxo, Uzo) generate shear waves. (Reprinted with permission. See Ref. [50]. 9 1994 American Chemical Society.)

elastic films, ffi ~ tlr3 ~ toh(p/G') 1/2 and t]~2~ toh(p/K') t/2. For polymer films, K' remains in the vicinity of 10 l~ dyne/cm 2 in both glassy and rubbery states, so that the compressional wave phase shift 4~2 remains small (<'r r/2) for typical polymer thicknesses. Thus, polymer films remain acoustically thin with regard to compressive displacement (Uyo) applied to the lower film surface. Since G' can be as low a s 1 0 7 - 1 0 8 dyne/cm 2 in rubbery polymer films, with ~bl and th3 reaching at/2 for films as thin as 80 nm (at 100 MHz), films do not remain acoustically thin with regard to shear displacements applied to the lower film surface. Since ca >> cl, in ST-cut quartz, ~b3 dominates the viscoelastic contribution to the response. Figure 3.31 (page 98) shows the attenuation and velocity responses calculated from Equation 3.60 vs the shear wave phase shift q~3 for various values of a film loss parameter r3. The loss parameter ri -- -Im(fli)/Re(fli) describes the intrin-

3. Acoustic Wave Sensors and Responses

98

sic lossiness of the film as experienced by the xi-polarized wave. This parameter, a ratio of power dissipation to energy storage, is analogous to a loss tangent, taking on values between 0 and 1 for all viscoelastic materials: ri = 0 for an elastic film and increases toward 1 for purely viscous films.

0.1 A olam

:3

0.2

es lb.

0.4

0.1 e u

0.4

c

.0 Im

0 o

-1

<3

-2 -3 -4 0.00

0.25

0.50

0.75

1.00

~31/I; Figure 3.31 Contributions to SAW velocity and attenuation vs the shear wave phase shift ~ for several values of the film loss parameter r 3. The dashed line is predicted from the Tiersten formula (Equation 3.59). (Reprinted with permission. See Ref. [50]. 9 1994 American Chemical Society.)

3.3 Acoustic Plate Mode (APM) Devices

99

We note in Figure 3.31 that velocity decreases linearly with tk3 for ~b3 "~ 7r/2, following the dashed line predicted from the acoustically-thin model (Equation 3.58). The response deviates substantially from this linear behavior near dr3 = ~r/2: attenuation goes through a maximum while velocity undergoes an upward transition. This combination of responses arises from film resonance, arising from interference between waves generated at the lower film surface and those reflected from the upper (film/air) interface. The resonant response at ~b3 = 7r/2 is predicted to recur at 3zr/2, 57r/2, etc., constituting harmonics of the fundamental film resonance. Martin et al. [50] have shown how the above model can be used to predict velocity and attenuation responses as polymer-coated SAW devices undergo temperature changes or are exposed to vapors. The response arises from temperature- or vapor-induced variations induced in the shear modulus G, bulk modulus K, film thickness h, and mass density p.~ Figure 3.32 (page 100) shows the velocity and attenuation responses measured (points) and calculated (lines, Equation 3.60) as pentane and TCE vapors were absorbed by a polyisobutylene-coated SAW sensor. The dashed lines show the predictions based on mass-loading by the absorbed vapors. At low concentrations, the mass-loading contribution accounts for 40% of the measured (low concentration) Av/vo response for pentane and 67% for TCE. The remainder of the response is due to film plasticization (softening) by the absorbed vapor molecules. This is consistent with a comparison of SAW and chromatography measurements by Grate et al. [53] that indicated that the mass response was a small fraction (25%) of the total Av/vo response. At high vapor concentrations, film plasticization due to acquired solvent volume causes the film to behave as acoustically thick. Film resonance occurs when solvent plasticization causes tk3 to reach Ir/2.

3.3

Acoustic Plate Mode (APM) Devices

This section describes a class of acoustic wave sensors utilizing a shearhorizontal (SH) acoustic plate mode (APM), which has been developed for sensing in liquids. SH modes have particle displacement predominantly parallel to the device surface and normal to the direction of propagation, as shown in Figure 3.33 (page 101). The absence of a surface-normal component of displacement allows each SH plate mode to propagate in contact with a liquid without coupling excessive amounts of acoustic energy into the liquid. By comparison, when surface acoustic waves are propagated at a solid-liquid interface, the surface-normal displacement radiates compressional waves into the liquid and severely attenuates the wave.

100

3. Acoustic Wave Sensors and Responses

2.5

2.0 A

O

1.5 X

2

1.0 II B

0.5

0.0

-I A t~

6 -2 X

al O

9 .

-3

~ =lww J

P

II B 9 ,

-4

.... |

-5

0

I

,

,, I ......

2

I ............

I

3

4

-,,j

II II]

5

Concentration (mole/I) Figure 3.32 Velocity and attenuation changes measured (points) and calculated (solid lines) vs absorbed (O) pentane and ( 1 ) trichloroethylene concentrations for a 97-MHz SAW device coated with a 0.70-/.tm polyisobutylene film. A QCM coated with an identical film was used to measure the mass of absorbed vapor, from which film concentration was determined. (Reprinted with permission. See Ref. [50]. 9 1994 American Chemical Society.)

3.3 Acoustic Plate Mode (APM) Devices

101

SH-APMs utilize thin single-crystalline quartz plates that serve as acoustic waveguides, confining acoustic energy between the upper and lower surfaces of the plate as the wave propagates between input and output transducers. This is in contrast to the SAW, for which nearly all the acoustic energy is concentrated within one wavelength of the surface. The consequences of this difference are two-fold: (1) the sensitivity of the SH-APM to mass loading and other perturbations depends on the thickness of the substrate; (2) both faces of the crystal undergo displacement, so that detection can occur on either surface of the device. SH plate modes may be thought of as a superposition of plane waves with inplane (shear horizontal) displacement reflected at some angle between the upper and lower faces of the quartz plate. These upper and lower faces impose a transverse resonance condition that results in each APM having displacement maxima at the surfaces, with sinusoidal variation between surfaces. In studying these devices as sensors, many salient features can be inferred by modelling the plate as an isotropic medium. This approximation greatly simplifies the analysis of APM sensors and leads to reasonable predictions regarding mode resolution and perturbation mechanisms acting on the device.

Figure 3.33 Schematic of an acoustic plate mode (APM) device showing the shear horizontal (SH) displacement of the mode as it propagates between input and output transducers. (Reprinted with permission. See Ref. [54]. 9 1989 Elsevier Publishers.)

102

3. Acoustic Wave Sensors and Responses

The particle displacement associated with the n th order SH plate mode (propagating in the z-direction) has only an x-component, given by [54] (nzry) Ux(y) = Uxo cos b e(Ja#-YNZ)' (3.61) where b is the plate thickness, Uxo is the particle displacement at the surfaces, n is a transverse mode index, and t is time. Since, unlike the TSM, modes are excited from only one side of the crystal, modes corresponding to all integer values of N can propagate. The exponential term in Equation 3.61 describes the propagation of the displacement profile down the length of the waveguide (along the z-direction) with angular frequency ~o and wave number YN, where

YN = J

Vo

-- --if-

(3.62)

where Vo is the unperturbed propagation velocity of the lowest-order mode. The cross-sectional (in the xy-plane) displacement profiles for the four lowest-order isotropic SH plate modes are shown in Figure 3.34. The mode index n corresponds to the number of nodes in the displacement profile. As illustrated in Figure 3.34, each mode has equal displacement on both surfaces of the APM sensor, allowing the use of either side for liquid-sensing applications. As with the SAW, a lithographically-patterned interdigital transducer on one side of the piezoelectric plate can be used to excite and detect APMs in quartz. Both the ST- and AT-cuts of quartz have been used; the latter has the advantage of greater temperature stability, wider spacing between modes, and without allowing SAW excitation. An IDT couples most efficiently to a plate mode when the transducer periodicity matches the mode wavelength along the surface, An. The frequency at which each mode is most efficiently coupled by a transducer is thus given by fn = vn/d, where vn is the phase velocity of the n th SH mode. Hou et al. [55] have shown that transducer coupling efficiency also varies inversely with the ratio of plate thickness to wavelength. Modeling the quartz plate as an isotropic medium, the Nth order SH plate mode will be generated most efficiently by a transducer of period d at a frequency approximated by [54]

fN=~

1+

-~

(3.63)

Equation 3.63 gives an approximation for the SH plate-mode spectrum found in an unperturbed quartz plate. The presence of surface features, including transducers, perturbs the wave velocity, and hence the excitation frequency, of each mode.

3.3 Acoustic Plate Mode (APM) Devices

103

Figure 3.34 Cross-sectional displacement profiles for the four lowest-order shear horizontal plate modes. These profiles are normalized for equal power flow per width of the plate. (Reprinted with permission. See Ref. [54]. © 1989 Elsevier Publishers.)

In order to avoid problems of mode interference, it is desirable when using APM devices as sensors to excite only a single mode. This can be accomplished by using a transducer whose bandwidth is less than the frequency separation between modes.

3.3.1

APM/LIQUID INTERACTIONS

A number of interactions can affect plate-mode propagation characteristics, particularly in a liquid environment. In the following sections, models of several of the important modes of interaction will be outlined and compared to experimental results. These include: (1) mass accumulation on the device surface, (2) viscous entrainment of the contacting liquid medium by the oscillating device surface, and (3) acoustoelectric coupling between evanescent plate mode electric fields and the liquid.

104

3.3.2

3. Acoustic Wave Sensors and Responses

MASS SENSITIVITY OF THE APM

When mass is bound strongly to either surface of the APM device, it oscillates synchronously with the quartz surface under the influence of the passing plate mode. The extent to which mechanical surface perturbations will influence APM propagation is proportional to V2xo/P, the ratio of surface particle velocity, Vxo, squared to acoustic power flow, P, down the "wave guide." The larger the surface particle velocity is in comparison with the power flow in the guide, the more sensitive the mode will be to surface mechanical perturbations. The crosssectional displacement profiles, shown in Figure 3.34, are normalized for equal acoustic power densities. It is apparent from the figure that the lowest-order mode (n = 0) has a smaller relative surface displacement (and particle velocity), and hence less sensitivity, than the higher-order (n >-- 1) modes. An ideal mass layer deposited at the surface results in increased kinetic energy which is offset by a decrease in propagation velocity [54]:

AV Vo

JnPs bpq

Cfps,

(3.64)

where cf is the mass sensitivity, pq is the density of the quartz substrate, Ps is the surface mass density (mass/area on one surface), Jo = 1/2, and Jn = 1 for n -> 1. Equation 3.64 predicts that velocity will decrease linearly with accumulated mass density and that the lowest-order mode will be half as sensitive to surface mass as higher-order modes. We note the similarity of Equation 3.64 to Equation 3.9 for TSM resonator mass sensitivity; the only difference is the Jn factor that accounts for the reduced sensitivity of the zero-order mode (which is not excited in the TSM resonator). Rayleigh wave devices exhibit sensitivity, when calculated on a relative basis (AV/Vo), that is proportional to frequency. In contrast, SH plate mode sensitivity displays no significant frequency dependence. This difference can be attributed to the fact that with surface waves, the acoustic energy becomes distributed closer to the surface as frequency increases. Like the TSM resonator, the energy density for each propagating SH mode is, dependent upon plate thickness rather than frequency, The mass sensitivity of an ST-quartz APM device was determined by depositing metal onto the unelectroded quartz surface, i.e., the side opposite the transducers. The plate mode velocity shift is plotted vs the surface mass density of deposited silver in Figure 3.35. As expected from the discussion above, the device is approximately twice as sensitive when higher-order modes (n > 1) are excited than with the lowest-order (n = 0) mode. The mass sensitivity measured

I

'

"1

"

I

I

A I

0 X

,I=,,

"

!

" '

,, n=O, cf= 9.5 <>n - l , cf=18.5 T n=2, cf=19.7 o n=3, cf=20.O

0 (,O

'1

-20 -40

I'

"

cm2/g cm2/g cm2/g cm2/g

-60 -80 <3 -100 0

@ m. t~

m t~ @

-120 0

2

4

6

8

Ps(l~g/cm 2) Figure 3.35 Fractional change in APM propagation velocity vs areal/mass density of silver deposited onto the device surface. (Reprintedwith permission. See Ref. [54]. 9 1989 Elsevier Publishers.)

"t ~

.r m. t~

t.~

106

3. Acoustic Wave Sensors and Responses

for the device is 9.5 cm2/g for the lowest-order mode and 19.4 cm2/g on average for the next three higher-order modes. The corresponding sensitivities estimated from Equation 3.64 (9.3 cm2/g and 18.6 cm2/g, respectively) are in good agreement with the experimental values. It is reasonable to ask how accurately the mass sensitivity in vacuum reflects the sensitivity when the device has liquid contacting the surface. This was investigated by monitoring the frequency shift of a single device both during vacuum deposition of a metal film and removal of the same film in an etching solution. The sensitivity in the liquid was approximately 6% less than the value measured in vacuum, a discrepancy that lies within our estimates of experimental uncertainty in this case [54]. The high mass sensitivity of the APM device enables it to function as a general purpose detector, serving as a microbalance in a number of sensor applications. Submonolayer accumulations of surface species can be readily measured. Through suitable chemical modification of the surface, the APM device can be sensitized to the presence of specific species or classes of species present in solution. One approach is to derivatize or chemically modify the properties of the sensing surface, enabling it to selectively bind species from solution. Species that are strongly bound move synchronously with the oscillating APM device surface and perturb the oscillation frequency, according to Equation 3.64, leading to a sensor response. Application of the high mass resolution of the APM to chemical sensing is discussed in Chapter 5.

3.3.3

APM LIQUID LOADING

The in-plane oscillation of the quartz surface contacting the liquid sensing environment leads to entrainment of a thin layer of liquid near the interface, similar to operation of the TSM resonator in contact with a liquid. This viscous coupling of liquid to the plate mode causes both a change in the propagation velocity, V, and attenuation a of the mode. The changes in APM velocity are analogous to changes in TSM resonant frequency, while APM attenuation is analogous to changes in TSM resonator admittance magnitude. In modeling the interaction of a liquid with plate modes, the high frequency of operation necessitates the consideration of viscoelastic response by the liquid. For the simple liquids examined, good agreement was obtained by modeling the liquid as a Maxwellian fluid with a single relaxation time r When the Maxwellian fluid is driven in oscillatory flow with to~-~ l, it responds as a Newtonian fluid characterized by the shear viscosity, T/. For to1-~> l, the oscillation rate approaches the rate of molecular motion in the liquid and energy ceases to be dissipated in

3.3 Acoustic Plate Mode (APM) Devices

107

viscous flow, being stored elastically instead [56]. Consequently, when driven at high frequencies, a Maxwellian fluid behaves as an amorphous solid with shear properties characterized by a shear modulus,/z. The relaxation time, ~', associated with the transition from viscous to elastic behavior in a Maxwellian liquid is related to these parameters by [57] r/ ~"= --. /z

(3.65)

Viscous coupling of plate modes to an adjacent fluid results in both attenuation of the plate mode and a change in propagation velocity. These can be estimated from a perturbation analysis and are given by [54] Aa =

k

Av Vo in which

~2 .

cfrIRe(') 2Vo 1 + jto'r c/film ( -2to

'

(3.66~)

!

)

1 + jto'r

(k . 2. . t~ /x

+j

top 7/

(3.66b)

(3.66c)

where cf is the mass sensitivity of plate mode velocity (see Equation 3.64). It is interesting to note that attenuation and velocity shift arise as the real (Re) and imaginary (Ira)parts of a single complex function describing the viscoelastic fluid response. The velocity shift arises from mass loading by the entrained liquid layer, while attenuation arises from power dissipation in the liquid. Since liquids couple to the surface displacement, it is reasonable that the viscous sensitivity of a device is proportional to mass sensitivity. The plate mode velocity shift and attenuation arising from liquid entrainment are shown vs 771/2in Figure 3.36 (page 108). At low values of viscosity, the fluid behaves as a Newtonian liquid with AV/Voand Aalk proportional to ('!7) 1]2. For viscosities exceeding about 10 cP, relaxation times become comparable to the wave period (6 ns) for the 158-MHz device and viscoelastic behavior results. The solid line is the calculated change in propagation characteristics based on the viscoelastic model of the liquid (Equations 3.66). A shear stiffness/x - 3.1 • 108 dyne/cm 2 was chosen to give a best fit of these equations simultaneously to the experimental velocity shift and attenuation measurements. Interestingly, this value of/x implies a shear relaxation time (from Equation 3.65) that agrees fairly closely with liquid dielectric relaxation times [57]. The dashed line is the pre-

108

3. Acoustic Wave Sensors and Responses

0 A

E -100 v

>o

e

-200

I -400

,

-

S

\

.

:

~ .....

|

i

, ....

,,I

,

.

I

~

, I

, .....

,,,

, ....

I

,.,

. . . .

i ....

,

......

i

,,,

~

,

_~

, . . - S"

I

,ot ,dh

~

~

.

0.5 0.0 0.0

0.2

0.4 V~

0.6

0.8

(Poise) 1/2

Figure 3.36 Change in APM velocity and attenuation vs liquid viscosity. The solid line is calculated using a Maxwell model for the liquid (Equations 3.66); the dashed line is calculated using a Newton]an model for the liquid. (Reprinted with permission. See Ref. [54]. 9 1989 Elsevier Publishers.)

diction when viscoelastic effects are neglected and the liquid is treated as a Newton]an fluid over the entire viscosity range, i.e.,/z = oo in Equations 3.66. Apparently, it is the viscoelastic nature of the fluid that leads to saturation in attenuation and a reversal of the velocity shift at higher viscosity levels [54,58]. The effect of liquid entrainment on APM propagation has several implications. First, the sensitivity of the device to liquid viscosity enables the device to

3.3 Acoustic Plate Mode (APM) Devices

109

be used as a microviscometer [54,56] in the Newtonian regime (co~",~ 1). The ability to detect perturbations on the unmetallized side makes the device attractive for in-situ monitoring of viscosity in engines, chemical process streams, etc. Second, increasing the mass sensitivity of the APM device (e.g., by using a thinner plate) results in a correspondingly higher viscous loss, resulting in a tradeoff between the mass sensitivity and the output signal level of the device. This trade-off is made less severe by decreasing the viscosity of the sensing environment and/or decreasing the operating frequency of the device. When operating the device in the oscillator configuration, the amplifier gain must be increased to offset the viscous attenuation. Third, since changes in liquid properties, such as density or viscosity, lead to changes in plate mode velocity or oscillator frequency, solution properties must be controlled or monitored closely; the relatively high sensitivity of the viscosity of water to temperature changes, for example, means that the temperature of test solutions must be well controlled.

3.3.4 APM ACOUSTOELECTRIC COUPLING Another sensing mechanism of APM devices results from acoustoelectric interactions. Like the SAW, a plate mode propagating in a piezoelectric waveguide generates a layer of bound charge at the surface (Figure 3.23). The evanescent electric field associated with this layer of bound charge extends into the adjacent liquid, coupling to ions and dipoles in solution [58,59]. This interaction is analogous to that found previously between SAWs and charge carriers in a conductive film overlay. Like the viscous entrainment of liquid by the surface, the electrical entrainment of ions decays exponentially with distance from the solid/liquid interface. Since the electric field has a decay length of A/27r, however, ion coupling extends several micrometers into the liquid. Ion, dipole, and induced-dipole motion resulting from this acoustoelectric coupling lead to a perturbation in plate mode velocity and attenuation. The effect of wave/ion coupling on APM propagation can be determined from an equivalent-circuit model analogous to that of Figure 3.24. The perturbation in APM velocity and attenuation arising from a given ion concentration can be related to the solution conductivity cr by [59]

Av Vo -

K2(~.s+~o) 2

o.2

Es + e---"---~ o"2 + oj2(Es + et)2

Aot K2(~.s+Eo) tOO'(Es + ,l) ko - T as q- ai 0 -2 q- to2(es + ai) 2 '

(3.67a)

(3.67b)

110

3. Acoustic Wave Sensors and Responses

in which K 2 is the square of the electromechanical coupling coefficient for the APM; Es, E~, and 6o are the dielectric permittivities of the substrate, liquid, and free space, respectively. Equations 3.67 are very similar to Equations 3.54 derived for the SAW/thin film acoustoelectric interaction. In the present case, however, o" refers to a bulk, rather than a sheet, conductivity. Furthermore, an additional term appears in the present equations that scales the acoustoelectric response inversely with liquid permittivity. This term was unity in the SAW calculation, under the assumption that the medium above the film was vacuum or air. Josse has treated the APM acoustoelectric interaction and obtained a slightly different result from that presented here [58]. The acoustoelectric interaction between plate modes and ions in solution was investigated by measuring variations in APM propagation velocity as a function of solution conductivity or, as shown in Figure 3.37 for four solvents [59]. Attenuation of the APM due to ionic conductivity is too small to measure with precision when using quartz devices, but may be significant with more highly piezoelectric plates such as lithium niobate. The dielectric constant of the solvent significantly affects both the rate at which velocity changes with conductivity and the overall magnitude of the change. This is consistent with Equations 3.67, which predict that velocity changes most rapidly when or = ages + el). Thus, lower dielectric solvents such as ethanol and methanol cause the velocity transition to occur at a lower conductivity than do higher dielectric constant liquids. The magnitude of the overall velocity shift is also diminished, as predicted from Equations 3.67, with higher dielectric liquids, e.g., water. The solid lines in Figure 3.37 are velocity shifts calculated using Equations 3.67 from the dielectric constant for each solvent s and a best-fit value of K 2 = 3.2 • 10 - 4 (same k 2 value used to fit all data). The model works well in the range of conductivities or < 2ore, where ore = co(Es + 61). In many sensor applications, responses resulting from conductivity variations are an unwanted interference. In the addition or removal of a conductive film in an aqueous solution, for example, the acoustoelectric velocity shift accounts for approximately 14 ppm of the overall shift. This would be even larger in most solvents; the large dielectric constant of water helps to minimize the acoustoelectric signals. In aqueous solutions, the acoustoelectric response from a conductivity variation between zero and crc is comparable to the mass response from an adsorbed monolayer. However, there are several approaches that can eliminate signals arising from ion coupling [59]: (1) solution conductivity can be main5The dielectric constants used for the solvents were values estimated at 158 MHz from literature values of the low-frequencydielectric constant and the dielectric relaxation time "r.

3.4 Flexurai Plate-Wave (FPW) Devices

111

-2

-4

-6

~E

A

E

o. o. o

<1

1 = 79.3

-8 -10

...~~r

g-"

: 52.5

-12

09

00

9 - KNO 3 IN H 2 0

-14 (1 : 3 2 . 9

-16

I

- LICI IN H 2 0

9

- LICI IN H 2 0 /

ETHANOL 9 - LICI IN M E T H A N O L

-18

~)~- LICI IN ETHANOL

(:1 = 2 4 . 2 O

0.5

1

1.5

2

2.5

(T (~--~-1 m - l ) Figure 3.37 Change in APM velocity due to the acoustoelectric interaction between electric fields generated in the piezoelectric plate and ions in solution; solid lines are calculated from Equations 3.67, while points are measured. (Reprinted with permission. See Ref. [59]. 9 1988 American Institute of Physics.)

tained much below or above o'c, where conductivity effects are small; (2) the conductivity can be maintained at a constant value throughout the measurement interval; or (3) a sufficiently conductive metal layer can be deposited on the quartz surface to shunt evanescent electric fields, thereby decoupling ions in solution from the APM without affecting mass sensitivity.

3.4

Flexural Plate-Wave (FPW) Devices

In a flexural plate wave (FPW) membrane, Figure 3.38 (page cussed---the TSM, SAW and device can sense quantities that

device, an acoustic wave is excited in a thinned 112). As with the other acoustic sensors disAPM devices m the flexural-plate-wave (FPW) cause its phase velocity, Vp, to change. A unique

112

3. Acoustic Wave Sensors and Responses

F L E X U R A L PLATE WAVE OSCILLATOR FREQUENCY < 1-200MHZ INSERTION LOSS OF ONE TRANSDUCER II

II

FREO r ~ fosr SHIFT DUETO LIQUID LOADING

floaded ---J ....

MEMBRANE USUALLYTHIN COMPAREDWITH WAVELENGTH VEL. f . ~ . - - SAW PIEZOELECTRIC-COATEDSUBSTRATE SILICON ALUMINUM VELOCITY<100-600m/s NITRIDE J SoMEMANY MODESMoDE OFDI S sPERSIvEPROPAGATION THICKNESS/WAVELENGTH

ZINC OXIDE

Figure 3.38 Schematic diagram of a flexural-plate wave (FPW) device.

feature of the FPW is that it can be dimensioned so that its phase velocity is lower than that of most liquids, which lie in the range from 900 to about 1500 m/s. When the FPW device contacts or is immersed in such a liquid, a slow mode of propagation exists in which there is no radiation from the plate. Thus, the FPW device functions well in a liquid environment, and is therefore a good candidate for biosensing and chemical sensing in liquids. Because the "plate" of a FPW device may be only a few micrometers thick, the mass per unit area of the thin plate can be increased significantly by mass-loading produced by the adsorption of chemical vapor molecules on the plate. This causes the phase velocity of an ultrasonic wave propagating on the plate to decrease. Other mass-loading effects that can be measured in fluid-loaded FPW devices by monitoring decreases in the real part of the phase velocity are increases in the density of a fluid on the plate, and the attachment onto the plate of protein molecules, cells, and bacteria from a liquid that contacts the plate. An opposite effect occurs if the tension in the thin plate is increased, for example, by establishing a differential gas pressure across it, by applying a force on the plate, or by bending the frame that surrounds it. The increased tension causes the real part of the phase velocity to rise. One finds experimentally that the amplitudes of the displacements associated with a flexural wave of given total power are large relative to those of the other acoustic sensors discussed here. Peak-to-peak normal displacements up to 100 nm have been measured, using laser diffraction, when only a few milliwatts of wave energy were propagating in a plate a few micrometers thick. As a result of

3.4 Flexurai Plate-Wave (FPW) Devices

113

this large-amplitude motion, one can produce useful kinetic effects, such as the transport of granular solids and the pumping and mixing of fluids. Thus, the FPW device can be both a sensor and an actuator. We will now discuss in detail the sensing and actuating properties of these waves.

3.4.1

FLEXURAL PLATE WAVES

The characteristics of flexural plate waves are found by a process similar to that used for surface acoustic waves: 1. Write the constitutive relations for the medium to relate stress to strain, assuming elastic linearity (Hooke's Law); 2. Formulate the relation between acceleration of the medium and the spatial variation of stress (Newton's First Law); 3. Express the conditions on stress and particle displacement at the boundaries of the plate; 4. Obtain expressions for the displacement components of the waves that satisfy all the relations above. One finds in the simplest case of an elastically isotropic plate that there is an infinite set of waves that can exist. These are known as Lamb waves, after Sir Horace Lamb who published their first detailed description [60]. Figure 3.39 (page 114) shows the phase velocities of the waves as a function of the product ktd, where kt -" 2"rr]At, At is the wavelength of the bulk transverse (shear) wave in the medium of which the plate is made, and d is the plate thickness. The waves divide naturally into two sets: symmetric waves (denoted by So, S l . . . . ) whose particle displacements are symmetric about the neutral plane of the plate, and antisymmetric waves (A0, Al . . . . ), whose displacements have odd symmetry about the neutral plane. Figure 3.38 shows that for sufficiently thin plates (ktd < 1.6), only two waves exist m the lowest-order symmetric mode (So) and the lowest-order antisymmetric mode (Ao). These are the modes shown earlier in Figure 2.0d. The plate mode that we will emphasize here is the A0 mode, in which the elements of the plate undergo flexure as the wave propagates. The shape of a plate during propagation of this flexural mode has been likened to that of a flag waving in the wind. The characteristics of Lamb waves have been derived and explored by a number of authors [61,62,63,64]. Here we will focus on the aspects of the waves that are most relevant for sensing and actuating in devices made by micromachining techniques. These techniques include many of those customarily employed in making silicon integrated circuits. Examples are processes for depositing thin

.

s~

A~,

A2

.

.

.

.

O

[

....9

.r

II

I_/

g~ O ='1

t~ g~ t~

Q

t

"g

3$

t,

3"

6

l

a

s

so n

/z I j

ktd Figure 3.39 Symmetric (S) and anti-symmetric (A) Lamb wave characteristics. Vertical axis: Lamb-wave velocity normalized to transverse bulk-wave velocity. Horizontal axis: Product ktd where kt = transverse wavenumber = 27flAt, where At is transverse wavelength and d is plate thickness. (Reprinted with permission. See Ref. [61]. 9 1967 Plenum Press.)

3.4 Flexural Plate-Wave (FPW) Devices

115

films, such as insulators and conductors consisting of metallic or doped semiconductors. For acoustic-wave transduction, one utilizes piezoelectric films that are typically deposited by sputtering. Key etching techniques for making microstructures are bulk and surface micromachining. In the former, one etches away silicon lying under a deposited film to leave a beam or membrane. In surface micromachining, one deposits and shapes films deposited on a so-called sacrificial layer. One then shapes these films by photolithography and etching, and finally, dissolves the sacrificial layer to free the shaped film. These micromachining processes are described in a recent book on semiconductor sensors [65] and in articles in a reprint volume about microsensors [66]. 3.4.1.1

Behavior of the FPW Velocities and Particle Motions

Figure 3.40 shows the phase velocity of the Ao and So Lamb waves in tensionfree silicon nitride, as calculated by a numerical analysis program by Nassar and Adler [67]. Silicon nitride, an amorphous glasslike substance, is a practical material to use in micromachined flexural-wave sensors since thin layers of it can easily be made on a silicon wafer by LPCVD (low-pressure chemical-vapor deposition). The underlying silicon can later be etched to leave a thin unsupported plate, as mentioned above. A silicon-rich formulation having nearly equal numbers of silicon and nitrogen atoms is preferred over stoichiometric silicon nitride, Si3N4, because it can have a very low residual stress. The behavior shown in Figure 3.40 (page 116) is typical: 1. For very small thickness-to-wavelength ratios, the phase velocity of the Ao mode approaches zero asymptotically. 2. As d/A increases, vp increases, finally becoming asymptotic from below to the surface-wave velocity for the medium. 3. The phase velocity of the So mode is maximum for a very thin plate, and it falls as d/A increases, finally becoming asymptotic from above to the surface-wave velocity for the medium. The rise in (2) is due to the increased effective stiffness of the medium as an ever-thickening plate is required to assume the sinusoidal wave shape. The approach to the surface-wave velocity as the plate becomes thick is to be expected, as a surface wave can be represented as a superposition of antisymmetric and symmetric plate waves. The particle motions that are indicated schematically by the ellipses near the curves of Figure 3.40 are predominantly normal to the plate for the Ao mode and predominantly tangential to the plate for the So mode. Fortunately, the most interesting applications of the FPW arise for very thin plates, for which d/A "~ 1. In this regime, we can fabricate plate-mode delay lines

SO ~~'

:

"-'-':, -

i

............ i .................................

i

Q

I= .< r

................ . ~ . ~

A

.......................................................... O

Q, =I gl. r "O O r~ r 9 . . . .

0.0

0.5

. . . o o . , . . . , , . o , o , , P , o , , , e , , i

d/~,

, e t o t o , t e t o e t e e ~ t t o * t e e e e ~ e o ~ e e e o

9

o

1.0

1.5

Figure 3.40 Calculated phase velocity of flexural plate waves vs ratio of plate thickness, d, to wavelength, A, for silicon nitride. Material is assumed to have the elastic properties of SiaN4 and no residual tension. The mode shapes are illustrated at the right with a greatly enlarged vertical scale for clarity. Ellipses at left show the retrograde elliptical particle motions of the lowest symmetric and antisymmetric modes for d/A = 0.03. (Reprinted with permission. See Ref. [62].)

3.4 Flexurai Plate-Wave (FPW) Devices

117

whose phase velocity is below the velocity of sound in water, and so one can use them for biosensing. Furthermore, because of the low phase velocity, the frequency of operation, f, of the device for a given wavelength is low, since

vp f = ~. A

(3.68)

A low operating frequency is an attractive feature as it implies relatively inexpensive associated electronic circuitry. Finally, it is possible in the thin-plate regime to approximate the phase velocity quite well by the simple asymptotic expression [68]

Vp =

(3.69)

where B is the bending stiffness of a homogeneous, elastically isotropic plate and M is the mass per unit area of the plate. For an Ao Lamb wave in a tension-free plate, the bending stiffness takes the form B =

12

(3.70)

where E'-

1-

E

v2

(3.71)

is the so-called effective Young's modulus, E being the actual Young's modulus and u the Poisson's ratio for the material. As do the SAW and APM sensors, the FPW device employs interdigital transducers and piezoelectric coupling to generate and detect the waves. Figure 3.41 (page 118) shows a cutaway view of an FPW device in which the supporting membrane is a low-stress silicon-rich silicon nitride layer formed by the LPCVD process. After the layer is deposited, the silicon is etched away to leave an unsupported membrane. A conducting groundplane is deposited, followed by the RF-magnetron sputtering of piezoelectric zinc oxide and then the sputtering or evaporation of a second conducting layer. The transducer electrodes may be formed in either conducting layer. The dimensions of a typical device are indicated in Figure 3.41. Note that in contrast with the SAW and APM transducers, for the dimensions given each transducer finger is quite close to the opposite groundplane, and so the electric fields in the piezoelectric are directed primarily perpendicular to the plate. (In the thicker SAW and APM devices, significant transverse electric fields are also produced by the transducers.) The electronic measurement techniques used with SAW and APM sensors can also be used with FPW devices. Thus, often a delay-line oscillator is formed by

118

3. Acoustic Wave Sensors and Responses

Figure 3.41 Typical flexural-wave device. Thickness of the surrounding silicon frame, typically 250-500 microns, is reduced here for clarity. P is the IDT periodicity. (Reprinted with permission. See Ref. [621.)

connecting an electronic amplifier between output and input transducers. Changes of wave attenuation arising from changes of viscosity are reflected in changes of the signal amplitude at the output transducer. The frequencies employed in FPW

3.4 Flexural Plate-Wave (FPW) Devices

119

devices are usually in the 1-10 MHz range, significantly lower than those used with SAW and APM sensors. Example 3.8: Find the mass per unit area, M, of the composite plate of a typical FPW device whose layer thicknesses are: SixNy, 1.8 I~m (density 3100 kg/m3); ZnO, 0.2/xm (density 5665 kg/m3); Al ground plane, 0.2 Ixm (density 2700 kg/m3).

Solution:

M, the sum of the thickness-density products for each of the layers, is 11.8 •

10 -3 kg/m 2.

Before examining the interactions between the plate wave and the ambient, we should note two important details: (1) The surface of the silicon nitride typically oxidizes and so it is actually silicon dioxide, a substance that lends itself well to use in biosensing. (2) In the fabrication process, usually a tensile stress develops in the plate that can affect the phase velocity. Thus, the plate has one aspect of a membrane: it has in-plane stress. This stress affects the phase velocity somewhat. Its effect can be included in the thin-plate approximation for the phase velocity, Equation 3.69, as v~ =

(Tx+B),/2 M

(3.72)

where Tx is the component of in-plane tension in the propagation direction (taken here as the x direction) per unit width in the y direction, perpendicular to the direction of propagation. Explicitly, /

.d

Tx = J ~'yy(~)d~

(3.73)

o

where ~'yy is the y component of tensile stress in the plate and ~: is a variable of integration normal to the plate whose bounding surfaces are at z = 0 and z = d. In typical FPW devices operated in air, the in-plane tensile stress may account for about ten percent of the phase velocity (in other words, Tx/B ~ 0.2).

3.4.2

FPW P E R T U R B A T I O N M E C H A N I S M S

We will now consider the response of the lowest-order flexural mode to various perturbations. For generality, we assume that there is some initial tension, T~, in the plate. For simplicity, we assume that the plate is quite thin (d/A ,~ 1), and so the approximate phase velocity expression of Equation 3.72 can be used as a basis for discussion. Figure 3.42 (page 120) summarizes the perturbations that we will discuss in Sections 3.4.2.1 to 3.4.2.5

120

3. Acoustic Wave Sensors and Responses

iii

i

i iii i

i

I

I U N L O A D E D PLATE one Flexural Mode: "AO Lamb" Mode

,,

I

Real Phase Ve'iocltg

I

i ii

,,

,,

ii

.

i

ii

I

FLUID-LOADED PLATE Two Flexural Modes: "AO Lamb" Mode --Always Lossy .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

"Scholte" ,M~

Non-viscous Fluid [

.

-- Vp < vF

!

Viscous Fluid

Real Phase Velocity. Complex Phase'velocltg I .=

Mess- I oedl nq c hange: Absolute pressure Chemical vapors Cells, bacteria ....

Mass- 1oedi ng r hanoe: E:Iect ro pl eft ng FIutd density change Protetn adsorption Cell growth Stiffness chanae: [lectropleting (thick)

Stiffness chenaeDifferential pressure Force Acceleration

Mes_s-loadlno r F1uld within vtscous decay distance

Attenuationcher~ge. Ytscosttychange

Figure 3.42 FPW perturbations for unloaded and fluid-loaded plates. The mode names are in quotes because in-plane tension modifies the behavior from that of conventional Lamb and Scholte modes. (See text for details.)

3.4.2.1

Effects of Increasing the Mass/Area of the Plate

Intuition correctly suggests that if we increase the mass per unit area of the plate by an amount m', the phase velocity for a thin-plate FPW device will become just

vp

( T x + B , ) '/2 M+m

=

(3.74)

Note that if m'/M ~ 1, we can expand the square-root expression in a Taylor series and show that the fractional change in velocity, Avp/vp, is approximately AVp __ (l,p)fina I -- (Vp)o,.iginal ~ Vp

(Vp)o,.iginal

m' 2M

(3.75)

where (Vp)fina I is the phase velocity after the mass increase and (Vp)o,.iginal is that before the mass increase. As was done earlier with the APM device, we can define a mass sensitivity, Sin, and obtain its value for the FPW device as S/71

=

1 AVp

m

1

vp

~

1

2M

The units of the mass sensitivity are [area/mass].

(3.76)

3.4 Flexural Plate-Wave (FPW) Devices Example 3.9:

121

Find the gravimetric sensitivity of the 3txm-thick FPW device of Ex-

ample 3.8. Solution:

As Sm ~ -1/2M, Sm= --42.4 m2/kg = 424 cm2/g.

Note that the value of Sm obtained for this typically dimensioned FPW device is much higher than those for the TSM and APM devices. If one wishes to increase the FPW mass sensitivity even further, one should make the device thinner, reducing the velocity (and incidentally reducing the frequency of operation). This increasing sensitivity with a lowering of the frequency is opposite to the situation for the TSM, SAW and APM devices, for which one increases the sensitivity by raising the operating frequency. Example 3.10: Assume that the FPW device of Exercise 3.8 is operated as a delayline oscillator whose unperturbed oscillation frequency is f, and suppose that the random fluctuation of frequency (noise) is Afnoise. Find the minimum detectable added mass per ! P unit area, m rain, that could be detected with a 3: I signal-to-noise ratio. Calculate m rain assuming f = 5 MHz and Afnoise = 0.4 Hz. Solution: For the delay-line oscillator, Avp/Vp = Aflf. Setting the minimum significant frequency shift, Af, equal to 3Afnoise, from Equation 3.57 we obtain

mmin = - 2 M ( Avp Vp )min = - 6 M ( Aff~

(3.76)

For the values given, m'mi~ = 5.7 X 10-9 kg/m2 = 5.7 • 10 --l~ g/cm2 (570 pg/cm2). If one wishes to reduce this value, one can reduce the membrane thickness, and hence, M. With the device of Figure 3.41, a lower limit on thickness of the composite membrane is set by the minimum thickness of the piezoelectric layer, as extremely thin ZnO layers tend to be randomly oriented and hence have low piezoelectric coupling. Much thinner membranes can be achieved if one dispenses with the piezoelectric and instead drives a very thin membrane with electrostatic forces produced by an opposing interdigital electrode array [62,69].

Example 3.11: For the sensor of Exercise 3.10, what fraction of a monolayer coverage could be detected of molecules having a specific gravity of 1.35 ? (This is the specific gravity of a typical protein molecule.) Assume that the molecules are spheres having a diameter of 1 nm located on centers that are one diameter apart. Solution: The fractional coverage, F, equals m'min/(mass of monolayer per unit area). For the values given, F = 5.7 • 10-9/7.1 • 10-7 = 0.008 (or 0.8% of a monolayer coverage).

Detecting Chemical Vapors with the F P W Sensor A practical FPW chemical vapor sensor typically employs a sorptive film on the plate, as do the TSM, SAW and APM devices (Figure 3.43, page 122). When calculating the mass sensitivity of the coated FPW sensor, we simply include the mass per unit area of

122

3. Acoustic Wave Sensors and Responses

Figure 3.43 Schematic cross-sectional view of polymer-coated FPW device for vapor sensing. The inset, with exaggerated vertical scale, shows the wave propagating along the membrane. (Reprinted with permission. See Ref. [62].)

the sorptive film together with that of the plate itself. Thus, if the density of the sorptive film is Ps and its thickness is ds, the approximate mass sensitivity of the coated FPW vapor sensor is sm= -

1 9 2(M + psds)

(3.77)

Figure 3.44a shows FPW sensor response to toluene vapor [68]. The sorptive coating was a 1.5-b~m-thick layer of poly(dimethylsiloxane), PDMS. The sorptire polymer was in its rubbery state at the measurement temperature of 24~ Very linear response was observed (Figure 3.44b). A different FPW device operating at 2.85 MHz and having a 0.5-/xm-thick coating of ethyl cellulose, which was expected to be better suited to toluene detection [70], had a measured mass sensitivity of Sm = 1064 cm2/g. Its estimated minimum detectible concentration was 70 ppb, based on an assumed 3' 1 signal-to-noise ratio and the measured short-term frequency instability of +0.04Hz. Example 3.12: Determine the mass sensitivity of the FPW device of Example 3.8 when it is covered with a O.1 lain layer of a sorptive polymer having a specific gravity of 1.05. By what percentage has the sensitivity been reduced from the value for the uncoated device?

Solution: For the values specified, psds = 1.05 x 10 -4 kg/m 2, yielding Sm = -42.0 mi/kg = -420 cmZ/g, a sensitivity reduction of 0.9%.

Figure 3.44 FPW response to toluene vapor. (a) Temporal responses of infrared spectrometer (MIRAN) and PDMS-coated FPW delay-line oscillator for different concentrations of toluene vapor in nitrogen carrier gas. Delay of FPW response was due to delay in traveling through a length of piping. (b) Concentration vs frequency shift for toluene vapor. Diameters of data symbols indicate probable experimental error. (Reprinted with permission. See Ref. [62].)

123

124

3. Acoustic Wave Sensors and Responses

3.4.2.2

Effects of Loading with a Non-Viscous Fluid

Let us suppose that we put a fluid having a speed of sound vF in contact with a FPW delay line whose phase velocity satisfies the inequality Vp < vF. Based on experience with light and radio-frequency electromagnetic waves, we might expect that the ultrasonic wave energy would not radiate away into the fluid, because the plate would act as a slow-wave propagation medium. The case is similar to the energy confinement that occurs in fiber optics: optical energy does not radiate from the high-refractive-index, low-velocity fiber core into the lowindex, higher velocity cladding. The wave in the faster medium (the fluid) becomes evanescent, its amplitude diminishing as an inverse exponential function of the distance from the plate (Figure 3.45). FPW experiments support this simple picture for the most part, but detailed differences must be noted. When a semi-infinite fluid contacts the FPW device, new modes of propagation exist that are not allowed in unloaded FPW devices. The lowest-order mode, which is useful for sensing, is similar to the Scholte wave of geophysics [71], which is guided along the boundary between the semi-infinite seabed and the liquid layer, the ocean. As shown in Figure 3.46 (page 126), the phase velocity for this wave in the thin-plate case ranges from zero to the velocity of sound in the fluid for plates that are thick compared with the wavelength. If the fluid is inviscid, this wave is lossless. It appears that this mode is the one that is responsible for most reported flexural-wave sensing results. In addition, there is a fluidloaded asymmetric Lamb wave that can have a very large attenuation factor, even for frequencies well below the speed of sound in the fluid. (Calculated attenuation factors for this Lamb wave for an inviscid water-like loading of a 2-micronthick plate at a 100-micron wavelength exceed 800 dB per centimeter!) It has been shown [68,72] that when a semi-infinite body of fluid contacts one side of a thin FPW device, the mass loading that the fluid produces can be described by simply adding an additional term to the mass per unit area, M, in the phase velocity expression of Equation 3.74:

Tx+B )1/2 Vp =

(3.78)

M + pFc$e

where Pr is the density of the fluid and Be, the so-called evanescent decay length, is given by

.

(3.79)

t~

m_ i

.r

--o

t~

Figure 3.45 FPW device in contact with a semi-infinite fluid showing evanescent disturbance excited in the fluid after [62]. Lengths of arrows in fluid represent amplitudes of particle velocity locally. Note that amplitudes decrease rapidly within a fraction of a wavelength into the fluid, showing that the disturbance in the fluid is localized near the membrane. (Reprinted with permission. See Ref [62].)

t,~ t~

126

3. Acoustic Wave Sensors and Responses

4000

] ..................................................................... ~ ~ ~

~ ~

i

3000

.I

.....

....,......****..,b

A

E 2000

............................................

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i .................. ............................

(a)

=,

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,,.,b.

~ . . . . . . . . . . .

.~:

.

.

.

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,, CPT .................... /

1000

.... ;.,.:.:

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, . . . . . . . . . . . . . . . . . . . . . . . . . .

.,..,.,,

.....

, ....

. ....

,~ ...........

,..,~

....

,

Iossless (Scholte)

0 0.00

0.04

0.08

O. 12

O. 16

0.20

d/k 70000 1 .....................'......................................................................................... I

"E'

~.

i oooo ,

..........

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........ '"

..................... ' ..................... ~..................... i"....................

(b)

30000 z.,

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0.16

0.20

Figure 3.46 Phase velocity (a) and attenuation (b) of fluid-loaded flexural plate modes plotted vs thickness/wavelength, d/A. The Iossless (Scholte) mode velocity approaches from below the velocity of the fluid, assumed to be water. CPT denotes result of classical plate theory for an unloaded plate. (Reprintedwith permission.See Ref. [62].)

127

3.4 Fiexurai Plate-Wave (FPW) Devices

For plates and fluids that satisfy vp ~ VF, the term in the brackets is approximately unity, and we have A

(3.s0)

Physically, Equation 3.80 means that one may consider the mass-loading effect of an entire half-space of fluid as being equivalent to that of a layer of the fluid having a thickness of only BE. Example 3.13: Determine the approximate and the exact values of the evanescent decay length for water, assuming that the wavelength is 100 microns, vp = 200 m/s and Vwater -" 1480 m/s.

Solution: Approximate evanescent decay length is t~Elapprox "~" (A/2~r) = 15.92 microns. Exact evanescent decay length 8F.lexact= ( A / 2 " t r ) [ 1 - - (Vp/VF)2]-1/2 = 16.06 microns.

Equation 3.80 has been verified in measurements made on a flexural-wave oscillator operated successively in air at STP (essentially zero loading) and then with various liquids on one side of the plate. Table 3.4.1 lists the liquids and their properties, and compares measured frequencies with those calculated from Equation 3.80. The mass-loading effect of a gas was evaluated in a room-temperature pressure cell filled with helium (whose speed of sound, VF, is 965 m/s at 0~ at from 1 to 4 atmospheres gauge (Figure 3.47). A linear dependence of velocity on gas density was observed, as expected [62]. The discrepancy between calculated and measured values was thought to be due to insufficient thermal equilibration between measurements. In this application of the FPW device, there is no differTable 3.4.1 FPW Density Determinations for Low-Viscosity Liquids [62]. Velocity of Sound in Fluid is Denoted by v~. The Measured Frequencies for Air Loading and Methanol Loading Yielded the Device Parameters M = 6.411 x 10 -3 kg/m 2 and Tx + B = 539.2 N/m Used in Calculating Predicted Responses for Other Liquids. Liquid

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128

3. Acoustic Wave Sensors and Responses

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Variation of FPW delay-line oscillator frequency vs pressure in helium-

filled

vessel.

pressure

( R e p r i n t e d with p e r m i s s i o n . See R e f [62].)

ential force on the plate, and hence the device has no obvious upper pressure limit. At high enough gas pressures, we would expect the velocity shift to depend nonlinearly upon gas pressure (or, actually, gas density) because of the nonlinearity of the mass-loading relationship and because ultimately the elastic stiffness of the m e m b r a n e could be affected. In spite of this, the sensor could be useful so long as the response was monotonic and reproducible. Let us consider the ability of the F P W device to measure small changes in fluid density. The basic gravimetric sensing expression of Equation 3.76 can be rewritten for a delay-line-oscillator F P W sensor as

af --

f

=

SmAm

(3.81)

3.4 Flexural Plate-Wave (FPW) Devices

129

where Am is the change of mass per unit area due to a change of fluid density, Ap. If the change is small '~ 1), we obtain

(SEAp/M af

(3.82a)

-7--- Sm~EAp = Spi~to where

~e Sp = - 2(M +

PFSE)"

(3.82b)

Measurements have shown [72] that for liquids whose density is near that of water, the discrepancy between literature density values and those deduced from FPW measurements are in the range of _.+0.2%. Strictly speaking, one needs to know the speed of sound in the liquid under test in order to determine accurately the value of ~ , and hence, the density. This can be done by using two FPW sensors operating at different wavelengths. Also, designing the FPW device to have the lowest possible phase velocity will reduce the importance of knowing the speed of sound in the liquid. 3.4.2.3

Gravimetric Detection of an Added Mass in a Liquid

There may be instances where one wishes to detect the absorption of molecules from a liquid into a polymeric film on the plate surface. And in biosensing, one may wish to detect the adsorption or attachment of a layer of protein molecules, cells, bacteria or other organisms on a surface. Figure 3.48 (page 130) shows an exploded view of a three-chip FPW liquid flow cell made for such applications. We can determine the velocity or frequency shift caused by such types of loading, which is in addition to the loading due to the liquid, by substituting into the denominator of the phase velocity expression of Equation 3.78 all the relevant masses per unit area: that of the plate itself, M; the equivalent loading of the liquid, that of any selective biological or chemically sorptive layer, and that due to the unknown itself, Am. If Am is much smaller than the sum of the other terms, as is usually the case when one is seeking the minimum detectable added mass, we can use the first term of the Taylor series expansion of the denominator of the square-root in the velocity expression, and write the approximate phase velocity as

PF~e,;

msorptive;

vp~( •

Tx+B M + pFt~E + msorptive +

)1/2 ~ (

Am

( 1 -- 2(':'M + pF6eAm-t-msorptive) ) "

Tx+B

)1/2

M "k- PF~E dr msorptive (3.83)

130

3. Acoustic Wave Sensors and Responses

Figure 3.48 Exploded schematic view of a flow-cell FPW liquid sensor. The silicon chip containing the thin silicon-nitride membrane, piezoelectric film and transducers is sandwiched between two etched silicon chips, The upper chip is a cap with fluid inlet and outlet fittings. It also provides vias for contact to a temperature-sensing polysilicon resistor deposited on the FPW chip below it. The lower chip introduces transducer contact leads and protects the underside of the membrane from contact with the fluid. (Figurecourtesy of Ben Costello,BerkeleyMicrolnstruments,Inc.)

3.4 Flexural Plate-Wave (FPW) Devices

131

For such a device the gravimetric sensitivity is

1

Sm

-- - 2(M +

PF~E + msorptive)"

(3.84)

We then find that the minimum detectable added mass, Ammin, in this fluid-loaded case with a sorptive film is just Ammin

-- am(

?)

Afmin

(3ss)

\

where Afmin is the minimum significant frequency shift.

Example 3.14:

For an FPW device having in a vacuum vp = 200 m/s, a lO0-micron wavelength, and the mass per unit area, M, of the device of Example 3.8, .find the fractional velocity decrease that would be produced by loading (a) one side with water (Pwater = lOakg/m3), (b) both sides with water, and (c) one side with methanol (Pmethanol = 0.89 X 103/kg/m3). Solution: The effective areal mass added to the membrane mass per unit area by liquid loading on one side of the membrane is pFSE, and twice that for two-sided loading. The values of this added areal mass for the three cases here are 15.77 • 10 -3, 31.54 X 10 -3, and 14.04 • 10 -3 kg/m2 respectively. These are comparable with M (= 11.8 • 10-3 kg/m2 from Example 3.8), so the fractional decreases of velocity are substantial. Using Equation 3.78 we find that the phase velocity is reduced from its original unloaded value by the factor 1/(1 + PFSE/M)1/2 for one-sided loading and 1/(1 + 2pFSE/M)1/2 for two-sided loading. The percentage fractional decreases are 34.6%, 47.8%, and 32.4%, respectively. The effect of liquid loading can be decreased substantially by reducing the FPW wavelength.

3.4.2.4

Effects of Loading with a Viscous Liquid

Analytical and experimental studies of FPW device response to loading with a viscous liquid show many similarities with the effects already described in this chapter in connection with the three other acoustic devices [62,72]. Representing the operating angular frequency as to and the viscoelastic relaxation time as ~', one can show that if toy ,~ 1, the attenuation of the FPW is proportional to (r/) 1/2, where 7) is the shear viscosity. There is also a mass-loading effect that may be thought of as being due to the mass of the entrained liquid that is viscously coupled to the plate. This loading can be accounted for analytically by adding a viscous mass-loading term in the approximate expression for the FPW phase velocity, viz., ( Vp =

Tx + B M +

pFtSE + M n

),/2 (3.86a)

132

3. Acoustic W a v e Sensors and R e s p o n s e s

where Mn -

~Sv 2

(3.86b)

and the quantity 3v is the so-called viscous decay length, the distance over which a shear disturbance in a viscous medium decreases to 1/e of its amplitude at the point of excitation: 3v(2"rl) 1/2 = ~ . COpE

(3.87)

3.15: Calculate the viscous decay length and the value of Mn for a 1GOmicron-wavelength, 5 MHz FPW device of Example 3.50 that contacts water on one side (the viscosity of water, ~, is one centipoise = 10-3 Pa-s). Example

Solution: The viscous decay length is 250 nm, which is much smaller than the evanescent decay length (16 microns, from Example 3.55). The value of M,~ is 1.3 x 10-4 kg/m2, or about one percent of the areal mass of the membrane itself. The effect of the viscosity on the real part of the FPW phase velocity is obtained by substituting M,7 for added mass per unit area m' in Equation 3.74. The dependence of the attenuation coefficient of the FPW, a, is given by [72] -

T + 2B + ~p~8~/(~/2~) 2

(3.88)

As a viscosity sensor, the FPW device has an advantage relative to APM sensors because of its low operating frequency" the viscosity for which ~o~"= 1 and the attenuation saturates is much higher than that for the SAW and APM devices. Also, the sensitivity of attenuation to viscosity should be higher than that of a TSM resonator operating at the same frequency because of the larger surface-tovolume ratio of the FPW device. Figure 3.49 shows results of measurements [72a] of the temperature dependence of viscosity for water and aqueous solutions of DMSO (dimethylsulfoxide). These tests were made in preparation for measuring the viscosity of a rare and expensive glycoprotein. In this case, measuring viscosity acoustically is a distinct advantage, as fewer than six microliters of sample are required. Experiments with aqueous solutions of DNA and of other polymers suggest that polymers having high molecular weights - - and hence large viscoelastic relaxation t i m e s - do not take part in the acoustic motion and thus do not contribute to the wave dissipation [72]. For operation at 5 MHz, the maximum molecular weight for which reliable viscosity measurements can be made acoustically is about 15,000 daltons.

3.4 Flexural Plate-Wave (FPW) Devices .

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curve

133

fit

water 5 N e

~

r~

o

r~

<>

0 -10

0

10

20

30

40

Temperature (oC) Figure 3.49 Viscosity as a function of temperature for 1M, 3M and 5M aqueous dimethylsulfoxide (DMSO) solutions. Solid curves are curve fits to the data based on the exponential expression r / = rlph exp [AEact'ffr ( l k T - D,Tph)], where T is absolute temperature in Kelvin, R is the universal gas content, AE,,ct is the activation energy, Tph is the phase change temperature, and r/ph is the viscosity of the solution at the phase-change temperature. The dashed curve is the exponential curve fit for water, and the dashed circles indicate the region of temperature where phase change occurred. (Reprinted with permission. See Ref. [72a]. 9 1993 ASME International.)

3.4.2.5

Other Perturbations

The ability to utilize an electrically conducting film on the FPW plate permits one to keep electric fields produced by the transducers from reaching a fluid in contact with the plate. Hence, the device can be made insensitive to the electrical conductivity of the medium, if desired. Unless temperature compensation is employed, the FPW velocity will depend fairly strongly upon temperature. The measured temperature coefficient of the relative phase velocity of the device of Figure 3.48 was - 1 2 0 ppm/~ This re-

134

3. Acoustic Wave Sensors and Responses

suits from a combination of thermal expansion of the frame (silicon) and the elements of the composite plate (silicon nitride, aluminum, zinc oxide). Owing to the small heat capacity of the thin plate, the phase velocity can change rapidly in response to heating from either an electric current in a resistive film on the plate or from absorbed thermal radiation [68]. A possibly useful feature of the FPW device is its ability to sense while coated with a layer of gel that is much thicker than the plate [73]. Water-based gels such as gelatin, poly(acrylamide), poly(vinylalcohol), agarose, and alginate having less than 2-5% solids content have shear moduli that are small compared with the elastic moduli of the plate's components (around 1011 Pa). Hence, the gels merely mass-load the plate. Recalling the evanescent FPW acoustic field structure, we note that the phase velocity will only be affected by loading within the evanescent decay distance, Be. Thus, one can use the gel to screen out large particles while responding to any small particles that diffuse to the gel-plate interface. Examples are shown in [73].

3.4.3

FPW KINETIC EFFECTS: PUMPING AND MIXING

We conclude this section with a brief overview of the kinetic functions that the FPW device can perform, in addition to the sensing just discussed. 3.4.3.1

Experimental Observations

The following experiments were made with FPW devices like that sketched in Figure 3.41.

Granule transport: In room air tests, when the lefthand FPW transducer was driven by a 10 V peak-to-peak RF source tuned to the center of its transducer response, granular particles sprinkled on the plate moved to the right at velocities of at least 3 cm/s [74]. The direction of motion was initially surprising, as one might have expected frictional forces to drive granules in the opposite direction owing to the retrograde flexural-wave particle motion (as indicated in Figure 3.40). This frictional drive is utilized in most macroscopic rotary ultrasonic motors. Liquid with marker spheres: In a similar experiment, deionized water containing 2.3-micron polystyrene spheres was transported to the right at velocities up to 300 microns/s. The experimental set-up is sketched in Figure 3.50. Initial measurements were made with marker spheres whose specific gravity, 1.05, differed from that of the liquid; thus the spheres settled onto the membrane. The speed

3.4 Flexural Plate-Wave (FPW) Devices

135

Figure 3.50 Experimental set-up for measuring flow velocity. (a) Cross-section view of silicon-based flow cell with FPW transducer on left side of bottom plate and glass slide to cover top of cell. (b) Cell on stage of optical microscope that is fitted with video camera and VCR for recording. (c) Schematic cross section of flow cell showing marker spheres and light rays converging from lens having small depth of field and large focal distance. (Neutrally buoyant spheres are depicted here; see text for details.) (Reprinted with permission. See Ref. [75]. 9 1994 IEEE.)

of fluid motion measured near the membrane was proportional to the square of the drive voltage, and to the square of the amplitude of the plate's normal motion, as measured by laser diffraction. The pumping speed measurements shown in Figure 3.51 (page 136) were made with 2.5-micron spheres that were near the membrane of the FPW device. Figure 3.52 (page 137) shows results obtained at various distances from the membrane of a device containing a dilute sugar-water solution in which such marker spheres were neutrally buoyant [75]. The observed recirculation is due to the closed-cell configuration. Detailed analytical study of the flow at heights below one micron suggest that flow velocities there could be as high as 250 microns/s under these experimental conditions.

136

3. Acoustic Wave Sensors and Responses

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Amplitude [ Angstroms I Figure 3.51 Pumping with flexural-wave device. Data: velocity measured from video recorded motion of polystyrene spheres vs amplitude of wave motion. Solid line: theoretical values based on acoustic streaming theory. (Reprinted with permission. See Ref. [74]. @ 1989 American Institute of Physics.)

Liquid with dye: In experiments where a dye (consisting of permanganate ions) was introduced into a covered water-filled well on the device, circulation of the water was evident. This test was performed to eliminate the possibility that the flow seen earlier was being caused by radiation pressure acting on the marker spheres (whose acoustic impedance differs from that of the liquid).

Electrochemical cell: The limiting current in an electrochemical cell was found to increase substantially when one electrode was a platinum-coated FPW device driven so as to produce either propagating or standing flexural waves [76]. The fractional increase in cell current was proportional to the square of the drive voltage, and hence to the square of the wave amplitude (Figure 3.53, page 138). 3.4.3.2

Phenomena Involved

These experimental observations can be accounted for by an approximate analysis based on the nonlinear phenomenon of acoustic streaming [77] in the fluid that contacts the FPW device. Briefly, the phenomena involved are the following:

3.4 F l e x u r a l P l a t e - W a v e ( F P W ) D e v i c e s

137

1. Because of its small volume, the displacement of the surface of the FPW plate is relatively large when even a small amount of acoustic power is used. For example, a few milliwatts at a few megahertz in a 3mm-wide, 2-micron-thick plate produces 100nm peak-to-peak displacements. 2. If the disturbance in the fluid that contacts the plate is evanescent (that is, if vp < VF), the energy in the fluid is concentrated within the evanescent decay distance, Be, from the plate. For the device illustrated in Figure 3.41, having a 100/xm wavelength, this distance is only 16/~m. Thus, the acoustic intensity can be relatively large near the membrane. 3. Because of the high amplitudes of particle motion in the fluid due to (l) and (2), nonlinear acoustic effects can be important. In particular, acoustic streaming can occur, so that a propagating sinusoidal wave produces a steady ("zero frequency") force in the direction of wave propagation. This steady force causes fluids in contact with the membrane to move. 4. In the electrochemical cell, circulation of the entire fluid (propagating wave) or local circulation (standing wave) stirs the electrolyte near the

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Figure 3.52 Flow velocity measured at different heights in closed flow cell of Figure 3.50. Below 170/zm liquid flows to the right in the direction of wave propagation. Above that height liquid flows to the left due to recirculation in the closed cell. (Reprinted with permission. See Ref. [75]. 9 1994 I E E E . )

138

3. Acoustic Wave Sensors and Responses

Figure 3.53 Electrochemical cell employing flexural-wave device as one electrode. Top: Cell with RF source to drive platinum-covered flexural-wave device in bottom of cell. Middle: Limiting cell current vs time as both transducers on FPW device are switched on and off, producing standing waves, at the different drive amplitudes shown as parameter. Bottom: Square-law dependence of increase of limiting current upon transducer voltage that produces mixing of the liquid in the cell. (Reprintedwith permission.See Ref. [76]. 9 1991 IEEE.)

3.4 Flexural Plate-Wave (FPW) Devices

139

electrode and so reduces the current limitation caused by relatively less effective mass transport by diffusion. An approximate analysis of FPW fluid pumping [74,75,78] indicates that acoustic streaming accounts well for the observed pumping speeds observed in the experiments with water and the marker spheres. The transport of granular particles is believed to result from pumping of the ambient air. In addition, the FPW wave intensity and relatively low frequency favor the production of sonochemical effects [79].

Applications

3.4.3.3

The ability to include FPW pumping and mixing along with sensing in microfabricated devices suggests that one might realize useful "microflow systems.,' The simplest such system might be a compact planar micropump included in the package with an integrated circuit to circulate coolant over the chip so as to reduce the tendency for hot spots to occur and degrade circuit performance. Another example is including an FPW micropump as a gas sampler in an FPW vapor sensing module, which could be used as an air-quality monitor or for sensing accidental release of toxic vapors in an industrial plant. Figure 3.54 shows schematically a generic microflow system that might be used to synthesize fine chemicals from reactants on demand, or to produce individual doses of a reconstituted lyophilized drug for medical treatment. A multiPROCESSING CHAMBER PARTICI~ TR'ANsF~RT"L--ih~ INPUT PUMP #1. I

|

i |

iJ

in

i

n

i

LIQUID INPUT PUMP #I |

IMI~R'I PROCESS SENSOR I HEATER ]

Figure 3.54 Conceptual view of integrated microflow system employing FPW pumps, mixer, process sensor and insonicator to produce ultrasound-assisted chemical reactions. Heater would be deposited metal or polysilicon meanderline formed on a surface of the chamber.

140

3. Acoustic Wave Sensors and Responses

plicity of input pump sections could be employed to bring a number of reactants together. In the processing chamber, FPW elements could be used to mix reactants or solvents and solutes. Other FPW elements could monitor liquid density and viscosity. The insonicator indicated could be used to produce sonochemical effects, such as in situ cell lysis as a first step in biochemical analysis of DNA [80] and access to alternative reaction pathways [81]. The mixing produced by a propagating flexural plate wave could be used to augment the effect of diffusion in bringing reacting ions to an electrode in an amperometric chemical sensor; the result would be to reduce the response time and effectively increase the signal-to-noise ratio for the sensor. As an indication of the magnitude of the improvements that ultrasonic mixing could bring, note that researchers working with an ELISA immunoassay found that insonication with bulk ultrasonic waves could produce increases in the rate of reaction of more than 500 times [82].

3.5

Comparison of Acoustic Sensing Devices

It may be helpful to close this chapter by discussing what the TSM, SAW, APM, and FPW sensors have in common and in what ways they differ. We will also describe several additional types of acoustic sensors.

3.5.1 3.5.1.1

R E C E N T L Y INTRODUCED ACOUSTIC SENSORS Thin-Film Compressional Bulk-Wave Sensor

As an outgrowth of research on piezoelectric filter elements incorporated into high-frequency integrated circuits, Lakin and co-workers [82a] have realized a thin-film compressional bulk-wave resonator that functions as a gravimetric sensor. Like the conventional TSM, this resonator is operated at the frequency for which its thickness is one-half a wavelength. The piezoelectric film is chemicalvapor-deposited aluminum nitride, having a thickness of approximately four micrometers, formed on a silicon or gallium arsenide wafer that is subsequently etched to leave an unsupported resonant diaphragm. Resonant frequencies near 1 GHz result. Because the membrane vibrates in a compressional mode, rather than shear as in the TSM device, this sensor is most likely to be useful in a gaseous rather than liquid ambient. A gravimetric sensitivity, Sin, of 555 cm2/g has been reported [83] for one of these 1 GHz devices; this value is in good agreement with what one would predict from the analysis cited in Section 3.5.2 below.

3.5 Comparison of Acoustic Sensing Devices 3.5.1.2

141

Surface Transverse Wave (STW) Sensor

In this device, a thin film or periodic grating on the surface of the crystal slows the wave and prevents radiation of energy into the interior of the crystal [84]. With proper choice of crystal orientation, a purely transverse particle motion at the surface can be obtained, permitting the sensor to operate successfully in liquids.

3.5.1.3

Love Wave Sensor

Another approach to obtaining a sturdy sensor substrate and a transverse particle motion to permit operation in liquids is the use of a structure that supports Love waves [85,86]. These waves are guided in a layer that is thin compared with the wavelength on a thick substrate. With the proper choice of materials one may also be able to achieve a significant degree of temperature compensation in this device.

3.5.1.4

Thin-Rod Flexurai.Wave Sensor

Just as flexural waves can propagate at low speeds in a plate whose thickness is much less than the wavelength, a low-speed flexural wave can propagate in a cylindrical rod whose diameter is much smaller than the wavelength [87]. Because of the low wave speed, operation as a gravimetric sensor in liquids is possible, as with the flexural plate-wave sensor. The gravimetric sensitivity for this sensor is typically Sm = -1/(2PFa), where a is the radius of the rod.

3.5.2

COMPARISON OF GRAVIMETRIC ACOUSTIC SENSORS

The gravimetric sensitivity, Sin, of each of our four main sensors can be expressed in a simple form that permits easy comparison of device sensitivity. The key is to focus on the dimensions of the "active region" of each device where wave energy is present. For the TSM, APM, and FPW devices, the dimension, d, of the active region is the device thickness. In the TSM resonator, the thickness, d, must be an integer multiple, n, of the wavelength, A: nA dTSM ......... 9 2

(3.89)

In the SAW, APM, and FPW devices, the wavelength is determined by the spatial periodicity of the interdigital transducer, while the thicknesses of the APM

142

3. Acoustic Wave Sensors and Responses

and FPW plates are chosen for mechanical strength or ease of handling. In the SAW device, the wave energy is concentrated within a wavelength or less of the surface, even though the SAW substrate may be tens or hundreds of wavelengths thick. It has been shown [87,88] that one can start from traditional expressions for the gravimetric sensitivities of these four devices and derive the simple approximate expressions for gravimetric sensitivity that are given in Table 3.5.1. The reader should consult the reference for the TSM, SAW, and FPW derivations, or Section 3.3.2 for the corresponding APM result. To interpret these expressions, recall that the gravimetric sensitivity Sm is defined as Sm -- ~ m \ Vp ]

(3.90)

where Avp = change of wave velocity from its unperturbed value, vp, produced by adding a mass per unit area, Am, onto the surface of the device. For delayline oscillator sensors in which Am causes a frequency shift, Af, from the unperturbed resonant frequency f, one can show that (Af/f) = (Av/v), and so Sm = -~m

"

(3.91)

By focussing attention on wavelength rather than frequency, one arrives at the simple expressions for gravimetric sensitivity tabulated at the left side of Table 3.5.1. The expressions show that to obtain high sensitivity for the TSM and SAW, one must reduce the operating wavelength; this can be done by increasing the operating frequency, since A = Vp/f. In the TSM, mechanical fragility limits the amount by which one may reduce the wavelength, since the plate thickness is related to the wavelength by drsM = nM2. (Overtone operation at odd multiples of a half-wavelength, or use of deposited thin-film resonators permits making moresensitive devices.) In the APM and FPW, higher sensitivity is obtained by reducing the plate thickness. Fragility sets a limiting minimum thickness of perhaps 100 micrometers for APMs made from mechanically lapped and polished oriented single-crystal material. In contrast, the FPW may be made by thin-film depositions, and so the thickness of its plate can even be less than one micrometer. Reducing the FPW plate thickness reduces the thickness-to-wavelength ratio, if the wavelength is held constant, and so reduces both the wave velocity (Figure 3.40) and the operating frequency. The gravimetric sensitivity is only one factor that affects the minimum added

Table 3.5.1

Gravimetric Sensitivities of Acoustic Sensors

Experimental Devices

Sensor Bulk-wave

Theoretical Sensitivity Sm -2/pA

or

Experimental

Calculated

Frequency (MHz)

Sm Value (cmZ/g)

Sm Value (cmZ/g)

AT-cut quartz

6

-14

-14

97

- 130 a

- 130b( - 133) c

97

--9.5 (zeroth

- 9 . 3 (zeroth

TSM

resonator Surface-wave

n/pd

Operating

Device Description

-K(tr)/pA

ST-cut S A W delay line

device (assumed elastically isotropic) Acoustic plate-mode

- 1/pd

mode); - 19.4

APM

device Flexural plate device

ST-cut quart

- 1/2pd

mode); - 18.6

ZnO-on-silicon

4.7

(higher modes) -442 d

(higher modes) -450 c

nitride FPW

2.6

-990 d

-951 e

delay line aExperimental value determined by deposition of nickel film. bExpected value for mass loading alone. CMass-loading value calculated for SAW in isotropic solid using from Sm= K(tr)/pA assuming Poisson's ratio tr = 0.35. dLiquid loading experiments verified functional dependences and gave value of M, membrane mass per unit area; experimental value of Sm is then Sm= - 1/2M. eValue of M is based on composite membrane thickness and densities. Sm is then given by Sm = -1/2M. (Reprinted with permission. See Ref. [88]. 9 1991 American Institute of Physics.)

Table

Qualitative Comparison of Acoustic Sensors

3.5.2

ii

Device p.t

4~

TSM SAW

Sm

Temperature Stability Uncoated

Motion at Surface of Device

Low Med

High High (Med) a

Transverse Normal and Transverse Transverse

APM

Low-

High

FPW

Med High

Med

i

Normal and Transverse i

i

i

ii

i

Wave Velocity Relative to that Liquid Fast (V > Cl) Slow (v < cD

Immersible?

Fast Fast

Yes

Low

Med

Discrete

R

No

Med-High

High

Discrete or

D or R D D or R

Frequency

of Operation

Mechanical Strength

Discrete or Multiple Fabrication

Fast

Yes

Med-High

Med

Multiple Discrete

Slow

Yes

Low

Low-Med b

Multiple

,

i

i

i

Delay-line or R_esonator

i

aST-quartz is a highly temperature stable single-crystal SAW cut. SAWs made with piezoelectric films deposited on silicon or other substrates typically have lower temperature stability. bFPW devices utilize thin membranes that are mechanically rugged if their transverse dimensions are not too large.

References

145

mass that these sensors can detect. Other important factors that are dealt with in later chapters are the instabilities (noise) of the device in its operating condition - - bare, coated with a sorptive layer, in contact with a liquid - - and the noise contributed by the associated electronic measurement equipment.

3.5.3

Q U A L I T A T I V E C O M P A R I S O N OF A C O U S T I C S E N S O R S

Table 3.5.2 summarizes qualitatively the characteristics of the four sensor families discussed. The reasons for many of the entries should be apparent from the preceding discussion. Additional points to note are: (1) The thermal stability of any of the devices made from temperaturestable crystal cuts is degraded considerably when the device is coated with a polymeric film used for vapor sorption. Contact with a liquid may also introduce temperature variations that affect the short-term noise of the entire system. (2) The devices whose particle motions are transverse only, or whose phase velocities are lower than the speed of sound in the liquid, can be immersed in a liquid without suffering excessive radiative loss. (3) A high frequency of operation may lead to a high gravimetric sensitivity, but at the expense of more costly electronics. In viscosity sensing, the higher the operating frequency the lower the maximUm viscosity that can be sensed. (4) Discrete devices can, of course, be connected in arrays to obtain better selectivity or higher accuracy. Devices fabricated concurrently may have more similar characteristics than discrete devices made at different times, and so be better suited for use in arrays.

References 1. 2. 3. 4.

Sauerbrey, G. Z. Phys. 155, 206-222 (1959). Numura, T. and Minemura, A. Nippon Kagaku Kaishi, 1621 (1980). Konash, P. L. and Bastiaans, G. J. Anal. Chem. 52, 1929-1931 (1980). Tiersten, H. In Linear Piezoelectric Plate Vibrations; Plenum: New York, Chap. 10 (1969). 5. Rayleigh, Lord Proc. London Math. Soc. 17, 4-11 (1885). 6. Benes, E. J. Appl. Phys. 56, 608 (1984). 7. Granstaff, V. E. and Martin, S. J. J. Appl. Phys. 75, 1319-1329 (1994).

146

3. Acoustic Wave Sensors and Responses

8. Rosenbaum, J. F. Bulk Acoustic Wave Theory and Devices; Artech: Boston, Sect. 10.5 (1988). 9. Martin, S. J.; Granstaff, V. E.; and Frye, G. C. Anal. Chem. 63, 2272-2281 (1991). 10. Reed, C. E.; Kanazawa, K. K.; and Kaufman, J. H. J. Appl. Phys. 68, 1993-2001 (1990). 11. Mecea, V. and Bucur, R. V. Thin Film Solids, 60, 73-84 (1979). 12. Granstaff, V. E. and Martin, S. J. J. Appl. Phys. 75, 1319-1329 (1994). 13. Cady, W. G. Piezoelectricity; McGraw-Hill: New York, 1946. 14. Martin, S. J.; Frye, G. C.; Ricco, A. J.; Senturia, S. D. Anal. Chem. 65, 2910-2922 (1993). 15. White, F. M. Viscous Fluid Flow; McGraw-Hill: New York (1974). 16. Glassford, A. P. M.; J. Vac. Sci. Technol. 15, 1836-1843 (1978). 17. Martin, S. J.; Frye, G. C.; and Wessendorf, K. O. Sensors and Actuators A44 209-218 (1994). 18. Kanazawa, K. K. and Gordon II, J. G. Anal. Chem. 57, 1770-1771 (1985). 19. Muramatsu, H.; Tamiya, E.; Karube, I. Anal. Chem. 60, 2142-2146 (1988). 20. Beck, R.; Pittermann, U.; Weil, K. G. Ber. Bunsenges. Phys. Chem. 92, 1363-1368 (1988). 21. Yang, M.; Thompson, M. Anal. Chem. 65, 1158-1168 (1993). 22. Tiean, Z.; Liehua, N.; Shouzhou, Y. J. Electroanal. Chem. Intelfacial Electrochem. 293, 1-18 (1990). 23. Ballato, A. IEEE Trans. Sonics UItrason. SU-25, 185-191 (1978). 24. Bruckenstein, S.; Shay, M. Electrochimica Acta 30, 1295-1300 (1985). 25. Schumacher, R. Angew. Chem. Int. Ed. Engl. 29, 329-343 (1990). 26. Beck, R.; Pitterman, U.; Weil, K. G. J. Electrochem. Soc. 139, 453--461 (1992). 27. Beck, R.; Pittermann, U.; Weil, K. G. Ber. Bunsenges. Phys. Chem. 92, 1363-1368 (1988). 28. Martin, S. J.; Frye, G. C.; Ricco, A. J.; Senturia, S. D. Anal. Chem, 65, 2910--2922 (1993). 29. Schlichting, H. Boundary-Layer Theory; McGraw-Hill: New York, 1979; Ch. 11. 30. Rajakovic, L. V.; Cavic-Vlasak, B. A.; Ghaemmaghami, V; Kallury, M. R. K.; Kipling, A. L.; Thompson, M. Anal. Chem. 63, 615-621 (1991 ). 31. Kipling, A. L.; Thompson, M. Anal. Chem. 62, 1514-1519 (1990). 32. Rajakovic, L. V.; Cavic-Vlasak, B. A.; Ghaemmaghami, V; Kallury, M. R. K.; Kipling, A. L.; Thompson, M. Anal. Chem. 63, 615-621 (1991). 33. Thompson, M.; Arthur, C. L.; Dhaliwal, G. K. Anal. Chem. 58, 1206-1209 (1986). 34. Thompson, M.; Dhaliwal, G. K.; Arthur, C. L.; Calabrese, G. S. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC-34, 127 (1987). 35. Mecea, V. M. Sensors and Actuators A, 41-42, 630-637 (1994). 36. Mecea, V. M. Sensors and Actuators A, 40, 1-27 (1994). 37. Haardt, H. Dissertation, Universit~it Kiel (1971).

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38. Martin, S. J.; Wessendorf, K. O.; Gebert, C. T.; Frye, G. C.; Cemosek, R. W.; Casaus, L.; Mitchell, M. A. Proc. of the 1993 IEEE International Frequency Control Symposium; IEEE: New York, 603-608 (1993). 39. Adamson, A. W. Physical Chemistry of Surfaces; Wiley: New York, p. 349 (1982). 40. Martin, S. J. and Frye, G. C. Ultrasonics Symposium Proceedings; IEEE: New York, 393-398 (1991). 41. Ramo, S.; Whinnery, J. R.; Van Duzer, T. Fields and Waves in Communication Electronics; Wiley: New York Sect. 1.18 (1965). 42. White, R. M. Proc. IEEE, 58, 1238-1276 (1970) 43. Datta, S. Sulface Acoustic Wave Devices; Prentice-Hall: Englewood Cliffs, NJ (1986). 44. Morgan, D. P. Sulface-Wave Devices for Signal Processing; Elsevier: New York (1985). 45. Frederick, D. K. and Carlson, A. B. Linear Systems in Communication and Control; Wiley: New York (1971). 46. Ristic, V. M. In Principles of Acoustic Devices; Wiley: New York, p. 127 (1983). 46a. Pfeifer, K. B.; Martin, S. J.; Ricco, A. J. "Surface Acoustic Wave Sensing of VOCs in Harsh Chemical Environments," Sandia Report, SAND93-0070, June 1993. 47. Slobodnik, A. J.; Conway, E. D.; Delmonico, R. T. Microwave Acoustic Handbook, Vol. IA. Surface Wave Velocities; National Technical Information Service, U. S. Dept. of Commerce (1973). 48. Martin, S. J. and Ricco, A. J. 1989 Ultrasonics Symposium Proc.; IEEE, New York, 621-625 (1989). 49. Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed; Wiley: New York, Ch. 1, (1980). 50. Martin, S. J.; Frye, G. C.; Senturia, S. D. Anal. Chem. 66, 2201-2219 (1994). 51. Landau, L. D.; Lifshitz, E. M. Theory of Elasticity, 3rd Ed.; Pergamon: New York, Ch. 1, (1986). 52. Tiersten, H. F.; Sinha, B. K. J. Appl. Phys. 49(1), 87-95 (1978). 53. Grate, J. W.; Snow, A.; Ballantine, D. S.; Wohltjen, H.; Abraham, M. H.; McGill, R. A.; Sasson, P. Anal. Chem. 60, 869-875 (1988). 54. Martin, S. J.; Ricco, A. J.; Niemczyk, T. M., Frye, G. C. Sensors and Actuators 20, 253-268 (1989). 55. Hou, J. and van de Vaart, H. Proc. IEEE Ultrasonics Symp.; Denver, CO, 573-578 (1987). 56. Ricco, A. J. and Martin, S. J. Appl. Phys. Lett. 50, 1474--1476 (1987). 57. Matheson, A. J. Molecular Acoustics; Wiley: New York, pp. 82-83, (1971). 58. Josse, F. Z.; Shana, A.; Radtke, D. E.; Kelkar, U. R.; Haworth, D. T. Electronics Letters 25, 1446-1447 (1989). 59. Niemczyk, T. M.; Martin, S. J.; Frye, G. C.; Ricco, A. J. J. Appl. Phys. 64, 5002-5008 (1988). 60. Lamb, H. Proc. Roy. Soc. (London), Ser. A, 93, 114 (1917).

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61. Viktorov, I. A. Rayleigh and Lamb Waves; Plenum: New York (1967). 62. Wenzel, S. W. Applications of Ultrasonic Lamb Waves, Doctoral Dissertation, EECS Department, University of California, Berkeley, CA (1992). 63. Grate, J. W.; Martin, S. J.; White, R. M. Anal. Chem., 65, Part I: 940A-948A; Part II: 987A-996A (1993). 64. Auld, B. A. In Acoustic Fields and Waves in Solids; Wiley: New York (1973). 65. Sze, S. M.Ed., Semiconductor Sensors; Wiley: New York (1994). 66. Muller, R. S.; Howe, R. T.; Senturia, S. D.; Smith, R. L.; White, R. M. Microsensors; IEEE Press: Piscataway, NJ (1991). 67. Nassar, A. A. and Adler, E. L. Proc. IEEE Ultrasonics Symp., 369 (1983). 68. Wenzel, S. W. and White, R. M. IEEE Trans. Electron Devices, ED-35, 735 (1988). 69. White, R. M. and Wenzel, S. W. U. S. Patent No. 5,189,914 (1992); U. S. Patent No. 5,129,262 (1992). 70. Personal communication, Jay Grate, Battelle Pacific Northwest National Laboratory. 71. Scholte, J. G. Mon. Not. Royal Astronom. Soc., Geophys. Suppl., 5:120 (1947). 72. Costello, B. J.; Wenzel, S. W.; White, R. M. Technical Digest, 7th International Conference on Solid-State Sensors and Actuators, Transducers '93, Yokohama, Japan, pp. 712-715 (7-10 June 1993). 72a. Eto, T. K.; CosteUo, B. J.; Wenzel, S. W.; White, R. M.; Rubiusky, B. J. Biomech. Eng., 115, 329-331 (1993). 73. Costello, B. J.; Wenzel, S. W.; Wang, A.; White, R. M. Proc. IEEE Ultrasonics Symp., 279 (1990). 74. Moroney, R. M.; White, R. M.; Howe, R. T. Appl. Phys. Lett., 59, 774 (1991). 75. Bradley, C. E. and White, R. M. Proc. IEEE Ultrasonics Symposium (1994). 76. Tsao, T. R.; Moroney, R. M.; Martin, B. A.; White, R. M. Proc. IEEE Ultrasonics Symposium, 937-940 ( 1991). 77. Nyborg, W. L. Acoustic So'earning, in Physical Acoustics, Mason, W. P. Ed., 2B, Academic Press 265, (1965). 78. Moroney, R. M.; White, R. M.; Howe, R. T. DSC-32, Symposium on Micromechanical Sensors, Actuators and Systems, ASME Winter Annual Meeting, 181-90 (1991 ). 79. Suslick, K. S. Ultrasound: Its Chemical, Physical, and Biological Effects; VCH Publishers: New York (1988). 80. Northrup, M. A.; Ching, M,; White, R. M.; Watson, R. Technical Digest, 7th International Conference on Solid-State Sensors and Actuators, Transducers '93, Yokohama, Japan, 924-6 (1993). 81. Mason, T. J. Ed., Chemistry With Ultrasound; Elsevier Applied Science: London (1990). 82. Chen, R.; Wenz, L.; Sizto, N. C.; Osoria, B. C.; Hsu, J.; Rodgers, R.; Litman, D. J. Clin. Chem., 30, 1446-1451 (1984). 82a. Lakin, K. M.; Wang, J. S.; Landin, A. R. Proc. 36th Ann. Symp. Freq. Coutr., 517-524 (1982). 83. Personal communication, Mark Porter, Iowa State University.

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Chapter 4

Materials Characterization

The field of materials science has grown dramatically in the past decade, with new materials being synthesized and/or developed for applications such as lubrication, corrosion protection, electronics, paints and coatings, and chemical separations. Many of these materials have complex properties quite different from those associated with simple "ideal" substances. Since the chemical and physical properties of a material determine its ability to meet the often stringent specifications required for a given application, characterizing the properties of materials plays a vital role in materials science. Thin film technology is an excellent example. Thin film materials are currently used in a wide variety of industrial applications. For example, thin films are used as protective or passivating layers [1-3], as conductive or photoactive (i.e., photoresist) layers [1], as dry lubricants [3], as catalysts [4], as gas separation membranes [5], and as optical layers [6]. Thin films can be formed by a variety of processes [ 1-8], including spraying, spin-coating, dip-coating, chemical vapor deposition (CVD), evaporation, and sputtering. To effectively optimize thin film properties, techniques to directly characterize thin film materials are critical. These techniques can be utilized as research and development tools to characterize new materials or, at the other extreme, as on-line probes of film properties during production. A major challenge in developing techniques for characterizing film materials is the limited amount of material present. For example, in a one-micrometer-thick film, there is only 10 -4 cm 3 of material for each cm 2 of film area. Thus, a 10cm 2 film has a volume of only one microliter and a mass on the order of one milligram. Many material characterization instruments do not have sufficient sensitivity to analyze these small volumes or masses [9]. In addition, those tech150 ACOUSTIC WAVE SENSORS

Copyright 9 1997 by Academic Press All righls of reproduction in any form reserved. ISBN 0-12-077460-7

4.1 Overview of Applications

151

niques with the required sensitivity (e.g., reflectance spectrometry, X-ray fluorimetry) have other disadvantages such as excessive cost, extensive sample preparation, long analysis times (no real-time monitoring), and restrictive sample environments (i.e., vacuum) [6,9]. Acoustic wave (AW) devices are ideally suited to thin film characterization due to their extreme sensitivity to thin film properties [10]. The sensitivity of AW devices to a variety of film properties (see Chapter 3), such as mass density, viscoelasticity and conductivity, makes them versatile characterization tools. The ability to rapidly monitor changes in device responses resulting from changes in thin film properties permits their use for monitoring dynamic processes such as film deposition, chemical modification (e.g., photo-polymerization, corrosion), and diffusion of species into and out of films. In this chapter, we explore the current and potential future applications of AW devices for materials characterization and process monitoring. Because of the limited mass of material that can be applied to the AW device surface, the majority of these applications deal with the chemical and physical characterization of thin-film properties. This thin film focus should not be thought of as a limitation of AW devices, but rather as a useful capability - - the direct measurement of properties of materials in thin-film form. Since material properties can depend on the physical form (e.g., film, bulk) of the material (see Section 4.3.1.3), AW devices are uniquely suited to directly characterize thin-film materials. These considerations also indicate that even though it is possible to use AW thin-film data to predict bulk material properties, such extrapolations should be performed with care.

4.1 4.1.1

O v e r v i e w of Applications C H A R A C T E R I Z A T I O N OF T H I N F I L M M A T E R I A L S

The development of AW thin-film characterization techniques has occurred largely because of the interest by various research groups in developing chemical sensors based on coated AW devices (see Chapter 5). Thus, many of the film characterization techniques described here were developed in an effort to characterize sensor coatings or to interpret the observed responses from AW chemical sensors in operation. As described in Chapter 3, mass detection limits for AW devices are typically at or below one ng/cm 2. These low detection limits translate into hundredths of a monolayer of atoms and film thicknesses of hundredths of nanometers. This

152

4. Materials Characterization

sensitivity permits quantitative detection of submonolayer mass changes in thin films formed on AW devices. This extreme mass sensitivity can be used to advantage in the characterization of film properties such as film thickness (Section 4.4.1) and surface area and pore size distribution (Section 4.3.1.2). In addition, it is useful for real-time monitoring of processes such as film deposition (Section 4.4.1), materials modification (Sections 4.4.2 and 4.4.5), corrosion (Section 4.4.3), and diffusion (Section 4.2.2). It can also be used to monitor adsorption at surfaces from both gases and liquids (Section 4.3). Using AW devices to monitor dynamic processes such as diffusion and corrosion can dramatically reduce the time required to quantify these processes. For example, as discussed in Section 4.2.2, diffusion equilibration times typically increase with the square of the diffusional length. For a thin film, this length scale, the film thickness (h), is very small. This enables the quantification of diffusion coefficients as low as 10-15 cm2/sec in less than one day, whereas months would be required using many conventional techniques that use thick films or bulk samples. For corrosion monitoring, the dramatic decrease in mass detection limits obtainable using coated AW devices, as compared with conventional balances and sample coupons, allows detectable mass changes to be achieved in minutes or hours rather than days or months (Section 4.4.3). AW device sensitivity to viscoelastic parameters and electrical properties can be used to advantage in some film characterization techniques. In these situations, a comparison of the AW device response to a model of the AW/thin film interaction is often crucial to the effective evaluation of thin film parameters. These additional interaction mechanisms typically involve changes in both the wave velocity and the wave attenuation for SAW, APM and FPW devices, and changes in both resonant frequency and admittance magnitude in TSM devices. In contrast, mass loading does not contribute to wave attenuation or decreases in admittance since moving mass involves no power dissipation (see Chapter 3). Having detectable changes in two sensor responses allows the amount of information that can be extracted regarding film properties to be increased, since agreement between both responses and predictions from the model aids in the discriminating power of the characterization technique. A demonstration of this can be found in the ability to determine viscoelastic parameters based on monitoring both sensor responses during a temperature cycle for a polymer-coated device (Section 4.2.1.2). These responses are also useful in elucidating the changes occurring during such processes as polymer cross-linking (Section 4.4.2), or the absorption of species in polymers (Section 4.2.1.3).

4.1 Overview of Applications 4.1.2

153

CHARACTERIZATION OF FLUID PROPERTIES

Another area of materials characterization involves characterizing the properties of a contacting fluid. Since the fundamentals of acoustic wave/liquid interactions are covered in detail in Chapter 3, this topic will not be repeated here. However, it seems relevant to provide a brief summary of some of the fluid properties that can be measured. Since SAW devices are excessively damped with liquids, these characterization techniques generally involve only APM, FPW, and TSM devices. Once again, the utility of using two sensor responses can be important. Two key properties that can be probed are viscosity (7/) and density (p). As discussed in Sections 3.1.5 (TSM), 3.3.3 (APM), and 3.4.2.4 (FPW), the responses are often proportional to the square root of the product (pr/); data showing trends vs (pr/) 1/2 have been reported using TSM (see Figure 3.10) [11-15], APM (see Figure 3.35) [16], FPW (see Figure 3.48) [17-19], and Love wave devices [20]. In some cases, one property is held constant to probe the other, for example probing viscosity at constant density [18,21 ]. In many cases, simple trends are shown such as the maximum in viscosity at intermediate concentrations of water/ethanol mixtures [15,22,23], or increasing response with increasing sugar content [22]. It has been observed with TSM devices that rough surface features result in liquid trapping and a term proportional to/9 and an ability to separate out p and 7) (see Section 3.1.6 and Figure 3.11) [24,25]. Similarly, since FPW devices have a velocity dependence proportional to density (see Section 3.4.2.2) and velocity and loss terms proportional to (pr/) 1/2 (see Section 3.4.2.4), it may be possible to use FPW device responses to characterize both p and r/simultaneously. Wave velocity in a fluid, which is a strong function of density, has been probed using longitudinal-mode resonators for analyzing gases (e.g., pressure or changes in composition) [26-28]. SAW devices have also been used with thin liquid layers and a reflector plate for probing liquid properties (e.g., changes in density due to changes in salt concentration) [29,30]. Both of these devices rely on probing the reflected compressional wave, and depend on the separation of the AW device and the reflector. Acoustoelectric interactions enable solution electrical properties to be probed with AW devices. It should be noted that these acoustoelectric interactions can be "shorted out" using a conductive (e.g., metal) layer between the substrate and the solution for APM and FPW devices. Similarly, for TSM devices, if the grounded electrode is placed in contact with the solution, no acoustoelectric effect should be present. The key parameter that has been monitored is solution conductivity. For example, measurements of AW responses vs conductivity have been reported using TSMs [ 11,15,31,32] and APMs (see Figure 3.36) [ 16,33-35].

154

4. Materials Characterization

The APM interaction is described in Section 3.3.4 while the TSM interaction is probably due to parasitic conduction through the solution. In one APM study, porous thin films were found to have an effect on conductivity trends, proposed in the study to be due to changes in solution conductivity in the porous regions [35]. Another explanation could be changes in the dielectric constant in the region of the film, since the dielectric constant has an effect on conductivity responses for APM devices (see Section 3.3.4) [16,34]. In another study, a TSM was used with a conductivity electrode to make a sensitive probe of conductivity that had little dependence on solution viscosity and density [36]. In addition, the parasitic contribution to the static capacitance in TSM devices has been correlated with solution dielectric constant [11,12]. Some sensors for extrinsic properties have also been demonstrated. For example, sensors for mass-flow rate using SAW [37,38] and APM [38] devices combined with either on-chip resistors [38] or acoustic absorbers [37] for device heating have been demonstrated. These devices use the temperature sensitivity of the devices to probe temperature changes induced by convective cooling by the flowing gas. Another investigation showed that the magnitude and direction (relative to the wave velocity) of an imposed shear stress could be monitored with a SAW device. This was proposed to be useful in developing a sensor for local and global turbulence [39]. Finally, a capacitance-dependent TSM sensor system has been demonstrated for measuring liquid volumes in the 0-1 ml range [40]. The demonstrations cited above illustrate how AW devices can be used to probe intrinsic and extrinsic fluid properties. This capability can be useful for providing in-situ probes of critical solution properties such as viscosity, density, and conductivity. This capability should prove useful in the monitoring of process streams or critical fluids (e.g., automotive oil condition monitoring [41 ]).

4.2

Characterization of P o l y m e r s

A polymer can be defined as a compound consisting of a large number of repeating units, called monomers. These monomers are joined together by covalent bonds to form a long chain. The degree of polymerization is defined as the number of repeating units in the chain. The properties of the polymer depend on the overall size of the polymer chain (i.e., average molecular weight) and on the inter- and intra-molecular forces that hold the polymer together [42--44]. The intramolecular forces consist of the covalent bonds that join the repeat units into chains, and any covalent bonds that may join adjacent chains together (crosslinkages). In addition, the polymer chains are held together by a variety of in-

4.2 Characterization of Polymers

155

termolecular forces, including hydrogen bonding, dipole-dipole interactions, and London dispersion forces resulting from the synchronization of electron motion in the interacting atoms (see Chapter 5 for a discussion of chemical interactions). The physical and chemical properties of the polymer depend on the types and relative strengths of these inter- and intra-molecular interactions. The sheer volume of polymeric material produced has increased dramatically in the last decade and, insofar as the chemical and physical properties of these materials can be modified, the number of applications for polymers has expanded [ 1,2,5]. In general, the polymer properties of interest can be categorized as diffusion/permeation properties or as mechanical (e.g., viscoelastic) properties. The measurement of diffusion/permeation properties is straightforward when diffusion of a species into a polymer film produces a simple mass-loading effect. Experimental determination of these properties using AW devices will be discussed in Section 4.2.2. In addition to the mass-loading effect, the presence of dispersed molecules in a polymer has a plasticizing effect, inducing changes in viscoelastic properties, as described in Section 4.2.1.3. Measurement of these viscoelastic properties is more complex. There are a number of texts that provide an excellent discussion of the viscoelastic behavior of polymers, including theoretical models to explain such behavior [42-44]. While an in-depth discussion of these models and their ramifications is beyond the scope of this work, a brief summary of viscoelastic behavior is supplied below.

4.2.1

VISCOELASTIC PROPERTIES

The viscoelastic properties of a polymer can be described in terms of how the polymer deforms in response to an applied stress. Elasticity refers to the ability of a material to return to its original shape after it has been stressed. Elastic behavior implies a linear relationship between stress, T, and strain, S, (T oc S). Viscosity is a measure of the flow resistance of the polymer or polymer solution. Viscous behavior implies a linear relationship between shear stress and the rate of strain (T oc OS/Ot). Rigid materials tend to display elastic behavior, whereas fluid or soft materials display viscous behavior. In many polymers, a combination of elastic and viscous responses arises as a direct consequence of the chain structure, hence the term "viscoelastic" properties. The concepts of stress, strain and displacement have already been introduced in Chapter 2 in describing the propagation of acoustic waves in an elastic medium, and in Chapter 3 in describing the various sensing mechanisms. The two deformation modes of interest are elongation and shear deformation. Elongation refers to the change in length

156

4. Materials Characterization

(in a given direction) of a polymer sample upon application of a longitudinal unit stress (i.e., stretching or compressing). Shear deformation refers to the deformation behavior of the sample under the application of a lateral force on one surface. How a polymer behaves under the force of an applied stress depends on a number of variables, including temperature, pressure, and the time frame (i.e., frequency) and nature (i.e., shear vs elongation) of the stress. As described in more detail in Section 3.1.8, the viscoelasticity of a polymer can be described by a complex modulus. The modulus is defined as the stress associated with a unit strain, and has units of force/unit area (dynes/cm2). It can be thought of as the stiffness or rigidity of the polymer, and is related to the inter- and intra-molecular forces at work within the polymer. In general, polymer film/acoustic wave interactions are dominated by the shear component of displacement (see Chapter 3). Thus, it is the shear modulus which can be effectively probed with AW devices. This shear modulus can be represented by G = G' + jG" where G', the storage modulus, is associated with energy storage and release during the periodic deformation associated with the oscillating stress, and G", the loss modulus, is associated with the dissipation of energy, usually as heat. The modulus depends on the molecular structure of the polymer, the average molecular weight, the temperature, and, in general, the rate (frequency) of applied shear stress. The interchangeability between temperature and strain rate in determining the modulus was first described by Williams, Landel and Ferry [45] and became the basis of the so-called "time-temperature superposition principle." This dependence can be explained in terms of the molecular motions in the polymer chain by examining the mechanism by which a polymer reacts to an applied stress. When the polymer is deformed on a time scale, Ts, that does not allow significant thermal motion of polymer chains with respect to each other (i.e., rotational freedom of the polymer chains is limited), the polymer behaves as a rigid or "glassy" material. The glassy state is characterized by large shear moduli, on the order of 101~dynes/cm 2. As temperature increases, thermal energy in the system becomes sufficient to overcome the molecular forces, permitting free rotation around the bonds of the polymer chain. This additional rotational freedom is manifested as a softening or "relaxation" of the polymer, and the polymer is described as an "elastomer." Modulus values of elastomers are on the order of 107 dynes/cm 2. The temperature at which the transition from the glassy to the elastomeric state occurs is called the glass transition temperature Tg. Another way to look at this is to consider that the polymer exhibits a characteristic relaxation time, ~'. If the stress is applied for a time period Ts that is much

4.2 Characterization of Polymers

157

shorter than the relaxation time (Ts < < ~'), polymer chains do not have time to move with respect to each other and the polymer behaves as an elastic solid characterized by a stiffness/x. As temperature increases, z decreases until Ts > > ~', at which point thermal motion allows (uncrosslinked) chains to move with respect to each other and the polymer behaves as a viscous liquid characterized by a viscosity r/. Tg can be defined as the temperature where Ts ~ I", at which point the polymer deforms both elastically and viscously, giving rise to viscoelastic behavior. It should be noted that Tg for an amorphous, glassy polymer is not the same as the melting temperature Tm for a semi-crystalline polymer. Both glassy and semi-crystalline materials are characterized by high modulus values, yet the two transition temperatures are associated with distinctly different phenomena. The former (Tg) is a relaxation, or second-order transition, and exhibits the time (frequency) dependence discussed above. In addition, this Tg transition generally occurs over a significant temperature range (i.e., is not abrupt) due to heterogeneities in the polymer and the fact that chain motion is an activated process. The latter (Tin) arises because of a chemical phase change, or first-order transition, and is independent of frequency. Melting transitions typically occur only in polymers having chains sufficiently linear to allow "packing" in a regular crystalline-like manner. Just like other melting transitions (e.g., ice to water), the temperature at which the transition occurs can depend on whether the temperature is being raised or lowered to induce the transition. This is due to the fact that nucleation of the crystalline phase during cooling does not occur until a lower temperature (i.e., supercooling) as a result of the high curvature of a newly nucleated phase [46]. In polymers, these melting transitions may not always occur at a single temperature. Instead, the presence of different molecular chain structures can result in multiple transitions, often denoted by Greek letters [45]. Even though these transitions are different in many ways, as demonstrated below, the way in which acoustic energy interacts with polymeric materials permits us to use AW devices to probe changes in polymer film viscoelastic properties associated with these transitions. It should be emphasized up front, however, that evaluating the viscoelastic properties (e.g., modulus values) requires an ability to effectively model the film displacement profiles in the viscoelastic layer. As described in Section 3.1.8, the film displacement effects are dictated by the phase shift, ~b, across the film. Since ~b depends on film thickness, perturbations in acoustic wave properties due to changes in viscoelastic properties (e.g., during polymer transitions) do not typically depend simply on the intrinsic polymer properties. This can lead to erroneous predictions if the film

158

4. Materials Characterization

dynamics are not taken into account. However, if these dynamics are effectively modeled, the AW device response can be used to quantitatively evaluate the shear modulus values (see Section 4.2.1.2).

4.2.1.1

Determination of Transition Temperatures

The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. Because of the oscillatory nature of the acoustic wave, probing of polymer viscoelastic properties using AW devices is analogous to the high rate/short time scale probing of polymers mentioned previously. The wave period, which is the inverse of the AW frequency, determines the time scale of the applied strain. Wave attenuation and velocity, or resonant amplitude and frequency, can be monitored at a relatively fixed frequency (rate) while scanning the temperature. The use of SAW devices to identify Ts and Tm for a variety of polymers has been reported. Both attenuation (output amplitude) [49,50] and velocity (frequency) [51,52] changes have been monitored. In two of these studies, relatively thick sample films were tested [50,51 ], and the results were consistent with Ts and Tm values from other experimental methods, such as differential scanning calorimetry (DSC). (It should be noted that the slow processes (large Ts) used in techniques such as DSC result in these techniques probing the static or low-frequency Tg values.) An example of this type of trend is shown in Figure 4.1 for a film being pressed onto the surface of a SAW device using a clamping system. No increase in T8 was observed, indicating that the measured attenuation/velocity changes were the result of changes in the AW/polymer coupling due to increased adhesion of the polymer to the AW device surface. This transition from a poorly coupled film, which has a correspondingly low perturbation in wave amplitude, to a film coupled to the acoustic wave, resulting in significant atten-

4.2 Characterization of Polymers

159

1.0

>

O O

E

V

uJ Q

0.8

l" ..J 11. ram=

'< ,.J

0.6

O

.< Z

0 m

U)

0.4

::) n_ I::)

0

Tg=75* 0.2

O 0.0

!~_ 30

I 60

C~o6itie~J 90

, I ...... 120

130

TEMPERATURE (oc) Figure 4.1 Glass transition detection using a polyethylene terephthalate film clamped o n t o the surface of a SAW device. (Reprinted with permission. See Ref. [50]. Copyright 9 1979 American Chemical Society.)

uation of the wave, occured when the polymer became softer as the temperature is raised above the static (low-frequency) Tg. Another technique for evaluating the static Tg uses an indirect approach that probes relatively slow processes. King [53] described how changes in diffusion rates (as indicated by the time to sorb 90% of the final sorption value) and solubility values could be used to probe the change from a glassy (slow diffusion) to a rubbery (diffusion several orders of magnitude faster) state. Using polystyrene on TSM devices, King showed that Tg values in agreement with those

160

4. Materials Characterization

obtained by other techniques could be determined, as well as showing that the transition occurred over a temperature range of about 20~ (interpreted as being due to the sample having a distribution of molecular weights). TSM-determined partition and diffusion coefficients vs temperature have also been used to probe transition temperatures in synthetic lipid multibilayer films [54]. Other studies have demonstrated the utility of FPW devices to identify both the static and dynamic Ts of polymer films simultaneously [55-57]. As shown in Figure 4.2, the static (low-frequency) Tg Was observed as a change in the slope of the acoustic velocity vs temperature curve; the change in slope was interpreted as a change in the rate of polymer expansion at the polymer static (low-frequency) Tg. The dynamic (or frequency-dependent) Ts was identified as a minimum in a plot of the acoustic wave amplitude vs temperature (indicative of a maximum in the loss modulus G"). These basic trends are consistent with results using bulk transducers to generate longitudinal waves at 2.5 MHz in polymer disks combined with a technique for measuring the thickness of the polymer disk with temperature [47]. For the one polymer (poly(vinylacetate)) where both the static and dynamic transitions were observed, the static transition was found to be about

4780

%

4760 A

N "I"

>.

4740

tO Z uJ =)

o

uJ

4720

u..

4700

4680

........ 0

1 10

I 20

.. I 30

..

TEMPERATURE

I 40

.....

I .. 50

I 60

.

.

.

.

.

.

(~

Figure 4.2 Frequency vs temperature for a poly(t-butyl acrylate)-coated FPW device

showing a slope change at the static (low-frequency) Ts. 9 1992 American Chemical Society.)

(Reprinted with permission. See Ref. [56].

4.2 Characterization of Polymers

161

60~ lower than the dynamic transition probed by the 5 MHz FPW device. Previous SAW studies have also reported detecting the dynamic Tg using thin films sprayed or cast on the SAW device surface. The observed Tg values (indicated by trends in the frequency response) were reported to be increased by ~50~ compared to DSC or other low-frequency techniques [50,52]. These results, indicating Tg values at AW frequencies significantly higher than the static Tg values, are consistent with the time-temperature superposition principle. To enable probing of the frequency dependence, one SAW study used a multi-frequency SAW device (i.e., a single ST-quartz substrate bearing five different SAW delay lines) to probe the temperature-dependent behavior of polymer films [58]. Multifrequency probing of viscoelastic properties has also been performed using TSM devices probed over many harmonics using a network analyzer [59,60]. The minimum amplitude (maximum attenuation) reported in the FPW study has also been observed during temperature ramps of polymer-coated SAW devices [61--65]. Examples of data for both velocity and attenuation are shown in Figure 4.3. In this study, it was determined that the observed trends were due to film resonance conditions (see Sections 3.1.8 and 3.2.7). This was strongly indicated by the fact that the temperature of the maximum attenuation decreased with increasing film thickness h; in fact, a more-than-60~ in the temperature of the maximum attenuation is demonstrated for only a three-fold increase in film thickness (0.44 to 1.37/zm). These results highlight the importance of considering film dynamics when investigating viscoelastic properties and transitions using AW devices [61,63,64]. Regarding the FPW work described above, it is important to consider whether this amplitude minimum is due to film resonance or if the films were thin enough (h about 0.5 to 1 /zm) that the phase shift ~b is much less than Ir/2 at the frequency of the FPW device (5 MHz). This latter condition would indicate that the observed amplitude minimum would represent the maximum in G" that occurs at the glass transition. FPW devices have the advantage for this application of high sensitivity at lower frequencies (smaller th values and an ability to stay in the acoustically thin realm). Thus, it appears that the film was acoustically thin for these FPW tests and that the responses are tracking changes in the film properties (i.e., h, G', and G"). This same question regarding film resonance is even more relevant for the earlier higher frequency SAW work [50,52], since film resonance results in frequency trends similar to those reported as being due to the glass transition. If film resonance effects are occurring in these studies, the reported Tg values would still be close to the actual Tg since it is the dramatic change in modulus values during the glass transition that would result in significant changes in the phase shift and the onset of film resonance. However, the

162

4. Materials Characterization 3.5

.....

~

. . I . . . . . . I. . . . . . . I . . . . . . I. . . . . . . I . . . . . .

[ PIB Film (~tm): 3.0 t_[_ , 0.44 ] 9 0.68

:

2.5

~,.,

9

4k)

2.0

1.o

..-'.--m

**

I ~/r

_ . f " _4)0 ,,=

/

&

"~

,'"

,*

-

9

AA A 9 9 0 oeo

an n

9r

aa""

.af

*

0.5 I

_ 9 .,,**,

,nul

t

/

4

~'*

I:]7

1.5[

I

9

'

/

.

AAAA***Q

]

~'Jbtm ' m - a L b ~ P ~ b qk 9

0.0

0

-1 9

,~

*~,

-2

I

. AA~ A

m

- - ~ & & A "

I ~0

~k%, A a.

"ml"

-3

"4 I

-4

"

9 4

.5

I

-20

0

,,

I

20

......

40

I

I

40

60

......

I

80

,

I

I

I00

120

Temperature (C) Figure 4.3 Attenuationand frequency vs temperature for 97-MHz SAW devices with various film thickness of polysobutylene (PIB). The maximum in attenuation and the sigmoidal frequency excursion are due to the onset of film resonance as the polymer softens with temperature. The temperature at which these AW trends occur depends on the thickness of the coating (thicker coatings yield lower temperatures). (Reprintedwith permission. See Ref. [61]. 9 1994 American Chemical Society.)

4.2 Characterization of Polymers

163

specific Tg value, and the interpretation that the AW trends are directly indicating changes in G' and G", would not be accurate if film resonance is causing the observed trends. This is clearly shown by the results in Figure 4.3.

4.2.1.2

Extraction of Storage and Loss Moduli

In this section we will describe how a proper accounting for film dynamics, based on a model of the thin-film/acoustic-wave interactions, can be used to quantitatively evaluate the shear modulus values as a function of temperature. As described in Section 3.1, an equivalent-circuit model can be used to relate the measured TSM electrical characteristics to the elastic properties, density, and thickness of a polymer film coating the device. Consequently, measurements made with polymer-coated TSM devices can be used to extract the shear elastic properties of the film. In order to separate properties of the film from those of the crystal, admittance-vs-frequency (Y-vs-f) measurements are made on the TSM resonator before and after deposition of a film. Fitting the equivalent-circuit model to measurements made on the uncoated device is crucial, allowing extraction of all of the circuit elements except Ze ~ the impedance element arising from the film (Figure 3.7). Once the uncoated resonator has been characterized, the impedance element Ze arising from a film coating. If measurements at only a single harmonic are used, film thickness and density must be known to extract G' and G". Admittance-vs-frequency measurements made at several temperatures on a polyisobutylene-coated TSM resonator were fit to the equivalent-circuit model of Sections 3.1.3 and 3.1.9 to determine values of G' and G" for the film [66]. These extracted values are shown in Figure 4.4, along with 5-MHz values obtained from the literature for polyisobutylene having an average molecular weight of 1.56 • 106 [44]. We note excellent agreement between the extracted and literature values of G' from - 2 0 ~ to 60~ and in G" from - 2 0 ~ to 10~ Above 10~ the extracted G" values are approximately 30% higher than the literature values. These results illustrate how AW devices can be used to quantitatively evaluate the viscoelastic properties of polymer films. Similar models for other AW devices, such as the model for SAW devices coated with viscoelastic layers (Section 3.2.7 and [61 ]), can enable these other devices also to be used to determine modulus values. However, the pure shear motion of the TSM does simplify the model, and the evaluation of the modulus values as compared with the more complex displacements of other AW devices such as the SAW device (a comparison of the models of Section 3.1.9 for the TSM and Section 3.2.7 for the SAW demonstrates this point).

164

4. Materials Characterization

10.0 04

E t~

9.5

c

~

"0 =

t3

i

01 0

S

kAA 9,0

--

8.5

-

'~

~-.

-- ~ --

G

kk

t!

8.0 -20

0

20

40

60

80

Temperature (~ Figure 4.4 Components of the shear elastic modulus extracted from admittance vs frequency measurements using a 15.6 /xm-thick polyisobutylene-coated TSM resonator. Lines are literature values for the polyisobutylene modulus [44] at 5 MHz. (Reprinted with permission. See Ref. [66] @ 1991 IEEE.)

4.2.1.3

Absorption P h e n o m e n a and Plasticization

Absorption of a solute liquid or vapor into a polymer film can profoundly affect the viscoelastic behavior of the polymer. The magnitude of this effect depends on the nature of the solute/polymer interactions and on the amount of solute absorbed. The solute/polymer interactions can range from simple dispersion to hydrogen-bonding and other specific interactions. The extent of absorption can be described by the partition coefficient, K, which quantifies the thermodynamic distribution of the solute between two phases (K = concentration in polymer divided by the concentration in the liquid or vapor phase in contact with the polymer). It has long been known that acoustic wave devices can be used to probe solubility and partition coefficients [53,67]. Due to the relevance of these topics to chemical sensors, more comprehensive discussions of these interaction mechanisms and the significance of the partition coefficient are included in Chapter 5. The major effects of solute absorption by a polymer are swelling (change in

4.2 Characterization of Polymers

165

volume) and plasticization. Both effects are a direct consequence of the solute/polymer interactions. As a solute absorbs into the polymer, it interrupts the intermolecular forces at work between the individual polymer chains, and the polymer swells. For polymers in which these forces are strong, due to a high degree of cross-linking or crystallinity, the swelling will be minimal. Lightly crosslinked or linear polymers can experience significant swelling. A theoretical analysis of the effect of compressive tensions resulting from this swelling is presented by Bartley and Dominguez [68]. The effect of vapor uptake on adhesion of polyimide films, possibly due in part to swelling effects, has been described [69,70]. Grate and coworkers [57,71 ] first proposed and documented, using predicted uptakes from gas chromatograph (GC) retention volumes, how these swelling effects can enhance the sensitivity of SAW chemical sensors over the predicted mass-loading values. This increased sensitivity has been confirmed by separate researchers [72]. Concurrent with the swelling phenomenon, the polymer may undergo significant changes in its viscoelastic properties. The presence of absorbed solute molecules in the regions between the polymer chains can act as a lubricant. Due to the interruption of the polymer intermolecular forces, the individual chains may move more freely and the polymer softens. The net results are a decrease in the Tg of the polymer that is dependent on the concentration of absorbed solute [73,74], and a broadening of the elastomeric region. This effect is called plasticization and has been observed using AW devices [51,61-65]. Mass changes associated with solute absorption will produce a change in the AW velocity without significant attenuation of the wave. Modulus changes associated with the glass transition will produce both velocity and attenuation changes. Examples of experimental results for solvent plasticization are shown in Figure 4.5. This plot is a parametric representation of data similar to that shown in Figure 4.3 for a temperature ramp, except the parameter being changed to move along a given curve is the concentration of the absorbing species in the vapor phase contacting the device [ 10,62,75]. As expected, significant velocity and attenuation changes are observed. In addition, the trends with different chemical species can be used to understand the plasticizing action. Since attenuation does not depend on the mass loading, a position on the curve at a given attenuation (e.g., the point of maximum attenuation) can be used as an indicator of the viscoelastic transition. If the velocity shift at the point of peak attenuation is plotted against the liquid density of the absorbing species, a linear relationship is observed [62]. Extrapolating the line to a density of zero should give the value of velocity shift due to changes in the viscoelastic properties. This is verified by the agreement of this extrapolated velocity shift with the value obtained in an ex-

166

4. Materials Characterization

1.5 PENTANE

1.0

: iN

0.5

"i g i

I

m

0.0

1.5 V VV

METHYLENE CHLORIDE

1.0 A

0.5

I

0 >r

"~

0.0

1.5 1.0

0.5 TRIC HL OROETHYLEN E

0.0

I

2.0

. ~ I DIBROMOMETHANE

1.5

I I

1.0 0.5 0.0

I

'

-1.5-1.0-0.5

A V/Vo

0.0

0.5

1.0

1.5

2.0

( x 10 "3)

Figure 4.5 Normalized attenuation-vs-velocity changes for a polymer-coated SAW device as vapor partial pressures are varied from 0% (at dashed line) to 80% of saturation. The polymer, Kraton D1102, is an ABA triblock copolymer, where A is polystyrene (approximately 28% by weight) and B is polybutadiene. (Reprinted with permission. See Ref. [62].)

4.2 Characterization of Polymers

167

periment where temperature changes were used to induce the viscoelastic transition. These trends are observed even though the maximum attenuations are not due directly to a maximum in the loss modulus (as stated in the original article [62]), but rather to film resonance effects that depend on the changes in the polymer modulus. The correlation with density is consistent with the plasticizing action depending only on the volume of chemical absorbed. This type of plasticizing action would be expected if no specific chemical interactions occurred between the absorbing species and the polymer. In contrast, results with a polyimide film and water, methanol, and ethanol vapors yielded trends which depended on the molecular weight of the absorbing species [76]. These trends indicate that the plasticizing action depends on the number absorbed, possibly indicating that the plasticizing is mainly due to the single hydroxyl group found for each species. Again, extrapolation to a molecular weight of zero can be used to extract the responses due to changes in the polymer properties. These results show that changes in viscoelastic properties with chemical uptake can result in significant AW responses, making these property changes important in developing and optimizing chemical sensors using polymer films (see Chapter 5) [57,61-64,71,72,76-79]. For example, the unique curves generated in a plot of attenuation vs velocity for different chemical species (see Figure 4.5) can be used to discriminate between chemical species, increasing the information provided by an AW chemical sensor [63,64,76,80,81]. These results, combined with those comparing SAW responses to predicted uptakes based on GC retention volumes, also indicate that the common practice of converting frequency shifts to amount absorbed assuming that the response is only due to mass loading can lead to erroneous results when working with viscoelastic polymers. Finally, they show that dual-response (attenuation and velocity) AW devices are particularly well suited for probing viscoelastic property changes. 4.2.2

4.2.2.1

DIFFUSION AND P E R M E A T I O N

Real-Time Monitoring

The wide variability of absorption and diffusional properties of chemical species in organic polymer films makes them useful as selective or complete permeation barriers (e.g., gas separation membranes and passivating layers [1,5,82]) and selective chemical sensor coatings [83]. For these applications, a method for rapidly and directly evaluating the solubility and diffusional properties in thin films is useful. Diffusional properties can be evaluated by monitoring the transient up-

168

4. Materials Characterization

take of a chemical species as it diffuses into a polymer sample. AW devices have sufficient sensitivity to monitor this transient uptake in real time in thin polymer films [84-86]. The use of AW-determined diffusion rates vs temperature for probing polymer transition temperatures is discussed in Section 4.2.1.1. A schematic of the device used in this AW technique is shown in Figure 4.6. A thin film of constant thickness h is formed on the impermeable substrate of the AW device. The film, initially in equilibrium with a partial pressure Pl of a gas-phase species, experiences an absorption transient as species diffuse into the film following an increase in the partial pressure to P2. Experimentally, this change in concentration is typically achieved using a gas test system with valves that can be activated to switch from one stream at Pl (typically Pl = 0) to another stream at P2. This absorption transient results in a transient AW frequency response that can be used to characterize the diffusional properties.

4.2.2.2

Fickian Diffusion

Even though diffusion in polymers is generally a complex process, it is possible to find systems that exhibit relatively simple Fickian diffusional behavior. For example, concentration-independent Fickian diffusion has been observed in many polymers when the temperature is far below the polymer's glass transition tem-

Figure 4.6 Schematic representation of a thin polymer film formed on an impermeable AW device substrate. The SAW device probes the concentration profile C(x,t) integrated over the film thickness. (Reprinted with permission. See Ref. [86].)

4.2 C h a r a c t e r i z a t i o n of P o l y m e r s

169

perature and/or diffusant activity is low [87,88]. In these situations, the concentration profile in the film can be determined from Fick's Second Law for a onedimensional system. For a constant diffusion coefficient D, the relevant equation is [89,90]

OC 02C = D~ Ot Ox2 '

(4.1)

where C(x,t) is the concentration of the absorbing species in the polymer, x is the distance from the polymer/substrate interface, and t is time measured from the onset of the change in the partial pressure of the absorbing species. The relevant boundary and initial conditions for this system are: (1) OC/Ox = 0 at x = 0 and all t, (2) C(h,t) = Co(P2) for t -> 0, and (3) C(x,t) = C0(Pl) for t < 0 and 0 -< x -< h, where Co(p) is the concentration in the polymer in equilibrium with a partial pressure p of the absorbing species. Equation 4.1 can be solved under these conditions to yield the following analytical expression [89]" oo

C(x,t) - Co(P2)

--

2AC0 ~

sin(~x/h)e-q'2~

,

(4.2)

n=l

where ~ = "rr(n- 1/2) and ACo = Co(P2)- Co(p1). Equation 4.2 can be integrated over the film thickness to give the following expression for the total moles, M(t), absorbed as a function of time:

M(t) = Mm~ 1 - 2 ~ e-~O~/h2 n=l 1~2 '

(4.3)

where Mmax is the incremental amount of species absorbed in the film after equilibrium is attained (Mmax - hAACo, where A is the area of the film). Equation 4.3 predicts an accumulation of species proportional to N/t until M(t) is approximately 60% of saturation (Mmax); thereafter, the inability of species m penetrate the substratr decreases the net flux into the film. A common technique for evaluating D is to use a gravimetric method to monitor M(t) [87,90] and then extract D and C0(p) by fitting the data to an equation similar to Equation 4.3 (the exact form of this relationship depends on sample geometry). Since equilibration times for Fickian diffusion are proportional to h2/D, the ability to monitor absorption transients in thin films (small h values) directly using AW devices enables a dramatic decrease in the equilibration time as compared to the use of bulk samples with conventional gravimetric techniques. In addition, since diffusional properties of thin films may differ significantly from bulk samples prepared from the same material [91 ], direct evaluation of thin-film properties can be advantageous.

170

4. Materials Characterization

Fickian diffusion was observed using a polyimide-coated SAW device for a wide variety of chemical species [86]. SAW frequency transients obtained for N20 and methanol are shown in Figure 4.7 (pages 172-173); p increased from zero to the indicated values. The expected behavior is observed: an increase in the response upon increasing p that saturates at a new level, indicating that the film has approached equilibrium with the new gas-phase concentration. The expected linear region of the data when plotted vs X/t is observed. These SAW frequency transients were used to determine diffusion coefficients using an alternative "frequency version" of Equation 4.3 where M(t) is replaced with Af(t)/fo and Mmax is replaced by Afmax/fo. The curve through the points represents a nonlinear least-squares fit of the data to this equation. The variable parameters in this fitting routine were: (1) D, (2) Afmax, and (3) to, the starting time for the change in partial pressure. The value of to was allowed to vary in order to account for the time lag between switching the valves and the arrival of the flow to the device. Excellent fits to the data were obtained with an rms error in both cases of less than 1% of Afmax. The D values obtained were 2.3 • 10-ll cm2/sec for methanol and 8.0 • 10-lo cm2/sec for N20. It should be noted that studies with this film at various methanol concentrations indicated that the diffusion coefficient is not constant, but rather increases with increasing concentration [86]. The use of Equation 4.3 is still justified, however, since the concentration steps shown in Figure 4.7 are small enough that the diffusion coefficient does not change significantly. This concentration dependence can be important for chemical sensors, since it requires challenging the sensor at the low concentrations expected in practice in order to evaluate the speed of the sensor response (see Section 5.3.6). Fickian diffusional behavior in polyimide has also been observed by Denton et al. [82] using a capacitive technique and, for the desorption branch only, by Bartley and Dominguez [68] using a SAW device. The absorption transient in the Bartley and Dominguez study exhibited a non-Fickian linearity with time. As described in detail below, non-Fickian behavior was also observed by Brace et al. [92] in their SAW study. This disagreement is not surprising considering that the various polyimide films differ significantly because of the use of different starting solutions and thermal treatments. These differences in the polymer films also show up in differences in the sign of the frequency response. The polyimide used to generate the data in Figure 4.7 exhibits a positive frequency response when challenged with relatively low concentrations ( P/Po < 0.1, where P0 is the saturation vapor pressure) of the various species tested. The other two SAW studies, however, report negative frequency responses to the vapor challenges. The positive response shown in Figure 4.7

4.2 Characterization of Polymers

171

must be due to a combination of a negative mass response and an additional positive response that is large enough to overwhelm the mass-induced response. This additional response is probably due to viscoelastic property changes caused by the plasticizing action of the absorbing species (see Section 4.2.1.3). These viscoelastic effects probably occurred in the other studies but to a smaller extent compared to the mass-loading effect. As described in Section 4.2.1.3, this makes the evaluation of concentrations in the films based on the frequency response questionable for all of these studies. When mass loading is not the dominant sensing mechanism, sensor response may not be linear with concentration in the film. This departure from linearity has been observed with polymer films [61,64,86]. An investigation into the possible effect of this nonlinearity on the evaluation of D values from SAW frequency transients indicated that errors in D values (factor of two error) could be obtained if the nonlinearity of the response is large [86]. However, using small steps in partial pressure, this nonlinearity in the response can be minimized, allowing the effective evaluation of diffusion coefficients based on AW frequency transients. It has been noted by other researchers that the molecular size of the absorbate has a dramatic effect on the diffusion coefficient [93,94]. An exponential relationship is observed between D and the size (represented by the b parameter in the van der Waals equation of state) of the absorbate [94,95]. As shown in Figure 4.8 (page 174), an exponential dependence on the molar volume of the absorbing species was observed with an almost four-order-of-magnitude decrease in D for only a 2.3-times increase in molar volume. The potential for using this variability in D values to advantage in the development of chemical sensors has been discussed [86,96,97]. The basic concept is to use the evaluation of D to determine the chemical species that is providing the sensor response and the magnitude of the response (e.g., Afmax) to evaluate concentration. The results presented above illustrate the utility of using AW frequency transients to evaluate diffusional processes in thin polymer films. The ability to use thin films allows the rapid evaluation of D values from 10 -9 to 10 -15 cm2/sec [86]. The upper limit on D is set by the requirement for multiple data points during the transient response, while the lower limit results from the long times required to approach equilibrium. Thus, thinner films (hundreds of nanometers) are better for probing slower diffusion, while thicker film (micrometers) are better for faster diffusion. An electronics scheme capable of rapid data acquisition [98] would enable larger D values to be quantified based on following the rapid transients. Another way to probe faster diffusion times is to use very thick films. As men-

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v~" (seconds) 1 / 2 Figure 4.7 Frequency shift as a function of V~ during diffusion of (a) methanol, and (b) N20 into a 1.8-pm polyimide film. The lines through the points are fits of Equation 4.3 to the data, giving D values of 2.3 • 10-11 and 8.0 • 10- lo cm2/sec for methanol

and N20, respectively.

(Reprinted with permission. See Ref. [86].)

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4.2 Characterization of Polymers

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4. Materials Characterization

- 9 ! . - ' ~ N20

1.8 pm POLYIMIDE FILM 25C

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tioned in Chapter 3, FPW devices can operate when coated with a thick gel having a solids concentration belc, w about 5%. The device behaves as if it were simply in contact with the liquid solvent for the gel, and no significant change in FPW device velocity or attenuation occurs as the gel sets because dilute gels have very low shear moduli [99]. The semi-logarithmic plot of Figure 4.9 illustrates the use of the FPW device to follow diffusion in a gel. Here, a 500-/xmthick, 2% wt./vol, agar gel was made on a FPW device, with deionized water as solvent. After the gel had set, it was exposed to a 0.1 M NaCI solution; the ions diffused into the gel and finally reached the mass-sensitive region within the evanescent decay length of the membrane, a distance of 16/zm in this case. From the observed mass loading, one can determine the diffusion constant of ions in the gel to be 9.8 • 10 - 6 cm2/s, two orders of magnitude higher than could be probed with thinner films on SAW devices [99]. A similar test was made with whole human blood; in this case, the gel acted as a filter that allowed only the smallest molecules to diffuse toward the membrane and be detected, while holding back blood cells and other large molecules.

4.2 Characterization of Polymers 10000 -

175

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TIME (seconds) Figure 4.9 Response of 5.6-MHz FPW device coated with 500-/zm-thick agar gel upon immersion in 0.1 M NaCI, showing gravimetric detection of ions that diffuse to within an evanescent decay length of the sensor membrane. (Data provided by Amy Wang and Ben Costello, U.C. Berkeley and Berkeley Microlnstruments, Inc., respectively.)

4.2.2.3

Non-Fickian Diffusion

The Fickian diffusion described above is relatively easy to analyze, and demonstrates the capabilities of AW devices for monitoring transient uptakes. However, Fickian diffusion in polymers is the exception rather than the rule. A wide variety of transient responses have been observed, often due to the long time constants required for relaxation of the polymer chains upon absorption of species into the film [93,95]. A detailed discussion of these trends is beyond the scope of this book, and the reader is referred to the polymer literature for these details [93,95]. Brace et al. [92] investigated polymer/water interactions using SAW devices coated with either polyimide or cellulose acetate butyrate (CAB). In this study thermodynamic parameters were evaluated from the absorption isotherms, and transient responses to step changes in concentration were monitored. The transient responses observed were not consistent with Fickian diffusion, but could be described using a generalized relaxation equation containing two additive terms. Results under various conditions indicated that relaxation in the polymer system is much slower than diffusion of water.

176

4. Materials Characterization

Laatikainen and Lindstr/Sm [ 100] used TSM devices to investigate absorption in cellulose acetate and poly-(hexamethylene adipamide). In addition to measuring absorption isotherms and partition coefficients, they reported on transient responses to changes in methanol concentration for a cellulose-acetate-coated TSM device (Figure 4.10). At low concentrations, the linear response with X/t is consistent with Fickian behavior, and diffusion coefficients can be evaluated (D = 4.8 X 10 -l~ and 1.6 x 10 -9 cm2/sec for steps 1 and 2, respectively). It is seen that the initial diffusion rate increases with concentration in the polymer (based on the initial slope of the curves), until, at higher concentrations, a two-stage absorption transient occurs. This behavior, which is typical of glassy polymers, is due to the fact that diffusion begins to become faster than the polymer relaxations [95]. Recent work investigating gas sensor applications using TSM devices coated with the conductive polymer poly(pyrrole) revealed in some interesting diffusional properties. In one study on absorption of various alcohols [ 101 ], methanol was found to show Fickian behavior (D = 2.2 • 10 -12 cm2/s), while larger alcohols were found to have slower diffusion rates (D = 1.3 • 10 -12, 6.4 X 10 -13, and 2.4 • 10 -13 cm2/s for ethanol, n-propanol, and n-butanol, respectively) and trends indicative of non-Fickian diffusion. In another study that used a TSM device combined with measurements of film conductivity [102], the trends were consistent with Fickian diffusion except for the TSM frequency response, which demonstrated non-Fickian trends for methanol. These observations were interpreted as indicating that the conductivity changes to methanol were due solely to one stage of the two-stage sorption observed with the TSM. This may be due to the conductivity only probing the swelling of the polymer and not any subsequent sorption. In this study, the TSM measurements helped in determining the mechanism of conductivity changes in poly(pyrrole)films. In a final study investigating dichloromethane absorption from aqueous solutions [103] into poly(N-methylpyrrole) and poly(N-methylpyrrole/polystyrenesulfonate), the sorption rate was found to be independent of film thickness. This was interpreted as being due to rapid diffusion through pores in the polymer, followed by slow diffusion into the bulk of the polymer. The effect of oxidation state on sorption rates was also investigated. The preceding results show that the ability of AW devices to follow the transient uptake of a species into a thin film allows these devices to be used to probe a wide variety of diffusional processes. As described for Fickian diffusion, a significant advantage of the AW technique is the ability to use thin films, which results in the rapid evaluation Of the diffusional properties even in polymers that exhibit very slow transient uptake.

4.2 Characterization of Polymers

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(seconds) Figure 4.10 Interval absorption of methanol in cellulose acetate measured using a TSM device. Each curve represents the transient response in going from an initial (tk~ to a final (tk*) volume fraction of methanol in the polymer. Fickian diffusion at low volume fractions turns into two-stage absorption at higher volume fractions. (Reprintedwith permission. S e e R e f . [ 1 0 0 ] . )

178

4. Materials Characterization

4.2.2.4

Permeation Rate Evaluation

There are some situations where permeation through a film is the property of direct interest. For example, for a film being proposed as a gas-separation membrane or a permeation barrier, the permeation rate through the film is the critical parameter. The diffusion coefficient can be misleading, since it measures the time required for absorption of the species into the polymer but does not effectively probe small holes (which can allow species to permeate rapidly through the film even though the calculated diffusion coefficient is low). This permeation through the film can be evaluated using a multilayer coating. For example, SAW responses for a polysiloxane film over a porous silicate coating upon exposure to methanol are shown in Figure 4.11. For comparison, the SAW responses due to the polysiloxane film alone are also shown. In each case, a rapid frequency decrease is observed upon exposure to the methanol. The small size of the response for polysiloxane alone could be due to the mass increase from methanol

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TIME (min) Figure 4.11 Experimental SAW frequency transients during exposure to methanol (P/Po = 0.05) for 360 nm-thick polysiloxane film deposited on bare quartz (m) and on a 150 nm-thick porous silicate film on the quartz substrate (e). The larger initial frequency drop with the porous film is due to permeation of methanol through the polysiloxane film and adsorption onto the surfaces of the underlying porous film. Data points are overlapping at early times. (Reprintedwith permission.See Ref. [86].)

4.3 Surface Adsorption and Characterization of Porous Films

179

adsorption on the interfaces of the film. However, the larger response for the device with the porous film underneath, due to adsorption on the high-surface-area silicate following rapid permeation of the methanol through the siloxane overcoat, verifies that this fast response is due to rapid diffusion in the polymer. Further results with this type of polysiloxane using a wide variety of species support this interpretation [80]. This type of multilayer coating is useful for effectively probing permeation rates.

4.3

Surface Adsorption and Characterization of Porous Films

4.3.1

PHYSISORPTION: CHARACTERIZING SURFACES AND PORES

Adsorption on a solid surface is the process of a species present in a gas or liquid phase "adhering" to the surface of the solid [46,104,105]. This adsorption occurs due to molecular interactions between the adsorbing species and the solid. If adsorption is characterized by relatively weak interactions, such as those typical of van der Waals forces, the process is called physisorption. Because such weak forces occur between all molecules, physisorption is typically reversible and will occur at any surface when the normalized concentration of the adsorbing species is sufficiently high. For a gas-phase species, the normalized concentration is equal to P/Po where p is the partial pressure of the species and P0 is its saturation vapor pressure. The endpoint for physisorption occurs when the concentration of the adsorbing species reaches its saturation value. For a gaseous contacting phase, condensation occurs at this point, (i.e., when p = P0). 4.3.1.1

Characterizing Surfaces and Adsorbed Layers

Physisorption on a surface can be used as a method of probing the molecular interactions occurring at a solid surface. Since the nature of the adsorbing species can be known, this provides a technique for probing the properties of the solid [106]. These measurements often utilize noble gases to provide an adsorbing species with minimal potential for specific chemical interactions. An example from one of these studies by Krim is shown in Figure 4.12 (page 180) for krypton on a gold surface. The adsorption isotherm labeled A was for adsorption onto a gold surface that was briefly exposed to air prior to being placed into the vacuum system where the measurements were taken. Due to surface contamination on the gold surface, this shows a relatively smooth curve without any specific adsorption steps. In contrast, the data for Curve B were obtained after heating

180

4. Materials Characterization

u.I r LIJ

~' O rO

2-

0.0

A

0.2

0.4

0.6

0.8

1.0

P/Po Figure 4.12 Adsorption isotherms for krypton on gold obtained using TSM devices in a vacuum chamber. Curve A was at 90~ before baking while Curve B was at 96~ after baking the gold film at 350~ for 12 hours. (Reprinted with permission. See Ref. [106].)

the gold surface to 350~ for 12 hours under vacuum prior to measurement. This isotherm clearly shows stepwise adsorption, with the first monolayer adsorbing at very low partial pressures and the adsorption, of a second monolayer occurring at a relative saturation of about 0.5. This stepwise adsorption was stated to indicate that the uniformity of the gold surface was sufficient to result in layerby-layer condensation of atomic layers [ 106]. The ability to monitor submonolayer mass changes on well-characterized surfaces using AW devices has resulted in their use in a variety of these studies [106-108], allowing interesting behavior including wetting transitions and step-wise isotherms to be observed. Comparison of the results to theories of gas-surface interactions enables these theories to be verified and optimized [107,108].

4.3 Surface Adsorption and Characterization of Porous Films

181

AW devices can also be used to probe the orientation and extent of adsorption. For example, using a gold-coated TSM device, Tsionsky and Gileadi [ 109] investigated the adsorption of various vapors. Based on the amount of adsorption, they were able to show that benzene adsorbed flat on the surface while pyridine attached in an upright orientation due to the nitrogen atom. In addition, they found that water, methanol, and 1-propanol occupied the same number of surface sites per molecule on the surface. This study also demonstrated the importance of considering the small but detectable effects of the pressure and the viscosity and density of the gas in contact with the surface when investigating the small responses due to monolayer adsorption onto the surface of an AW device. They proposed that performing the experiments by changing the partial pressure of the adsorbing species in an inert atmosphere maintained at a constant total pressure (common technique used in most AW adsorption experiments) minimized the effects of these additional interactions compared with varying the total pressure to change the partial pressure of the adsorbing species. The "nanotribology" of adsorbed layers has been investigated by Krim and coworkers using TSM devices. They observed changes in the Q (eletrical quality factor): of gold- and silver-coated TSM sensors upon adsorption of Kr, Xe, and N2 at cryogenic temperatures, and for water and cyclohexane at room temperature [ 110,111]. These changes were attributed to slippage of the adsorbed layers at the surfaces due to the large velocities imposed by the high frequency of the TSM device [ll0,111]. Models to account for these results in terms of film-substrate interfacial viscosity [ 112] and in terms of a characteristic slip time [112,113] have been developed. This information is relevant to topics such as dendritic film growth, fluid flow and slip near boundaries, phase transitions in adsorbed films, and adsorbed monolayers on liquid surfaces [ 112]. These considerations may also explain the nonmonotonic frequency responses with vapor partial pressure observed for adsorption of non-polar molecules onto the quartz surface of a SAW sensor [114]. Since it is well known that surface coverage increases monotonically with partial pressure, these trends are inconsistent with a simple mass-loading interpretation. In this paper, the authors proposed a coverage-dependent SAW-adsorbate interaction to explain the anomalous results for the weaker binding non-polar species (no anomalous trends were observed with polar adsorbates). 4.3.1.2

Characterizing Film Surface Area and Pore Size Distribution

There are applications of thin films where it is important to obtain information regarding properties relating to the microstructure of the coating. Some exam-

182

4. Materials Characterization

pies are: (1) gas separation membranes where the size of the pores and their accessibility from the gas phase are critical; (2) chemical sensor coatings where a high surface area is important for films being used to selectively adsorb species [ 115]; and (3) passivating and protective coatings where a lack of porosity is necessary. A standard technique for characterizing the microstructure of bulk samples is the use of adsorption isotherms [ 116-118]. These measurements can provide information regarding sample surface areas, pore size distributions, and total pore volumes. Obtaining an adsorption isotherm involves measuring the extent of uptake of a chemical species (typically called an adsorbate) by a sample as a function of the partial pressure (p) of the adsorbate in the gas phase over the sample. In general, the adsorbate partial pressure is increased from zero to a value near the saturation vapor pressure (Po) and then back to zero. Uptake of the adsorbate occurs due to adsorption onto the accessible surfaces of the sample, as well as condensation into the accessible sample pores. The most commonly used adsorbate is nitrogen at its boiling point (77~ [ 116]. A variety of commercial instruments are available for performing nitrogen adsorption measurements on bulk samples. These instruments measure the extent of uptake using volumetric, gravimetric, or flow-through methods [ 117]. Sample surface area is determined from a nitrogen adsorption isotherm using the well-established BET model developed by Brunauer, Emmett, and Teller [116,119]. This model accounts for adsorption onto the surfaces of the sample using two binding energies: one between the surface and the adsorbate for the first monolayer, and a second binding energy between the adsorbate molecules for adsorption of subsequent monolayers. The isotherm described by this model is given by [116,119] n nm

=

c(p/po)

(4.4)

(1 - P/Po)[ 1 + (c - 1)( p/po)]

where n is the number of adsorbed molecules, nm is the number of adsorbed molecules in a single monolayer on the available sample surfaces, and c is a constant that depends on the two binding energies. For a molecule like N2, which exhibits high-affinity adsorption (large c value), this model predicts a Type II [ 120] isotherm shape (see Figure 4.13 for an example, or Figure 5.7 for schematic examples of Type I-V isotherms) consisting of: enhanced adsorption at low P/Po values due to adsorption of the first monolayer on the surfaces, a knee in the isotherm indicative of the completion of the adsorption of this initial monolayer, and slow uptake at intermediate p values until multilayer adsorption begins to

4.3 Surface Adsorption and Characterization of Porous Films

183

become significant as p approaches the value for condensation (P/Po = 1). For ease of analysis, Equation 4.4 is typically rearranged to the form: fl _

P/Po

n(1 - P/Po)

=

1

+

nmC

l) P_ nmC Po

(c -

(4.5)

where/3 is defined here for simplification. If the BET model is applicable, a plot of/3 vs P/Po yields a straight line. In practice, due to surface heterogeneities altering the adsorption energies at low P/Po values and the onset of capillary condensation at higher P/Po values, this plot is typically linear only in the P/Po range from about 0.1 to 0.3 [ 116,117]. The slope and intercept of this linear region can be used to evaluate c and nm" c-" 1 + slope/intercept and nm "- 1/(slope + intercept). Using the well-characterized area of an adsorbed N2 molecule (am = 0.162 nm 2 [116]), the sample surface area, As, can be calculated using As = nmam. This BET analysis can be effectively applied to samples that exhibit Type II or IV (described in the next section) isotherms. Pore size distributions are determined based on the fact that condensation in small pores occurs at a lower partial pressure than is required to obtain condensation on a flat surface. The relationship quantifying this effect is the Kelvin equation which, for a hemispherical meniscus of radius rc, has the form [ 116]: In P'__.L= 2trVm Po - rcRT

(4.6)

where p,. is the partial pressure at which capillary condensation occurs, tr is surface tension, Vm is molar volume, R is the gas constant, and T is the absolute temperature. The expression 2trVm/RT is equal to 0.96 nm for nitrogen. This capillary condensation results in enhanced uptake over what would be expected for adsorption onto the surfaces of the film. As the pores fill, however, the surface area decreases until finally, at high P/Po values, the pores are completely filled and N2 uptake ceases. The value of adsorption at this plateau can be used to determine the total volume of pores using the liquid density of the adsorbate (0.808 g/cm 3 for nitrogen at 77~ If the total volume of the sample is known by some independent means, this pore volume can be used to determine the fractional porosity of the sample. Due in large part to geometric constraints, the partial pressure at which pore filling and pore evacuation occur are not identical. This results in hysteresis in the adsorption branch (p increasing) falling beneath the desorption branch (p decreasing). These trends result in what is called a Type IV isotherm shape [120] (see Figure 4.14 for an example). To extract a pore size distribution (volume of pores as a function of pore size)

184

4. Materials Characterization

from an adsorption isotherm, one uses a reference point at high partial pressures (P/Po near 1.0) where the isotherm is fiat. In the first step, the change in amount of N2 uptake by the sample as P/Po is decreased is used to indicate the amount of capillary condensation that occurred over this P/Postep. Using the Kelvin equation to determine the size of the radius of the evacuated area and accounting for the thickness of the adsorbed layer at this P/Po value, the size and the volume of pores of this size can be determined. Before proceeding, the surface areapresent in these evacuated pores is calculated so that in subsequent steps, changes in N2 uptake due to changes in the thickness of the adsorbed layer on these surfaces can be accounted for in the calculations. By continuing to lower P/Po values in this way, a pore size distribution can be determined. Pores from 3 to 50 nm in diameter, typically called mesopores, can be characterized in this manner. Further details on these calculation procedures are presented elsewhere [116,117,121]. Samples with pores smaller than this range (i.e., pore diameters < 2 nm), typically called micropores, provide the final type of commonly observed nitrogenadsorption isotherm. The interaction of the nitrogen molecules with a microporous solid is enhanced due to the close proximity of the surfaces of a pore which has a diameter that may be only a few times the diameter of the nitrogen molecules (approximately 0.4 nm). This enhanced interaction is seen in large amounts of adsorption and pore filling at low P/Po values. This type of adsorption isotherm is called Type I. This different mechanism for pore filling results in an overestimation of the surface area using the BET analysis, and an inability to determine a pore size distribution using the Kelvin equation. Because of these limitations in applying standard calculation procedures, research on new techniques for the quantitative evaluation of microporosity is ongoing.

4.3.1.3

AW Device Results with Porous Films

Nitrogen adsorption isotherms obtained for two films using an AW technique are shown in Figures 4.13 and 4.14 (page 186). These films were both prepared by dip-coating SAW devices using solutions containing oxide precursors prepared by sol-gel processing, a technique that can be used to tailor the microstructure of oxide coatings [3,122,123]. The measurements were made by monitoring SAW frequency changes as the concentration of nitrogen flowing over the device was varied from zero to about 95% and back to zero, using mass-flow controllers to control the dilution of nitrogen with helium, a nonadsorbing species at 77~ [ 117]. The device temperature was maintained at 77~ by immersing the test fix-

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I. . . . . .

I

....

'

0.4

,

'

0.6

'

I,

0.8

, ,,

'

' -

O

1.0

P/Po Figure 4.14 Nitrogen adsorption isotherm for a SAW device dip coated using a sol containing four oxide precursors ("four component"). This coating was prepared from a solution aged for two weeks at 50~ and pH 3. The large amount of adsorption relative to the film thickness and the Type IV isotherm shape indicate that this film is highly porous. (Reprinted with permission [10] by courtesy of Marcel Dekker, Inc.)

r "l

mj ..~ N ..~ g~

4.3 Surface Adsorption and Characterization of Porous Films

187

ture containing the device in liquid nitrogen. An alternative method for varying the nitrogen partial pressure is to monitor pressure as the test fixture containing the AW device is first evacuated, then refilled by slowly bleeding in nitrogen, and finally reevacuated. This technique has been demonstrated using TSM devices in a vacuum chamber [ 124] and for SAW devices by fabricating a test fixture that attaches to a Micromeritics A S A P - 2 0 0 0 nitrogen adsorption instrument [125]. Using the ASAP-2000, the wide pressure range available with this commercial system allows an effective probing of microporosity (P/Po from 10 -6 to 0.1 range) and of larger mesopores (P/Po values very close to 1.0). The data in Figure 4.13 were obtained for a film formed from an acid-catalyzed sol-gel solution ("A2") that is known to produce relatively dense coatings [ 126]. The isotherm shape resembles a Type II isotherm indicative of a sample with no porosity in the mesoporous range. BET plots (/3 vs. P/Po) are linear for both branches of the isotherm, and the calculated BET surface area is 0.95 cm2/(cm 2 of film), very close to the value of 1.0 cm2/(cm 2 of film) expected for a flat, nonporous film on the device surface (BET values are typically thought to be accurate to within 20% [ 116,117]). This data set is useful for demonstrating the extreme sensitivity of SAW devices, since it verifies that submonolayer mass changes can be detected even on a flat surface (full scale is only 120 ng/cm2). For comparison, a single monolayer of nitrogen on a flat substrate contributes a mass loading of 29 ng/cm 2. Analysis of a bulk sample prepared from this same A2 solution using a conventional instrument (Micromeritics DigiSorb 2600) showed a large uptake of nitrogen [123,127] with a Type I isotherm shape, indicative of microporosity. Thus, these data also demonstrate the importance of being able to directly characterize thin film samples rather than risking the erroneous predictions that can occur by using the common procedure of characterizing bulk samples and attributing their properties to thin films. The data in Figure 4.14 were obtained from a film formed from a sol-gel system in which the number and the size of pores can be varied by altering the reaction time prior to film preparation [ 128]. Adsorption isotherms for films formed from the as-prepared solution resemble the data in Figure 4.13, and have low calculated BET surface areas (1.3 cm2/cm 2) [ 129]. This solution contains small precursor polymers (hydrodynamic radius --3 nm) that collapse under the large capillary pressures that occur during film drying [123,128]. However, aging the solution at pH 3 and 50~ results in an increase in the polymer size and, due to the inability of these polymers to interpenetrate [122,123], an increase in the amount and size of porosity in the film. The data from Figure 4.14 were obtained from a film prepared using a solution aged two weeks. The total amount of ad-

188

4. Materials Characterization

sorption is much larger than that observed with the acid-catalyzed A2 film (see Figure 4.13). The BET plot of these data is shown in Figure 4.15. The data are linear in the range expected, and the BET surface area (based on a linear leastsquares fit to the data for P/Po from 0.1 to 0.35) is 46 cm2/cm 2, significantly larger than the value obtained with the A2 film. This value can be converted into the more conventional units of m2/g by calculating the film mass/area (mr): mf = h(l -fp)psk, where h is film thickness, fp is the fractional porosity, and Psk is the skeletal density of the oxide matrix. Based on ellipsometric analysis, this film is 165 nm thick and has a refractive index of 1.21. Using the Lorentz-Lorenz relationship [ 130] and a skeletal refractive index of 1.45, a fractional porosity of 0.50 is estimated. However, from the total amount of adsorption in the plateau region at high P/Po values, a fractional porosity of 0.33 is determined. Since nitrogen adsorption only probes the open porosity, the refractive index estimate, which is sensitive to all porosity in the film, may be more accurate for determining my. Using this porosity value and a skeletal density of 2.1 g/cm 3 yields mf = 1.7 • 10 -5 g/cm 2 and a surface area of 270 m2/g. This relatively large surface area and the fact that the isotherm is of Type IV indicate that this film has porosity in the mesoporous range. A pore size distribution using the desorption branch of the isotherm is shown in Figure 4.16 (page 190). A fairly unimodal distribution is obtained with a median pore diameter of 3.8 nm. Results obtained with samples at aging times up to three weeks indicate that the microstructural properties can be varied over a wide range based solely on the sol-gel aging time; percent porosities ranged from 0 to 52%, median pore diameters ranged from <0.2 to 6.1 nm, and surface areas ranged from 1.5 to 270 m2/g [84,123]. Microporous samples have also been analyzed using AW devices. For example, Bein and coworkers have measured adsorption isotherms for N2 at 77~ and for vapors at 25~ using TSM devices coated with zeolites [131-133] and with layered silicate materials that have been ion exchanged with alkylammonium cations [134]. As expected for these types of materials, Type I isotherms indicative of microporosity were observed in many cases. In addition, Hietela and coworkers [125] used the ASAP-2000 system with a SAW device to look at the A2 sol-gel film described above. In agreement with the results shown in Figure 4.13, the BET surface area calculated from the N2 adsorption isotherm gave a value of 1 cm2/(cm 2 of film). However, tests using CO2 at 196 and 273 ~ gave large uptakes and a Type I isotherm shape, indicative of a microporous sample. The surface area (calculated using the Dubinin-Radushkevich equation useful for microporous samples) was 55 cm2/(cm 2 of film). They interpreted the lack of porosity to N2 to be due to activated diffusion limitation for entrance of the N2

, ,

0.4

,,

,~

9 ADSORPTION II DESORPTION ,

,

i

1

Ilimlll

I

~, 0.3 01 @

E

O

@

c~ 0 . 2 m.

r

r

O.1

m.

N

i

O.0 O.O

@ =3 @ o @ =

O.1

0.2

0.3

0.4

0.5

P/Po Figure 4.15 BET plot of 13 (see Equation 4.5) vs P/Po for the film formed from a two-week-aged, four-component sol (see Figure 4.14). Based on a linear least-squares fit to the data from P/Po = 0.1 to 0.35, a BET surface area of 46 cm2/(cm 2 of film) or 270 m2/g is obtained. (Reprintedwith permission [10] by courtesy of Marcel Dekker, Inc.)

mo

1.o ! ........... i ..........

~

.........I. . . . .

I

W

I

...... I "

I

FOUR COMPONENT TWO WEEK AGE DESORPTION BRANCH

~Z 0.8 ,,,,J

tm~ t~ m/ mm. t~ m

0 >

I,,IJ

~r

0.6

"I

O

tm~ eD m. N

..J

mt @

0.4

z

I,U

13: I,,U IJ.

r

0.2

0

4

8

PORE

12

DIAMETER

16

20

(nm)

Figure 4.16 Pore size distribution obtained from the desorption branch of the nitrogen adsorption isotherm for the film formed from the two-week-aged, four-component sol (see Figure 4.14). Median pore diameter is 3.8 nm. (Reprinted with permission

[ I 0 ] by c o u r t e s y o f M a r c e l D e k k e r , Inc.)

4.3 Surface Adsorption and Characterization of Porous Films

191

molecules into the micropores at 77~ This is commonly observed for coals but was unexpected with the thin film sample used with the SAW experiment. The results described above demonstrate the utility of this AW technique [ 135] for characterizing thin film microstructure. This technique uses the wellestablished nitrogen adsorption isotherm technique commonly used to evaluate porous bulk samples. By increasing the sensitivity to the amount of adsorbed Ng, this AW technique allows thin films to be characterized directly. 4.3.2 4.3.2.1

CHEMISORPTION Overview of Chemisorption

Chemisorption occurs when strong interactions, including hydrogen bonding and covalent and ionic bond formation, occur between the adsorbate and the solid surface. Chemisorption typically occurs even at very low concentrations, and the chemisorbed species are often "irreversibly" bound to the surface, i.e., they will not readily desorb under ambient temperature conditions. The endpoint for chemisorption is when all the active sites on the solid surface are occupied by chemisorbed molecules. The specific interactions that occur during chemisorption raise a broader range of questions to answer in order to characterize the solid/adsorbate interactions. AW measurements of equilibrium adsorption, as well as adsorption and desorption kinetics, can be exceptional tools for evaluating such parameters as activation energies and heats of adsorption, particularly for the study of the submonolayer regime. Czandema [136] has reviewed many of these types of studies using very sensitive conventional microbalances along with the types of information that they can provide. The simplicity of using acoustic wave devices, as compared with sophisticated balance systems, to obtain the required sensitivity for these studies on low surface area samples should be a significant advantage. Studies of corrosion processes, detailed in Section 4.4.3, have demonstrated the capability of SAW devices to monitor relatively low rates of chemisorption, including the conversion of a thin copper film to Cu2S at an initial rate of 4% of one molecular monolayer/day. The use of SAW devices to monitor the real-time desorption of species from a metal film in response to a temperature ramp has been shown to yield information about both the energy and extent of chemisorption [I 14]. TSM studies of chemisorption of O2 and CO on very thin Ti films were used to determine that the oxide being formed is Ti203 and that the oxidation depth is approximately one nm [ 137]. For further discussion and additional examples of chemisorption, the reader is referred to Section 5.4.4.3, where these

192

4. Materials Characterization

interactions are described in some detail because of their relevance to the development of highly sensitive chemical sensors. 4.3.2.2

Self-Assembling Films

Self-assembling films rely on a unique combination of three interactions to produce highly ordered, durable films ranging in thickness from one to tens of molecular layers [138]. The process is best illustrated using an example, the self assembly of a hexadecanethiol (CH3(CH2)IsSH) monolayer on a gold substrate. When the gold surface is exposed to a low concentration of this molecule in either the gas or liquid phase, the SH "head" group of each thiol molecule chemisorbs onto the gold surface, creating a thiolate bond. The creation of a thiolate bond results in the sulfur molecule being bound to a three-fold site on the gold (11 l) crystal lattice accompanied by the loss of hydrogen [ 139]. This head group binding of the thiol, the strongest of the three interactions, ensures that all the chemisorbed molecules are oriented in roughly the same direction. The second interaction involves van der Waals forces, which are relatively weak on a "per bond" basis (measured to be 3.3 kJ/mole per methylene unit using temperature-programmed desorption (TPD) [140]). However, these forces can be cumulatively quite strong (16 C-C van der Waals bonds form between two properly aligned hexadecanethiol chains), bringing all the chains into alignment. Thus, the sulfur atom determines the spacing on the gold lattice while the van der Waals interactions between adjacent chains determine the orientation. Another weaker interaction that should be considered involves the nature of the tail group, in our example, a methyl group. As the monolayer forms, the solvent is excluded from the film as the surface free energy of the film is maximized at the solvent-monolayer interface favoring a more highly ordered structure. For this reason, the tail group along with the solvent properties influence monolayer formation, especially for the last 5% of the monolayer's formation. For tail groups such as carboxylic acid groups (-COOH), the interactions between the tail groups in the monolayer can also be important. The sum of the headgroup chemisorption energy, the van der Waals interactions for the long hydrocarbon tails, and the properties of the tail group/solvent interactions results in a relatively robust, anchored film. These materials show promise in applications including electronic and optical devices, chemical sensors, lubricants, model biological membranes, permeation barriers, and catalysis [141,142]. Work using SAW devices has focused on the gas-phase self-assembly process [143,144]. Figure 4.17 (page 194) shows the utility of a SAW device in monitoring the assembly of a hexadecanethiol monolayer on a polycrystalline gold

4.3 Surface Adsorption and Characterization of Porous Films

193

film on the device surface [143]. Not only is the SAW device's mass resolution sufficient to show that the equilibrium coverage exceeds that calculated for a single crystalline gold surface by about 15% (a result of the polycrystalline film having a roughness factor exceeding unity), but the kinetics of this chemisorption/assembly process are readily discerned in real time. Analysis of the kinetic adsorption data reveals a good fit to a simple, first-order Langmuir rate law, meaning that the rate of adsorption is proportional to the product of the partial pressure of the thiol and the unoccupied concentration of gold adsorption sites on the surface. Significantly, this result indicates that the process of chemisorption of the thiol head group, as opposed to the process of alignment of the adsorbed chains through van der Waals forces, limits the overall rate of film assembly [143]. Chemical reactions between a surface-bound self-assembled monolayer (SAM) and a second species that reacts with one-to-one stoichiometry and modifies the chemical properties of the surface layer, have also been studied with submonolayer accuracy [144]. In solution-phase work, Buttry and coworkers have shown that the TSM oscillator can monitor the process of electrochemically inducing changes in the adsorption of redox centers attached to long alkyl chains [145,146]. In particular, changing the oxidation state of the redox center results in the rapid desorption of the adsorbed layer, a process that is readily followed using the TSM oscillator's mass sensitivity. For sufficiently long alkyl chains, the process slows enough that the kinetics of desorption can be followed in real time. When a thiol or disulfide moiety is attached to the redox center, the resulting chain will chemisorb strongly on silver or gold electrodes on the surface of the TSM oscillator, allowing the oxidation state of the redox center to be changed without desorption occurring. In this case, it is possible to monitor the flux of charge-compensating ions into and out of the film during the electrochemical process [147,148]. Karpovich and Blanchard [149] also looked at adsorption kinetics of SAMs using TSM devices. They found that the adsorption was rapid and was described by the Langmuir adsorption isotherm. Based on a concentration dependence of the monolayer formation rate, they concluded an equilibrium exists for the adsorption/desorption process.

4.3.3

ADSORPTION AT SOLID-LIQUID INTERFACES

Adsorption from liquids can involve both physisorption and chemisorption; however, one needs to consider the molecular interactions between the adsorbing species and the liquid, as well as those with the solid. The relative magnitudes of the liquid/adsorbate and solid/adsorbate interactions will determine the extent

-0

0 - N2 A

E

O H 3 ( 0 H 2 ) 1 5 SH in N 2 - 0.2

-5

r "I m, m

- 0.4 ::= m,mml

O

-I0

~')

- 0.6 -15

O O

- 0.8

O m

Q r

(/)

-20

- 1.0

13" 0 ,-,- -25

- 1.2 I

I

!

I

0

20

40

60

......

!

80

,I

1O0

,!

120

! .....

140

Time (min) Figure 4.17 Frequency shift as a function of time measured for a gold-coated SAW device exposed to an N2 gas stream containing CH3(CH2)IsSH at approximately 25% of its saturation vapor pressure. Leveling of the frequency shift at approximately 1.15 monolayers indicates that the polycrystalline gold film has a roughness factor of 1.15. The kinetic data fit a simple, first-order Langmuir rate law. (Reprinted with permission. See R e f . [ 1 4 3 ] . 9 1991 A m e r i c a n Chemical Society.)

gr

4.3 Surface Adsorption and Characterization of Porous Films

195

of adsorption at a given concentration. An interesting example of the importance of this concept is adsorption of surfactant molecules, which contain a hydrophilic "head" making them soluble in water, but a hydrophobic "tail" that causes ordering of water molecules. The entropy decrease upon removal of this tail from water upon adsorption at a surface results in an additional driving force for adsorption. This interaction is sometimes called hydrophobic bonding [104]. The ability to use TSM, APM, and FPW devices in contact with liquids enables them to monitor adsorption at the solid-liquid interface. This ability is probably most useful in evaluating the adsorption of polymer or surfactant molecules, since this adsorption is used in a variety of applications [46,104,105]: modification of surface wettability, removal of dirt and oils using surfactants (e.g., detergents), and the dispersion of small particles (e.g., pigments in paints). Limited studies on this ability have been performed with AW devices. Figure 4.18 shows data for adsorption of bovine serum albumin (BSA) onto the surface of an FPW device [150]. Similarly, Laatikainen and Lindstr6m [ 151 ] monitored the adsorption of BSA on a polysulfone-coated TSM device. They found the adsorption trends were in agreement with expectations; however, the absolute magnitude of

5.94

-

[i

i

i

El 9

i i ii 9

i

i 9

i

it

ii

9

iiii qr a

i

iiiiii

i

i / Ii

iii 9

5.93 'k ~ 5.9'2 0r

::2

o" 5.91

5.90 ""~0

0.5

1

1.5

2 Time

2.5

3

3.5

4

(minutes)

Figure 4.18 Response of a 5.9-MHz FPW device as bovine serum albumin (BSA) deposits onto the device surface from a phosphate buffer solution. (Dataprovided by Ben Costello, Berkeley Microlnstruments, Inc.)

196

4. Materials Characterization

the adsorbed amount, calculated based on assuming that the frequency shift was due solely to the mass increase due to the adsorbing BSA, was too large. By allowing adsorption to occur from the liquid and then drying the crystal, significantly smaller values (approximately 30% of those from the in-situ measurements) were obtained. They interpreted the larger response for the in.situ measurement as being due to the fact that the TSM was sensitive to the hydrated mass of the adsorbed layer, and thus, was also detecting the mass of the water and electrolytes bound to the BSA layer. Adsorption of other biomolecules has also been monitored with AW devices. For example, TSM devices were monitored with a network analyzer during adsorption and denaturation of proteins [152] and during adsorption, immobilization, and hybridization of DNA [153]. The multidimensional information was used to look at the amount of adsorption, the kinetics, and to probe the conformation of the protein molecules on the surface [152] or the viscoelastic properties of the DNA layers [153]. A Love plate device was used to follow the kinetics and amount of adsorption of human IgG, anti-human IgG, and protein A onto polymethylmethacrylate polymer layers [154]. Similarly, an APM device was used to measure kinetics and amounts of adsorption for antigen-antibody reactions [155]. The adsorption of a variety of surfactants onto the quartz surface of APM and TSM devices has also been monitored [145,156]. Values in reasonable agreement with the literature were obtained in several cases by assuming that the frequency shift was due to the adsorbed mass of the surfactant. However, anomalous results (i.e., frequency increasing with solution concentration) were also observed under some conditions. These studies demonstrate that one of the challenges in using AW devices for monitoring adsorption at the solid-liquid interface is the ability to quantitatively convert the device response to an adsorption level (mass/area or moles/area). Additional responses are the result of the sensitivity of these devices to such effects as the mass of bound or entrained liquid, changes in the liquid properties in the vicinity of the surface due to changes in the electric double layer (the layer of ions formed around a charged surface [104]), or modification of the wettability of the surface (this has been proposed to result in slipping of the liquid layer at the surface [ 157]). Even with these challenges, the simplicity and speed of measurement possible with an AW device as compared with other measurement techniques can make these studies useful even if only to evaluate adsorption trends quickly. The sensitivity of AW devices to these additional effects, which here is put forth as a complication, may be used to advantage to study these effects. For example, the ability to probe a thin liquid layer near a charged surface may permit study of the liquid properties in the electric double layer. This layer is typi-

4.4 Real-Time Monitoring of Chemical and Materials Processes

197

cally less than 10 nm thick [104] and thus is difficult to monitor with conventional techniques. As demonstrated in some of the studies described [152,153], monitoring of more than one sensor response can be helpful in determining the amount of adsorption and the properties of the adsorbed layer.

4.4

Real-Time Monitoring of Chemical and Materials Processes

Because acoustic wave devices are sensitive and respond rapidly, they are ideally suited for real-time monitoring of chemical and physical systems. As discussed in the introduction to this chapter, thin films represent a growing industrial and technological concern for a variety of applications. The use of acoustic devices to characterize the physical properties of these films has been dealt with in the previous sections. Here we describe how these devices can be used to monitor film formation or dissolution processes, or to observe and characterize film properties as a function of time (similar to the monitoring of diffusion in polymers described in Section 4.2.2). 4.4.1

MONITORING FILM AND PARTICLE DEPOSITION AND REMOVAL

Perhaps the simplest application of real-time monitoring is to monitor the deposition or removal of a thin layer. The use of TSM devices for deposition monitoring is well known, and commercial instruments using TSM devices are routinely used for such applications as monitoring the thickness of metal films formed by vacuum evaporation, as shown in Figure 1.5 [158,159]. Other types of deposition can be monitored; for example, the deposition of Langmuir-Blodgett (LB) films on TSM devices was studied by McCaffrey, et al. [160]. They observed a linear decrease in the resonant frequency of the device as multiple layers of a calcium stearate LB film were deposited. From the slope of the resulting plot (Hz/layer), they calculated a surface mass density in the film of 322 ng/cm 2, significantly greater than the theoretically calculated value of 266 ng/cm 2. This result suggested that water was trapped in the film during formation or that the surface topography of the substrate may provide a slightly larger effective surface area for film formation than previously assumed. In addition, the straight-line plot had a negative intercept, from which they concluded that the first layer of film was less dense than subsequently deposited layers. Wohltjen, et al. [161 ] also measured SAW frequency shifts as a function of the num-

198

4. Materials Characterization

ber of LB layers. Using devices operating at three different frequencies (31, 52, and 112 MHz), they were able to verify the dependence of SAW response on the square of the operating frequency (see Section 3.2.4). However, the absolute magnitudes of the responses were significantly lower (about 50%) than predicted based on mass loading. This discrepancy was interpreted as being due to elastic effects in the LB film. In contrast, Grate and Klusty [ 162] found excellent agreement with predictions based on mass loading using 2t)0-400 MHz SAW resonators and LB layers of soft organic polymer materials. In two final LB studies, Hanley, et al. [163] used TSM devices to estimate the molecular area and percent ionization of LB layers composed of fatty acids, while Ariga and Okahata [164] used TSMs to determine the amount of water incorporated into LB films as a function of parameters such as deposition rate and surface roughness. The use of SAW and APM devices for real-time monitoring of film deposition processes is demonstrated by the results shown in Figures 3.22, 3.26, and 3.34 for the vacuum evaporation of thin metal films. In these examples, the film thickness and deposition rate was monitored with submonolayer accuracy. In addition, for the deposition shown in Figure 3.26, the conductivity of the film could be probed along with the film thickness by monitoring both the velocity and attenuation of the wave, and relating these total responses to the combined effects of the mass-loading and the acoustoelectric interactions. For monitoring deposition of viscoelastic polymers, it should be possible to probe the viscoelastic properties of the film being deposited based on the relative magnitudes of velocity and attenuation (or frequency and admittance) values. This ability to probe film properties while monitoring the deposition rate makes AW devices uniquely suited for studying film deposition processes. Conversely, AW devices can effectively track the loss of film material as the result of some chemical or physical process. For example, Joshi utilized a dual delay-line SAW oscillator to monitor the plasma-etching of a photoresist film [165]. One delay line was coated with the photoresist film, while the other delay line was left uncoated to act as a reference. Because plasma-etching produces significant heating of the substrate, the dual-device approach was used to correct for temperature-induced frequency changes: changes in frequency difference between the two delay-lines were attributed to film loss from the device surface. The TSM has also been used to study sputtering yields [ 166] (i.e., loss of material from a surface under ion bombardment) by monitoring frequency changes due to mass loss as a function of ion dose. While these studies have usually been performed using metal or silicon films [ 167], recent studies have investigated the sputtering process associated with ion bombardment of organic films. UUevig and Evans monitored the frequency of TSM devices coated with polystyrene (PS)

4.4 Real.Time Monitoring of Chemical and Materials Processes

199

and polymethyl methacrylate (PMMA) films during bombardment with 1 keV argon ions [168]. In addition, TSM devices have also been used for laser ablation studies. In one study, the TSM sensor served as a precise probe of etch rates in the region of the ablation threshold intensity [ 169]. In another study, the TSM was used to measure variations in the amount of sample ablated for normalizing results of laser ablation-inductively coupled plasma atomic emission spectrometry [ 170]. AW devices have also been demonstrated for real-time monitoring of attachment of particles. For example, early work looked at the ability of TSM devices to measure particles and found that detection efficiency decreased with particle size above 2/zm on uncoated devices but could be improved for these larger particles using viscous coatings [171,172]. The use of an electrostatic precipitator was demonstrated for determining mass concentrations of suspended particles [ 171,173], while a portable instrument was demonstrated for monitoring changes in particle concentrations due to short-term changes such as starting a machine or the presence of a smoker [171,174]. In more recent work, SAW devices have been used to increase the sensitivity for mass detection [ 175]. In addition, TSM devices have been combined with a cascade impactor to provide data on size and amount of particles. This particle-sizing capability has been used to measure changes in stratospheric particle concentrations due to volcanic eruptions [ 176-178]. In a serendipitous experiment designed to measure removal of SiO2 layers by cosmic radiation, a TSM device on Saliut-6, a Soviet-Romanian joint space flight, was able to quantitatively measure accumulation of cosmic dust after a solar explosion [28]. The delay time from the explosion to the start of deposition enabled an estimate of the solar wind at 697.7 km/hr. The lack of a frequency increase indicative of mass loss prior to the arrival of the cosmic dust also demonstrated the good stability of SiO2 in space. Real-time monitoring of deposition or dissolution from liquids can be performed using TSM, APM, or FPW devices. For example, Kanazawa and Doss [ 179] demonstrated the use of TSM devices as real-time rate monitors of electroless nickel deposition, while Ricco and Martin [ 180] demonstrated a similar use of APM devices for electroless deposition of copper directly onto the quartz substrate. TSM devices have also been used to monitor surface accumulation of thermal degradation products from jet fuels [181]. The ability to rapidly quantify the rate of accumulation can be used in designing jet fuels with improved thermal stability [182,183]. Turning to material removal, monitoring the dissolution of metals in aqueous environments has also been demonstrated [ 184]. In addition, by intentionally contaminating a TSM with a surface layer similar to the anticipated contamination on a component to be cleaned, a real-time moni-

200

4. Materials Characterization

tor of contaminant removal has been demonstrated [ 185]. This capability could be used for optimizing cleaning processes, as an in-line process monitor, or as a probe to determine cleaning efficiency in order to extend the life of cleaning baths. An important parameter for many photoresist materials is the rate of dissolution in the developer as a function of light exposure. Hinsberg et al. [ 186] utilized TSM devices in a special cell that enabled flow of developer across a photoresist layer on one side of the device. They demonstrated the ability to monitor the removal of the photoresist material in real time as a function of the exposure. Rapid dissolution rates could be monitored (e.g., total removal of the layer in less than 30 seconds), as well as verification of the lack of removal of the unexposed resist. Using a previously formed conductive layer, electroplating processes can also be monitored. Of the AW devices discussed in this book, TSM devices have an advantage for this application since the electrode metalization (used for AW transduction) can also be used as an electrode for the electroplating process. Commercial instruments using TSM devices are currently available for monitoring the thickness of electrodeposits (see Appendix D). Electrodeposition has been used for calibrating FPW sensors while they are in contact with a liquid, since liquid loading affects their gravimetric sensitivity [ 187] (see Section 3.4.2.3). Using APM devices, the ability to use both velocity and attenuation to simultaneously measure film thickness and probe deposit roughness has been demonstrated [ 188]. The film roughness is detected by an increase in the attenuation observed at higher electroplating currents, interpreted as being due to the generation of compressional waves from the roughened surface. The ability to probe surface roughness with TSM devices by monitoring the admittance magnitude has also been demonstrated (see Section 3.1.6). AW devices have also been used in solution to measure the attachment or binding of various biomaterials. For example, TSM devices have been used to measure attachment of cells to the surface of the TSM [ 189-191 ]. As might be expected, the cells were found to behave viscoelastically [ 189]. In addition, the removal of cells by a virus infection has also been monitored [ 190]. By improving stability to enable long-term monitoring, the slow attachment and growth of biofilms was monitored in one study [192]. 4.4.2

POLYMERIZATION REACTIONS

Reaction rate and time to completion are two important yet difficult-to-measure parameters in many polymerization processes. The mass changes that" occur during polymerization provide a velocity or resonant frequency response for a

4.4 Real-Time Monitoring of Chemical and Materials Processes

201

polymer-coated AW device. In addition, the formation of cross-links affects the elastic properties of a polymer. The free movement of one polymer chain relative to its neighbors, which is possible in the uncrosslinked polymer, is severely inhibited by the formation of crosslinks between chains. As a result, crosslinking significantly increases the film's shear modulus while simultaneously decreasing viscous damping in the polymer [193]. Thus, the shear modulus of the film gives an indication of the crosslink density and the extent to which a polymerization reaction has proceeded. The combination of these elastic property changes with the mass changes that occur during polymerization enables the use of acoustic wave devices to monitor polymer film crosslinking reactions in situ and in real time. For example, Hager et al. [ 194] demonstrated the potential of a TSM for characterizing the curing process for a gelatin-based photoresist film. By monitoring amplitude and frequency of the acoustic wave simultaneously during the photocuring process, they were able to differentiate between solvent evaporation and photo-hardening processes occurring in films of varying thickness. The early stages of film drying were characterized by concurrent increases in both amplitude and frequency, consistent with solvent evaporation. The loss of solvent mass produces an increase in frequency, while the effective increase in viscosity and density of the film as the film "dries" was thought to result in a decrease in energy dissipation in the film (i.e., output amplitude increases). By contrast, illumination of a well-dried film produces further increases in frequency at essentially constant amplitude. This was interpreted as an effective mass-increase due to greater coupling efficiency for photo-crosslinked films. Martin and Ricco [ 195] monitored photo-polymerization in negative photoresist films (Waycoat HR-100 [196]) using APM devices. Shown in Figure 4.19 (page 202) are changes in APM propagation velocity and attenuation measured as the film crosslinks upon exposure to 380 nm illumination. This wavelength is near the peak spectral sensitivity reported [ 196] for photo-polymerization of HR100. During the reaction, APM velocity increased while attenuation decreased. After an exposure time of 140 minutes, velocity and attenuation reached stable values, indicating the completion of the cross-linking reaction. Martin and Ricco state that each cross-link formed in the HR-100 film has two effects that can perturb the APM propagation velocity: an increase in the elastic storage modulus (G') and a decrease in the surface mass density (ps) through the liberation of two N2 molecules. Both of these effects should result in an increase in APM velocity, consistent with the positive velocity shift observed during cross-linking. In addition, cross-linking typically decreases the loss modulus (G"), a result of restricting dissipative processes [193]. This is consis-

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EXPOSURE ENERGY ( 3 / c m 2 ) Figure 4.19 Fractional velocity shift and change in attenuation as a function of time, measured during cross-linking of HR100 negative photoresist film. (Reprinted with permission. See Ref. [ 1951.)

4.4 Real-Time Monitoring of Chemical and Materials Processes

203

tent with the decrease in attenuation observed during cross-linking. A plot of attenuation vs velocity change [ 195] is linear during this cross-linking process, indicating a linear relationship between incremental changes in the storage and loss moduli. More work is needed to develop a realistic model to relate cross-link formation to changes in viscoelastic parameters. This model would permit the evaluation of film properties as a function of cross-linking. The wavelength dependence of the photosensitivity of the resist film was determined by measuring the rate at which APM velocity changed in response to cross-linking as a function of incident optical wavelength A0. The rate of change of APM velocity at each wavelength is defined by" R(h~o) =

1 dv Vo dt

hO"

(4.7)

Wavelength was stepped from 200 to 650 nm in 10 nm increments. The 15second dwell time at each wavelength was sufficient for a change in film properties to be measured without appreciably cross-linking the film: the entire spectral response experiment cross-linked the film by less than 20%. The relative spectral sensitivity for film cross-linking is R/I, where l(h0) is the spectral density of the source. A plot of R/I vs optical wavelength is shown in Figure 4.20 (page 204) for an HR-100 photoresist film. The peak in spectral sensitivity is at approximately 370 nm, in reasonable agreement with the sensitivity peak of 360 nm cited by the manufacturer [ 196]. Also shown in Figure 4.20 is a UV-visible absorbance spectrum recorded for a similarly prepared HR-100 film on a quartz optical flat. The absorbance spectrum has a peak at 355 nm, corresponding to the peak observed in the acoustic measurement of R/I. The film also exhibits very high absorbance at wavelengths below 300 nm, a result not observed in the acoustic measurement. The spectral response measured using an acoustic device is an action spectrum in that it registers only optical absorptions that lead to a chemical reaction and thereby contribute to changes in the elasticity or density of the film. Not all absorbed photons lead to chemical reaction. The peak in the absorbance spectrum (Figure 4.20) at 355 nm is due to photoinitiator absorption, which leads to the formation of cross-links in the polymer and a corresponding peak in the acoustic R/I response at 370 nm. The strong absorption at wavelengths less than 300 nm, however, is likely due to the polymer backbone (cyclized polyisoprene), which is not photoactive; thus, its optical absorption affects neither mass density nor the elastic properties of the film. This method of obtaining cross-linking photoaction spectra in real time using acoustic wave devices is a unique analytical technique for characterizing photoactive films.

9

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WAVELENGTH (nm) Figure 4.20 Acoustically probed photoaction specmnn of 1.I/zm thick HR-100 photoresist (left axis); rate of change of APM velocity R(Ao), normalized to spectral density l(Ao), indicates rate of film cross-linking as a function of optical wavelength Ao. Optical absorption spectrum of identical film on quartz flat (right axis); spectrum peaks at 355 nm due to absorption by photoinitiator, while strong absorption below 300 nm is due to the polymer backbone. (Reprintedwith permission.

See Ref. [195].)

mmm

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4.4 Real-Time Monitoring of Chemical and Materials Processes 4.4.3

205

CORROSION MONITORING

The ability to use SAW devices for real-time monitoring of corrosion of thin metal films in gaseous environments has been demonstrated. Metal films, ranging in thickness from a few Angstroms to a micron, were deposited on the propagation path between transducers. Since the acoustic-wave propagation velocity depends upon the mass and mechanical properties of the film, any change in these properties due to corrosion alters the velocity. Results with a copper film that was vacuum-deposited between the transducers on a 100-MHz SAW device upon exposure to 5 ppm of H2S in dry nitrogen are shown in Figure 4.21 (page 206). During this initial sulfidation process, an overall frequency shift of - 2 3 ppm occurred. If elastic effects are negligible, this would correspond to a mass change of 180 ng/cm 2. The presence of a minimum in the response may be due to the presence of adsorbed H20 that is formed by the reaction of H2S with a surface layer of copper oxide. On this time scale, the reaction appears to stop after only a few minutes. However, experiments for longer times indicate that after this relatively fast reaction and apparent stabilization upon initial contact with H2S, the frequency again begins to decrease [ 184]. For example, in another experiment with a copper film challenged by 100 ppb H2S, 150 ppb NO2, and 60% relative humidity at 40 ~ a second frequency decrease began after about 10 hours of exposure. The rate of corrosion, assuming that mass loading dominates, ranged from 22 ng/cm2-hr at the early stages of this linear decrease to 15 ng/cm2-hr at the end of this eightday experiment. In addition, a copper film passivated by a corrosion inhibitor (benzotriazole) showed a much slower rate of corrosion; frequency shift (after the initial rapid decrease) is approximately 7% of that observed with the untreated copper film. Hager et al. used TSMs as electrode substrates to monitor corrosion processes occurring at the surface of an iron-coated electrode [ 197]. The frequency response of a TSM in solution depends on the combined effects of mass gain, film stress, hydrodynamic coupling, and electrokinetic coupling. Since the dependence of the electrokinetic coupling on solution conditions is not presently well-modeled, interpretation of data is problematic for systems where electrokinetic effects may be significant. For system responses dominated by mass or hydrodynamic coupling effects, however, the TSM can be used to study corrosion processes quantitatively. These results demonstrate that acoustic wave sensors can be used as real-time corrosion monitors. Their small size enables them to be used in situ in corrosive process environments or as a component to warn of the impending failure of a

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TIME ( s e c o n d s ) Figure 4.21 Monitoring of the corrosion of a copper film by a dilute H2S stream. The corrosion reaction can be seen in real time using the SAW device as a sensitive probe. ( R e p r i n t e d w i t h p e r m i s s i o n [10} b y c o u r t e s y o f M a r c e l D e k k e r , Inc.)

4.4 Real-Time Monitoring of Chemical and Materials Processes

207

circuit or structure. In addition, they should prove useful in research by providing real-time kinetic data on corrosion rates. Extreme sensitivity allows rapid evaluation of even relatively slow corrosion processes, as well as testing of corrosion inhibitors. 4.4.4

ELECTROCHEMICAL STUDIES

There is a growing body of literature on the use of acoustic sensors for in-situ experiments, particularly in conjunction with electrochemical measurements [198]. These studies are most commonly performed using a quartz resonator (TSM) device that has been designed or adapted for use in solution. When used in this manner, these acoustic devices are commonly referred to as electrochemical cluartz crystal _microbalances (EQCM). To be consistent with the terminology used in this book, these devices will be referred to here as electrochemical TSMs or ETSMs. In a typical experiment, one of the electrodes used to excite the acoustic wave mode in the substrate is used concurrently as the working electrode in an electrochemical cell. This configuration allows for the simultaneous monitoring of electrochemically-induced mass changes at the electrode surface and the consumption of charge (electron flow) associated with the electrode process/reaction. An example of some typical results is represented in Figure 4.22 (page 208). The ETSM provides information on changes in surface mass (film or solution property changes can also be monitored) concurrent with the measurement of the current-voltage properties. This ETSM information is useful in the characterization of charge-transfer electrode processes, including the influence of the solution/electrode interface (e.g., depletion layer effects [199]), solvent effects (e.g., differences in frequency shifts for H20 and D20 have been used to probe hydration of polymer layers [200,201]), and kinetics [202-204]. The diversity of ETSM studies is evident in several recent reviews [ 198,205,206] and references contained therein. Some examples of these applications are briefly discussed in the following paragraphs. The high mass sensitivity of ETSM sensors renders them particularly suited for the analysis of monolayer and submonolayer films. In fact, the earliest applications of the ETSM involved studying the electrochemical deposition of monolayers, including the formation of metal oxides [207], electrosorption of halides [208], and the underpotential deposition of metal atoms [209-213]. In some cases, the electrovalency (i.e., the ratio of moles of electrons transferred at the electrode to moles of adsorbate deposited) was found to vary with adsorbing species; the adsorption of iodide onto gold, for example, occurs with complete charge transfer from the halide to the electrode, whereas the adsorption of bro-

208

4. Materials

Characterization

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Figure 4.22 Simultaneous idealized representation of ETSM processes. Curve a (solid line) represents the current flow in the cell for a redox cycle, while curve b (dotted line) represents the concurrent frequency shift associated with the adsorption (forward arrow) and desorption (reverse arrow) of mass at the electrode surface during the redox electrode reaction. The reference electrode is a saturated calomel electrode (SCE). mide on gold occurs with only partial electron transfer [208]. Studies of reductive desorption of self-assembled monolayers also provided key information on processes occurring at the electrode surface [214]. The ETSM has been used to study the adsorption characteristics of surfactants containing electroactive groups, and how the adsorption and micellization of these species could be altered by electrochemical reactions at the electrode [ 145]. Bubble evolution during electrochemical processes has also been investigated [215]. In addition, these devices have been used to study thick (multilayer) films of electroactive materials, including charge-transfer salts [216], electrochromic (colored) materials [217,218], and a variety of oxide films [219-221]. The use of the ETSM to study polymeric systems, especially redox and conducting polymers, is a rapidly growing area of research. It has been used to elucidate the mechanisms of film formation, ion and solvent transport phenomena, and compositional changes that occur in these films upon redox cycling. Among the redox polymer systems that have been studied are poly(vinylferrocene)

4.4 Real.Time Monitoring of Chemical and Materials Processes

209

[222-224], nickel ferrocyanide [201,225,226], and ferrocene-siloxane copolymers [227]. Conducting polymer systems that have been investigated include poly(pyrrole) [228-230], poly(aniline) [203,231], poly(bithiophene) [232,233], and a variety of co-polymer and composite polymer films [231,234]. Because viscoelastic effects may come into play for polymer films, special care must be taken in the interpretation of frequency data for these materials [227,233]. 4.4.5

MISCELLANEOUS M A T E R I A L S / PROCESS CHARA CTERIZA TION

The use of AW devices to monitor relaxation and phase transitions in polymeric materials was discussed previously. These devices can also be used to monitor phase transitions in other materials. Changes in the general fluidity or viscoelasticity upon transition from solid to liquid crystalline (LC) states can be detected as frequency changes in TSMs coated with these materials. Okahata and Ebato [235] studied the behavior of smectic and nematic LC materials, as well as lipid bilayers, as the ambient temperature was increased above the phase transition temperature (Tc). For the smectic LC phases, they observed a dramatic increase in frequency upon transition to the LC state, whereas for the nematic phase, there was minimal frequency change at To. From these results, they concluded that the smectic materials form multilayers that are oriented perpendicular to the crystal surface, while the nematic materials do not form a similarly layered structure. Below To, the solid coating vibrates with the crystal. Above To, the multilayered smectic LC coatings become fluid and slippage occurs between layers, the effective mass coupled to the surface decreases, and the AW-device frequency increases. This behavior is observed for smectic LC materials in both air and in water, and is readily reversible. Similar behavior is observed for lipid bilayers in contact with aqueous solution; for films in contact with air, however, no frequency change at Tc is observed. Miramatsu and Kimura [236] also used a TSM to study transitions in Langmuir-Blodgett films with two phase transitions, and their results suggested that the viscosity and mass increased at the first phase transition, while the elasticity decreased and viscosity increased at the second transition. In addition to the characterization of polymers and liquid crystals, AW devices have been used in the characterization of layered metal films, especially superlattices [237-239]. Metal superlattice structures are of interest because they display interesting characteristics including, in some cases, superconductive properties. Superlattice metal films can exhibit a "supermodulus effect" (i.e., an increase in the Young's and torsional modulus) or an anomalous softening (---35%)

210

4. Materials Characterization

in the elastic shear modulus compared to single-metal films. The correlation of anomalous elastic behavior (i.e., modulus changes) with the layer dimensions and/or composition of these films can provide insight into the superconductivity effect. The moduli of these films are usually determined by Brillouin scattering, an optical technique requiring an extremely high-quality surface. The SAW technique permits the nondestructive evaluation of thin superlattice films to obtain moduli data that are comparable to Brillouin scattering results. The SAW has also been used to monitor the effects of contaminants or dopants on the elastic behavior of superlattice structures [240]. Acoustic sensors have also been reported as alternatives to existing pharmacochemical animal test procedures. Okahata and Ebato [241] report on the use of lipid-coated TSM devices as an alternative to the Draize test, which involves using animals to predict eye-irritant potential. As shown in Figure 4.23, they found excellent agreement between the partition coefficient obtained from the TSM response and the Draize score for a variety of surfactants. These results indicate the potential for using AW devices as an inexpensive, fast, and humane alternative to the controversial Draize test. Kurosawa et al. [242] used actomyosin from fresh carp and monitored the changes when adenosine 5'-triphosphate (ATP) was added, and noted changes that were not observed with aged actomyosin, potentially making this useful for a meat-freshness sensor. Some final notes refer to studies showing real-time monitoring of chemical modifications of films. For example, acoustoelectric interactions with metalcoated SAW devices have been shown to be useful for probing chemisorptioninduced mass and conductivity changes [243]. TSM devices have been used to monitor DNA hybridization [244]. CdS particle formation in cadmium arachidate Langmuir-Blodgett films upon exposure to hydrogen sulfide [245]. SAW devices have been used to determine rate laws and activation energies for the reaction of styrene vapor with an organoplatinum complex in a polymeric matrix [246]. Finally, using TSM devices to monitor uptake of water and calcium ions in phospholipid LB films as a function of temperature, significant differences in uptake above and below the phase transition temperatures have been observed [247,248].

4.5

Summary

For some film-characterization techniques, the sensitivity of AW devices to film mass density allows these devices to be used as sensitive microbalances (nanogram mass changes can be effectively quantified). This thin-film mass balance can be used to monitor absorption into polymers and adsorption onto sur-

4.5 Summary

211

50 A

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Ik==

O O

30

O Ik==

O O

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13 Ik== E3

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O

0 2.0

2.5

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log 10 P Figure 4.23 Comparison for the same surfactants of the partition coefficient (P) obtained from TSM measurements with the Draize score (cornea) obtained from animal e x p e r i m e n t s . (Reprinted with permission. See Ref. [241]. 9 1991 American Chemical Society.)

faces. By measuring nitrogen adsorption isotherms, thin-film surface area and microstructure can be evaluated. AW devices can also be used for real-time monitoring of: (1) diffusional transients (allows the rapid evaluation of diffusion coefficients as low as 10 -15 cm2/sec), (2) film deposition processes, and (3) corrosion and etching processes. For other film characterization techniques, the sensitivity of the AW device to the mechanical or electrical properties of a film is used. The presence of two sensor responses (i.e., velocity and attenuation or, equivalently, the frequency and admittance magnitude) has the significant advantage that the amount of in-

212

4. Materials Characterization

formation about the film is increased. This additional information helps in discriminating between sensing mechanisms and applying models for the interactions that allow the evaluation of thin-film properties. For example, these two responses enable one to determine thin-film viscoelastic properties and glass transition temperatures. In addition, they facilitate the understanding of dynamic processes such as polymer crosslinking and corrosion reactions. The results presented here demonstrate that thin films can be characterized based on acoustical monitoring of changes in film mass density, conductivity, and viscoelasticity. Additional sensing mechanisms are available to probe film properties. Some examples are thin-film dielectric constant, stress, and structure (e.g., roughness). Some of these sensing mechanisms will be hard to quantify since they involve a complex interaction (e.g., wave attenuation based on wave scattering due to film roughness); however, they may still be useful to provide a qualitative monitor based on empirical data. In conclusion, the results presented in this chapter demonstrate the extreme versatility of AW devices for the characterization of materials. The inherent sensitivity of AW properties to the mechanical and electrical properties of thin films can be used to advantage to directly monitor a wide variety of film properties. Since the properties and behavior of thin-film materials can be very different from those of similar bulk materials, this ability to directly measure thin film properties can be a significant advantage in materials research and development. The ability to use thin films instead of bulk samples has the added advantage that the time required to perform an evaluation of dynamic processes such as diffusion and corrosion can be greatly decreased. The number of applications of AW devices to thin-film characterization continues to increase, and is limited only by the ingenuity of AW device researchers and developers.

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Chapter 5

Chemical and Biological Sensors

5.1 Introduction Preceding chapters have described the detailed operating principles of acoustic wave (AW) devices and how these devices can function as sensors of various physicochemical phenomena in surrounding media. This chapter describes the extension of these capabilities to the detection and quantitation of chemical and biochemical species. An introduction to the fundamental background of various important physical and chemical interactions is presented for those not especially familiar with these topics. Coated bulk-wave oscillators operating in the thickness shear mode (TSM quartz devices, commonly referred to as quartz crystal microbalances--QCMs) were first demonstrated as viable organic vapor sensors by King in 1964 [ 1]. The subsequent proliferation of reports on this class of TSM sensors for the measurement of airborne and dissolved species has been reviewed by several authors [2-8]. The advent of the interdigital transducer provided the capability for generating surface waves in piezoelectric media [9,10], and the development of chemical sensors based on surface acoustic-wave (SAW) technology soon followed [11,12]. Compared to TSM chemical sensors, coated-SAW sensors are relative newcomers to the chemical sensor arena. The advantage of higher sensitivity with SAW sensors, coupled with the ability for mass production using planar microfabrication methods, are key factors responsible for the increasing interest in this class of chemical sensors, which have also recently been reviewed [13-15]. Shearhorizontal acoustic plate mode (SH-APM) sensors [16], and flexural acoustic plate wave (FPW) sensors [ 17-20] can be considered close relatives of SAW de-

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Copyright 9 1997 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-077460-7

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vices wherein a different type of wave or mode is employed. They are the most recently developed AW sensors and their capabilities for chemical sensing have only recently been characterized. With a few notable exceptions, obtaining adequate sensitivity and selectivity for the measurement of a given analyte requires a chemical or biochemical interface, henceforth referred to as "the coating." The coating, which should be physically or chemically bound to the sensor surface, may consist of a solid adsorbent, a chemical reagent, or a sorptive liquid or polymer. The coating acts as a chemically sensitive and selective element that immobilizes a finite mass of some chemical species from the environment. Resultant changes in physical and/or chemical properties of the coating, in turn, perturb the underlying AW device. Perturbations of AWs resulting from interactions of the coating with one or more analytes constitute the basis for detection and quantitation. The ultimate performance of the sensor depends on both the device configuration (substrate material, acoustic mode, operating frequency) and the nature and extent of coating-analyte interactions. Perturbation mechanisms for the various acoustic devices were discussed in general terms in Chapter 3. In this chapter, these mechanisms are reviewed specifically in the context of chemical and biochemical analysis. Performance criteria are discussed, and the fundamental coating-analyte interactions giving rise to sensor responses are presented as a basis for classification. Relevant physical and chemical models of these interactions are described, and examples of analytical applications employing each type of interaction are given to illustrate their advantages and limitations. While references have been included to illustrate specific points, this chapter is not intended to comprise an exhaustive review of the literature, particularly for TSM resonators, for which the number of references is far too great to be fully reviewed here. For more detailed information on the diversity of sensor applications, the reader is referred to the many review articles that have been published on these topics [2-8,13-15].

5.2

Detection Mechanisms

The detection of chemical analytes can be based on changes in one or more of the physical characteristics of a thin film or layer in contact with the device surface. Some of the intrinsic film properties that can be utilized for detection include mass/area, elastic stiffness (modulus), viscoelasticity, viscosity, electrical conductivity, and permittivity. In addition, changes in extrinsic variables such as

224

5. Chemical and Biological Sensors

temperature and pressure can also produce a sensor response, affecting the AW either directly or via changes in the film's intrinsic properties. Not all detection mechanisms are of practical significance for all types of sensors, and several mechanisms can operate simultaneously (synergistically or antagonistically) to affect a response. The range of detection mechanisms is thus a double-edged sword that leads to a high degree of versatility and a broad range of potential analytes, but that can also make interpretation of sensor responses difficult in certain cases. The development of equivalent circuit models or network analysis has recently been used to assist in the evaluation of sensor response behavior, and can provide insight into the relative importance of a given transduction mechanism for a specific sensor application. As with the materials characterization applications described in Chapter 4, the transduction mechanisms employed in analytical applications involve changes in the velocity and/or the amplitude of the acoustic waves. Although wave velocity is generally the preferred measurement, wave attenuation sometimes provides an additional indicator of a particular interaction and, importantly, aids in distinguishing one sort of perturbation from another [21,22]. In many cases, the relevant perturbation mechanisms can depend on the nature of the environment contacting an AW sensor. For example, all the AW devices discussed in this book have been examined in detail in vapor-phase environments and, under typical laboratory conditions, the density and viscosity of the contacting gas(es) are of little consequence. In contrast, the effect of contact by a liquid phase is such that only TSM, SH-APM, and FPW sensors operate effectively in such an environment ~ a consequence of the nature of the waves they propagate. For SAW devices, propagating waves are excessively attenuated by liquids, leading to inefficient operation [16,23]. SH-APM and FPW devices have the added advantage that acoustic energy is present on the surface opposite where the electrodes are placed, permitting isolation of the electrical contacts from a liquid-phase environment. The nature of the sensitive coating ~ both its inherent physicochemical properties and the physical particulars (thickness, uniformity, etc.) of a specific layer deposited on a specific device ~ often influences the detection process. Thickness, uniformity, and other characteristics are affected by the method of deposition, be it painting, dipping, solvent casting, spraying (air-brushing), spin-casting, or subliming. These methods are detailed in Chapter 6. LangmuirBlodgett and self-assembling monolayer films represent a special case wherein molecularly ordered film layers are deposited [24-26]. Coating uniformity over the device surface can vary greatly with the deposition method. For situations

5.2 Detection Mechanisms

225

involving equilibrium sorption, only the average thickness is important, so film nonuniformities can be tolerated within limits. Particularly for liquid-phase analysis, adhesion of films to the sensor surface can be problematic, requiring chemical immobilization (i.e., chemical bonding) of the coating on the sensor surface. Such methods of attachment are fairly well developed [ 16,27-29], although some limit the coating thickness that can be deposited, thereby limiting analytical sensitivity. The selection and/or design of a coating appropriate for a given sensing application requires consideration of the predominant detection mechanism(s) to be utilized. These are discussed in the following section, along with the relevant coating properties that affect chemical sensor response. 5.2.1

MASS LOADING

Of all the detection mechanisms listed previously, changes in the wave velocity (or, equivalently, oscillation frequency) by the addition or removal of mass at the surface of the sensor is the most commonly used and easily interpreted. Simple mass loading perturbs the wave velocity without producing attenuation effects, a fact that distinguishes it from the other modes of detection discussed in the following. Furthermore, this effect is accessible to all acoustic-wave modes. As a result, the vastmajority of analytical applications have sought to utilize changes in mass loading. TSM and SAW sensors have often been referred to in the past as "gravimetric sensors" because of the supposed predominance of mass changes in causing velocity (frequency) shifts. It is now clear that other factors, including changes in mechanical and electrical properties of the coating, can affect the sensor response, making such a generalization inappropriate in many cases (vide infra). Surface mass changes can result from sorptive interactions (i.e., adsorption or absorption) or chemical reactions between analyte and coating, and can be used for sensing applications in both liquid and gas phases. Although the absolute mass sensitivity of the uncoated sensor depends on the nature of the piezoelectric substrate, device dimensions, frequency of operation, and the acoustic mode that is utilized, a linear dependence is predicted in all cases. This allows a very general description of the working relationship between mass-loading and frequency shift, Afm, for AW devices to be written: Afro = - KSmAmA,

(5.1)

in which Sm is a device-specific constant that depends upon the factors mentioned above, K is a geometric factor for the fraction of the active device area being per-

226

5. Chemical and Biological Sensors

turbed, and AmA is the change in mass/area on the device surface. (Mathematical expressions that give explicit details of the relationship between mass changes and frequency/velocity shifts can be found in Chapter 3.) Note that r can be as simple as the fraction of the center-to-center spacing between IDTs that is coated with a uniform chemically sensitive film in the case of delay lines, or it can be a complex function that relates some nonuniform coating geometry with the (nonuniform) distribution of acoustic energy for resonators. As defined in Equation 5.1, Sm includes dependencies on frequency and substrate thickness of various orders for the different categories of AW devices. Table 5.1 summarizes these dependencies and also gives expressions for Sm that allow the operating frequency or substrate thickness to be accounted for, yielding a numerical value for Sin. The relationship among sensitivity, operating frequency, and substrate thickness was previously a limiting factor in the applicability of TSM sensors. As the plate thickness decreases, the operating frequency and mass sensitivity increase proportionally. The mechanical stability of the substrate, however, constrained the TSM configuration to an upper limit operating frequency of about l0 MHz. Recent evaluation of chemically milled substrates has demonstrated that stable operation at frequencies of 30 MHz can be achieved in liquids [32], and that even higher frequencies may be possible. The last column of Table 5.1 must not be misinterpreted: although a larger S,, value is indicative of a greater inherent mass sensitivity, the minimum detectable mass (MDM) change is limited by the noise level of the AW device-containing circuit, which can vary by orders of magnitude from one device/circuit combination to the next. As an example, the AIN thin-film resonators have the highest Sm value of any of the examples in Table 5.1, a result of their being extremely thin and thus operating at relatively high frequency. But initial results with these devices give noise estimates of nearly 1000 Hz, leading to a MDM of about 1.7 ng/cm 2 [33]. In contrast, the 97-MHz SAW delay lines of Table 5.1 have a shortterm noise level of about 1 Hz, yielding a MDM of 80 pg/cm 2, better by a factor of greater than 20. Noise levels are highly dependent upon the design of the circuit and the RF fixturing (see Chapter 6), as well as the method used to calculate the noise. Comparison of noise levels is, therefore, of limited utility; data on noise levels for these AW devices have been purposely omitted. The operation of AW devices in liquids has been reported and models have been developed to interpret observed behavior for the TSM [37-41 ], FPW [20] and SH-APM devices [ 16]. For sensing in liquids, the effective surface mass depends on the thickness of the liquid/coating layer that is "coupled" to the propagating AW. The thickness of this layer depends on the density and viscosity of the contacting liquid as well as operating frequency. For thin-film, acoustically

Table 5.1 Typical Mass Sensitivities of Acoustic Wave Devices i

Device Description AT-cut quartz T S M resonator

i

i

Examples

Refs.

Theoretical Mass Sensitivity (Sin)a (Hz "cm2/ttg)

Freq. Range (MHz)

Frequency (MHz)

[30]

2.3 .fo ~

5-30 b

6

0.26

[31]

5.7/t 2

30

0.055

[32]

Substrate Thickness (ram)

1111

(Hz-cm2/ttg) 84 2170

Sputtered A1N thin-film

-,i

longitudinal-mode resonator

[33]

0.59 .fo E 16.3/t 2

900-1000

957

0.0055

X-propagating S A W delay lines ST-cut quartz Y-cut quartz

[34] [35]

1.32. fo 2 1.35 9f02 e

25-500

97 112

N/A N/A

12,200 16,900

ST-quartz S A W resonator

[36]

1.26.fo 2

ZnO/AI/Si3N4 F P W delay line

[7]

0.019/t 2 d 0.022/t 2 d

200 4.7

N/A 0.003 c

50,400 2,110

2.6

0.003 e

2,470

ST-quartz S H - A P M delay line i,i

[16]

80/t 2 f

[16]

400It 2 g

25-500 25-500 1-10 25-200

i i

539,000

104

0.20

2,000

158

0.19

11,000

i

ii

,

value tO be used with Equation 5.1. Unless otherwise noted, these values have been experimentaUy confirmed within 5% or better. Multiply by (J'o in M H z ) 2 or divide by (t in mm) 2, as indicated, to obtain working value of S,,,. bConventional wisdom usually places the upper limit for the fundamental mode of quartz TSM devices between 10 and 15 MHz. Alternative device structures, however, can achieve a fundamental frequency significantly greater than this, with operating frequencies of up to 100 MHz. CNot experimentally confirmed to better than 50%, but believed accurate. aExpedmentally confu'med within 7%. eBecause the membranes through which the FPW propagates are three-layer, microfabricated composites, the thickness of each layer, as well as effects of residual strain, must be accounted for to give accurate Sm values. 9 or n -> 1 modes; sensitivity is one-half as great for n = 0 mode (see Chapter 3 and ref. 15). gFor unresolved modes. Value is experimental only, as calculation is not possible for mixed modes (see ref. 25). N/A = not applicable. aS m

228

5. Chemical and Biological Sensors

rigid coatings that are strongly bound to the surface, mass accumulation in or on the coating yields a proportional frequency decrease as in Equation 5.1. Most physical and chemical interactions between analytes and sensor coatings lead to changes of mass. Thus, this sensing mechanism offers the greatest latitude in the selection of sorptive or reactive coating materials, including a wide variety of organic polymers [42]. In addition, the performance of a given coating can sometimes be predicted a priori through knowledge of chemical reactions or by reference to solubility theory and/or appropriate models, as described in Section 5.4. The key challenge to implementing this detection mechanism in a useful sensor is imparting selectivity. Strategies for accomplishing this are discussed in later sections.

5.2.2

MECHANICAL PROPERTIES

Interactions with an analyte can cause changes in the mechanical properties of the coating. An increase in mass loading alone produces a decrease in frequency without affecting attenuation. In contrast, changes in mechanical properties of the coating can produce changes in both the frequency and the attenuation of the AW, as described in Chapters 3 and 4. Furthermore, these changes can either increase or decrease either or both of the two AW propagation parameters, depending on the details of the relationship between film thickness, acoustic wavelength, and the complex modulus of the film at the frequency and temperature of operation. The mechanical properties of a thin film can be generally classified as either elastic or viscous in nature. In many cases, these two properties are so interdependent that treating one without the other is neither practical nor realistic, so they are considered together as viscoelastic properties. The case of purely viscous interactions was treated in Chapter 3 for the contact of liquids with AW devices. A few liquid absorbent films and liquid-like, low molecular weight polymer films (which might be adequately treated as liquids in terms of their physical interactions with acoustic waves), have been examined [43-47]. Similarly, there are some cases where mechanical effects are (almost) purely elastic; this case is discussed next. In general, however, many thin-film materials, including most polymers, must be treated as viscoelastic materials to fully account for their interactions with acoustic waves. Investigation of viscoelastic effects on acoustic wave sensor response represents a particularly active area of research.

5.2 Detection Mechanisms

229

In the instance that mechanical effects can be adequately treated as purely elastic, the frequency of a SAW device is perturbed by modulus changes according to A f e = S ef 2oA - 7

A + 21a,

'

(5.2)

where S e is a constant that depends on the substrate material, h is the coating film thickness, v is the surface-wave velocity, and/x and A are the shear modulus and Lam6 constant (bulk modulus) of the coating, respectively. Note that the presence of the "A" outside the term in parentheses indicates that the change in the entire term is utilized to compute the elastic perturbation. This form is convenient because it applies to either the deposition of an elastic material (in which case h changes from zero to the thickness of the deposited film), or changes in the elastic moduli and/or thickness of a film already present on the device surface. Organic polymers comprise the most common type of coating used with AW sensors due to their capability to reversibly sorb vapors and liquids. For those polymers whose interactions with AWs can be treated as perfectly elastic, the fact that h is invariably larger than/z means that the value of the term (A + /z)/(A + 2/x) is constrained between 0.67 and 1; thus, this ratio can be approximated using a value of 0.84. The magnitude of a purely elastic perturbation is then proportional to the product of shear modulus and thickness, with no more than a 16% error. In much of the work published on the use of polymer coatings for SAW vapor sensing, the polymer's elastic modulus has been considered small enough for modulus effects to be neglected; most of these studies did not, however, consider viscoelastic effects at all. Furthermore, the modulus values assumed in such cases have been based on static or low-frequency determinations. This is a likely source of additional error, because the effective modulus of a polymer increases with the frequency of applied stress. In fact, for (nonacoustic) measurements performed in the range of 1-30 MHz (the highest frequencies reported), shear moduli in the range of 108-109 N/m E are found for many organic polymers that have low-frequency/z values of 106-107 N/m 2 [48-51 ]. Shear-modulus values in this range are sufficiently large so that they must be accounted for if the effect of adding a polymer film to an AW device surface is to be properly modeled. The frequency shift obtained upon deposition of such a coating is smaller ( ~ 10%) than that predicted from mass effects alone, because the sign of the righthand side of Equation 5.2 is opposite to that of Equation 5.1.

230

5. Chemical and Biological Sensors

Just as in the case of film deposition, exposure of a polymer to an analyte must generally be considered in the context of viscoelastic changes in the film. Again, there are some cases in which the perturbation is largely elastic. In such instances, absorption of the analyte more commonly causes a modulus decrease, thereby enhancing the magnitude of the negative frequency shift attributable to mass loading. Recent reports suggesting a greater role for changes in the stiffness or viscosity of the coating film are preliminary and, in some cases, contradictory. Bartley and Dominguez suggested that internal stress created during vapor sorption in polymers might lead to an increase in frequency [52]. They derived an expression for the sensor response that included terms for mass loading and elastic stiffness changes (as in Equations 5.1 and 5.2), as well as a third term to account for the increase in frequency expected if compressive stresses were created within the coating upon vapor sorption. For typical polymers, however, this term is expected to be about an order of magnitude less than the mass-loading term. Interfacial stress was implicated by Thompson et al. to explain transient frequency increases in liquid-phase bioassays using TSM sensors with immobilized coatings [53,54]. Zellers et al. reported on the relative responses of polymercoated FPW and SAW sensors to changes of mass, density, and elastic stiffness [ 18] using a computer model developed previously. Results using high-frequency modulus values for different devices operating at the same acoustic wavelengths indicated that the fractional change of velocity resulting from changes of elastic stiffness were small relative to thickness- and density-induced changes. In contrast, a follow-up of earlier work [55] by Grate et al. compared partition coefficients, K, determined by gas chromatography to those determined using the same stationary phases as coatings on a SAW device [56]. They found that the SAW-derived values were four to six times greater than chromatographically determined values, with the latter reflecting only mass uptake. Typical comparisons are presented in Figure 5.1 for various polymers. Although differences between the chromatographic support material and the planar SAW device surface might account for part of the disagreement, the discrepancies were largely attributed to changes in the modulus of the coating upon vapor sorption and the effect of such changes on SAW frequency. Several factors hinder a complete analysis of these results, including uncertainties in modulus values at high frequency, as well as the effects of absorbed vapors on the moduli as a function of vapor concentration. The conclusion derived from this work was that responses of polymer-coated SAW vapor sensors might be dominated by modulus effects rather than mass-loading effects.

5 A

L.

0 C

I

4

W m nxm DI23

3 E

I

e

rn x

x rn x

2 io

0 ..J

taalb O

1

2

3 Log K (from G LC)

4

5

Figure 5.1 Comparison of K values (partition coefficient) calculated from SAW response data with K values from GLC retention. The K values are for fluoropolyol (FPOL - 1 ) , poly(epichlorohydrin) (PECH - F]), and polyisbutylene ( P I B - x) exposed to a variety of organic vapors. The solid line is the line of perfect correlation. (Adaptedwith permission. See Ref. [56]. 9 1992 American Chemical Society.)

t~ IT i.mo

I',O

232

5. Chemical and Biological Sensors

Other studies have reported frequency increases for polymer-coated SAW devices upon exposure to water vapor at elevated temperatures (<80~ consistent with a predominance of elastic stiffening of the coating [57]. At lower temperatures (25-35~ the same sensors exhibited frequency decreases upon exposure to water vapor of the same concentration, a response consistent with mass loading. Thus, the dominant mechanism may be determined by a variety of factors, including the type of vapor-coating interactions and the ambient temperature. Note that ambient temperature can have profound effects on film viscoelastic properties (see Chapter 4), which in turn can influence the results of vapor exposure. At least some of the controversy might be resolved by applying models that account for viscoelastic and film resonance effects, as described in Chapters 3 and 4. The apparent discrepancies in the studies may arise from the assumption underlying Equation 5.2, namely that the entire coating moves synchronously with the device surface. This assumption is valid only for rigid films (in the case of polymers, glassy or crystalline) that are acoustically thin: the film thickness should be less than approximately 1% of the acoustic wavelength in thefilm I. For thicker films of viscoelastic materials, the assumption of synchronous motion is not generally valid. Martin and Frye [58] recently derived an equivalent-circuit model relating the near-resonant electrical characteristics of a TSM to the viscoelastic properties of the coating. They demonstrated that the resonant frequency of the TSM can either increase or decrease, depending on the relative acoustic thickness of the film. Evidence of film resonance effects has been reported for polymer-coated SAWs exposed to organic vapors [59a]; and a formal film resonance model has been developed for SAW/polymer interactions [59b]. Lu and Lewis [60] also investigated the response of coated TSM devices with respect to elastic effects. They related the frequency response upon coating deposition, and subsequent interaction with the analyte, to the acoustic impedance of the overlay film. The relative importance of the mass-loading and viscoelastic contributions to the observed acoustic sensor response is an issue that has yet to be resolved. Capitalizing on these effects to improve chemical selectivity and detection sensitivity requires further characterization of sensor response, in terms of both velocity and attenuation changes, in addition to more accurate models describing how coating-analyte interactions affect relevant film properties. ~Note that the acoustic wavelengthin the film depends on the velocityof sound in that material and can therefore be very different (often much smaller) than the wavelengthin the AW device substrate. Consequently,the "1% rule" is an approximation,at best, unless correction is made for the acoustic wavelengthin the film.

5.2 Detection Mechanisms

5.2.3

233

RHEOLOGICAL PROPERTIES

AW propagation velocity is sensitive to changes in the density of any medium in contact with the substrate surface. Inspection of the mass-loading term for AW devices (Chapter 3; Equation 5.1) reveals an implicit dependence of wave velocity on the density of a coating layer. Note that a density change need not occur in a surface-immobilized film in order to be detected: changes in the ambient medium produce an effect as well. TSM [61], SAW [ 11 ], and FPW devices have been utilized to monitor the pressure (via the density) of gases. For liquid-phase sensing, both density and viscosity, as well as the nature of the acoustic mode, play a role in AW perturbations. For TSM and SH-APM devices, in-plane motion of the substrate surface entrains a thin layer of liquid through viscous coupling. Entrainment of a liquid layer by the sensor surface constitutes a mass load proportional to the product of thickness and density of the coupled liquid layer, giving rise to a velocity change. The inelastic nature of the liquid layer also results in attenuation of the AW, the magnitude of which depends upon frequency, density, and viscosity. For highfrequency SAW devices, this attenuation is far more severe than for shear-mode devices: Rayleigh waves have a substantial surface-normal component that generates compressional waves in a contacting liquid, dissipating most of the SAW energy (the extent of the attenuation is about 4 dB/cm-MHz). As a result, liquidphase sensing using SAW devices is limited to frequencies below approximately 10 MHz [23,62]. At first glance, the fact that FPWs also possess a substantial surface-normal component would appear to preempt them from liquid-phase applications as well. But the velocity of FPWs is extremely l o w - lower than the velocity of sound in ordinary l i q u i d s - so dissipation of energy through compressional wave generation is minor [17] and these devices function well in contact with liquids. While rheologically-based detection mechanisms have value for characterization of liquids (see Chapter 3), they are generally impractical for most chemical sensing applications due to limited sensitivity. For most solutes, sizable changes in concentration are required to produce a measurable change in density and/or viscosity, and viscosity is often not a monotonic function of concentration. Furthermore, the sensitivities of both density and viscosity to temperature changes mean that exceptional temperature control and/or compensation are required for such measurements to be meaningful. Two possible exceptions are (1) a few analytes, e.g., sucrose or glycerol, that cause very dramatic changes in viscosity with concentration [63], and (2) chemical reactions in a bulk solution or thin liquid layer that dramatically alter viscosity. Examples of the latter case are the

234

5. Chemical and Biological Sensors

gelation/agglutination reactions involving biochemical species discussed in Section 5.4.7 [64-66].

5.2.4 ELECTRICAL PROPERTIES Because piezoelectric substrates are used for AW chemical sensing applications, an electric field accompanies the propagating wave as it travels through the substrate. This field can interact with mobile charge carriers in a surface layer/ coating and affect both the velocity and amplitude of the wave, as discussed in Section 3.2.5; changes in acoustic velocity and attenuation due to the interaction of charge carriers are given by Equations 3.35a and b. Taking advantage of this detection mechanism in the design of a chemical sensor requires judicious selection of the piezoelectric substrate [34]. Changes in the attenuation and velocity of surface acoustic waves depend on the square of the electromechanical coupling coefficient of the substrate, K 2, which varies by orders of magnitude from one material to another. YZ-lithium niobate (LiNbO3), for example, has a/(2 value of 0.048, which is more than 40 times higher than that of ST-quartz (K2 = 0.0011). Thus, LiNbO3 is a more appropriate substrate to choose if this detection mechanism is to be employed. Appropriate temperature controls will be essential, however, since the temperature coefficient of LiNbO3 SAW devices is over 20 times that of comparable ST-quartz devices. If a coating material is used to concentrate the analyte near the sensor surface, it must be a semiconductive material with a sheet conductivity (the product of film thickness and bulk conductivity) that falls within a "window of sensitivity" determined by the substrate. Using values for LiNbO3 [from ref. 67] maximum sensitivity is obtained in the range of 10-7-10 -5 ~ - l , and the maximum possible frequency shift (Af/fo) is K2/2 = 24,000 ppm. For quartz, the window of sensitivity is an order of magnitude lower (10-8-10 -r l-l-l) and the maximum shift obtainable is only 550 ppm; this is, however, more than adequate for the observation of a significant effect (i.e., sensor response) under the proper conditions [34]. If interaction with an analyte increases the conductivity of the coating film (in the appropriate range), the frequency decreases and the conductivity change enhances frequency shifts due to increased mass or decreased modulus. If it is desired to isolate the conductivity effects from mass and mechanical effects, a reference device can be coated with an initial layer of metal whose sheet conductivity significantly exceeds the window of sensitivity, thereby shorting the electric field (this does not affect sensitivity to mass changes). The chemically sensitive coating material is then applied over the metal film [67]. The signal from this device can be compared with that from a sensing device having no

5.2 Detection Mechanisms

235

metal layer, and the resulting difference in frequency shifts depends only on conductivity changes. The substrate material can also be important in isolating the conductivity effect; LiNbO3 is again the material of choice, with a mass sensitivity less than half that of other common substrates such as quartz and ZnO-onSi [67]. In addition to having sheet conductivity within the aforementioned window of sensitivity, the sheet conductivity of the coating material must be altered as a result of a (bio)chemical stimulus. Much of the earlier applications used films of phthalocyanine (H2Pc) or metal phthalocyanine (MPc, where M = Pb, Cu, Co, Fe, etc.) [24,67-70]. Pc-based films are attractive as coatings because they exhibit suitable conductivity and are thermally stable to 400-500~ although their propensity for sublimation limits extended operating temperatures to about 250~ and below. Films of H2Pc, MPcs, and their derivatives can be deposited by a variety of techniques, including vacuum sublimation [68], Langmuir-Blodgett transfer [24,26], and plasma polymerization [70]. Interaction with electronegative gases, such as NO2, can enhance the p-type conductivity of these materials by several orders of magnitude; this is a result of the creation of mobile holes via electron transfer to the electrophile [71,72]. Changes in conductivity within the range of 10-9-10 -6 l'~-1 have been reported for MPc films upon exposure to 2.8 ppb of NO2 [72]. The conductivity and sensitivity of the Pc film to a given analyte can be modified by varying the central metal atom [70], by using substituted Pc materials, or by adding dopants to the coatings after deposition [71 ]. Ricco and Martin [67] used the metal-coated reference-device scheme described above to confirm their calculations comparing mass and conductivity effects. Their results are presented in Figure 5.2, showing the SAW response to NO2 for a Pc-coated SAW device with and without a conductive metal layer. The calculations indicated that the frequency change due to NO2-induced conductivity variation in PbPc on a LiNbO3 SAW device was orders of magnitude greater than the frequency shift from mass loading for that particular system. 2 More recent studies have focussed on the characterization of the conductive polymer, polypyrrole, and its use as a coating for acoustic wave vapor sensors [74-77]. One advantage of polypyrrole is that it can be generated directly on an 2Nieuwenhuizen et al., performed similar studies using PbPc on quartz SAW devices [73] and concluded that, for quartz substrates, both mass-loading and acoustoelectric effects contributed to the observed response. This is consistent with data provided in a table in reference 67; the greater mass sensitivity and smaller K 2 value for quartz relative to LiNbO3 combine to result in a ratio of acoustoelectric to mass effects of about 10, rather than the value of 1000 calculated for LiNbO3, for the same film thickness and operating frequency. This difference serves to reinforce the point made earlier, that the choice of substrate is crucial when examining such effects.

L~

t,n

rg r

r162

B

am 9

mini

lg

m9

z o

am..

r~ r om/

Figure 5.2 Response of lead phthalocyanine-coated SAW to NO2 with (or decoupled) and without (or coupled) a metal subcoating. The data indicate that the response of the LiNbO3 SAW is due to acoustoelectric effects, rather than mass loading. The "single" designation indicates that the response is from an individual SAW sensor (i.e., no reference sensor was employed). (Reprinted with permission. See Ref. [67]. 9 1985 Elsevier Publishers.)

5.2 Detection Mechanisms

237

electrode surface by electropolymerization, which makes it particularly suited for the TSM (quartz resonator) devices. The conductance of the polypyrrole film changes upon sorption of organic vapors, with nucleophilic vapors producing an increase in film resistance and electrophilic vapors causing a decrease in resistance [77]. The oxidation state of the deposited film also appears to influence its sorptive capabilities [75]. The observed response of polypyrrole-coated TSM sensors, however, is likely dominated by physical effects (e.g., mass loading and/or stiffness changes). The polypyrrole films are particularly well suited for hybrid sensor configurations. For example, the use of a SAW sensor (for mass measurements) in tandem with a chemiresistor (for conductivity measurements) is feasible; such hybrid devices have been previously reported using phthalocyanine coatings [78]. A unique advantage of the TSM devices is the presence of an electrode that can function as a working electrode in an electrochemical cell. Thus, sorption of vapors into the film can produce a mass loading response and, if the vapor is electroactive, the vapor may also be involved in redox reactions (current flow) with the film at the electrode surface [76]. Such a configuration could provide additional means of discriminating between sorbed vapors. An uncoated substrate can also be affected by the interaction between polar analytes and the electric field associated with the propagating acoustic wave. This effect may have contributed to SAW sensor responses to high relative humidity levels by Huang [79]. Using lithium niobate substrates, increased attenuation of the SAW was observed in the RH range of 89% to 98%; minimal frequency shifts were observed during these studies. Increases in attenuation may have occurred as a result of electrical leakage between electrode finger pairs in the IDTs. Other studies have reported liquid sensing/detection of ionic species using uncoated acoustic devices, where the frequency of the device changes in response to the conductance of the solution. Yao et al. reported the use of a TSM device to monitor acid-base [80] and compleximetric titrations [81]. The frequency of the TSM changed with the specific conductance of the solution, which depends strongly on the ion(s) present and their respective concentrations. By plotting frequency shift vs titrant volume, the endpoint was determined as a change in slope. This sensor was subsequently used for the multi-component determination of aspirin and salicylic acid in solution [82]. Nomura and Kanazawa also used an uncoated TSM to analyze for metal ions in solution [83]. They concluded that the negatively charged quartz surface attracted and adsorbed metal ions; the frequency shift observed was likely the result of mass loading. While uncoated devices lack selectivity, the general response to charged and/or polar species may be an advantage for some applications, for example as a detector for ion chromatography.

238

5.2.5

5. Chemical and Biological Sensors

THERMAL EFFECTS

The AW velocity in piezoelectric media is sensitive to changes in temperature. For most practical sensors, this fact necessitates some means of temperature control and/or compensation, as discussed in detail in Chapter 6. For most chemical sensing applications, substrates such as ST-quartz for SAW sensors and ATquartz for TSM sensors, which have small temperature coefficients, are selected. There are cases where the temperature sensitivity of acoustic-wave devices is of potential, but thus far undemonstrated, value. Pyroelectric materials, e.g., ZnO, LiTaO3, and VOx (2 < x < 3), have the property that a temperature gradient causes a potential drop across the substrate [84,85]. This enthalpimetric capability has been used to measure the heats of chemical reactions occurring at a sensor surface, the most common application being the detection of biological species via enzyme-catalyzed reactions [86-88] because of the considerable heats generated (up to 100 kcal/mole [89]). The temperature sensitivity of AW velocity makes similar enthalpimetric measurements feasible without the need for a pyroelectric layer. As in the case of the acoustoelectric effects discussed above, maximum sensitivity would be obtained through judicious choice of the substrate; YZ-LiNbO3, with its very large temperature coefficient (80 ppm/~ is a likely choice for SAW sensors. Minimizing the thermal mass of the AW device and its (reactive) coating film, relative to the active area of the sensing film, also serves to enhance sensitivity.

5.3

Performance Criteria

In the development of a sensor for a given application, numerous factors affecting performance must be considered. Among these are sensitivity, selectivity, reversibility, response time, dynamic range, stability, reliability, and environmental (e.g., temperature) effects. Some of these concerns dictate the preferred substrate and/or acoustic mode; others are important in the selection of the coating, or in establishing optimal operating conditions. These criteria play a large role in the design of a complete sensor system, as discussed in Chapter 6. Of the aforementioned factors, selectivity and reversibility will be discussed in greatest detail, since they alone are unique to bio/chemical sensors. The remaining criteria are practical concerns common to sensors of all sorts and therefore are discussed in more detail in Chapter 6.

5.3 Performance Criteria

239

5.3.1 SELECTIVITY Selectivity refers to the ability of a sensor to discriminate between the analyte of interest and possible interferences. For acoustic-wave chemical sensors, this characteristic is determined in most cases by the properties of the coating material. Perfect selectivity for a single analyte is virtually unattainable if one uses simple polymer, organic, and inorganic films, but can be realized for some biologically-based coatings. In many cases, however, adequate selectivity for a particular application can be achieved if the nature and number of potential interferants is known. This constraint applies to most monitoring systems and should not be considered a limitation unique to the present, or any other, sensor technology. The focus of much of the work in acoustic-wave sensor development has been achieving selectivity through the use of different types of coating materials. The ideal coating will exhibit high sensitivity (defined more fully later) toward the analyte, but low sensitivity toward other species. This concept is illustrated in Figure 5.3 for two SAW devices coated with fluoropolyol (FPOL), a polyfluorinated polymer of moderate-to-high polarity, and polyisobutylene (PIB), a nonpolar hydrocarbon polymer. The FPOL-coated SAW exhibits good response to butanone, but significantly less response to isooctane; i.e., FPOL exhibits greater selectivity toward the butanone. The PIB-coated SAW, in contrast, exhibits greater selectivity toward the isooctane. As would be expected, the sensitivity and selectivity of a sensor coating depend on its chemical properties (e.g., polar vs non-polar). As discussed in Section 5.4.1, tailoring the chemical properties of the coating to match those of the target analyte represents one strategy for improving the selectivity of acoustic sensors. Considering the volume of literature on the subject of coating development and evaluation, comprehensive testing of selectivity for most target analytes has been disappointingly limited. Because water vapor is ubiquitous and therefore often constitutes an interference, it would seem imperative to evaluate the response of every sensor as a function of relative humidity (RH); this has rarely been done [92a,b]. In those instances where the response to potential interfering compounds has been investigated, it was usually by exposing the sensor to target and interfering analytes individually; rarely have sensors been simultaneously exposed to more than one species [92c,92d,99a]. In some cases, it can be argued that the separate responses accurately indicate the presence (or absence) of an interfering signal. Unfortunately, additivity of responses has not been extensively demonstrated [92c]; at high vapor concentrations or when analyte and interferant have significant intermolecular interactions, responses may be non-additive.

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5.3 Performance Criteria

241

The issue of selectivity continues to represent a most active area of research for this class of sensors and will be discussed further in the context of coating-analyte interactions.

5.3.2

REVERSIBILITY: SENSORS AND DOSIMETERS

Reversibility is the ability of a sensor to recover, or retum to its original background/baseline condition, after exposure to an analyte. More particularly, a coating-analyte interaction is considered reversible if removal of the analyte from the ambient phase results in its complete desorption from the coating/sensor, with no permanent physical or chemical change having occurred. The reversibility of analyte/coating interactions will depend on the relative strength of the interactions, and on the kinetics and thermodynamics of those interactions. These issues are discussed in greater detail in Section 5.4 Because they are indistinguishable in terms of sensor performance, interactions that are slow to reverse at room temperature are often lumped together with interactions that are "truly irreversible," in one of three senses. (1) If the energy required for removal of the analyte is sufficiently high, the sensor and/or coating may be damaged before a high enough temperature is attained for removal to proceed at a reasonable rate. (2) Some interaction processes lead to the formation of new compounds, permanently changing the chemical nature of the coating. An example is the detection of H2S using a silver film: 2Ag + H 2 S ( g ) ~ Ag2S + H2(g). In this case, both the hydrogen gas that is formed (and lost) in the reaction process, as well as fairly high temperatures, would be necessary to regenerate metallic silver. (3) Highly reactive analytes and/or coating materials can cause permanent alteration of the physical structure of the coating material, e.g., the scission of C-C bonds in a polymer coating as a result of the action of a powerful oxidant such as ozone. The observed signals for reversible and irreversible coating-analyte interactions are fundamentally different, so detection and quantitation criteria differ accordingly. For a reversible sensor, the frequency or amplitude change is proportional to analyte concentration. Sensitivity (defined more fully in Section 5.3.3) in this case is determined by the equilibrium value of the signal, relative to its baseline; upon removal of the analyte the sensor signal returns to its original baseline value. For an irreversible sensor, however, exposure to the analyte produces a change in signal from which the sensor does not recover; repeated exposures produce a corresponding permanent shift in the baseline value. Thus,

242

5. Chemical and Biological Sensors

sensors utilizing irreversible interactions are often referred to as dosimeters, since the signal at any particular moment is an indication of the cumulative dose of analyte received by the sensor, provided the sensor is operating within its linear dynamic range (see Section 5.3.4). In this case, sensitivity is defined as the change in signal as a function of dose, which is the product of concentration and exposure time. Irreversible interactions do not preclude the measurement of instantaneous concentrations; the rate of change of the signal at any instant in time can provide a real-time measure of analyte concentration. Because of these distinctions, irreversible and reversible interactions are best suited for different applications. For long-term monitoring of ambient vapor concentration profiles the reversible sensor has the advantage of unlimited lifetime. The irreversible sensor has a limited lifetime; once the available coating has completely reacted, further interactions with analyte produce no additional response. Thus, such sensors are constrained to applications where the total dose is unlikely to exceed the "capacity" of the coating, or to cases where the reagent in the coating can be regenerated, in situ. The two advantages of dosimeters derive from the fact that the final signal represents a record of total exposure over a given period. The dosimeter need not be continuously monitored, reducing power requirements substantially; and a permanent record is available for documentation, important for such applications as health and safety monitoring. To obtain a comparable total-exposure record for reversible sensors requires maintaining a continuous record of response data for the entire time period of interest. An operating parameter that must be considered in the context of reversibility is mass flow of analyte to the sensor. For reversible interactions where the response depends on an equilibrium distribution process, response is a function of analyte concentration and is independent of flow rate. This holds true provided the analyte concentration remains constant long enough for equilibrium to be attained; higher rates of delivery of analyte to the sensor can result in more rapid attainment of equilibrium but will not change the magnitude of the equilibrium response. If a sensor system is not carefully designed, the response of a dosimeter (change in signal/unit time) can depend on the mass flow of the analyte. This occurs when the overall rate of interaction/reaction per unit area for the coating is comparable to or exceeds the rate of impact per unit area of the analyte, creating a layer near the sensor that is significantly depleted of analyte. In the limit of low analyte concentration and rapid interaction/reaction kinetics, the rate of change in the signal is proportional to the amount of analyte introduced to the coating per unit time. For either type of sensor, variation of the flow rate is the

5.3 Performance Criteria

243

surest way to determine if mass flow rates are important. The issue of reversibility is inextricably intertwined with sensitivity and selectivity, insofar as all three are dependent on the nature and extent of coating-analyte interactions. As discussed in Section 5.4, interactions that tend to increase sensitivity and/or selectivity usually are less reversible. As a result, the selection of an appropriate coating for a given application often requires trade-offs. In many cases, the construction of an effective sensor depends not on the ability to identify or synthesize the perfect coating, but on the ability to compromise in the face of apparently conflicting requirements.

5.3.3

SENSITIVITY 3

For a reversible sensor, sensitivity is defined as the change in sensor output signal obtained for an incremental change in the concentration or mass of the analyte, i.e., the slope of the response-vs-concentration curve. Sensitivity for a reversible AW sensor typically has units of [frequency change]/[concentration change], e.g., Hz/M (M - mol/L), Hz/(/xg~), or even ppm/ppm (normalized frequency shift/concentration). For an irreversible sensor, sensitivity is more appropriately defined in terms of frequency change/integrated exposure, e.g., Hz/M-min. The overall sensitivity of an AW-sensor system, including the device, its coating, and in some cases much of the supporting hardware, should not be confused with the coefficient of mass sensitivity (Sin) described in Section 5.2.1. While the overall sensitivity does depend on Sin, it takes into account many other factors as well. For a given device employing a given acoustic mode, sensitivity to an analyte is determined by the amount of coating (thickness and/or available surface area) and the strength of the analyte-coating interaction, i.e., the constant for equilibrium between ambient-phase and sorbed analyte. Given the limits on the amount of coating, coating-analyte interaction strength is of paramount importance in determining overall sensitivity and detection limits; this issue is discussed in more detail under the individual sections on analyte-coating interactions.

3Sensitivity is often confused with detectability, yet the distinction is important for analytical measurements. Detectability, or the limit of detection (LOD), is the smallest amount or concentration of a substance required to produce a sensor response that can, with some level of statistical confidence, be differentiated from zero. Because the LOD sets the lower end of a sensor's dynamic range, it is discussed further in Section 5.3.4.

244 5.3.4

5. Chemical and Biological Sensors DYNAMIC RANGE

The dynamic range is the concentration interval over which a sensor provides a continuously changing response. The linear dynamic range (LDR) further constrains this interval to that region in which linear proportionality between response and concentration is maintained. Dynamic range is bounded by the limit of detection (LOD) at the low end and by saturation effects at the upper end, which is often termed the saturation limit. It should be noted that saturation can occur as a result of chemical limitations of the system or from saturation of the electronic circuitry. Analyte concentrations below the LOD give no detectable response (i.e., indistinguishable from noise), while concentrations at or above the saturation limit all give the same response. Like sensitivity, LOD depends on the inherent sensitivity of the device itself, as well as the kinetics and thermodynamics of the coating-analyte interaction and the quantity (thickness and/or surface area) of coating available. Unlike sensitivity, however, LOD also depends on the system noise level. The LOD is expressed in terms of the ratio [response when analyte is present]/[noise level when there is no analyte present]. Commonly, LODs are defined as signal-to-noise (S/N) ratios of two or three, corresponding roughly to situations where the signal exceeds the noise at statistical confidence levels of 95% and 99%, respectively [91]. Thus, in the latter case, the LOD can be defined as 3N/sensitivity. The LOD is expressed in units of concentration (e.g., M,/.,g/L, or ppm). The saturation limit can be set by any one of several factors. Factors relating to the limitations of the electronic circuitry are discussed in Chapter 6; the physical and chemical limits will be discussed here. For a given amount of coating, there is an upper limit to the concentration or mass of analyte that can be sorbed/reacted before either the sorptive/reactive capacity of the coating is reached or the physical properties of the coating are irreversibly altered. The upper limit of coating thickness, in turn, is determined by several factors. Few realworld thin-film materials are perfectly elastic, the consequence of which is filmthickness-dependent attenuation of the acoustic wave. This is particularly true for polymers above their glass-transition and/or melting temperatures. Even some metal and metal-oxide films can be inelastic to some extent. Any material that is significantly inelastic has an upper limit of thickness beyond which operation of the AW device becomes impractical due to excessive attenuation. Furthermore, the sorption of an analyte by an inelastic material can result in significantly more attenuation than that attributable to the "unloaded" film itself; a prime example is the case of viscoelastic polymer films, where sorption of an analyte plasticizes the film, increasing AW attenuation by large amounts (see Chapter 4).

5.3 Performance Criteria

245

In the somewhat rare instance that the coating (even when loaded with analyte), remains highly elastic, mass loading may be the only operative interaction mechanism. In this case, as the total coating-plus-analyte thickness reaches and exceeds several percent of one acoustic wavelength, the mass sensitivity deviates significantly from that derived from perturbation analyses for acoustically thin films, and is difficult to predict. For reversible interactions, the linear dynamic range is determined by that portion of the coating-analyte sorption isotherm (discussed in Section 5.4) that lies between the LOD and the saturation limit. For irreversible interactions, the LDR will depend on the sorption/reaction kinetics and the coating capacity. For practical reasons, it is desirable to have the widest LDR possible, although inexpensive microprocessors and associated memory make correction for minor nonlinearities straightforward. For an example of a wide linear dynamic range, refer to Figure 5.13.

5.3.5

STABILITY, REPEATABILITY, RELIABILITY, AND REPRODUCIBILITY

Four concepts are important for a discussion of stability: short-term effects, longterm effects, noise, and drift. Short-term effects are rapid compared to the typical time interval over which a sensor response occurs, while long-term effects are slow on that same time scale. Noise describes positive and negative fluctuations about an unchanging (on a long time scale) average value. In contrast, drift refers to a unidirectional change in signal that results in the average value changing monotonically (though not necessarily linearly) with time. In the short term, minimal noise and short-term drift are the goals. Noise has a detrimental effect on the LOD and on the precision of the response. Short-term drift, often associated with short-term changes in ambient parameters such as temperature, pressure, and relative humidity, can exceed oscillator noise, in which case drift dictates the LOD. While it is possible to partially compensate for noise by averaging several consecutive data points, this is more difficult for short-term drift. Long-term aging of the sensor components - - the coating, the device, and the electronic c i r c u i t r y - typically results in drift and may also necessitate frequent recalibration, particularly if the physicochemical properties of the coating change with time. Long-term baseline drift resulting from, e.g., slow temperature variations or "bum in" of a device and its circuitry, is readily compensated using baseline subtraction strategies. Some of the effects of both long- and short-term drift (not noise) can be cor-

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5. Chemical and Biological Sensors

rected by performing a differential measurement using a dual-device configuration (sensing and reference), provided the observed drifts are comparable for the two devices. Note that this strategy works best when both sensing and reference devices have the same coating, the properties of which may determine sensitivity to changes in such variables as temperature and relative humidity; the coated reference device must of course be isolated from the analyte. Differential measurements are not particularly helpful when environmentally induced aging of the coating is the main source of drift, since the reference device in this configuration is not constantly exposed to the same ambient as the sensing device. Repeatability is the degree to which an individual coated sensor repeatedly yields the same signal for the same analyte concentration under the same operating conditions. Repeatability necessarily depends on stability. A high degree of repeatability requires either that the coating-analyte interaction be reversible, either spontaneously or under suitable conditions, or that the response lie within the linear region of dynamic range. Reliability is the same as repeatability, except that the responses are obtained under the variety of ambient conditions expected for a particular sensor application. Both reliability and repeatability are often confused with reproducibility, which quantifies the extent to which two nominally identical (coated) sensors--fabricated according to the same set of procedures, but at different times and/or at different facilities ~ yield the same response to a given stimulus. A high degree of reproducibility means that a single sensor from a large batch can be used to obtain calibration data for all other sensors in that batch. To date, problems with precisely and uniformly reproducing sensor coating layers and, to a lesser extent, problems with practical aspects such as packaging, have prevented attaining the sort of reproducibility necessary for such "one-of-many" calibrations of AW chemical sensors.

5.3.6 RESPONSE TIME The response time of a chemical sensor should be appropriate for the application for which it is intended. For example, if the sensor is used to monitor acutely toxic (lethal) substances in the workplace, the response time should be faster than the biological/toxicological response ~ perhaps only a few seconds. On the other hand, some applications, such as monitoring the spread of a chemical waste plume underground, have characteristic time scales of days to years, permitting utilization of sensors that respond more slowly. Response time depends on the properties of the sensor system (such as cell volume and gas/liquid-delivery system --- see Chapter 6), on the properties of the coating (i.e., thickness), and on sorption/reaction kinetics. Rates of adsorption

5.3 Performance Criteria

247

and desorption determine response times for sensors that utilize either a flat, impermeable surface or a coating that is sufficiently thin and/or has high enough diffusivity that permeation is comparatively rapid. For reactive coatings, reaction rates can be affected by reagent surface area: small particle sizes and/or highly porous supports that maximize area/volume ratio yield a larger response in a shorter period of t i m e - so long as the rate of delivery of analyte to the device is not the limiting factor. Kinetic factors are discussed in more detail in Section 5.4.3. Many of the AW sensors that have been examined to date utilize films of materials, often organic polymers, for which transport within the film is not rapid compared to adsorption/desorption. In these cases, the rate of transport within the film affects response times. For polymeric films, those in the glassy or crystalline state generally exhibit lower diffusion rates (and correspondingly slower response times) than rubbery, amorphous (elastomeric) polymers (see Chapter 4). Assuming Fickian diffusion in the film, the time to reach equilibrium is proportional to the square of film thickness, so thinner films respond more rapidly at the expense of lower sensitivity and limit of detection. Regardless of the ratelimiting mechanism, response time invariably improves with increasing temperature. 5.3.7

ENVIRONMENTAL EFFECTS

The most significant environmental factor affecting sensor performance is temperature. The sensor temperature, and changes thereof, can affect the response in a variety of ways. The effect of temperature on the oscillation frequency of an AW device, which has been discussed previously and is discussed further in Chapter 6, can be minimized by selection of a substrate, such as ST-quartz for the SAW, having a small or zero temperature coefficient in the temperature region of interest. Devices based on thin piezoelectric layers (polycrystalline ZnO, A1N, etc.) can utilize a "stack" of other metal and/or oxide layers of appropriate thicknesses to yield a composite structure exhibiting minimal temperature coefficient. Additional temperature-drift compensation can be accomplished by using a dual-device configuration, although this may not be completely successful due to the difficulty of precisely matching thermal stress effects for the sensor and reference devices. In addition to the inherent temperature dependence of the acoustic-wave device, the AW velocity in the coating is invariably temperature dependent to an extent, particularly in the case of polymers, that can dwarf the temperature sensitivity of the bare device; analyte-coating interactions are temperature dependent as well. Thus, for many practical applications, thermostatting the sensor may be necessary.

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5. Chemical and Biological Sensors

Temperature effects on coating response behavior are varied. For reversible equilibrium-based sensors, increased temperature results in decreased sensitivity. An example of this temperature-dependent response behavior is provided in Figure 5.4 for a PIB-coated SAW device exposed to dichloroethane (DCE) vapor. From Figure 5.4(a) it can be seen that the response (in Hz) increases steadily as the concentration of DCE increases, but that the slope of the response curve decreases with increasing temperature. This decreased sensitivity is due to the Arrhenius-type decrease in the equilibrium constant, K (see Sections 5.4.1 and 5.4.2); a plot of K values calculated from SAW responses vs 1/T is given in Figure 5.4(b). Although the equilibrium response decreases, diffusivity usually increases with temperature to provide faster response times. Since the change of sensitivity with temperature can vary from one analyte to the next, temperature can be varied to improve the selectivity of the sensor for a given analyte [92a]. For irreversible (non-equilibrium) sensors that utilize activated reaction/interaction mechanisms, sensitivity usually increases as a result of increased reaction rates at higher temperatures. This type of response behavior is illustrated in Figure 5.5 for the reaction of a Pt-olefin-complex with ethyl acrylate [92d]. In contrast to the steady decrease in sensitivity for the reversible sensor, the SAW response rate (in Hz/min) increases with temperature. Thus, depending on the type of coating-analyte interactions being utilized, the sensor sensitivity can be improved by selecting an operating temperature consistent with the predominant response mechanism. Another significant environmental factor for vapor-phase applications is humidity. The ubiquitous nature of water vapor requires development of means to exclude or correct for interferences from water [92a,b]. Careful selection of coating materials, for example, can minimize the effect of water vapor on the sensor response. Alternatively, a coating with appropriate sensitivity to water can be used in the development of correction algorithms [93]. Other instrumental or system approaches, such as preconcentrators or sensor arrays with pattern recognition [94a-c], will be discussed in Section 5.5 and in Chapter 6.

5.4

Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

Regardless of the detection mechanism(s) involved, the response characteristics of an AW sensor are a function of the nature of the interaction between the analyte and the sensor coating. A fundamental understanding of the types of inter-

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

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250

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

251

actions is necessary to interpret sensor responses and to design useful sensor coatings for analytical applications. The interactions utilized for chemical sensors can be organized into two broad categories: physical and chemical, with a significant gray area between the two. Within each category, there are further distinctions according to the precise nature of the interaction. The classification of these assorted interactions is the topic of Section 5.4.1. In the context of this chapter, the "sorbent phase" is a coating on an AW sensor surface, where sorption can refer to adsorption (onto a surface or sorption site) and/or absorption (dissolution in the bulk). In the discussion following Section 5.4.1, adsorption and absorption are treated separately, and each of these interactions is discussed in terms of its energetics, or thermodynamics, which control the amount of analyte in/on the coating under equilibrium conditions. Kinetic factors, which determine the rate of response and also bear upon the reversibility of the sensor, are then considered. The kinetics of adsorption are described in Section 5.4.3; details of absorption kinetics, which are essentially diffusional in nature, can be found in Chapter 4. With this groundwork in place, a number of instances where these effects have been utilized in AW chemical sensors are described. Section 5.4 concludes with a discussion of biochemical/biological AW sensors.

5.4.1 PHYSICAL AND CHEMICAL INTERACTIONS Physical and chemical interactions involving adsorption are referred to as physisorption and chemisorption, respectively, with the distinction between the two based primarily on energetic differences. Physisorption often has little or no energetic activation barrier, and involves relatively weak, long-range van der Waals interactions. It is, therefore, a relatively low-energy process on the order of 5-12 kcal/mol, comparable to the heat of condensation of covalent, non-hydrogenbonded adsorbates. As a result, physisorption is typically quite reversible at room temperature, but relatively nonselective. Chemisorption, which is generally characterized by energies in excess of 10 kcal/mol, involves greater redistribution of electron density and, very often, the formation of a chemical bond with a strength of 25-100 kcal/mol or more. In addition, the chemical bonds of the sorbing species may be broken as new bonds are formed via reaction with the coating, causing the adsorbate to lose its original identity. More often than physical interactions, chemical processes are activated, meaning that a finite energetic barrier must be overcome for adsorption

252

5. Chemical and Biological Sensors

to occur. Chemical interactions tend to be far more specific than physical interactions, but are also more likely to be irreversible (see Section 5.3.2). The gray area between physical and chemical interactions arises when the energy of an attraction places it in the physical realm, but the interaction displays a degree of specificity that requires invoking the concepts of chemical bonding, albeit on an energetically weak scale. Examples are the sharing of a lone pair of electrons by donor and acceptor atoms or molecules, hydrogen bonding, or even extensive van der Waals interactions (all explained in the following paragraphs). All of these are typically nonspecific, but can be made specific to certain analytes when particular geometric and electronic structural matches are necessary for the interaction to occur. Such concepts are the basis for much of the specific but readily reversible chemistry upon which biochemical interactions are based. Physisorptive interactions can be classified by the component forces giving rise to the overall intermolecular attractions. The predominant forces include hydrogen bonding and van der Waals forces, which is a broad classification covering dispersion (London), dipole-induced dipole (Debye), and dipole-dipole (Keesom) interactions [95]. The nature of these forces is illustrated in Figure 5.6.

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5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

253

London forces result from the transient creation of weak dipoles in a molecule as a result of fluctuational polarization of the electron cloud. Such a momentary dipole is capable of polarizing the electron cloud of an adjacent molecule, creating an induced dipole of opposite polarity and resulting in a net attraction between the two molecules. Since all substances engage in dispersive interactions to varying extents, London forces are inherently nonselective. For nonpolar materials, like saturated hydrocarbons and noble gases, London forces are the only significant intermolecular forces of attraction. Even for more polar molecules (which are typically more polarizable), London forces can be quite strong. Within an homologous series, per-molecule London forces generally increase with the number of atoms in the molecule [95], a consequence of the fact that the total London force between two molecules is the sum of those between all the individual atoms. Dipolar interactions require that one or both of the molecules possess a permanent dipole, i.e., a separation of charge. If only one of the molecules possesses a dipole, it can induce a dipole in an adjacent molecule. The energy of the resulting interaction depends on the dipole moment of the permanent dipole and the polarizability of the adjacent molecule. If both molecules have a permanent dipole, then the attractive energy depends on the product of the magnitudes of the two dipole moments and a function related to probability that the dipoles are in an attractive orientation. In an isotropic system, the volume-averaged magnitude of the probability function decreases significantly as temperature increases, due to increasing random molecular motion. Hydrogen bonding can be considered a special case of dipolar interactions. For hydrogen bonding to occur, the proton must be covalently bonded to a very electronegative atom, most commonly nitrogen ( e . g . , = N - H ) or oxygen ( - O - H ) . The electron withdrawing power of this atom leaves the proton with a significant fractional positive charge. This charged proton is, in turn, attracted to a nonbonding pair of electrons on a second electronegative atom, forming the hydrogen bond. The original electronegative atom to which the proton is covalently attached can also act as an electron-pair donor, the result of which is a two- or three-dimensional network of hydrogen bonds, as illustrated in Figure 5.6. Weaker proton acceptors include less polar functional groups that also have nonbonded lone-pair electrons, (e.g., O = N - and > C = O ) , as well as the halides. Very weak proton acceptor capability can also be exhibited by functional groups having high electron density, including carbon-carbon multiple bonds and aromatic ring structures. The strength of hydrogen bonding interactions, 3-7 kcal/mol, puts them into the physical interaction category, but the high degree of specificity of these interactions is more characteristic of chemical interactions.

254

5. Chemical and Biological Sensors

If the analyte is a charged species, electrostatic forces can also contribute to analyte-coating interactions. 4 Unlike molecular dipoles, ionic species are characterized by integral positive or negative charges associated with a given atom or molecule. Ionic interactions are, in general, stronger than dipolar interactions. In fact, electrostatic attraction is an important component of some very strong chemical bonds, such as the bond between Na + and CI- in table salt. Note that the strength of such ionic bonds (98 kcal/mol for NaCI) does not prevent them from readily breaking apart when the energy of solvation of the ions by a good solvent (e.g., water) is comparable to, or exceeds, the energy required to dismantle the solid-state structure. There are two important distinctions between the electrostatic forces that hold ionic solids together in a crystal lattice and those that are of interest in the context of sensor analyte-coating interactions" (1) it is rarely the case that an organized ionic crystal structure is formed as a result of binding ions in the coating layer; (2) the change in solvation of the ionic species upon being bound in a coating is typically much less than that associated with crystallization. The important consequence of these two distinctions is that the net energy change associated with the binding of ionic species by a coating layer typically lies at the strong end of the physical interaction energy scale and/or the weak end of the chemical energy scale. While simple coulombic interactions are inherently nonspecific (hence classified as physical), there are cases in which molecular geometries are crucial in facilitating ionic interactions, making them highly chemically specific. Many biological interactions fall at least partially into this category. Finally, it should be noted that electrostatic interactions are also sensitive to factors such as the polarity and dielectric constant of the surrounding medium (i,e., the ambient phase or the coating material). For example, interactions of solvent dipoles with charged ions can mediate ion-ion interaction strength. A class of interactions that generally lies on the low end of the chemical energy scale is coordination and complexation. Coordination compounds are formed when the unfilled orbitals of transition metals accept electron density from one or more relatively electron-rich ligands; the molecule thus formed is known as a complex, or complex ion if it is charged: While this might sound like a specialized sort of physical interaction, a close fit in terms of both ener-

4Although systems involving ionic interactions are most often liquid phase, there are a number of solid-state ion conductors whose chemical interactions with analytes are dominated by ionic interactions, even at room temperature.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

255

getic and geometric structure is often necessary between complexing/coordinating agent and analyte, conferring a significant degree of chemical specificity. In certain cases, complex formation can be highly selective and at the same time readily reversible; there are two general ways in which this can occur. The straight-forward case is when the ligand-metal interaction is relatively weak, as indicated below for the complexation of ammonia with an equilibrium constant, K, Ni 2+ + NH3 ~ Ni(NH3) 2+

Kl = 525

Thus, isolated amine functionalities within a polymer are likely candidates for a reversible, liquid-phase Ni 2+ sensor. In the more complicated case, the fact that many coordination complexes involve a central metal atom and two to six (or even more) ligands is key: while the first couple of ligands often interact with energies characteristic of chemical bonds, each additional ligand has a progressively weaker interaction, so that the last couple of ligands added to the complex can exchange readily with the ambient environment. Consider, for example, the progressive binding of chloride to mercury, where (a)

Hg 2+ + 2C1- ~ HgC12

(b)

HgCl2 + 2Cl- ~ HgCl42-

K12 = 1.7 • 1013 K 3 4 "-

80

Thus, immobilized HgCl2 could form the basis of a readily reversible sensor for aqueous chloride at moderate to high concentrations, though a tiny concentration of Cl- would have to be present at all times in the contacting solution to prevent dissociation of the HgC12 complex. The coordination complexes discussed above need to be distinguished from charge-transfer complexes. For coordination complexes, the charge distribution within the complex is essentially the same in the ground and the excited states. By constrast, charge-transfer complexes exhibit electronic transitions in which an electron moves from a molecular orbital associated with a donor atom or region (e.g., ligand) to an orbital associated with an acceptor atom or region (e.g., metal). Thus, these complexes are characterized by a significantly different charge distribution in the ground and excited states. Such charge-transfer transitions can be identified by the appearance of new, intense bands in the UV-visible region of the spectrum. For example, solutions of iodine in many organic solvents are highly colored as a result of charge-transfer phenomena. 5The term complexion is also used on occasion to describe charged molecules with nonmetallic central atoms,e.g., PF6-, althoughthe term complexis not used to refer to analogousneutral species, e.g., SF6, which are simply called molecules.

256

5. Chemical and Biological Sensors

The strongest chemical interactions result in the formation of a chemical bond between coating material and analyte. Bond formation requires a certain "range of compatibility" in terms of both electronic and physical structures, hence bond formation is inherently a selective process. But selectivity carries a price: to break the chemical bond the energetic barrier that must be overcome, Ed, is the sum of the chemical bond strength (Ec) plus the activation energy of bond formation (Ea): Ed = Ea + Ec. As a result, Ed can often exceed 50 kcal/mol, making bond formation irreversible at room temperature. Chemical bonds range from purely covalent, in which a pair of electrons is shared equally between two atoms, such as the H - H bond in H2 (Ec = 104 kcal/mol), to highly ionic, with a grossly inequitable distribution of charge between the two atoms, such as Li - F (Ec = 137 kcal/mol), whose bond is approximately 80% ionic in nature [96]. As discussed in Section 5.3.2, chemisorptive processes can also involve loss of byproducts and/or significant morphological changes in the coating, both of which can affect the degree of reversibility. When neither of these complicating factors pertains, heating can sometimes regenerate the initial reactants, although in many cases heating leads to decomposition of the coating instead. An alternative to thermal regeneration is chemical regeneration, whereby the analyte is removed from the coating via a chemical reaction that forms a more readily-desorbed product. This strategy has been used successfully in several reported sensor applications [ 16,27,92d, 97-99c]. The distinction between molecular interactions discussed here provides a useful framework for understanding the nature of interactions between analyte and coating. The progression in energies from simple physical interactions to strong chemical bond formation is shown in Table 5.2. It should be kept in mind that these are generalizations and that overlaps in the energies between the different types of interactions are common. In the sections that follow, the use of these interactions in the development of chemical sensors is discussed. Where appropriate, some discussion of models describing the extent of the interactions has been included. Such models can be useful in the selection of coating materials, in the prediction of sensor coating performance (i.e., sensitivity, selectivity, and reversibility), and in the interpretation of sensor response mechanisms. 5.4.2

THERMODYNAMICS OF ADSORPTION: ADSORPTION ISOTHERMS

For an equilibrium p r o c e s s - one in which there is rapid (on the time scale of the sensor measurement) exchange of analyte between the ambient and sorbed p h a s e s - the amount of analyte that is adsorbed depends upon the change in

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors Table 5.2

Classification of Coating-Analyte Interactions and Approximate Energies .

,

....

,

,

.,

,

General

Physical/Chemical Physical/Chemical Weak Chemical Chemical

,

Energy Range

Classification

Physical/ van der Waals

257

Specific Interaction

London Dipole-induced dipole Dipole-dipole Hydrogen Bonding Electrostatic Bonding Coordination/Complexation/ Charge-Transfer Bonding Covalent/Ionic Chemical Bonding

,

,

,

,,

(kcallmol) a

0.1-1 b 0.1-1 b 0.1-1 b 3-7 2-12 2-50 25-250 ,,

,,

,

alnteraction energies are given on a per-bond basis. Thus, large molecules forming a large number of van der Waals, hydrogen, or other sorts of bonds can have cumulative interaction energies many times those given in the table. bref. [100], pp. 203-206.

Gibb's free energy (AGa) associated with adsorption. This relationship can be expressed as Ka

=

aa a

~

=

e - AGa/RT

~.~.~.

where Ka is the equilibrium coefficient for adsorption, R is the ideal gas constant, aa is the chemical activity of the adsorbed analyte, and a is analyte chemical activity in the ambient phase. 6 At low concentrations or partial pressures, analyte activity is often adequately approximated by concentration or partial pressure, respectively. Equation 5.3 reveals that negative values of AGa favor the adsorbed form of the analyte; it also shows that the dependence on temperature is exponential, with higher temperatures resulting in less adsorbed analyte, provided AGa < O. The G i b b ' s free-energy change depends on two terms, the heat (en-

6For those not conversant in chemical thermodynamics, chemical activity is best thought of as a sort of linearized concentration scale: nonlinearities in concentration-dependent behavior are accounted for by converting concentrations to activities. For a solution species X, its activity ax and concentration [X] are related by ax = [X]yx, in which Yx is known as an activity coefficient. If X is in the vapor phase, then its activity is typically referred to as fugacity fx, which is related to partial pressure Px by fx = YxPx.

258

5. Chemical and Biological Sensors

thalpy) of adsorption AHa and the entropy change ASa associated with adsorption at temperature T, according to

AGa = A l i a - TASa,

(5.4)

Nearly all adsorption processes are exothermic, i.e., AHa < 0. The change in the phase of the analyte upon adsorption from a liquid or gas onto a solid coating causes a loss in the degrees of motional freedom, the consequence of which is a negative ASa value (decrease in entropy). Thus, for equilibrium to favor the adsorbed form of an analyte, AHa must be sufficiently negative and T small enough that AHa < TASa: the enthalpy term must at least compensate the loss of entropy. Additional insight into the effect of temperature on adsorption equilibria is gained by combining Equations 5.3 and 5.4 to yield

K a = e-AHa/RT, eASa/R.

(s.s)

Although both AHa and ASa have implicit temperature dependencies, these are relatively minor compared to the temperature dependence expressed explicitly in Equation 5.5. Bearing in mind that both AHa and ASa are less than zero for typical adsorption processes, it should be clear from this equation that increasing temperature decreases the magnitude of the enthalpy-containing term, leading to a lower concentration of adsorbed analyte. The value of the equilibrium constant of adsorption is often evaluated as a function of ambient-phase analyte activity at a constant temperature by acquiring an adsorption isotherm. The ambient-phase analyte concentration is typically varied from zero, through the concentration range of interest, and on to near its saturation value 7 (if practical). A constant value of Ka over a broad range of analyte concentration implies a linear relationship between aa and a, which is often not the case. Nonlinearities in the isotherm are a consequence of the activity-dependent thermodynamic relationship between surface-adsorbed coverage (number/area) of an analyte and its concentration in the ambient phase. This is due to a number of factors, including the finite number of adsorption sites available, physical inhomogeneities (e.g., pores and capillaries) in/on the substrate, and adsorbate-adsorbate interactions. Thus, the isotherm reflects the concentra-

7Because more of the classic adsorption studies have been done with gaseous adsorbates, concentrations are usuallyexpressed in terms of partial pressures, hence the terms concentration and partial pressure are used somewhat interchangeably throughout this section. For gaseous species, the term saturation means that any increase in analyte concentration will result in spontaneous condensation of any additional analyte from the gas phase.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

259

tion-dependent Ka value, and is indicative of the relative strength of the interactions, the specific surface area of the solid (see Section 4.3.1.2), the distribution of interaction energies and pore sizes, the occurrence of monolayer or multilayer adsorption, and the process of condensation in pores. With respect to the detection of analytes, the shape of the isotherm characterizes the sensitivity, dynamic range, and, for irreversible interactions, ultimate capacity for a given adsorbate/coating combination. Note the implication of an isotherm whose slope decreases with increasing analyte concentration: sensitivity to the analyte declines as the ambient-phase concentration increases. Since the greatest sensitivity is often desired at the lowest concentrations, this is not a major shortcoming. Several models have been developed to describe the thermodynamics of adsorption on solid surfaces. They are typically considered in the context of gasphase species interacting with solids, although most can be applied to adsorption from liquids as well. There are five basic isotherms that have been found to describe the majority of all systems [ 101 ]. Figure 5.7 shows these along with their standard designations, Types I-V [ 102]. Type-I adsorption describes a situation wherein the adsorbate coverage approaches a limiting value of one monolayer as the concentration in the ambient phase approaches saturation. Types II and III depict multilayer adsorption wherein the number of layers is unbounded. Types IV and V are special cases of multilayer adsorption that involve capillary phenomena on mesoporous substrates (pore diameters from 3-50 nm); surface coverage reaches a plateau when all the pores are full (see Section 4.3.1), followed at higher partial pressure by unbounded multilayer formation. Since the adsorption isotherms for many materials are known or can be readily determined, the performance of an adsorption-based sensor can be predicted to some extent using the appropriate adsorption models discussed in the following section. It should be stressed that spontaneous desorption of analyte upon removal of analyte from the gas phase does not always occur. While Equation 5.3 and Figure 5.7 imply an equilibrium between adsorbed and ambient analyte, as will be discussed in Section 5.4.3, desorption of analyte often requires elevated temperatures. 5.4.2.1

Langmuir Isotherm

The Langmuir-adsorption model predicts an asymptotic approach to monolayer surface coverage as adsorbate partial pressure approaches saturation; this is the Type-I isotherm of Figure 5.7. The Langmuir model, though proven for many ultraclean, well-ordered surfaces interacting with small-molecule adsorbates, is oversimplified for many real-world systems. Nonetheless, it is the foundation upon which much of adsorption theory is built and as such provides a useful con-

260

5. Chemical and Biological Sensors

m

a

f

0 W "U m

plPo '

III

o

plPo

plPo

to)

8 q) al,..,,.

0 M .

plPo

.

.

.

.

.

.

II

plPo

Figure 5.7 Classification of typical adsorption isotherms (I-V) showing vapor adsorption as a function of relative pressure p/po; see discussion in text. (Adapted with permission. See Ref. [102]. 9 1940 American Chemical Society.)

5.4 C o a t i n g - A n a l y t e Interactions and A c o u s t i c - W a v e C h e m i c a l S e n s o r s

261

ceptual basis for understanding the process. Indeed, many of the other adsorption models outlined below treat the first monolayer as Langmuirian, then simply add on further terms to describe the adsorption of subsequent layers. For adsorption to cease at one monolayer, the tendency for bulk condensation of the adsorbate must be small under the selected experimental conditions of temperature and pressure. Thus, "pure" Langmuir-type behavior, in which there is no detectable adsorption beyond the first monolayer, is most often observed for species that strongly chemisorb onto a substrate. The fundamental thermodynamic assumption that characterizes the Langmuir model is that the chemical activity, aa, of the surface-bound adsorbate is proportional to the fraction of occupied surface sites, (0), aa = ~ (1-0)

(5.6)

where 0 = N/No (N is the number of filled sites/area, and No is the total number of surface sites/area). The model further assumes that the surface is energetically uniform (i.e., all sites have the same binding energy for a given adsorbate), that adsorbed molecules attach to definite surface sites (localized adsorption), that each site can accommodate only one adsorbate molecule, and that the binding energy of each molecule is independent of the presence or absence of adsorbates on neighboring sites (the energy of adsorption is independent of surface coverage). Upon exposure to a given partial pressure, p, of a gas-phase analyte, equilibrium is established when a certain fraction, 0, of adsorption sites are filled. The activity of adsorbate in the ambient phase can typically be approximated by the partial pressure of the adsorbing gas, so that Equation 5.3 can be written as: aa Ka = P

0 p(1 - 0)'

(5.7)

which leads to the more familiar "Langmuir expression" for fractional site occupation as a function of partial pressure: Kap 0 = ~

.

1 + Kap

(5.8)

For multiple adsorbing species, this equation becomes

o=2o,=2, ,

Ka,i Pi +

where Oi is the fractional coverage of the ith species.

(5.9)

262

5. Chemical and Biological Sensors

For acoustic wave-device applications, it is convenient to consider adsorption models in terms of adsorbed mass/area. The simple relationship among the number of occupied sites/area, the molecular weight of the adsorbate M, and the mass/area of adsorbate ma, is ma = N" M/Na, where Na is Avogadro's number. This allows the fraction of the surface sites occupied to be written as 0 = mA/mMt.,, where mMt, is the adsorbed mass/area at monolayer coverage. Substituting into Equation 5.8 yields ma =

mMt.,Kap 9 (1 + Kap)

(5.10)

The equation is conveniently evaluated by rearrangement to the linear form:

e =P mA

+

mML

1 (KamMt.)

(5.11)

By plotting p/mA versus p, the constants mML and Ka can be obtained from the slope and intercept, respectively, of the resulting line. With these constants evaluated, the value of 0 can be determined for each p from Equation 5.8. Note that the partial pressure, p, is proportional to the gas concentration, while mA is proportional to the frequency shift of the AW sensor, provided mass loading is the sole operative response mechanism. 5.4.2.2

Freundlich Adsorption Isotherm

Most "real-world" surfaces are nonuniform, possessing surface sites that have a range of potential energies for a given adsorbate. Even when all sites (on an empty surface) are energetically equal, filling of sites may lead to a progressive decrease in adsorption energy due to repulsive interactions between adjacent adsorbates. In either case (or for a combination of both), the consequence is that as 0 increases the heat of adsorption decreases. The inability of the Langmuir model to account for a reduction in the heat of adsorption with increasing coverage led to the empirical derivation of the Freundlich model, which assumes an exponential decline in the heat of adsorption with increasing coverage: mA = krp I/'p,

(5.12)

where kr and nF are empirical constants. Again, the surface coverage is expressed in terms of adsorbed mass/area, mA. Plotting log mA versus log p results in a straight line with slope 1/np and intercept of log kr. It is important to note the qualitative similarity between the Freundlich and Langmuir models. At very low pressures, the Langmuir model indicates a more

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

263

nearly linear variation in mA with p (i.e., Henry's- or Raoult's-Law behavior) than does the Freundlich model. But, at intermediate pressures, both models predict a dependence on a fractional power of p. In fact, for certain values of the relevant constants, plots of ma vS p nearly coincide for the two models, as illustrated in Figure 5.8. For this reason, it is sometimes difficult to distinguish between them, particularly over a narrow range of concentrations. Variation of partial pressure over several orders of magnitude often reveals non-Langmuirian behavior, as does the examination of a wide variety of adsorbates. In both cases, the Freundlich model works better when the decline in the heat of adsorption with increasing coverage is non-negligible. 5.4.2.3

BET Adsorption Model 8

The Brunauer-Emmett-Teller (BET) adsorption model was developed to account for multilayer adsorption. The BET model can be thought of as the sum of two terms; the Langmuir model is used to account for coverage from zero to the completion of the first monolayer, while the second and all subsequent layers (not treated by the Langmuir model) are assumed to have a heat of adsorption equal to the heat of vaporization of the bulk liquid phase of the adsorbing species. The heat of adsorption of the first monolayer usually exceeds the liquid's heat of vaporization. Although it might seem a crude oversimplification, the BET model works well for many systems that involve physisorption of "simple" molecules, i.e., species that do not interact with one another on a surface in a concentrationor orientation-dependent fashion. Thus, water adsorption does not typically follow the BET model particularly well, but the adsorption of argon or nitrogen at their respective boiling points often yields an excellent fit. While the BET model is most often associated with physisorptive interactions, the allowance it makes for a strongly bound first monolayer suits it to some chemisorptive systems, where chemisorption of the first monolayer is followed by condensation of more weakly bound multilayers. The mathematical expression of the BET model, given in Section 4.3.1.2, is not repeated here. Plotting the measured quantity/3 from Equation 4.5 versus partial pressure permits evaluation, from the slope, of the mass/area of an adsorbed monolayer that covers both external and all accessible internal surfaces.

SBecause of its importance in the characterization of a key property of porous thin-film materials, namely their total surface area, the BET model was treated in some detail in Chapter 4. A cursory treatment is included here for the sake of continuity and completeness.

tO

1.0

m

4~

0.8

8 W W

--.o

m

gl gh

0.6

mo

r o

mo

"0 _a

I_.

0.4

0 W "0

0.2 0.0 ! 0

0.2

0.4

I

I

0.6

0.8

PlPo Figure 5.8

Comparison of Freundlich (I-I) and Langmuir (1) isotherms. Data calculated from Equation 5.10 and Equation 5.12.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

265

From this mass/area, the total surface area of the adsorbent layer can be calculated, provided the area of a single adsorbate molecule is accurately known. The constant c, which is related to the strength of the interaction between adsorbate molecules in the first monolayer and the substrate, is evaluated from the intercept. The Type II and Type III isotherms shown in Figure 5.7 can both be described by the so-called infinity-form of the BET expression, which allows for an infinite number of adsorbate layers. The difference in the shapes of these two isotherms arises from differences in the strength of the adsorbate-adsorbent interaction.

5.4.2.4

Capillary Condensation; Other Models

The Type IV and V isotherms in Figure 5.7 are described by a combination of the BET model and a second model that accounts for capillary condensation in small pores or capillaries. The Kelvin equation relates a lowering of the saturation vapor pressure in the ambient phase of an adsorbate to the radius of curvature of a concave surface with which the adsorbate equilibrates. Qualitatively, a concave surface provides a larger number of sites/area with which the condensing liquid can interact, lowering the vapor pressure at which condensation begins. For quantitative relationships describing BET adsorption in combination with capillary condensation, the reader is referred to Section 4.3.1.2. Other adsorption models include the Dubinin~adushkevich isotherm equation [103], which is based on the theory of micropore-volume filling in combination with the Polanyi adsorption potential concept, and the Hacskaylo-Levan equation [ 104], derived from the well-known Antoine equation for vapor pressures. From the preceding discussion, it is clear that sensor coatings employing solid adsorbent layers inevitably yield nonlinear response curves unless the concentration range is narrow. The equations for the appropriate isotherm can be used to linearize such responses once the adsorption behavior of the coating has been characterized for selected adsorbates. It should be stressed, however, that a good fit to one of these models under a given set of exposure conditions does not unequivocally indicate adherence to that particular model under all conditions. To unambiguously determine the appropriate model, both temperature and analyte concentration should be varied over a substantial range and the fit to the model examined for each temperature. The preceding models are likely to have limited value in quantitative a priori prediction of sensor responses, in as much as the shapes of the isotherms vary with adsorbent surface area which, in turn, depends on the methods of producing and depositing the films.

266 5.4.3

5. Chemical and Biological Sensors KINETICS OF A D S O R P T I O N

Thus far, only adsorption equilibria have been discussed. It is also important to consider the rate at which equilibrium is attained. To understand the dependence of adsorption kinetics upon the various energies involved, a simple "reaction coordinate" diagram is helpful. Figure 5.9 is a simplified representation of the process of adsorption, with the horizontal axis representing the progress of the interaction/reaction and the vertical axis representing energy. An adsorbing species would follow a path moving from left to right along the horizontal axis, while a desorbing species would traverse this path in the opposite direction. In the following section, expressions are given for rates of adsorption and desorption assuming that activation energies and overall energies of adsorption (see Figure 5.9) are independent of surface coverage, in accordance with the Langmuir adsorption model described in Section 5.4.2.1.

5.4.3.1

Rate Expressions

For adsorption from the gas phase onto nonporous, impermeable surfaces, physisorption and nonactivated chemisorption are governed largely by gas-phase kinetics and are instantaneous on the time scale of chemical sensor measurements.

Reactants t-i o

(ambient species) Products

(adsorbed species)

Reaction Figure 5.9 Typical reaction coordinate for adsorption interactions, indicating the activation energy of adsorption (Ea) and desorption (Ea).

5.4 C o a t i n g - A n a l y t e Interactions and A c o u s t i c - W a v e C h e m i c a l S e n s o r s

267

Many chemisorptive interactions, however, are activated processes so that consideration of gas-surface collisions exclusively is insufficient to explain adsorption phenomena. To fully appreciate the factors affecting adsorption equilibria, it is useful to examine the processes of adsorption in more detail. In order for a molecule to ultimately adsorb, it must first collide with the surface with sufficient energy to overcome any activation barrier, indicated as Ea in Figure 5.9. The Ea can be negligibly small, as in physisorption, or can be significant, as in the case of chemical reactions. The rate at which adsorption proceeds will depend on an adsorption rate constant (ka), on the concentration or partial pressure of the adsorbing species (p), and on the fraction of adsorption sites that are unoccupied. Thus, we can express the adsorption rate as

'a,,1

0,

(5a3)

The adsorption rate constant can be expressed as

ka =

SoNo e -EamT. X/'2"n'MRT

(5.14)

where So is a "sticking coefficient" that indicates the probability of a collision with an empty site resulting in adsorption, No is the number of adsorption sites/area available on the bare surface, M is the molar mass of the adsorbing species. Note that when the activation energy of adsorption is negligible (Ea 0), the dependence of adsorption rate upon absolute temperature is ka ~ I~/'-T. While this might seem counterintuitive, it is a consequence of the decrease in gas density that occurs with increasing absolute temperature (at a constant pressure), which leads to lower impact rates. In the case of activated chemisorption (Ea > 0), the exponential term usually dominates the temperature dependence. Unlike many cases of adsorption, desorption has a significant activation energy barrier (the molar desorption energy, Ed), which is always greater than or equal to the analyte-substrate interaction energy. Desorption depends on a desorption rate constant (kd) and on the number of occupied sites, so that a general expression for the desorption rate can be written as

( d-~tt)des = --kdO'- --Ofae -ed/Rr

(5.15)

268

5. Chemical and Biological Sensors

in whichfa is an attempt frequency 9, typically in the range of 1012-1014/sec. The Arrhenius temperature dependence of desorption is determined by the exponential activation energy term. In terms of adsorption-based sensors, the net effect of desorption being more temperature-dependent than adsorption is two-fold. First, the equilibrium concentration of adsorbed analyte depends significantly upon temperature, with higher temperatures resulting in lower adsorbed analyte concentration. Second, the rate at which a sensor "recovers" when the ambient concentration of analyte diminishes to zero is very temperature dependent. The above expressions for adsorption and desorption rates were derived assuming that the two processes occur independent of one another. In reality, however, the two processes are not entirely independent. When adsorption raises the surface concentration of an adsorbate to an appreciable level, desorption begins to compete. Also, in many "real-world" situations, nonzero concentrations of ambient-phase analyte are present during desorption as well as adsorption. The relationship between thermodynamics and kinetics for the process of adsorption can be examined. Equilibrium is achieved not when adsorption ceases, but when the rates of adsorption and desorption precisely balance one another. This is why equilibrium is sometimes referred to as dynamic: to stress its nonstatic nature. When this is the case, surface occupancy is no longer changing with time, i.e., dO/dt = 0. Setting Equations 5.13 and 5.15 equal to one another and rearranging reveals k~ kd

=

0 p ( l - 0)

.

(5.16)

The righthand side of Equation 5.16 is the same as that given in Equation 5.7 above for the Langmuir adsorption model, with K,, = ka/kd. The experimental significance of Equation 5.16 is that measuring any two factors (adsorption rate, desorption rate, or equilibrium constant) uniquely determines the third. The expressions given above for/ca and kd lead to

ka Ka =

SoNo f x/2 Mer

s.17)

This rather cumbersome expression for the equilibrium constant is useful for the insight it gives into dependencies on a range of parameters. For example, one 9Attempt frequency is roughly correlated with the vibrational frequencies associated with the adsorbate-surface bond. Thus, the lower end of the range for f,, (1012/sec) is typical of the weaker bonding associated with physisorption, while the upper end of this range (lOm4/sec) is characteristic of stronger chemisorptive bonds.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

269

can tell at a glance how changes in the molecular weight of the adsorbate, the number of sites on the surface, or the activation energy of desorption will perturb a given equilibrium between ambient-phase and adsorbed analyte. Such information is useful in designing or selecting adsorbent materials for sensing applications. In addition, it demonstrates the temperature dependence of Ka: increasing temperatures translate into a decrease in the equilibrium adsorption coefficient. In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorption. The power-law model assumes a Freundlich adsorption isotherm. Both models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a monolayer with increasing gas concentration. The LH model assumes that the adsorption process is at equilibrium and that the chemical reaction at the surface is the rate-limiting step. The LH expression for the rate, r, of an irreversible gas/solid reaction is r =

kK~p l +Kop

,

(5.18)

where k is the reaction rate constant, Ka is the equilibrium adsorption constant for the gaseous reactant, and p is the partial pressure. The equilibrium constant, Ka, would be expected to exhibit a temperature dependence as discussed above, i.e., Ka decreases wtih increasing temperature. The reaction rate constant k, however, would be expected to increase with temperature, so that the overall dependence of the reaction rate on temperature cannot be determined a priori. Rearranging Equation 5.18 into the following form allows comparison of sensor data with the model using linear-regression analysis: p= r

1 kKa

p k

.

(5.19)

Since p is proportional to the gas concentration and r is proportional to the rate of change of the sensor response, plotting [gas concentration/rate of response] vs concentration yields a straight line.

270

5. Chemical and Biological Sensors

The power-law kinetic expression for a reaction that is first-order in the adsorbed gaseous reactant is [ 106] r = Fp line,

(5.20)

where F is a combined reaction-rate/adsorption constant and nr is a constant > 1. Adherence to this model is indicated if there is a linear relationship between the logarithm of the rate of the chemical reaction and the logarithm of adsorbate concentration. Application of the LH and power-law models to responses from reagent-coated SAW sensors has been described by Zellers et al. [108].

5.4.3.2

Transport Through Films

To this point, it has been assumed that only the outermost layer of the coating, be it perfectly smooth or highly porous, is involved in the adsorption process. When this is not the case, the simple surface adsorption-based models discussed above are inadequate. For physisorption on/in porous solids, transport into mesopores and micropores often limits the rate of adsorption. Two-stage equilibria are frequently observed: the more accessible outer surfaces equilibrate rapidly and remain in equilibrium with the ambient phase, acting as a source for slower transport of the adsorbate into the interior of the solid. Establishment of complete equilibrium can be a slow process. Hindered diffusion, the primary transport mechanism in porous solids, can be qualitatively described as a series of "hops" by the analyte, via gas-phase diffusion, from one surface site to the next. Thus, hindered diffusion is composed of two main components: a pure diffusion-related term, often Fickian in nature, associated with movement of the analyte in the gas phase; and a term describing the noninstantaneous equilibration between gas-phase analyte and the solid surface at each point where the analyte "touches down" (adsorbs). In extended porous solids (e.g., a chromatographic column tightly packed with porous beads), transport is often more complex, requiring the consideration of such factors as eddy diffusion and Knudsen effusion. This is important if there is a significant pressure drop along the path of the analyte [109]. Finally, the presence of any external fields (thermal, electric, etc.) must be considered as well. Differences in mass transport rates provide a potential means for discriminating between different gases and vapors, it is known, for example, that transport through molecular sieves can be a sensitive function of molecular size and shape [ 110]. For gases and vapors that have only weak physical interactions with a porous adsorbent layer, however, transport rates are often too high to allow

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

271

collection of enough data during the initial phases of adsorption to allow such discrimination [ 111 ]. For many chemisorptive interactions, particularly those involving chemical bond formation, reaction may proceed beyond the surface and into the bulk of the coating layer, providing far greater dynamic range but complicating kinetic analysis considerably. Bulk reaction between analyte and coating can alter the coating surface area; furthermore, as surface reaction sites saturate, the analyte must diffuse below the surface to reach unreacted sites. While a simple, exposure-dependent linear correction might be devised to account for surface-area changes, treatment of transport into the bulk is more difficult. The mass-transfer resistance associated with diffusion into a viscous liquid or solid reagent layer often slows the overall rate of reaction. When a nonvolatile product is formed during the reaction, analyte molecules must diffuse through a progressively thicker product layer. The Fickian model for diffusion is often appropriate, with the caveat that the thickness of the film through which diffusion occurs must be continuously adjusted according to integrated analyte exposure. Under these conditions, the so-called unreacted-core model described by Levenspiel [ 112] may be appropriate for describing the chemical reaction. This model depicts the gas-solid reaction as proceeding from the outer surface of the solid inward, with production of a progressively thicker product shell around a shrinking core of unreacted starting material, as illustrated in Figure 5.10. The use of this model to predict kinetic behavior is complicated by the need to specify the

Figure 5.10 Representation of the unreacted-core gas/solid reaction model for a particle of unchanging size. As reaction time progresses from left to right in the figure, the reaction surface recedes into the particle, the unreacted core shrinks, and the "ash layer" (containing the reaction product) increases in thickness.

272

5. Chemical and Biological Sensors

amount of available surface area: for solid reagents, the morphology of the asdeposited solid and its evolution with progressive exposure are important. This is also true for viscous liquids that are not deposited as uniform films on the sensor surface. In terms of sensor response, the result of the growth of a product layer upon a reactive coating layer is a gradual reduction in sensitivity, measured as (change in signal)/(integrated exposure) [ 108]. The issue of reagent depletion has received surprisingly little attention considering the number of reagent coatings reported in the literature. The effect of increasing temperature is to increase mass transport rates for all categories of diffusion. The obvious implication of more rapid mass transport for equilibrium-based interactions is more rapid sensor response. In addition, sensors based on the consumption of a reagent layer generally show enhanced sensitivity with increased temperature, because reaction rates and diffusion rates both exhibit a positive Arrhenius temperature dependence.

5.4.4

ADSORPTION-BASED ACOUSTIC WAVE SENSORS

For vapor-phase species, adsorption onto an uncoated (smooth) sensor surface is, in some cases, inadequate for sensitive detection, although measurement of small fractions of a single molecular monolayer have been reported [113,114]; furthermore, nonspecific adsorption (i.e., adsorption that is general to many different species) has been reported as a possible interference on uncoated reference devices [90]. Nonspecific adsorption can be minimized by "deactivation" of the surface, accomplished by replacing polar groups (e.g., OH) with nonpolar functionalities, such as the methyl groups associated with chlorotrimethylsilane, CI(CH3)3Si (see Figure 5.11 for a schematic depiction of this reaction). The result of this so-called "silanization" reaction is a "low-energy" (in the sense of its strength of interaction with potential adsorbates) surface covered with unreactive methyl groups. Surprisingly few volatile compounds or gases interact strongly enough with methyl-covered surfaces to yield appreciable equilibrium surface concentrations. Note, however, that low-volatility species (e.g., oils and many high-molecular-weight organics) condense on any available surface they contact, no matter how chemically inert it may be. For liquid-phase applications, lowenergy surfaces can prevent many cases of nonspecific adsorption as well. With lack of specificity and low sensitivity established as two major drawbacks of uncoated surfaces, it is clear that an important key to the performance of adsorption-based AW chemical sensors is the adsorbent coating material. All

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

273

Figure 5.11 Generic silanization reaction for immobilization of coating/reagent on sensor surface. In step (1), the silylating reagent react with -Si-OH groups on the (quartz) surface. Subsequent reactions, indicated in step (2), can produce a polymeric coating.

other properties being equal, a film having higher surface area results in a larger number of analyte molecules being adsorbed for a given ambient-phase analyte concentration, the consequences of which are enhanced sensitivity and limit of detection. For reactive and (irreversible) adsorptive coatings, higher surface area translates to higher capacity and thus greater dynamic range. Thus, many of the materials described in the following section are porous, with high internal surface areas. For equal gas-phase concentrations, physical adsorption "favors" the deposition of low vapor-pressure species, in the sense that such molecules have a large heat of vaporization and thus a propensity to remain condensed upon surfaces. This results in some measure of selectivity (although a low concentration of a low-volatility species can give a response identical to a high concentration of a high-volatility species). Additional physical discrimination is obtained by controlling the polarity and hydrogen-bonding capability, with selectivity for analyte(s) determined by the film structure and/or subsequent surface modification. A potentially high degree of discrimination is achieved by the use of sizespecific materials, having a tightly-controlled pore size just larger than the kinetic diameter of the desired analyte. This excludes all larger species from the pores entirely; molecules significantly smaller than the chosen analyte, though able to fit into the pores, have a smaller interaction energy due to the size mismatch.

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5. Chemical and Biological Sensors

5.4.4.1

Common Materials for Physical Adsorption

Examples of high-surface area solid adsorbents suitable for sensor coatings are granular microporous materials such as activated charcoal, silica gel, alumina gel, porous polymers, and molecular sieves--in particular, zeolites. For most such materials, high adsorption capacity arises from the presence of large numbers of micropores and/or mesopores. The total surface area of a single gram of such materials can exceed 1000 m E [ 115]. Bulk samples of these materials are often used in packed beds for collecting airborne or dissolved species in environmental sampling procedures. Table 5.3 lists several adsorbents along with some of the types of compounds that can be collected with them. The adsorption capacity for different vapors varies widely with the structure and volatility (saturation vapor pressure) of the adsorbate as well as the process used for activation of the adsorbent. When porous adsorbents are used in packed beds, analytes that are efficiently trapped (have significant interaction energies) on these materials must be removed by solvent or thermal desorption [116]. However, if the adsorbent is in thin-film form (vide infra) and the analyte loading is relatively low, adsorption can be spontaneously reversible at room temperature [ 117,118], For AW sensor applications, grains of porous powders must be immobilized by some form of thin-film physical support layer on the device surface. This requirement is nontrivial, as it is a complex problem to create a uniform, wellbound layer of tiny, porous particles that is effectively "glued" to a flat surface without plugging the pores with the "glue" used for attachment. One class of materials that has been studied as a means to immobilize high-surface-area grains

Table 5.3

Adsorbent Materials and Typical Adsorbates

Adsorbent

A dsorbates (vapors)

Activated Charcoal

Most nonpolar and moderately polar organic vapors; alkanes, alkenes, chlorinated aliphatics, ketones, esters, ethers, higher alcohols

Silica and Alumina Gels, Zeolites

Polar vapors: water, alcohols, phenols, chlorophenols, glycols, aliphatic and aromatic amines

Porous Polymers (Tenax, XAD, Chromosorb)

Higher boiling-point organics: acidic and basic organics, multifunctional organics, pesticides, polynuclear aromatic hydrocarbons, etc.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

275

in a thin film, and also as high-porosity thin films in their own right, are sol-gels or hydrogels [119]. These materials are synthesized via hydrolysis and condensation of metal alkoxides to form inorganic polymers in solution. Application of a thin layer of the sol-gel solution by dipping or spin-coating, followed by appropriate thermal treatment, produces a porous, rigid, oxide-based thin film. The pore sizes and sorption capacities of sol-gel-derived films are highly dependent on precursor materials and reaction conditions, as well as the final thermal treatment [ 120]. The suitability of an adsorbent for a particular analyte is a function of the presence or absence and strength of each of the physicochemical interactions discussed in Section 5.4.1. The polarity and hydrogen-bonding capabilities associated with M-OH moieties (M = Si, AI) in silica gel and porous alumina render these materials attractive toward polar and hydrogen-bonding analytes. This feature also causes these materials to be highly hygroscopic; in the context of AWsensor coatings, adsorption of water can lead to premature saturation of binding sites, interfering with the detection of all other analytes. The term "molecular sieve" describes a material having pores that closely match the dimensions of a specific molecule. The best-known molecular sieves are composites of microcrystalline zeolites embedded in an inert clay binder. Zeolites are composed of regular clusters of tetrahedral aluminosilicates, with varying percentages of bound cations and water molecules, whose crystal structures incorporate small molecule-sized cavities. Because zeolite pore size is different for each of the numerous different crystal structures in this family, the sizeselective nature can be tailored for specific applications. Studies of the transport of liquid and gaseous organic species in molecular sieves indicate that the diffusion rate and equilibrium concentration of sorbed analyte are sensitive functions of their molecular dimensions, as well as zeolite pore size and shape [ 110]. To broaden the range of chemical species lining the (internal) surfaces of porous oxides and also broaden the application of these materials, chemical surface-modification techniques can be utilized [119]. The most prevalent reagents for this purpose are silane-based coupling and derivatizing agents, which are compatible with many metal and oxide-based surfaces and provide a wide chemical variety of terminal groups [ 121 ]. Figure 5.11 shows the reaction of a "generic" silane with an OH-covered surface. X can be any one of C1, Br, I, OCH3, OC2H5, or OC3H7, with chloro, methoxy, and ethoxy being the most common. R can be one of hundreds of different functional groups, from simple alkyl or aryl groups to organic ligands for transition metals to complicated chelating moieties. When R contains accessible X-like groups, formation of a surface-bound polymer is possible, rather than a discrete surface moieties. Silane-based surface modifica-

276

5. Chemical and Biological Sensors

tion can be carried out in the gas phase, typically using the more volatile CIbased species, in water, or in organic solvents, often with a low concentration of water intentionally added to speed hydrolysis. Many of these reactions proceed readily under mild conditions, reaching completion at room temperature in a few minutes. In addition to silane-based chemistry, virtually any other species that reacts with OH functionalities to produce a strong chemical bond can be used for surface modification of porous oxide-based materials. Examples include highly reactive metal alkyl species such as triethyl aluminum and dimethyl zinc. Most activated charcoal is produced in a low-oxygen environment that creates a largely nonpolar surface [115]. This adsorbent is not greatly affected by atmospheric water below 50% relative humidity (RH). At higher RH levels, however, activated charcoal begins to adsorb water and lose its capacity for other adsorbates. Adsorption on charcoal involves predominantly dispersive interactions whose energies are of the same order as the heat of condensation of many vapors. As a result, less volatile species tend to replace more volatile compounds bound to charcoal adsorption sites. Table 5.4 lists the adsorption capacity of charcoal (in grams of vapor per gram charcoal) for various organic vapors. Treatment of activated charcoal or other carbon-based films with a water/O2-based plasma results in reaction-condition-dependent coverages of OH groups, imparting surface properties intermediate between unmodified charcoal and the more polar oxides discussed above. OH surface functionalities also make it possible to utilize the silane-based reagents described above to chemically modify carbon-based films.

Adsorption Capacities of Organic Vapors on Activated Charcoal

Table 5.4

Adsorbate Vapor Acetone Chloroform Hexane Carbon tetrachloride Ethanol

Capacity at Saturtm'on* (g vaporlg adsorbent) 0.4 1.1 0.4 0.9 0.5

*Based on extrapolations from low-level adsorption assuming a Langmuiradsorption model. See Ref. [122].

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors 5.4.4.2

277

Physisorption-Based Sensors

Physisorption-based acoustic wave sensors have been applied to both gas- and liquid-phase detection. In liquid-phase applications, aqueous metal ions have been detected using TSM devices via deposition on the sensor surface as a result of electrostatic adsorption [81]. This adsorption is sensitive to pH: in the pH range where formation of hydroxide complexes occurs, metal adsorption was not observed. In addition to metal ions, other cationic species were found to adsorb, whereas nonionic or anionic species did not. By adding masking agents such as EDTA (ethylenediaminetetraacetic acid), analyses for specific metals (Ag) were performed [123]. Analysis of halides (Br-, I-) can be performed by adsorption onto a Ag electrode [124-126] (in some cases, the strength of the silver-halide interaction is strong enough to be classified as weak chemisorption rather than physisorption). While some interferences were noted, these were avoided by appropriate sample pretreatment [125]. The analysis of organic analytes has also been performed by taking advantage of reaction of analytes with bromine or iodine; the concentration of halide is then measured by the sensor and analyte concentration calculated indirectly [ 127,128]. As outlined in the previous section, the use of high-surface-area granular adsorbents on piezoelectric devices can provide good sensitivity for the detection of vapor-phase species. King used alumina, silica, and molecular sieves for monitoring humidity [ 1]. Detection of low concentrations of nitrobenzene vapors was reported using a TSM sensor coated with a fine layer of activated charcoal [ 118]. While the charcoal coating exhibited good sensitivity and reproducibility, recovery times upon purging with clean air were on the order of 8-10 min. One of the more unique adsorbent films used for vapor sensing is sputtered polycrystalline zinc oxide, ZnO. Under the appropriate conditions, the crystallites deposit with a common crystallographic orientation (c axis normal to the substrate) on a layer of SiO2 on silicon (ZnO-on-Si); grain boundaries provide adequate surface area for the adsorption of gases and vapors [13,129]. An advantage of this material is that it can simultaneously function as the piezoelectric transduction layer for the construction of thin film-based SAW and FPW devices supported on Si (or virtually any other) substrates [12,17,18]. Some typical adsorption-based acoustic sensor applications are summarized in Table 5.5 on page 278. Suspended in a sol-gel-based thin film as previously described, zeolites have been claimed to provide sensitive response to alcohols (MeOH and PrOH) while excluding other organic vapors (isooctane) solely on the basis of molecular size [ 132]. The excluded molecule is also highly nonpolar, in contrast to the polar alcohols that were detected; the potential role of solute polarity on exclusion has

278

5. Chemical and Biological Sensors Table 5.5

Examples of Adsorption-Based Acoustic Wave Sensors

Analyte

Adsorbent

Device

Detection Limit

Ref.

TSM TSM TSM TSM TSM TSM

0.5/,tM 0.6 ~g/L 0.02/zM -0.5 • 10-12 M 0.2/,tM N

[ 125] [124] [ 127] [ 128] [126] [123] [83]

TSM

0.1 ppm

TSM TSM SAW SAW TSM

<0.7 ppm 2/xL/L m < 1 ng --

Liquid Phase Isulfa drugs a o-cresol/m-cresol b BrAg + metal ions (Cd 2+, Co 2+, Mn 2+ , Ni 2+ , Zn 2+)

Ag electrode Ag electrode Ag electrode Ag electrode Ag electrode Pt electrode --

Vapor Phase water

nitrobenzene H2S organics organics (e.g., methanol) ethanol

,,,

,

Silica gel, molecular sieves, alumina Activated charcoal CdI2/urea Polycrystalline ZnO Molecular sieves sol gel modified molecular sieves; organo-clays t,

,

,,

,

1,,

,

[1]

,1

[ 118] [ 131 ] [ 129] [ 132] [ 133] [ 134] ,

,,

1,

"Indirect method based on reaction of sulfa drugs with bromine. Reduction of the resultant bromoderivative with iodide forms 12, which is extracted and detected with TSM sensor. blndirect method based on pH-sensitive reaction of cresols with iodine; concentration of I2 as a function of time is monitored with sensor.

not yet been carefully examined for these materials. Coating materials that combine molecular sieving properties with selective surface interactions have been reported [ 133]. These coatings consist of a crystal molecular sieve (silicalite) that was chemically anchored to the TSM gold electrode surface using thiol-organosilane 'chemistry. These molecular sieves were then further coated with an amorphous, porous silica layer prepared using a sol-gel process. The mol-sieve excludes larger molecules, while the porous sol-gel layer exhibits hydrophobic properties. The resulting sensors were capable of preferentially adsorbing ethanol even in competition with isooctane and water. Similar selective capabilities can be designed into coatings that utilize "organo-clays," which consist of layered silicate materials intercalated with alkylammonium cations [134]. The spacing between the silicate layers varies with the cation used for intercalation. These

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

279

coatings exhibited greater sensitivity for organics (compared to water) than Nasilicate coatings. In addition, the combination of size exclusion (based on layer spacing), and partitioning into the organic phases in the sandwiched interacalation layer, resulted in unique selectivies for aromatics relative to other hydrocarbons. Although nonporous surfaces do not provide the sensitivity and limit of detection associated with porous layers, smooth surfaces have nonetheless been investigated. Nonspecific adsorption of a range of volatile organic compounds on smooth quartz and metal surfaces was given a degree of specificity by directly heating the device surface using a metal meander line. The form of the resulting thermal desorption signature depended upon the adsorbed species [ 135], and can be used in some applications for identification of adsorbed vapors. 5.4.4.3

Chemisorption-Based Sensors

The high degree of selectivity afforded by carefully choosing an analyte/coating chemical interaction makes this class of sensors particularly attractive. Unfortunately, the price of selectivity is often an irreversible response and limited lifetime. In applications where expected concentrations/doses over a given measurement interval (an eight-hour workday, for example) are small compared to coating capacity, and when a permanent record of total dose (i.e., net Af) is important, irreversibility is actually beneficial and a limited lifetime is unimportant. Snow and Wohltjen demonstrated the use of a poly(ethylene maleate) (PEM)coated SAW device for the detection of cyclopentadiene at a level of 200 ppm with a response time of one minute [ 136]. As indicated in Figure 5.12, the PEM polymer exhibits reversible interactions with many organic vapors, but reacts irreversibly with cyclopentadiene to form a Diels-Alder adduct; the reaction was nonreversible even after heating to 185~ It is worth noting that the PEM exhibits some reversible sorption of cyclopentadiene; the irreversible reaction, however, results in a net decrease in the SAW frequency even after removal of the sorbed cyclopentadiene vapor, as indicated in Figure 5.12. The sensor exhibits a large linear dynamic response, shown in Figure 5.13, over the range of 200-10,000 ppm (0.5-27 mg/L) of cyclopentadiene for short-term exposures. In other work, Fog and Rietz used a polybutadiene-coated TSM resonator to detect ozone in workplace environments [137]. Ozone reacts irreversibly with unsaturated hydrocarbons to form ozonides, which typically react further with moisture to give ketones and hydrogen peroxide. They reported stable operation at a concentration of 20 ppb for up to 4 hours, with a 10% decrease in sensitivity during a 15-minute exposure to 100 ppb of ozone.

_

b~

OO

t~

-0.25 -

t~

A

N "r"

t~ Ig

acetone 9

-0.5 -

r~ c O Q.

gg gg.

methylene chloride

me o O me Ig mm

benzene

(D

n,, -0.75 -

r gl

methanol

<

O

-1cyclopentadiene -1.25

i

0

2

~

I

4 6 T i m e ( s e c x 10^3)

t

8

10

Figure 5.12 Response of poly(ethylene maleate) (PEM)-coated SAW with organic vapors. Reversible interactions with acetone, methylene chloride, benzene and methanol are indicated by the near return to the original response after removal of the vapor. Exposure to cyclopentadiene results in a net, irreversible response due to formation of a Diels-Alder adduct. (Adapted with permission. See Ref. [ 136]. 9 1984 A m e r i c a n C h e m i c a l Society.)

200 .|

oO .,~

A

~~ ~176176 ~

= 150 -

~

r O

o.

l, ==

== l=

. l

E

o-'~176, . - ~

1111=

"r-

,.L.,'

"0 1 0 0

~176

-

~

~ o ..o~176 1

~ oO-

o

~

o.,-~ ~~176

Ill == till= =I I= t~ tile= l* O ==

.oO"

t,~

~176 .o~ o

n,

o.O ~o~176

1

== ==

ooO-~" O

oo~176

<

co

r~ 1111= l9

o. - " l

50-

,.~

!

oo.O~"

....-=

r

=

t==, .o,

...=

0

I'D == r~ O ='1 r~

2000

4000

6000

8000

10000

Concentration Cyclopentadiene (ppm) Figure 5.13

Linear dynamic range for irreversible response (-Hz/min) of the PEM-coated SAW sensor to cyclopentadiene.

(Adapted with permission. See Ref. [136]. 9 1984 American Chemical Society.)

t'~ OO

282

5. Chemical and Biological Sensors

Thin metal films (Pt, Pd) have been used for the adsorption and detection of gases such as HE and NH3 [ 138,139]. While the interaction mechanisms for these sensors were not specified, it is well known that H2 dissolves to a significant extent in Pd, with concomitant changes in the density, electrical conductivity, and mechanical properties of the film. The H2/Pt interaction as well as the interaction of NH3 with both Pd and Pt undoubtedly involves chemisorption on surface sites. Metal thin films deposited by nearly all techniques are polycrystalline; chemisorption along grain boundaries can often lead to a response that is considerably larger than predicted from the properties of metal single crystals. Various metal oxide films have also been applied with some success. Tungsten trioxide (WO3) was used for the detection of H2S using SAW devices [140,141]. This sensor was operated at elevated temperatures (>100~ since high-temperature, oxide-based semiconductor films have been used in conductivity-based sensors, it is possible that the response mechanism in this case is due to an electronic effect. Edmonds reported using manganese dioxide for the detection of NO2 using a TSM device [142]. The amalgamation of noble metals, specifically gold (Au), by mercury (Hg) has been used for the liquid- and gasphase detection of several species. In water, an Au-coated TSM device was used to detect aqueous concentrations of Hg(II) [143] in the range of 2-30/zM; repeated analysis resulted in a gradual decrease in sensitivity. Au-coated TSM devices have also been used to detect ambient Hg levels in the atmosphere [144], and for the collection of evolved elemental Hg vapor after the reduction of aqueous Hg species [ 145]. The amalgamation reaction has also been used for the detection of atmospheric SO2 [146]. Bubbling an SO2 stream through a solution of mercurous nitrate produces elemental mercury via the reaction: 2SO2 + 2H20 + Hg 2+ ~ Hg(SO3)22- + Hg ~ + 4H + The quantity of evolved elemental Hg, which is proportional to the SO2 concentration, is measured by amalgamation onto an Au TSM device electrode surface. The collected Hg can be thermally stripped from the electrode and the TSM resonator reused for subsequent analyses. Coordination and charge-transfer interactions are commonly used for the detection of electronegative vapor species or species having lone or nonbonding pairs of valence electrons (e.g., NO2, SO2, NH3). For example, semiconducting phthalocyanine (Pc) films have been studied extensively as coatings for (partially) reversible detection of NO2 [67-70,72,147]. The structure of the Pc molecule is illustrated in Figure 5.14; different metals can be complexed in the center of this structure, leading to a range of physical and chemical properties for

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

283

Figure 5.14 Molecular structure of the metal-phthalocyanine (M-Pc) complex. The central metal atom (M) can be a transition metal (i.e., Cu, Fe, Ni) or a heavy metal (Pb). The metal atom can act as an Lewis acid (electron pair acceptor) and interact with electron donors, whereas the extended aromatic ring structures on the periphery of the complex can interact with electronegative species (electron acceptors).

this class of materials. The delocalized 7r-electron system associated with this highly conjugated molecule can interact with electronegative species (electron acceptors); metal cations in the center of the ring can form complexes with electron donors as well as acceptors. Depending on the choice of AW device substrate, the sensor response arises partly or largely from changes in film conductivity (see Section 5.2.3). As expected, the sensitivity of the Pc film depends in

284

5. Chemical and Biological Sensors

part on the central metal atom, with copper and iron providing the highest sensitivity to NO2 [72], but lead was often reported to give better reversibility. These coatings exhibit excellent selectivity for NO2 over other vapors such as halogen gases, CO2, SO2, H20, and NH3 [147]. In the case of NH3, as well as higher NO2 dose levels, there does appear to be some irreversible interaction resulting in some loss of sensitivity with prolonged exposure. Plasma-polymerized Cu-Pc films have also shown high affinity for planar aromatic compounds (benzoic acid, phenol, etc.) and higher alcohols [66]. While there may be significant charge-transfer interaction with the Pc film in the case of the former compounds, other modes of interaction (e.g., dispersion, H-bonding) are probably operative for the alcohols. Other transition-metal complexes have been used for the selective detection of various compounds. Karmarkar et al. used trans-chlorocarbonyl-bis(triphenylphosphine) iridium(I) [t-IrCl(CO)(PPh3)2] suspended in Nujol (mineral oil) for the selective detection of aromatic hydrocarbons. The iridium complex exhibited less sensitivity to olefinic and aliphatic hydrocarbons [148]. Zellers et al. have performed extensive work with a series of SAW sensor coating reagents of the general formula PtCl2(olefin)(amine) [92a,92c--d,97]. Responses to olefin gases and vapors are based on the mass change accompanying displacement of the initially-complexed olefin. Where ethylene and pyridine are used as the initial ligands, low-ppm sensitivity to several olefin vapors was demonstrated and regeneration of the initial reagent was possible by exposure to ethylene gas in situ. Remarkably high selectivity was possible based on steric factors. For example, 1-butene could be monitored with complete selectivity in the presence of isobutylene; ethyl acrylate could be detected with no interference from methylmethacrylate. Electronic factors were also important, with electron-deficient olefins, such as vinyl chloride, neither reacting with the reagent nor influencing the reaction of several other olefins with the reagent. Replacing ethylene by 1-hexene in the initial reagent permitted detection of butadiene at ppb concentrations; mass amplification resulted from displacement of two hexene molecules for every butadiene that reacted. Low-ppm concentrations of ethylacrylate could be measured with the ethylene complex, but did not react with the 1-hexene complex. A variety of organophosphine transition-metal complexes have been used for the detection of SO2 [149]. Cook et al. used triphenyl- and tribenzyl phosphine compounds as ligands bound to Cu and Mn. Varying the ligand affects the Lewis acid strength of the metal complex, and hence, its ability to bind SO2. One complex (bis(tribenzylphosphine)copper(II) thiophenolateR [Cu(PBz3)2)SPh])exhibited a reversible response to SO2 that was linear in the range of I0-1000 mg/L.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

285

The coating exhibited good stability in laboratory air, and retained sensitivity to SO2 even after 2-3 months. Selectivity was also favorable, with little or no interference from 02, CO2, NH3, CO, or NO2. Other transition metal compounds which engage in irreversible redox reactions with SO2 have demonstrated good sensitivity [150]. A wide variety of amines have been employed for sensitive detection of SO2 as well, as reviewed by Guilbault [2] and Alder and McCallum [3]; NO2 appears, however, to act as a significant interference with many of these coatings. Other coordination and/or charge-transfer reagents have been used successfully for the detection of NH3 [ 151], toluene diisocyanate [ 152], phosgene [ 153], and organophosphorous compounds [154]. Due to their importance as model compounds for chemical-warfare agents, much effort has been devoted to the detection of a class of compounds known as organophosphonates. While much of this work has utilized polymer-based coatings (see Section 5.4.6), a number of workers have utilized chemisorptive interactions [155 and references therein]. Using the reported ability of Cu 2+ to act as a catalyst for the hydrolysis of organophosphates as a starting point, Kepley et al. designed a self-assembling monolayer film terminated by coordinatively unsaturated Cu 2+ ions [156]. A SAW device coated with this film responded reversibly to organophosphonates in the gas phase at concentrations from 100 ppb to saturation, with and without relative humidity present. The response of this coated device to organophosphonates was consistent with mass loading in the range of a fraction of one monolayer up to tens of layers. In contrast, the (reversible) response to a wide range of common organic solvents was a positive frequency shift, suggesting a change in film elastic properties and providing a unique form of selectivity. Complexation interactions have also been used for liquid-phase detection of metals. Martin et al. used an immobilized ethylenediamine coating on an SH-APM device to detect aqueous Cu 2+ [ 16]. The ethylenediamine molecule is a bidentate ligand capable of strongly binding transition metals via the amine groups. The sensor readily detected Cu 2+ at a concentration of 2.5 • 10 -4 M. While the metal response was not spontaneously reversible, the bound metal was released upon acidification to give a 10 mM HCI solution. Nomura et al. used oleic acid (deposited as copper oleate) on a TSM device for the analysis of metal ions [ 157]. The coating could be regenerated (bound metals removed) by addition of EDTA to the solution. Interferences from some metals (Cu 2+, AI3+, Fe 3+) were eliminated by the addition of the masking agent acetylacetone. These and other examples of chemisorption-based sensors are listed in Table 5.6, page 286.

Table 5.6

Chemisorption-Based Acoustic Wave Sensors ,,,

Analyte

Coating

Detection Limit

polybutadiene poly(ethylene maleate) polymerized Pc [trans-IrCl ( CO )PPh3 )2] PtCl2(ethylene) (pyridine)

10 ppb/min 200 ppm/min <1 ppm < 1 ppm 0.6 ppm

butadiene

PtCl2(1-hexene)(pyridine)

24 ppb

toluene diisocyanate phosgene

tri-n-octyl phosphine oxide methyltrioctyl phosphonium dimethylphosphate XAD-4 resin + Cu2+ diamine complexes gold film gold film gold film

0.1 ppm

ozone

cyclopentadiene aromatics olefins (styrene, ethyl acrylate)

organophosphorous compounds Hg (air) Hg (water)

5 ~g~ < 1 ppb . . . _ .

25 ng/m3/min 2 X 10 -3 M

,l l

J

Comments

irreversible irreversible selective vs. aliphatics no interference from hindered or electron deficient olefins; regenerate with ethylene 2:1 substitution leads to mass amplification minimal interference up to 60% RH high NH3 causes loss in sensitivity possible interference from auto exhaust gases amalgamation (thermally reversible) reduction to Hg~ amalgamation of Hg(II)

i

ill

Re$. [137] [1361 [701 [1481 [97,98]

[991 [1521 [1531 [154] [144] [145] [143]

continued

Au 3+

Au electrode

H2 NH3

Pd Pt pyroxidine-HC1 l-glutamic acid WO3 MnO2 metal-Pc Au film [Cu(PBz3)2SPh] triethanolamine (TEA) TEA, others trioctylmethylammonium dichromate ethylenediamine oleate/oleic acid

[-I2S NO2 SO2 oo

metal ions

0.15/zg/mL

interferences from Ag, Pt, Hg, Pd eliminated by pre-extraction

minimal interference SO2 displaces Hg from Au amalgam reversible coordination reversible charge transfer reversible charge transfer irreversible redox reaction

[138] [139] [151] [159] [141] [142] [73] [146] [149] [140] [16o] [150]

reversible upon addn. of acid reversible upon addn. of EDTA

[1571

50 ppm <1 p,g/dm3 10 ppb 7 ppm <1 ppm 20 ppb 10 mg/L l O ppb (SAW) 5 ppm (TSM) <10/xg/m 3

[158]

large HCI(g) interference operates at high temperature

[16]

288

5. Chemical and Biological Sensors

5.4.5 ABSORPTION AND POLYMER SORPTION Absorption implies intimate mixing at the molecular level of two substances (e.g., a coating and a vapor); the absorbed species literally dissolves in the absorbent material. In other words, absorptive interactions are not restricted to interfacial surfaces or fixed sites as in the case of adsorption. Partitioning of vapor into liquid, where the vapor becomes uniformly distributed in the liquid, is a perfect illustration. Sorption is a general term, used to describe the penetration and dispersal of liquids, gases and vapors into polymers, that encompasses the processes of adsorption, absorption, filling of microvoids, and other mixing phenomena. The coexistence of these processes, coupled with the typical lack of well-defined internal surfaces in polymers, warrants the use of this general term [ 130]. As discussed above for simple adsorption, polymer sorption can be treated in both thermodynamic and kinetic contexts. The quantity of an analyte that is sorbed by a polymer at equilibrium is referred to as the solubility of the analyte, while the rate at which the analyte is transported through the polymer is referred to as permeability. Although high solubility is generally a prerequisite for high permeability (on any reasonable time scale), there are some notable exceptions. Polysiloxanes and polytetrafluoroethylene (Teflon| for example, are quite permeable to water, but the solubility of water is not particularly large in either material. Polymers, specifically rubbery, amorphous polymers, have several inherent advantages as chemically sensitive sensor coatings: they can be deposited as thin, adherent, continuous films of fairly uniform thickness by solvent casting or spray coating techniques; they are nonvolatile and of homogeneous composition; and their chemical and physical properties can be modified to some extent by judicious choice of monomers and synthetic procedures. The individual molecules making up polymer chains are held together by strong covalent chemical bonds, whereas the interactions between adjacent chains involve lower-energy forces. Many of the physical properties of polymers depend on the strength and nature of these interchain forces. Since the interactions between a polymer and a penetrant molecule are governed by similar forces, the comparative strength of chain-chain and chain-penetrant interactions determine the solubility of the penetrant. Several polymer properties are important in determining the ability to sorb vapors. The glass transition temperature, Tg, is the temperature at which a polymer changes from glassy to rubbery, as described in Chapter 4. Above Tg, (in the rubbery state), permeability is governed entirely by diffusional forces and sorption proceeds rapidly and reversibly. The sorption process is very much like absorption into a liquid and, as discussed later in the context of sorption mod-

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

289

els, the polymer behaves much like a liquid solvent. Another consequence of the rubbery state is that the solubility of a penetrant is, in some cases, relatively large. For example, Table 5.7 lists the sorption capacity of natural rubber for the same vapors given in Table 5.4 for activated charcoal. The activated charcoal has similar adsorption capacities for all of these vapors. Natural rubber, which is well above its Tg at room temperature, exhibits a significantly higher sorption capacity and generally also shows greater selectivity for nonpolar vapors (hexane, carbon tetrachloride). For polymers that exist in a (partially) crystalline state, Tm is the melting temperature at which crystallinity gives way to an amorphous structure. In amorphous glassy polymers, sorption rate is governed by a combination of diffusion and segmental relaxation. The latter process has a relatively long time constant, resulting in slower attainment of sorption equilibrium. Often, these relaxations are irreversible, causing hysteresis and aging effects [161]. For partially crystalline polymers, solubility is proportional to the amorphous fraction because penetration is almost completely inhibited in crystalline regions. Highly crosslinked polymers, where adjacent chains are connected by many covalent bonds, also exhibit limited sorption of penetrants due to the restrictive nature of the crosslinks. For polymers that are glassy or crystalline, absorption into the bulk of the polymer as well as adsorption at specific sites can occur simultaneously: so-called dual-mode sorption [ 162,163]. Even in rubbery amorphous polymers, if there are specific functional sites along the chains where a sorbate interacts very strongly, then behavior resembling dual-mode sorption can occur. A final advantage of rubbery, amorphous polymers is that their sorption isotherms are often linear over relatively large ranges in penetrant concentration. Appendix C lists some common polymers that have been used as sensor coatings along with their Tg, Tin, and monomer repeat unit structure. Table 5.7 Sorption Capacity of Natural Rubber for Several Organic Solvents ,,

,

Vapor Acetone Chloroform Hexane Carbon tetrachloride Ethanol Values from Ref. [161].

,,

,..

.

.

.

.

.

.

.

.

.

.

.

Capacity at Saturation (g solventlg rubber) 0.104 1.444 9.111 0.008

290

5. Chemical and Biological Sensors

5.4.5.1

Overview of Polymer Sorption Isotherms

Figure 5.15 presents typical sorption isotherms for polymers. The ideal case (i.e., Henry's- or Raoult's-Law behavior) represented by Figure 5.15(a) occurs when the penetrant is dispersed randomly throughout the polymer and penetrantpenetrant interactions are energetically similar to, or much less than, penetrantpolymer interactions. This behavior is usually found for gases below about one atmosphere pressure and for many organic vapors over fairly large pressure ranges as well. For systems following this behavior, the sorbed molecules and polymer chains are highly mobile and the system can be modeled as a solution of the penerrant (solute) in the polymer (solvent). For polymer/penetrant combinations where strong interactions between specific functional groups occur and binding to specific sites predominates, a localized sorption model is more appropriate. Figure 5.15(b) represents such a model, which is equivalent to the Langmuir and Freundlich isotherm models presented in the context of adsorption in the previous section. This behavior has been oh-

a. Henry'sLaw

i J

0

0

r~

i i

c. Flory-Huggins

b. Langmuir/Frcundlich

,,

,,

d. BET site J saturation emo i auram o o m mm o o maapanm~

/: ' moommooum

Figure 5.15 Typical sorption isotherms representing different polymer sorption models, as indicated.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

291

served for the sorption of polar vapors by polar polymers [54] and for the sorption of certain dyes by ionic polymers [ 161 ]. Figure 5.15(c) represents the case where there is a preference for penetrantpenetrant pairs to be formed, such that solubility increases with the concentration of penetrant in the polymer. This type of behavior is observed in systems where the polymer is strongly plasticized by the penetrant, and localized penetrant clusters form, into which additional penetrant molecules preferentially accumulate. Figure 5.15(d) resembles a BET adsorption isotherm and represents a combination of two interactions indicated by the broken curves: specific localized sorption at low concentrations, followed by clustering or aggregate formation at high concentrations (note that clustering is not associated with capillary condensation as it is in the BET case). Sorption of water by hydrophobic polymers such as cellulosic materials follows this behavior. The majority of investigations involving polymer-coated acoustic-wave sensors for vapor detection have employed liquid or rubbery, amorphous, solid polymer coatings and have been restricted to vapor concentrations that are well below saturation. As a result, linear sorption isotherms have been found to prevail. Insofar as a sorption isotherm depends on the distribution of analyte between two phases (ambient and coating), models describing the extent of the distribution process are useful in a-priori prediction of coated-sensor performance. Like adsorption, the distribution of a species between a sorptive phase and an ambient medium (liquid or gas) can be described by a partition coefficient, Kc, such that

Cs Kc = Ca

(mgVs) Ca

(5.22)

where Cs is the concentration of analyte in the sorbent coating in equilibrium with Ca (the concentration in the ambient), and ms is the mass of analyte sorbed into the coating of volume Vs1~ This process, which is analogous to that occurring in a gas-liquid chromatography (GLC) column, where retention and sepa-

I~ value of the partition coefficient in this derivation, K,., is the ratio of the concentration of solute in the coating to the concentration of solute in the ambient (vapor) phase, with all concentrations being expressed in units of mass of solute per unit volume. Alternative expressions for the partition coefficient can be derived for concentration units of (moles of solute/coating volume) or (mass of solute/coating mass), or on a mole fraction basis. The value of K will be dependent on the concentration units used. For our purposes in the remainder of discussion, Kc will refer specifically to the partition coefficient using the concentration units of mass per unit volume as described above.

292

5. Chemical and Biological Sensors

ration of analytes depend on the distribution between a stationary and a mobile phase, is illustrated in Figure 5.16. For an AW sensor where mass loading is the predominant response mechanism, the frequency shift, Arc, occurring upon deposition of the coating and that due to sorption of an analyte, Afs, are both proportional to the mass changes associated with each material (see Equation 5.1). Thus, these two shifts are related by Afs

ms

Afc = mc

ms Vcpe

(5.23)

where Vc is the volume of the coating and pc is the coating density. Rearranging this result and substituting into Equation 5.22 yields

AAo

Ke = ~ . Afr C a

(5.24)

This equation has been used in the estimation and comparison of Kc values derived from SAW data with Ke values derived from GLC data [55,56,166]. In addition, this relationship is independent of both the specific substrate used (pro-

Figure 5.16 Illustration of the distribution of analyte between ambient phase and the sensor coating. The partition coefficient Kc = Cs/Ca, where Cs and Ca refer to the analyte concentration in the sorptive coating and ambient phases, respectively.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

293

vided it has no effect on coating properties) and the device oscillation frequency. There are abundant examples in the literature of methods for describing and/or predicting the retention behavior of solutes in chromatographic systems (GLCgas/liquid chromatography; GSC-gas/solid chromatography; LLC-liquid/liquid chromatography; LSC-liquid/solid chromatography). These methods can also be applied to the characterization of sensor coatings for the purpose of predicting response behavior. Two approaches have developed for predicting chromatographic retention behavior. The empirical approach consists of classification or correlation of solute retention based on systematic features (e.g., molecular structure), and has been applied successfully in a large number of investigations as discussed in a later section. The limitation of this approach is that it generally lacks a strict theoretical framework and provides limited insight into the fundamental basis of separation and retention. Results so obtained are usually valid only for solutes and phase systems contained in the original data set; extrapolation of results to unrelated solutes or solvents is not recommended. The alternative approach is the development of theoretical models to describe the solvation/partition process(es) in terms of relevant known or measurable properties of the solute and/or chromatographic material(s). The advantage of the latter method is that results obtained from a given system can be used to predict retention behavior in other systems, as long as the relevant properties of the solutes/solvents in that system are available. The following section examines a few of these models and their applicability and limitations in predicting sensor response behavior. 5.4.5.2

Normal Boiling-Point Model

The partitioning of a vapor into a polymeric or high-boiling liquid sensor coating depends on the solubility of the vapor in the coating. The solubility, in turn, depends on the volatility of the vapor, the interaction forces between the vapor and the coating, and the ambient temperature. The free energy change for the absorption/solvation process, A G s , can be described using relationships identical to Equation 5.3. For the case of an infinitely dilute vapor forming an infinitely dilute solution in the coating, the entropy change associated with the transfer of vapor to the coating can be considered negligible compared to the heat of solution, AHs. Under these conditions, a general expression for the temperature dependance of the partition coefficient can be written as Kc = e - a G s m r ~ e - z ~ d R r

(5.25)

where Kc is the equilibrium partition coefficient, AHs is the heat of solution, R is the gas law constant, and T is absolute temperature in Kelvin. The dissolution

294

5. Chemical and Biological Sensors

of a solute vapor in a coating can be conceptualized as a two-stage process' condensation of the vapor as pure solute, followed by mixing/dilution of the solute in the solvent coating. The heat of solution, then, can be expressed in terms of the molar heat of condensation, AHcond, and the partial molar heat of mixing, AHm:

AHs = AHcond + AHm

(5.26)

For ideal solutions, A H m is zero. For real solutions, however, AHm is finiteand its value can be estimated by the regular solution theory of Hildebrand as described in the next section. For most vapors, AH~ond is negative and it dominates the value of AHs. As a result, AHs is usually negative and the partition coefficient decreases with increasing temperature. According to Trouton's Rule, the (absolute) boiling point, Tb, of a vapor is directly proportional to AHcond for that vapor (with the exception of associated liquids such as alcohols, amines, and water). Thus, at a given temperature (assuming A H m is negligible or approximately the same for all vapors), the log of the partition coefficient,K~, should have an approximately linear relationship to the boiling point of the vapor. Alternatively,non-linear empirical equations have been developed for compounds within a homologous series (i.e.,chemically similarcompounds differing only in the length of the carbon chain) that describe the relationship between the boiling point (Tb in K) at 760 Ton" and AH~o~d. For nonpolar and slightlypolar solutes, this can be approximated (at 25~ by [164]

-AHcond

-2950 + 23.7Tb + 0.02T 2

(5.27)

Both Trouton's rule and the above relationship give reasonable estimates of AHco~d for liquids having Tb values below about 80~ for Tb values greater than this,the lastterm in Equation 5.27 becomes increasingly significant,resulting in overestimates in some cases. For nonpolar substances, cohesive forces between molecules are predominantly the result of dispersive interactions,which are dependent on the polarizability of the molecule. As polarizability or polarity increases, the strength of the intermolecular interactions increases. Logically, as the attractive forces between solute molecules increase, the energy required to separate the molecules also increases, resulting in an increase in Tb. Early work by King [I], Janghorbani and Freund [160], and Karasek et al. [165] showed, for homologous seriesof nonpolar vapors interactingwith polymer-coated T S M sensors that, indeed, the response was linearly related to the boiling points of the vapors. Recent work by Patrash and Zellers has shown that this relationship is, in fact, quite general; polymer-coated S A W responses were predicted within a

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

295

factor of two for vapors from several different chemical classes on polymer coatings varying widely in polarity.

5.4.5.3

Regular Solution Theory (Hildebrand Solubility Parameter)

The above discussion was based on the assumption of ideal mixing of components to form dilute solutions. For ideal solutions, the heat of mixing is zero, a condition that is seldom true for real systems. Hildebrand defined a "regular solution" as one in which the entropy of mixing is ideal (ASm - 0), no volume change occurs (AV = 0), and deviations from ideality arise entirely from the enthalpy of mixing (AHm) [164]. Under these conditions, the partition coefficient can be related to the free energy change as R T InK = - A G e = - ( A E E + P A V ~ - TAS E)

(5.28)

where AEE represents the excess energy change associated with the transfer of solute from one phase to another [ 167]. (Note that the partition coefficient K in this expression has concentration units of mole fractions, rather than mass/ volume as in the case of Kc.) Again, treating the dissolution of a solute vapor in a solvent coating as a two-stage process, then the energy change can be expressed in terms of AEv and AEm, where the subscripts v and m refer to the processes of vaporization and mixing, respectively. The energy of vaporization is equal in magnitude, but opposite in sign, to the energy of condensation due to the reciprocal nature of the two processes. In the absence of entropy effects, a solubility parameter, 6i, is defined for pure solute i as 82i_ AEv Vi

'

(5.29)

where Vi is the molar volume of pure solute i. (Note" AEv = A/Iv - R T ) . The solubility parameter can then be considered as a measure of the interrnolecular interaction energy per unit volume of pure solute. Deviations from ideality can be described by the solute activity coefficient, 3', which can be related to the energy of mixing, AEm: In Yi,s =

AEm RT M

Vi(Si - ~s)2 RT '

(5.30)

where Yi,s, is the activity coefficient for solute i in solvent s, and ~s is the solubility parameter for solvent s [164]. As indicated by Equation 5.30, the mixing energy depends on the difference in the intermolecular interaction energies for the solute and the solvent. The greater this energy difference, the greater the value

296

5. Chemical and Biological Sensors

of AEm and the subsequent deviation from ideality. Taking advantage of Raoult's Law and the Ideal Gas Law, Equation 5.22 can be rewritten as

Cs

~.: -^c =

RT ,ipop,

= M,

s.31)

where R is the gas constant, T is absolute temperature in Kelvin, Ms is the solvent molecular weight, Ps is the solvent density, ~'i is the solute activity coefficient and pO is the saturated vapor pressure of pure solute I 1. For the distribution of a solute vapor between the gas phase and a liquid or polymer solvent coating, the partition coefficient, Kc, can now be expressed as

lnKc = In MsPOiOsTi

Msp~ps

- - ~ (8i - 8s)2.

(5.32)

Note that as the difference between 8i and 8s decreases, the value of Kr increases. In other words, the ( 8 i - 8s) term is inversely related to the solubility of the solute in the solvent/coating. The partition coefficient is largest when 8i and 8s are equal (i.e., ideal solutions, Ti = 1). For distribution between two liquid phases, the solubility of the solute in each

t tldeal solutions behave in accord with Raoult's Law, which relates the partial pressure of a solute vapor to the mole fraction of solute in solution and the saturated vapor pressure of pure solute. Deviations from ideality can be accomodated by use of the activity coefficient such that

Pi = XfyiP ~ where Xi is the mole fraction of solute in solution. The partition coefficient, Kc, can be expressed either in terms of mass (m) or moles (n) of solute, such that

Kr ,

" - "

(mi/Vs) (mi/Va)

m

(ni/Vs) (ni/Va)

where mi is the solute mass, and Vs and Va are the volumes of solvent and air, respectively, in which mi is contained. The denominator can be expressed in terms of the partial pressure of solute using the Ideal Gas Law. The solvent volume can be expressed as the product of the moles of solvent (ns), solvent density (ps), and solvent molecular weight (Ms). For dilute solutions, the ratio of (ni/ns) is essentially equivalent to solute mole fraction, X~, so that the partition coefficient can now be expressed as

Kc=

ni/(nsMsps)

(p,mr)

( x i ) RT = ~ M~p/

Rearranging the Raoult's Law expression and substitution into this expression for Kc yields Equation 5.31.

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

297

phase determines the value of Kc. That is, Kc depends on the relative activity coefficient of the solute in each phase, such that m

lnKc = In Yi,x

Vi

where the subscripts i, x, and y refer to the solute and the two solvent phases, respectively. Thus, the regular solution theory permits the description of the properties of the mixture (i.e., partition coefficient) by reference to the properties of the pure components, specifically the solubility parameters. Snow and Wohltjen [136], Jarvis et al. [ 168], and Patrash and Zellers [ 166] found semi-quantitative agreement between experimental SAW sensor responses and those predicted using Equation 5.31 or 5.32 for most of the vapors tested. While the assumptions inherent in the model are valid for mixtures where dispersion forces predominate, the model breaks down in systems involving significant dipolar or hydrogen bonding interactions. To extend the solubility parameter treatment to more polar systems, several researchers have divided the solubility parameter into components that account separately for specific interactions such as dispersion, dipole-dipole, and hydrogen bonding [ 167,169-171 ]. Values for the total solubility parameter and the expanded parameters have been tabulated for a great number of liquid solvents [ 172a]. In addition, the extended solubility parameter approach has been used to derive equations for estimated energies of distribution processes involving solid, liquid, and gaseous phases [170]. Unfortunately, in many instances the materials employed as sensor coatings are nonvolatile solids (polymers) for which 8 values cannot be calculated directly. Solubility parameters for these materials can be estimated, however, by immersion testing [172b], inverse gas chromatography [ 173,174] or from coatedSAW sensor responses [ 166]. In inverse chromatography, the polymeric coating material is used as a stationary phase on a GC column, and the specific retention volumes (Vg) for several solutes are determined. Since the Vg is directly related to, Kr the solubility parameter for the polymer coating can be derived from relationships similar to Equation 5.32. A similar approach is used to derive ~s from SAW sensor response data [ 166]. Another limitation of the regular solution theory is the assumption that ASm is negligible. While this assumption may be valid for solutions in which all components (solute and solvent) are of similar sizes, it breaks down when the molar volumes of the components are significantly different, i.e., in the case of high molecular weight (polymeric) solvents and low molecular weight solutes. For such cases, more rigorous models that include entropic considerations, such as

298

5. Chemical and Biological Sensors

Flory-Huggins theory, have been used to predict solute uptake [ 175a] and chromatographic behavior [175b], and may also prove useful in predicting sensor coating performance.

5.4.5.4

Linear Soivation Energy Relationships (Solvatochromic/Soivation Parameters)

Linear solvation energy relationships (LSERs) have been used successfully to characterize solubility properties in a number of diverse systems, including gas/liquid chromatography (GLC), gas/solid chromatography (GSC), and liquid chromatography (LC) [176-179c]. These relationships take the form of a multivariate linear regression, such as SP = S P ~ + l l " logL~ 6 + Sl" 7/"2 W a l " or2 + b l ' f l 2

+ r l " R2,

(5.34)

where the parameters having the subscript 2 (e.g. ' log L 216) refer to solubility properties of the solutes, and the coefficients having subscript 1 (e.g., l~) refer to the corresponding properties of the solvent in the system. SP is the solubility property under investigation, and SP ~ is a constant. The number of terms included in the equation depends on the system under investigation; other terms (e.g., molar refraction, dipole moments) may be included or substituted to provide a higher degree of correlation. The solubility properties most often correlated by such methods include the specific retention volume (Vg) from GLC and the partition coefficient (Kc). The LSER approach models the solvation process insofar as the individual terms provide a measure of the relative ability of the solutes to engage in specific solubility interactions. For the above equation, the log L 16 term is the Ostwald solubility (partition) coefficient of the solute in hexadecane (C16H34) at 25~ This term provides a measure of dispersive interactions. The or* term measures the dipolarity/polarizability interactions and is approximately equal to the molecular dipole moment for compounds having a single, strongly polar functional group. The a and/3 terms measure the solute hydrogen-bond donor acidity and acceptor basicity, respectively. Non-bonded electron interactions are represented by the R2 term. The solvent terms (coefficients) provide a measure of the respective solvent solubility interaction strengths. For example, Ii is an estimate of the dispersion strength of the solvent, whereas a l provides a measure of the solvent's ability to act as a hydrogen bond acceptor with a hydrogen bond donor (or2) solute. These parameters were originally developed to explain solvent-induced chromic shifts, i.e., shifts in wavelengths of maximum optical absorbance, for a variety of compounds; hence, the term "solvatochromic" param-

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

299

eters. The increasing use of these parameters to study solvation properties has led to the more recent use of the term "solvation parameters." Extensive studies and continuing refinements by Kamlet, Abraham, Taft, and coworkers use the above parameters [179b,c]. Similar approaches and solubility factor sets have been developed and used successfully by other groups to characterize solute/ solvent systems [ 180-182]. The coefficients in the LSERs are determined by multiple-linear-regression analysis after determining the SP for a representative set of solutes in the solvent system under study. In this respect, the LSERs have been considered by some to constitute an empirical approach [ 183]. The fact that the LSER approach has been used to successfully describe hundreds of physicochemical, biological, toxicological, and pharmacological properties that depend on interactions between solutes and solvents lends credence to the argument that these relationships do, in fact, model the fundamental effects of solubility processes [ 184 and references therein]. It should be noted that the quality of fit is entirely dependent on the identification and inclusion of sufficient and appropriate terms in the regression equation to adequately describe the solubility processes responsible for the observed solute behavior (e.g., solubility interactions, solvophobic interactions, cavity formation). Once the solvent coefficients have been determined, then the property under consideration (Vg,Kc) can be determined for any solute for which the required solvation parameters are known. These parameters have been tabulated for a large number of solutes and solvents [176-179c and references therein]. The LSER approach is currently being used to characterize the properties of an increasing number of polymeric and biological materials that have potential application as (bio)chemical sensor coatings [185]. In fact, partition coefficients calculated from SAW response data have been compared with Kc values from an LSER, with good agreement in most cases [56,166,186a-d]. Thus, the method holds promise as a rapid means of predicting coating sensitivity and selectivity. The models discussed previously by no means represent an exhaustive list. In addition to the solubility models, approaches using molecular orbital computations have been used to study hydrogen-bonding mechanisms and to compare the results with SAW sensor data [ 187]. These ab-initio computations have been used successfully, but can currently only be applied to molecules of limited size because of the high cost and long computing time involved. 5.4.5.5

Empirical Methods

Empirical methods have been used to characterize the retention behavior of a variety of solutes in GLC and HPLC (high-performance liquid chromatography)

300

5. Chemical and Biological Sensors

systems, including nitrated and unsubstituted polycyclic aromatic compounds (PAC, PAH) [188-192], poly-chlorinated biphenyls [193,194], dibenzofurans [195], a variety of aliphatic, aromatic and olefinic hydrocarbons [196-198], pyrazines [199], alcohols and fatty acids [200,201], and diverse drug compounds [202]. These methods apply a variety of statistical analytical tools to a given data set, such as multiple-linear-regression (MLR) or principal-component analysis (PCA), to predict retention based on features of the solutes and/or solvents. The vast majority of these studies predict retention behavior based on molecular structural features, and are thus classified as quantitative structure retention relationships (QSRR). The structural features are represented by molecular descriptors, which are numeric quantities related directly to the molecular structure rather than physicochemical properties. Examples of such descriptors include molecular weight, molecular connectivity indexes, molecular complexity (degree of substitution), atom counts and valencies, charge, molecular polarizability, moments of inertia, and surface area and volume. Once a set of descriptors has been developed and tested to remove interdependent/collinear variables, a linear regression equation is developed to correlate these variables with the retention parameter of interest, e.g., retention index, retention volume, or partition coefficient. The final equation includes only those descriptors that are statistically significant and provide the best fit to the data. For more details on QSRR and the development and use of molecular descriptors, the reader is referred to the literature [ 188,195,198,200202 and references therein]. Although empirical methods do not necessarily provide insight into the fundamental processes involved in solvation, their predictive value for a given system has been effectively demonstrated. Because the solubility behavior of a substance is influenced by the presence or absence of specific functional groups, it is logical to infer that the magnitude of the solvation parameter values discussed in the preceding section will be sensitive to these structural features. Correlation of solvation parameters with structural descriptors has, in fact, been performed for limited data sets, and shows promise for uniting these two approaches [203]. 5.4.6 ABSORPTION-BASED SENSORS

Thin films of many polymeric materials exhibit good adhesive properties and are easily applied to most substrates. In addition, relatively rapid diffusion and a high capacity for organic solutes make amorphous rubbery polymers attractive as sensor coatings. An example of this rapid and sensitive detection is shown in Figure 5.17, the response of a polyisobutylene-coated SAW device to trichloroeth-

I . . . .

,,

n

__

i

. . . . .

J. . . . . .

.

i

I

i

i

I

i

i

.........

ii

iii I

n

n,.

i

o ..........

I

..

.J

i

.....

. . . . . . . .

u

I

-i-

|

.

--

=

O0

0

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

. . . . . . . . . .

m

.......

m,

"~ ~)

301

0

o--~ o

o

c~,c: o ~

m

o

9

~ .

E

o

302

5. Chemical and Biological Sensors

ylene in the 10-100 ppm range. Equilibrium is attained in just a few seconds, and 10 ppm is easily discerned from background noise (noise levels with this type of coated SAW device are typically about 2 Hz or 0.02 ppm). Upon removal of the chemical from the environment, the response rapidly returns to baseline. The variety of functionalities that can be incorporated into polymers makes it possible to optimize selected sorptive interactions and maximize sensitivity for given solutes/analytes. Poly(ethyleneimine)-coated TSM resonators, for example, have demonstrated good sensitivity to organic acids (phenol, o-cresol) in hydrocarbon solvents [205], while not responding to aromatics. However, because of the nature of these interactions, the selectivity of polymer-coated sensors is often limited, and other strategies have been developed to enhance selective detection capabilities, such as sensor arrays (see Section 5.5). Even when not used as the chemically selective element, polymer films can be used as a supporting matrix to bind the reagent/adsorbent to the sensor surface, or as reference coatings [92d,98]. The versatility as well as potential sensitivity of polymer-coated acoustic sensors is indicated by the range of analytes listed in Table 5.8. These examples represent only a few of the typical polymer-coated AW sensors; extensive reviews are included in references 2,3,7,14, and 15. A more comprehensive listing of polymeric materials that have been used as coatings for acoustic sensors is provided in Appendix C. One demonstrated advantage of using polymer coatings to detect organic solvents is that two independent acoustic-wave propagation parameters (i.e., frequency and attenuation) can be measured for a single device/coating combination, enhancing the information content of the sensor response. This is due to the fact that two different acoustic-wave perturbations are generally involved when solvent is sorbed by a polymer layer: changes in mass loading and changes in polymer viscoelastic properties; the latter results from plasticization (i.e., softening) of the polymer by the absorbing solvent. Response curves for both propagation parameters are shown in Figure 5.18 for a polyisobutylene-coated SAW device. The attenuation (i.e., insertion loss) response is due solely to changes in viscoelasticity, while the frequency response results from a combination of viscoelastic and mass-loading effects. Because each of the two perturbations depend on a different combination of the physicochemical properties of the absorbed species, they are, in general, independent of one another. This is demonstrated by plotting the attenuation response vs the frequency (velocity) response in Figure 5.19. Each point along the curve for a given analyte corresponds to a particular concentration of that analyte. The fact that a unique curve is generated for each of the species examined verifies the independence of these two responses for the chosen set of analytes. It also illustrates a key advantage of monitoring

Typical Examples of Polymer-Coated Acoustic Wave Sensors

Table 5.8

Coating

Analyte(s)

polysulfonic acid fluoropolyol (FPOL) gelatin Na-polystyrene sulfonate Carbowax dinonyl phthalate silicone-based greases Carbowax 1000

water

sulfur dioxide anaesthetic gases (halothane, enflurane) explosives

silicone grease OV-275

toluene diisocyanate propylene glycol dinitrate organophosphorous compounds

FPOL poly(ethylenemaleate) (PEM) collodion, others 4 polymers

organophosphorous, organosulfur cmpds isooctane trichloroethylene toluene o-xylene acetone organic vapors

polyisoprene polyisobutylene polyamidoxime Pluronic L64 Carbowax 20M 6 polymers ll|

i

*Additional polymer-based sensor coatings are listed in Appendix C.

Sensitivity/ Detection Limit > 4 Hz/%RH 11 ppm < 1 ppm m 5 ppm 5 ppm 2.6-3.0 Hz//zg coating @0.75%v/v halothane 1 ppb < 10 ppb 0.05 ppm 0.030 ppm 0.070 ppm various 0.01 mg/m 3 0.5 mg/m 3 260 ppm 0.4 ppm 90 ppm 7.2 ppm 106 ppm various i,

i,

Comments

Rey.

limited to <70% RH

[2061 [2071 [208] [209] [160] [160] [210]

high selectivity linear range 20-79% RH some NO2 interference some NO2 interference minimal N20 interference some interference from perfumes, solvents large drift at high RH m

sample pre-concentration coupled with SAW sensor array

[211] [212] [213] [207] [207] [2141 [94]

[207] detects other organics as well

[204]

[207] [2~5] [215] [92c]

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CONCENTRATION

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Figure 5.18 Frequency and attenuation (shown as insertion loss) responses for a PlB-coated SAW device upon exposure to trichloroethylene vapors.

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306

5. Chemical and Biological Sensors

both AW perturbations: molecular discrimination can be achieved for an isolated chemical species using a single sensor [216,217]. The additional information provided by simultaneously monitoring both responses should also prove useful in sensor arrays (see Sections 5.9 and 6.5.3). The use of polymer-coated acoustic sensors as chromatographic detectors (GLC, HPLC) has also been demonstrated [ 1,43,218]. In such applications, a lack of selectivity for a given analyte is actually beneficial, since the function of the coated sensor is to detect each and every species passing the detector after preseparation by the chromatographic column (see Chapter 6). 5.4.7

BIOCHEMICAL INTERACTIONS AND ACOUSTIC WAVE SENSORS

In no area have the AW sensors seen such dramatic increase in recent years as in the field of biochemical analysis. The increasing development of acoustic devices as biochemical and immunological probes, as well as for the investigation and/or monitoring of biochemically significant processes, suggests that these applications be treated as a unique subset of AW sensors. The chemical interactions considered here are no more than combinations of those discussed previously. The potential for very high selectivity arises from the three-dimensional structure of biomolecules and the specific arrangement or location of functional groups. A useful analogy is that of a lock-and-key configuration. The geometry of the molecules acts to screen out substances that are not of a complementary structure; i.e., "key" molecules of the wrong size or shape will not fit into the "lock." The functional groups located within the 3-D structure engage in selective, mostly polar, interactions with molecules having complementary functional groups in the proper orientation. Although most biosensor coatings consist of naturally occurring materials, there is significant research involving the development of synthetic materials capable of mimicking the molecular recognition exhibited by biochemical materials [219,220]. Examples of biochemically-based acoustic sensors are listed in Table 5.9. Sensitive, selective detection of biochemically active compounds can be achieved by employing antigen-antibody, enzyme-substrate, and other receptorprotein pairs, several of which have been utilized in the development of piezoelectric immunoassay devices. The potential analytical uses of these materials has been reviewed, particularly with respect to the development of biochemical sensors [221-224]. The receptor protein (e.g., enzyme, antibody) can be immobilized directly on the sensor surface, or it can be suspended in a suitable film or membrane. An example of the sensitivity and response range that can be

Table 5.9 Analyte endotoxin fibrinogen formaldehyde

Coating~Reagent limulus amebocyte lysate thrombin

Detection Limit

Comment

1 pg/mL

viscosity change/gelation reaction viscosity change/gelation reaction reversible, gas-phase, excellent selectivity vs. alcohols, other aldehydes silane-immobilized antibody silane-immobilized antibody linear response up to 5 x 104 cells/mL sensor responds to agglutination of latex in solution in presence of antibody long analysis times (30 min.) needed for microbial reaction

0.50 mg/mL

human erythrocytes

formaldehyde dehydrogenase + glutathione + NAD goat antihuman IgG protein A anti-glycophorin A/PEI

antistreptolysin O antibody

streptolysin O coated latex particles

< 130 IU/mL

Candida albicans

anti-Candida antibody

106 cells/cm

glucose

hexokinase

human IgG

,,4

Examples of Biochemical Acoustic Wave Sensors

10 ppb

13/xg 10 -6 mg/mL < 1 x 103 cells/mL

1 mM

eel. [641 [651 [227]

[271 [242] [243] [234]

[2441 [281

continued urea

urease membrane

<3/zM

adenosine 5'phosphosulfate (APS) reductase human chorionic gonadotropin (hCG) human serum albumin (HSA) herpes virus

anti-APS reductase

5 ng/mL

galactosyl transferase parathion

horseradish peroxidase + polyvinylferrocene anti-HSA virus-specific monoclonal antibodies glucosamine misc. proteins

<600 ng/mL

5 pmol 0.01 ng/mL

response due to change in solution pH, conductance (AMISA)

[236]

AMISA

[236]

no response to BSA; does not require drying stage exhibits excellent selectivity, long shelf life liquid-phase reaction/device dried before measurement nonspecific protein adsorption

[2451

i i

i

[235]

[225] [226] [230]

5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

309

achieved with an AW biosensor is provided in Figure 5.20. It should be noted that, in many cases, the extent of affinity-based reactions increases with time, so that the detection limit for such biosensors will depend on the analysis time utilized. The degree of specificity that can be achieved is demonstrated by an immunosensor for herpes viruses reported by Koenig and Gr~itzel [225]. By immobilization of appropriate anitivirus antibodies, they were able to selectively detect herpes-type viruses in human specimens without significant interference due to non-specific protein adsorption. In addition, even with a complex mixture of structurally similar herpes-type viruses, the sensors were capable of selectively detecting a specific virus, increasing their utility in a clinical setting. In addition to receptor-type proteins, bilayer lipid membranes (BLMs) have been investigated for the detection of species of biochemical interest [221, 231,232]. The lipid film can be used alone, or chemical receptor agents can be incorporated into the membrane to enhance selectivity for inorganic ions or organic compounds/ions. Responses for BLM-coated devices are related to the mass loading of the analyte in/on the lipid film and to changes in interfacial conditions, e.g., elastic and viscous coupling effects [53,221-223]. Okahata et al. reported that BLM-coated TSM devices provided sensitive and selective response to bitter (e.g., papaverine, strychnine, quinine) and odorous (e.g., octanol, coumarin, vanillin) compounds [231]. In contrast, TSM devices coated with other polymers or proteins, such as keratin or albumin, exhibited little or no response to these substances. The BLM coatings, such as dimyristoylphosphotidylethanolamine (DMPE) and dioctadecyldimethyl-ammonium poly(styrenesulfonate), exhibited large partition coefficients ( 2 - 3 • 103) for these compounds. Furthermore, the BLM-coated devices did not respond to sucrose or L-glutamic acid (a naturally occurring amino acid). The relative sensitivity to the bitter and odorous compounds was correlated with threshold concentrations for human detection, indicating that the response of these films may be related to gustatory/olfactory reception. Similar studies focused on odorant detection and recognition have been reported by Muramatsu et al., using BLMcoated [232] and mixed-lipid-coated [233] TSM quartz resonators. Although the majority of AW biochemical sensors rely on changes in either mass loading, impedance, or interfacial tension for detection, changes in solution viscosity can be used in some instances. The advantage of this approach is that, since it takes advantage of changes in solution properties, immobilization of a selective coating is not required. Muramatsu et al. have reported the piezoelectric determination of endotoxin [64] and fibrinogen [65]. Upon addition of the appropriate reagent, the viscosity of the solution increases as a result of gela-

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5.4 Coating-Analyte Interactions and Acoustic-Wave Chemical Sensors

311

tion reactions. The viscosity change in the solution produces a corresponding change in resonant frequency or in the equivalent resistance of the oscillator circuit. Gelation times were correlated with concentration of the analyte. The same principle has more recently been applied utilizing the agglutination of appropriately treated latex particles [66,234], and the method has been dubbed latex piezoelectric immunoassay (LPEIA). The technique has been demonstrated for the detection of C-reactive protein [234] and antistreptolysin O (ASO) antibody [66]. Another less-utilized transduction mechanism for biosensors involves the acoustoelectric effect. In principle, any biochemical process that produces a change in the electrical properties of the solution, can be monitored by observing changes in the frequency and/or attenuation of the device if its surface is not metallized. For example, a SH-SAW device has been reported for the detection of pH changes associated with the enzyme-catalyzed hydrolysis of urea [235]. Using an immobilized urease membrane on the sensor surface, it was anticipated that urea concentrations as small as 3/xM could be reliably detected. Most immunochemically based sensors to date have been developed for liquid-phase measurements; thus, the TSM resonator has been the device of choice. Of course, other plate-mode devices (SH-APM, FPW) would be equally well suited for liquid-phase detection and may have advantages in terms of sensitivity. A low-frequency (20 MHz) SAW liquid-phase immunoassay device has been reported [27], but operation of SAWs of higher frequencies in liquids is not feasible due to excessive attenuation of the SAW by the liquid. An alternative to in-situ detection is to expose a protein-coated AW device to a liquid-phase sample for a period of time, then dry it [226]; the observed frequency shift is proportional to analyte concentration. When using this technique, it is crucial that careful control experiments in the absence of analyte be performed to obtain an accurate idea of the reproducibility of the baseline oscillation frequency throughout the procedure. The use of protein-coated acoustic wave devices for detection of gas-phase species has also been reported with claims of good sensitivity and selectivity. Guilbault et al. reported TSM sensors for the reversible gas-phase detection of formaldehyde [227], and organophosphorous pesticides [228,229]. More recent studies have cast some doubt as to whether the gas-phase sensitivity was the result of selective immunochemical binding, or simply due to nonspecific adsorption. In work reported by Thompson et al. [230], sensors coated with parathion antibody exhibited sensitivities to the pesticides parathion, malathion, and disulfoton that were remarkably similar to sensors coated with nonspecific proteins (valproic acid antiserum, human immunoglobulin G, and bovine serum albumin). The fact that the previous study [228] reported significantly larger sensitivity at

312

5. Chemical and Biological Sensors

higher humidities supports the idea that extensive hydration of the protein coating is required to ensure the integrity of the immunochemical binding sites. In the absence of hydration, nonspecific adsorption appears to play a significant role. Immunologically based sensors show great potential, but there are a number of problems that may limit their performance. For example, the nonspecific adsorption of proteins and other large molecules can adversely affect the apparent sensitivity and selectivity. Strategies for minimizing this effect include the use of a reference crystal coated with a protein that does not specifically interact with the antigen or compound of interest [27], and deactivation of nonspecific adsorption sites. The nature of immobilized reagent proteins has a major effect on sensor response parameters: the number of complementary binding sites per unit area of protein film and their binding constants determine the sensitivity and dynamic range of the biosensor. In addition, detection limits are poorer for low molecular weight analytes, for which the mass change per binding site is smaller. One solution to this problem is the amplified mass immuno_sorbent assay (AMISA) approach [236], illustrated schematically in Figure 5.21. In simple immunoassay methods, the analyte is selectively bound via the immobilized antibody or other complementary protein (Step 1). In AMISA techniques, the adsorbed analyte is further reacted with a conjugate enzyme to form a bound sandwich complex (Step 2). This complex subsequently reacts with other reagents in the solution to produce either an insoluble dimer product, which also adsorbs on the AW device surface, or a massive ion (I3- was used) that inserts into an ionic binding site in the surface film. Thus, the areal mass increase per bound analyte is significantly amplified. While these and other immunosensor detection schemes can involve rather complex reagent and/or buffer systems, the relative advantages of piezoelectric sensors in terms of cost, speed, and safety make them attractive alternatives to radioimmunoassay and other standard assay techniques. In addition to the detection of species of biological interest, these sensors have also been employed as tools to monitor a variety of biochemical processes, including rates of attachment of oseoblasts [238] and rates of bacterial growth [239]. The specific protein/ligand interactions of antifluorescyl antibody and Fab with fluorescein lipids was investigated [237]. The extent of interaction between free species in solution was found to be significantly reduced when the lipid was attached to a surface via Langmuir-Blodgett deposition onto a gold electrode. In addition, the protein/ligand binding strengths increased when spacer molecules were incorporated into the surface anchor compared to direct attachment of the lipid, indicating that freedom of movement of the lipid translates into greater ac-

5.5 Selectivity Revisited: Sensor Arrays and Pattern Recognition

313

Figure 5.21 Representation of immunoassay-based detection schemes. A reagent pro-

tein immobilized on the sensor substrate binds the complementary target protein (Step 1 - direct detection). In a_mplified mass i_mmuno_sorbentassay (AMISA), a conjugate enzyme is added to form a bound sandwich complex (Step 2), that can react with other reagents to amplify the mass increase on the sensor surface. (Adapted with permission. See Ref. [263]. 9 1988 American Chemical Society.)

cessibility of the binding sites. Several studies have focused on the attachment and hybridization of DNA molecules [240--241]. In these studies, the extent of attachment was quantitatively determined using radiolabelled DNA; the immobilized single-stranded DNA could then be used to monitor the rate of hybridization to complementary proteins. The sensor signals were interpreted using electrical equivalent-circuit analysis [241], or network analysis [240]. This technique has the potential to replace the more cumbersome radiochemistry based assays currently used extensively in clinical analysis.

5.5

Selectivity Revisited: Sensor Arrays and Pattern Recognition

The sensitivity and selectivity of a chemical sensor to an individual analyte (or class of analytes) can be improved by taking advantage of selective molecular interactions as discussed in Section 5.4. Some measure of selectivity can also be achieved by taking advantage of the inherent steric limitations of different coat-

314

5. Chemical and Biological Sensors

ing materials, such as molecular sieves [ 132], bilayer lipid membranes [221,23 l l, and nematic liquid crystals [246]. The anisotropic domains created in the latter two materials can afford selectivity for rod-like or planar molecules while excluding bent or branched molecules. The probability is still small, however, of identifying a single coating material having the required sensitivity, selectivity, and reversibility for a one- or two-analyte application that includes potential interferants. In addition, applications that require simultaneous monitoring for multiple analytes require multiple sensors. In such cases, the use of arrays containing multiple AW sensors, each bearing a coating with a different degree of selectivity for the solute(s) of interest, has been investigated for several microsensor technologies [247-252,90,92c,94]. The development of an effective array detector must address two problems: first is the selection of appropriate coatings for each element in the array, and second is the interpretation of the sensorarray data to identify and quantify the detected species. Both of these tasks can be simplified by the use of chemometrics, the general science of applying statistical techniques to the solution of complex analytical chemical problems. Pattern recognition uses multivariate statistics and numerical analysis to classify data and to elucidate relationships in multidimensional data sets [253-255]. A data point is located in an N-dimensional or hyperspace. The location in this space is defined by N components, criteria or properties of the data, with each component defining an axis in the hyperspace. Similarities between data points can be identified by cluster analysis: closely related data lie in clusters in the N-dimensional space. Typically, the N components are the responses from N different sensors, though this is not necessarily the case. For example, the use of individual SAW devices to recognize organic vapors via simultaneous measurement of AW frequency and attenuation changes [217] can logically be extended to array-based sensing, leading to 2N responses from N devices. The same idea could be applied to the five-frequency polymer-coated SAW device reported by Ricco and Martin to simultaneously measure velocity and attenuation changes (i.e., a total of ten responses) as a function of organic solvent vapor pressure for several species [22]. Applications of pattern-recognition techniques for the selection of coatings and for the interpretation of sensor-array data are discussed below.

5.5.1

COATING SELECTION

For practical reasons, the ideal array consists of the minimum number of sensors/coatings that can adequately represent the data. Thus, coatings exhibiting similar or redundant responses should be eliminated, and those exhibiting unique behavior retained. In terms of pattern-recognition analysis, a coating can

5.5 Selectivity Revisited: Sensor Arrays and Pattern Recognition

315

be classified according to its response to a set of solutes; the axes defining the hyperspace could represent retention indices or partition coefficients for the N solutes in that coating. This approach has been used to characterize GLC stationary phases and to define groups of stationary phases with similar properties [256]. Figure 5.22, for example, graphically displays the cluster of coatings from reference 257 in the form of a dendrogram. The identities of the individual coatings are listed, as Groups A-E, in Table 5.10. The dendrogram is a graphical representation of the similarity of coatings. Each line in the dendrogram represents a numbered coating whose position indicates where that line merges with another coating or set of coatings. Lines that merge close to the left edge (similarity value = 1.00) exhibit similar properties, whereas lines that merge far to the right (similarity value = 0.00) exhibit very different properties. For example, Coatings 3 and 6 are very similar, since their lines merge at a value of 0.85; other sets of similar coatings are 1 and 7, 10 and 16, and 20 and 27. Coatings 11 and 13, on the other hand, are not very similar and merge at a value of 0.30. They are closer to each other, however, than to any of the other coatings in the data set since their lines do not merge with the other coatings until the similarity value approaches zero. In terms of coating selection, such clustering simplifies the process by identifying differences and similarities among coating candidates. Once the coatings have been grouped, then a single coating can be selected from each group based on practical considerations such as sensitivity, stability, or cost. For more sophisticated coating selection, see [92c]. Since solubility interactions are related to structural features (as discussed previously), it is not surprising that coatings in a given cluster exhibit similarities in structure. For example, all of the poly(butadiene)-based coatings are found in Group A, whereas Group B consists mostly of vinyl polymers. Each of these groups would be expected to display similarities in solubility interactions. Thus, pattern-recognition analysis can also be used to group similar sets of fundamental processes responsible for the observed solubility behavior [258,259]. In this manner, results from pattern-recognition studies can be used to refine existing models [166-186a--d] or to provide feedback for the selection/design of better coatings for sensing applications. 5.5.2

SENSOR-ARRAY DATA INTERPRETATION

Each sensor in an array is designed with a different coating, with each coating selected to respond differently to the members of a set of analytes as described above. The resultant combination of responses should produce a unique finger-

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1986 A m e r i c a n C h e m i c a l S o c i e t y . )

5.5 Selectivity Revisited: Sensor Arrays and Pattern Recognition

317

Table 5.10 Cluster Classification of Coatings for Use in a TSM Sensor Array i

Group/ID

B

C

D

E

F

5 3 6 2 8 10 16 14 20 27 17 12 22 25 18 15 24 19 21 26 23 11 13

i

Compound poly(butadieneacrylonitrile) poly(butadiene) ( - O H term. liquid) poly(butadiene) ( - O H terminated) octadecylvinyl ether/maleic anhydride copolymer blend poly(vinyl stearate) poly(butadiene methacrylate) poly(1-butadiene) poly(p-vinyl phenol) methyl vinyl ether polystyrene poly(vinyl butyral) poly(vinyl carbazole) poly(ethylene glycol methyl ether) phenoxy resin poly(methyl methacrylate) poly(vinyl chloride) poly(caprolactone)triol abietic acid polyethylene collodion carnuba wax ethyl cellulose poly(caprolactone) DCll poly(caprolactone)triol 2X poly vinyl isobutyl ether poly- 1-butene

i

Comments generally exhibited highest sensitivity to test vapors, especially phosphonates (DMMP, DIMP) and octane

exhibit some selectivity to dimethyl phosphite, and esters

semi-selective response to water vapor

exhibit sensitivity/selectivity for DIMP; collodion exhibits greatest response to phosphonates of all coatings in the set of 27 coatings some selectivity for dichloropentane v s . most test vapors (except DIMP) generally poor sensitivity/selectivity for test vapors ,

,,

,

,,

, ,,,,,,

Based on data in Ref. [257]. Numbers provide locations of coatings as shown in Figure 5.22.

print for each analyte. The sensor response can be thought of as encoding chemical information about the analytes in numerical form. The response of each sensor in an array represents an axis in N-space. Identification of the analyte is achieved by the appropriate pattern or fingerprint in the array data. Examples of the response patterns of a four-coating sensor array toward different vapors are given in Figure 5.23. Note, for example, the similarity between response patterns for methanol and 2-propanol, and the similarity between chloroform and

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5.5 Selectivity Revisited: Sensor Arrays and Pattern Recognition

319

dichloroethane. While there are similarities within a given class, the typical response patterns of the two classes (e.g., alcohols vs chlorinated hydrocarbons) are quite different. Sensor-array response patterns of this sort can thus be used as a basis for identification of compounds according to their chemical class. When it is necessary to discriminate compounds within a single class, minor differences in the overall response pattern, or differences in the signal magnitude, may be useful. Acoustic sensor arrays have been used to study hazardous vapors and vapor mixtures [90,92c,94], for odor recognition [250], to determine o-cresol and m-cresol in water [ 128], and to monitor an industrial drying process [247]. A number of methods have been developed for establishing correlations between the pattern of responses from an array of chemical sensors and the identity of the corresponding analyte [260-262]. Principal-component analysis (PCA) and cluster analysis (CA) are usually performed on the matrix of sensor responses to obtain a qualitative assessment for the uniqueness of the response patterns for one or more analytes. In the ideal case, responses for different analytes are located in discrete clusters in N-dimensional space, where N is the number of sensors used. Classification methods are then used for the identification of an unknown analyte provided that its sensor responses are contained in the training set. Classification criteria are established using methods such as the K-nearest neighbor (KNN) or the linear learning machine (LLM). For mixtures, responses are usually located between those of the individual components comprising the mixture [90,263]. An unknown mixture can be identified provided that the spatial locations associated with the mixture responses, over the range of component concentrations, have been previously defined. Following identification of an unknown, methods such as multiple linear regression (MLR), partial least squares (PLS), or principal-component regression (PCR) can be used to determine the concentration(s) of the analyte(s) [251,260]. For sensors that give nonlinear responses with concentration, a method called transformed least squares (TLS) can be used to linearize the responses prior to quantitation [264,265a]. The use of MLR on matrices containing redundant sensor responses can lead to large quantitation errors, whereas PLS and PCR are less sensitive to this condition [260]. For advanced methods, see [265b]. Disjoint principal components modelling [266] and SIMCA (soft independent modelling of class analogy) [261,262,267] are examples of PCR wherein principal components models are developed for individual groups of responses within a data set. For these methods, classification is based on quality of fit of an unknown response pattern to the model developed for a given analyte [268-270]. This approach differs from standard PCR, where principal components are derived from the data matrix as a whole.

320

5. Chemical and Biological Sensors

The concepts underlying these methods can be extended to permit identification of both individual vapors and the components of vapor mixtures from the sensor response patterns [271 ]. A useful feature of this "extended" disjoint principal components regression (EDPCR) method is the integration of the qualitative and quantitative aspects of the sensor responses. Implementation of EDPCR has been demonstrated for arrays of polymer-coated SAW sensors exposed to a range of vapors and vapor mixtures [92a,92c,271]. Accurate identification and quantification of individual vapors and vapor-mixture components was achieved. One final problem that must be addressed in the interpretation of sensorarray data is the reliability of the final result. Each sensor response contains a certain degree of error, and the propagation of error for a sensor array is not trivial. This fact has important ramifications in terms of identification of an analyte in the presence of interferences, as well as in the selection of coatings for inclusion in the array. The efficacy of the array depends on the uniqueness of coating responses: as colinearity increases, error in the final result is amplified and the detection limit is adversely affected. These concerns have been addressed and the effects on the analytical result from the sensor array have been described quantitatively [260,272].

5.6

Summary

Clearly, AW sensors are versatile analytical tools having applications in nearly all areas of chemical analysis. Successful implementation of this technology for chemical sensing requires a broad-based interdisciplinary approach, Accessing the desired acoustic mode or transduction mechanism depends on the design and engineering of the sensor. Maximizing the sensitivity and selectivity of the sensor for a given analyte often depends on selection of the optimal coating or set of coatings which requires a detailed knowledge of the chemical/biochemical behavior of the analyte(s) in question. Interpretation of the response from the sensor or sensor array may require the use of sophisticated pattern recognition algorithms. Clearly, the production of a reliable chemical sensor of any type is possible only when all aspects of sensor operation are adequately understood.

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Chapter 6

Practical Aspects of Acoustic-Wave Sensors

6.1 Introduction The previous chapters have provided the essential theoretical underpinnings of the functioning and interactions of acoustic-wave (AW) sensors, along with specific examples of how these devices have been used for chemical analysis and materials characterization. This chapter offers some details about the practical aspects of designing both the sensors and the systems that permit one to obtain the physicochemical information that AW sensors can provide. The first practical problem to be addressed is the fabrication of acoustic-wave sensor devices. While some devices are commercially available (see Appendix D), a researcher may need a unique device in order to investigate some previously unexplored aspect of AW sensors and their interactions with their environment. It is therefore quite valuable to understand basic device configurations, fundamental design principles, the different properties of the range of materials that can serve as device substrates, fabrication practices, and coating technologies. These issues are addressed in Section 6.2. Radio-frequency (RF) excitation and detection of acoustic waves in a piezoelectric substrate constitute another significant challenge. Precise measurements with high-frequency (HF) to ultra-high-frequency (UHF) voltages can be difficult because of the relative complexity of HF-RF circuit design. Unlike modem digital and analog integrated circuits, which have evolved into extremely easyto-use, cookbook building blocks, RF circuits are often extremely sensitive to layout topology, transmission distances, and component selection. The difficulty of RF design is modest at frequencies below 50 MHz but it grows as the fre-

331 ACOUSTIC WAVE SENSORS

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332

6. Practical Aspects of Acoustic-Wave Sensors

quency increases. In this regard, low-frequency TSM resonators and FPW devices offer a significant advantage. Practical schemes for exciting and detecting AWs in TSM, APM, SAW, and FPW devices are described in Section 6.3. Yet another significant challenge to the successful use of AW sensors is the isolation of their sensitivities to numerous different perturbations, so that only a single, desired interaction is observed. As an example, AW sensors are sensitive to environmental variables such as temperature, pressure, and gas or liquid flow rate; in mass-sensing applications, excessive response to these variables can be a serious problem. Controlling the AW sensor environment is the focus of Section 6.4. Once the device has been fabricated, the chemically sensitive coating applied, and the supporting RF electronics turned on, acoustic-wave sensors sometimes do not perform as expected or desired. Drift may be excessive; sensitivity or selectivity may be inadequate to solve the immediate problem. Section 6.5 outlines several popular strategies for enhancing AW sensor performance through careful system design. Together, the practical details described below provide a realistic description of the current state of the art in acoustic-wave sensing. Armed with this snapshot of the present state of the technology, and having a vision of desirable future directions, the technical bottlenecks that must be passed for the vision to become a reality are apparent. These system design challenges are outlined in Section 6.6.

6.2

Basics of A c o u s t i c - W a v e S e n s o r D e s i g n and F a b r i c a t i o n

6.2.1

DEVICE CONFIGURATIONS

The "configuration" of acoustic-wave devices, in terms of the type and geometry of transducers, as well as the electronic circuitry to which the transducers are connected, has several variations. Some of these variations are a necessary result of fundamental differences in the nature of the AW device (and the AW itself), while others are attempts to optimize particular aspects of the sensor and its response. Initially, distinction will be made between different types of AW device according to the number of "ports" utilized, i.e., the number of separate electrical connections I (and hence the number of transducers) that each has. IBecause all the devices considered in this book operate at relatively high frequency (> 1 MHz), a "single connection" always consists of two electrical contacts. In cases wherethe associated circuitry is remotely located from the device itself, these two contacts connect, via an appropriately designed RF-compatible connector, to the center conductor and the outer conductor (the shield typically at ground potential) of a coaxial cable.

6.2 Basics of Acoustic-Wave Sensor Design and Fabrication 6.2.1.1

333

One-Port: Bulk and SAW Resonators

An example of a one-port device is the bulk resonator shown in Figure 6.1, which has a single, planar electrode on each side of a slab of piezoelectric material (these two electrodes together comprise a single port). Most often, the material takes the form of a disk and the electrodes are circular, coveting less than the entire surface of the disk. Connection to an external circuit is typically made via a coaxial cable, with one of the two electrodes connected to the shield and the other to the center conductor. This device is known as a resonator because an external circuit (see Section 6.3.3.2) excites the piezoelectric substrate in such a way that a standing wave is set up in the crystal, which thus resonates. Though a disk shape is not required for the substrate itself, it is highly desirable for the electrodes, since the high symmetry and lack of sharp comers make the acoustic mode and its perturbations easier to model and understand. The thickness of the substrate ranges from a few/xm in the case of thin-film-based devices (see Section 6.2.2) to several hundred/xm for quartz thickness-shear-mode (TSM) resonators; the diameter of the electrodes ranges from tens of/xm to a few cm. For liquid-phase applications, the ground electrode (which may be used as the working electrode of an electrochemical cell) is often significantly larger in diameter than the RF electrode, in order to eliminate fringing fields in solution; the ground electrode is also sometimes significantly larger for reasons associated with the fixture used to hold the device. In either case, the diameter of the smaller RF electrode determines the active device area regardless of where the mass deposition or other perturbation occurs. Note that both the frequency of resonance and the sensitivity to surface perturbations increase with diminishing substrate thickness. A couple of "typical" commercial TSM devices have the dimensions and characteristics specified in Table 6.1. There are no clear design rules regarding the ratio of the diameter of the electrodes to the thickness of the substrate, but the static capacitance of the quartz disk can be held constant by scaling the RF electrode diameter in proportion to

Figure 6.1 The thickness-shear mode resonator (TSMR); the pair of electrical leads comprise a single port.

334

6. Practical Aspects of Acoustic-Wave Sensors Center Frequency and Dimensions of Commercial TSM AT-Quartz Resonators

Table 6.1

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,

,

Frequency

Substrate Diameter

Substrate Thickness

Ground Electrode Diameter

RF Electrode Diameter

6 MHz 5 MHz

14 mm 25.3 mm

0.26 mm 0.34 mm

14 mm 12.3 mm

6.7 mm 6.3 mm

Resonant

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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.

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(1/thickness) 1/2. While the most common of the bulk resonators support a TSM in AT-cut quartz, devices fabricated from other materials support nonshear modes; an example is the thin-film resonator fabricated from AIN, which resonates longitudinally [ 1]. The second category of one-port device is the SAW resonator. To make a high-stability resonator, the quality factor, 2 or Q, of the device must be higher than for the two-port delay-line configuration discussed below. One way to accomplish this is to provide a structure that will support a standing wave, namely a series of ridges, oriented perpendicular to the direction of wave propagation and having a periodicity of one-half wavelength (M2), that can be thought of as forming an acoustic cavity [2]. A single IDT launches the standing wave, and this IDT requires fewer finger pairs than those used for delay lines. A typical resonator design is shown in Figure 6.2. Due to the half-wavelength grating periodicity, reflections from the ridges interfere constructively, giving rise to the standing wave. The details of IDT design are given in Section 6.2.3.

6.2.1.2

Two-Ports: SAW, APM, and FPW Delay Lines and Resonators

An example of a two-port device is the surface acoustic-wave (SAW) delay line shown in Figure 6.3. Acoustic plate mode (APM) devices utilize a two-port configuration that is conceptually identical to that of the SAW; for the flexural plate wave (FPW), there is typically a third connection to its ground plane (see Section 6.2.3). In principle, the ground plane connection is unnecessary, but in practice more stable operation results when this connection is made. Notice that there 2In the context of resonant acoustic devices, Q -fR/BW, wherefR is the resonant frequency and BW is the bandwidth; it can equivalently be defined as caUp/Pa,where ca is the angular frequency, Up is the peak total energy present in the device, and Pa is the power dissipated by the device. For resonant systems, BW is the range of frequencies over which the reflected power is within 3 dB (a factor of two) of its minimum value, attained at fR; for non-resonant systems (e.g., delay lines), BW is the range of frequencies over which the transmitted power is within a factor of two of its maximum value.

6.2 Basics of Acoustic-Wave Sensor Design and Fabrication

335

Figure 6.2 Schematic design of a two-port SAW resonator; the series of parallel lines on either side of the IDTs represent the array of ridges that forms a resonant acoustic cavity. One of the IDTs furnishes the signal to set up the standing acoustic wave; the second samples this wave, feeding back to the circuitry that drives the input IDT.

Figure 6.3

Schematic design of a two-port SAW delay line. The electrical signal is launched by one IDT and reaches the second after a delay determined by the spacing of the two transducers.

are two IDTs, one of which serves as the input to the device, while the other is the output. Often, the input and output IDTs are of identical design. Each transducer is comprised of two "combs," one of which is connected to the shield (ground) and the other to the center conductor of a coaxial cable. 3 This configuration is known as a delay line, rather than a resonator, because an electrical signal incident on the input IDT generates a propagating wave which, after a delay of some finite time (typically a fraction of one to several/xs), reaches the output IDT and generates an electrical signal. This configuration lends itself very easily to creating an oscillator circuit, as detailed in Section 6.3.3.3. The spac3Grounding one comb of an IDT means the transducer is unbalanced, i.e., one comb stays at ground potential while the second comb oscillates positively and negatively with respect to the first. An IDT can also be operated in a balanced configuration by interposing a balun transformer between the IDT and the remainder of the circuit, causing the two combs to be driven symmetrically about ground potential.

336

6. Practical Aspects of Acoustic-Wave Sensors

ing between IDTs is an important parameter: it must be large enough that direct electromagnetic coupling between input and output IDTs is small compared to coupling via the acoustic wave. In addition, if the coating material of interest is electrically conductive, or becomes conductive upon sorption of an analyte, then the inter-IDT space, to which the coating must be confined in order to avoid shorting the IDTs, must be significant compared to the total number of wave periods defined by the IDT itself to produce a readily measurable perturbation. As a rule of thumb, a wave path of 100-300 acoustic wavelengths works relatively well for SAW and SH APM delay lines. Two-port SAW resonators, on the other hand, normally have the IDTs spaced just a few wavelengths apart. The SAW device utilizes a mode whose wavelength is set by the periodicity of the input IDT; because it is a true surface wave, the SAW is not affected by the thickness of the substrate, provided it exceeds several acoustic wavelengths. With wavelengths typically of the order of several/xm to over 100/zm, substrates are usually 200/zm or more in thickness. As the substrate thickness approaches a few wavelengths, the"back face" of the substrate comes into play, and the SAW can degenerate into a plate mode. Two classes of plate mode are described in detail in Chapters 2 and 3 of this book: the shear-horizontal (SH) APM and the FPW. These modes have features in common with both the SAW and bulk resonators. Like SAW devices, the wavelength in the plane of the surface is set by the transducer periodicity; for plate modes, however, there is also a substrate-thickness-dependent mode variation in the direction normal to the surface. Just as for bulk resonators, the fraction of the wave energy present at (either) device surface and, hence, the sensitivity of these devices to surface perturbations, is inversely proportional to substrate thickness, the practical consequence being that thin substrates are necessary to achieve high sensitivity. Thin substrates have been obtained in the case of FPW devices via Si micromachining techniques to achieve wave-carrying membranes as thin as two/zm [3], while SH-APM devices have relied on conventional lapping and polishing to provide substrates in the 150-250/xm range [4]. To complicate matters, appropriately designed two-port devices can readily be operated as resonators (though one-port devices are not practical for use as delay lines). One need only consider the second IDT, located a few acoustic wavelengths from the launching transducer, as shown in Figure 6.2, to understand how one- and two-port SAW resonators differ in their fundamental design. A discussion of the function of the second IDT is contained in Section 6.3, Acoustic-Wave Measurement Technology. Unlike a delay line, where the interaction between AW and external stimulus must occur in the region between IDTs, the standing-wave pattern (and hence

6.2 Basics of Acoustic-Wave Sensor Design and Fabrication

337

the interaction region) for a SAW resonator extends well beyond the transducers. The distribution of wave energy over the resonating surface is non-uniform, leading to marked spatial variations in the sensitivity to surface perturbations (e.g., mass loading) [5]. For both delay lines and resonators, direct calculation of perturbations such as mass changes using literature sensitivity values requires that the change occur uniformly over the entire width of the wave path. Such uniform-width perturbations ensure that the straight-crested nature of the acoustic wave is preserved, the consequence of which is a more coherent signal (hence better signal-to-noise ratio) at the output transducer. To use literature sensitivity values for resonators, there is an additional constraint: the perturbation must generally occur uniformly over the entire length of the wave path as well. This is a consequence of the dependence of sensitivity to the local distribution of stored energy, rather than the total integrated power flow as is the case for delay lines. An exception to length-uniform perturbation for resonators is the region between, and in the first several wavelengths on either side of, the two IDTs, where the energy distribution is relatively fiat. Thus, if the sensitivity constant for this nearIDT region is known, then a measured fraction of said region can be perturbed and a reliable calculation of the magnitude of the causal effect made. Requirements for uniformity are relaxed for either type of device if the precise region of the surface over which the perturbation is to occur can be directly calibrated, for example by deposition/removal of a known mass to/from that particular area; but it is never wise to use a non-rectangular perturbation region, as disruption of the straight-crested waves will result.

6.2.2

SUBSTRATE M A T E R I A L S

The acoustic-wave sensors considered in this book all utilize piezoelectric transduction, hence the substrates considered are all piezoelectric materials. 4 Section 2.2 discusses in some detail the crystallographic requirements for a material to be piezoelectric. Quartz, a crystalline form of SiO2, is by far the most commonly used platform for AW sensors, a result of its relatively low temperature coefficient (compared to other piezoelectric materials). Though it is far from trivial to grow, 4While a thin transduction layer below and/or above the input and output transducers must be piezoelectric, there is no such restriction upon the balance of the substrate. A piezoelectric thin film (such as crystallographicaUyoriented polycrystallineZnO or AIN) can be deposited on a non-piezoelectric substrate to provide a medium for AW excitation and detection. Thus, (non-piezoelectric) silicon wafers often serve as the substrate for SAW or FPW devices, with piezoelectric transduction provided by a layer of ZnO. Note also that this transduction layer need not extend laterally past the regions in which the IDTs are defined.

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6. Practical Aspects of Acoustic-Wave Sensors

quartz's widespread use has led to its availability in comparatively large sizes (3" polished wafers) and large quantities from several suppliers (see Appendix D). In addition, various crystallographic orientations that minimize the temperature coefficient (near room temperature) of AW devices have been characterized over the years and are now widely available; these include the ST cut for SAW devices and the AT and BT cuts 5 for TSM resonators. Several other substrate materials are worthy of mention here. These include lithium niobate (LiNbO3), whose relatively large electromechanical coupling coefficient (K 2) allows two-port acoustic-wave devices to utilize IDTs comprised of nearly an order of magnitude fewer pairs of fingers than quartz. Unfortunately, LiNbO3 suffers from a very large temperature coefficient--approximately 80 ppm/~ for a SAW device with propagation in the Z direction on Y-cut LiNbO3. The consequences of this are that LiNbO3 is thermally quite fragile and that exceptional temperature stability is necessary when using LiNbO3 to detect anything other than temperature changes. The silver lining to this cloud is that one can measure changes as small as 10 -4 ~ using this material as the substrate for a SAW delay line-based thermometer. In contrast to silicon, which is piezoresistive but not piezoelectric, GaAs is a material from which integrated circuits can be fabricated and that is also piezoelectric. Owing to the relatively covalent nature of its bonding, however, GaAs has a very small K 2, which has perhaps prevented it from being used to any appreciable extent for AW sensors. The suitability of GaAs for extremely highspeed electronic devices makes it a candidate for incorporating microwavefrequency (GHz) electronic components on the same substrate with GHz-, and hence highly mass-sensitive, AW devices. With the aid of a particular class of materials (thin-film piezoelectrics), incorporation of AW devices and conventional integrated circuit components on the same silicon substrate is in fact possible. Under the proper conditions, a number of piezoelectric materials can be deposited in thin-film form, typically by RF sputtering, and retain their piezoelectric nature. For this to occur, the crystallites that grow during deposition must be predominantly oriented in a single, piezoelectrically active crystallographic direction. Two such materials are ZnO and AIN; the former has been used as an overlayer on Si wafers to fabricate all of the FPW devices studied for sensor applications to date, and also for SAW resonators. Because extremely thin piezoelectric films are readily fabricated, both ZnO and AIN have been used to make bulk resonators that operate at much higher 5The "T" in the designations"AT," "BT," and "ST" stands for temperature; AT and BT were the first two widely recognized temperature-coefficient-optimizedcuts for TSM quartz resonators.

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frequencies (e.g., 100 to 3,000 MHz) than TSM resonators made from quartz disks, which typically resonate at 5-20 MHz.

6.2.3

INTERDIGITAL TRANSDUCER DESIGN

The excitation and detection of surface acoustic waves, flexural plate waves, and other plate waves on piezoelectric substrates is most readily accomplished by use of an interdigital transducer (IDT) first reported by White and Voltmer [6]. The comb-like structure of the IDT, illustrated in Figure 6.4, is typically made from a lithographically patterned thin film that has been deposited onto the surface of a piezoelectric substrate or thin film. The metal film used to make the IDT must be thick enough to offer low electrical resistance and thin enough so that it does not present an excessive mechanical load to the AW. Typical IDTs are made

Figure 6.4 Characteristic features of the interdigital transducer (IDT) used for acoustic wave excitation. The transducer periodicity, d, is equivalent to the acoustic wavelength.

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from aluminum that is nominally 1000 A thick. Another popular IDT metal is gold, but this often requires the addition of a thin (ca. 100 A) layer of chromium or titanium/tungsten to assure adhesion of the gold. The design of the IDT determines the electrical impedance of the AW device, as well as the operating frequency, bandwidth, and sensitive area. An IDT excites an acoustic wave in the piezoelectric substrate when a radiofrequency voltage is applied to it. This time-varying voltage results in a synchronously varying deformation of the piezoelectric substrate and the generation of an AW. The wavelength A most effectively excited by the IDT is equal to the periodicity of the transducer pattern (d in Figure 6.4). The velocity of an unperturbed AW is a constant and is equal to the product of wavelength and frequency. Thus, the IDT finger spacing determines the center frequency: fo = v/d. For a typical piezoelectric substrate material like ST-quartz, whose Rayleigh wave velocity is 3158 m/s, an IDT with a periodicity (wavelength) of 100/zm generates surface acoustic waves having a frequency of 31.58 MHz. Design of the optimal IDT for a specific application is a complex task, which, in the case of commercial filtering, frequency-control, and delay-line applications, is most often accomplished with the aid of sophisticated computer programs. These programs model IDT response by considering the electromechanical effects of each finger, connected via appropriate electromechanical elements to its neighbors. Not all workers in the sensor field have access to such programs, so designs are often less precise, relying instead on designs reported in the literature and/or trial and error. The electrical impedance of the IDT depends on a variety of factors including the electromechanical coupling coefficient (K2), the dielectric permittivity of the substrate (Es), and the geometry of the IDT: electrode width, spacing, number of finger pairs, and acoustic aperture (i.e., IDT finger overlap length). Table 6.2 gives typical design parameters used for IDTs in SAW sensor applications. For the 31-MHz device, the acoustic aperture was selected according to a literature report that 50-II IDT impedance requires an acoustic aperture of 72 wavelengths (7200/xm for this periodicity) [7]. The acoustic apertures for the 25., 50,100-, and 200-MHz devices [8] were chosen based on past favorable experience with 50-wavelength apertures. The 97-MHz design has been used for a number of years for a range of chemical sensing and materials characterization applications [9,10]. Finger lengths (apertures) of less than approximately 30 wavelengths are inadvisable, as the transducer can act in a manner acoustically equivalent to a slit for optical radiation:diffraction of the acoustic beam results in it diverging considerably before reaching the output IDT. To efficiently couple power into and out of the IDT, thereby promoting

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IDT Design Parameters for ST-Quartz-Based SAW Sensor Devices

Table 6.2

Center

No. of finger pairs

Finger width/ finger spacing, n~ a

Acoustic

Acoustic

aperture,

path length,

MHz

Periodicity (Wavelength), ltm

n~ a

n~ a,b

31 25/50/100/200 c 97

100 124/62/31/15.5 32

50 25 50

0.25/0.25 0.25/0.25 0.25/0.25

72 50 50

350 200 230

Frequency,

,,,

ii

|

, |

i i

i

i

i

i

Number of acoustic wavelengths bAcoustic path length is an overall SAW device design parameter, but is included here with the IDT parameters for completeness. CDesign parameters for a multifrequency SAW device described in [8]. an;t =

low-loss and low-noise operation of the AW device, it is important that its impedance be matched as closely as possible to that of external components (invariably 50 1) and resistive). Due to its physical nature, the impedance of the IDT is largely capacitive. This capacitance can be "tuned out" by placing an appropriately chosen inductor in series with the non-grounded comb of the IDT. If the IDT static capacitance is Co, then the tuning inductor should have a value of Lr = 1/(to2C0); for example, an IDT capacitance of 4 pF requires a series tuning inductor of 633 nH at 100 MHz. Impedance matching techniques are described in more detail elsewhere [ 11 ]. The number of finger pairs in the IDT affects the bandwidth B W of the transducer: BW ocfo/N, where fo is the center frequency and N is the number of finger pairs. The bandwidth of the IDT is important for use in delay line-based oscillator circuits, since a narrower bandwidth results in higher stability and lower oscillator noise. Unfortunately, one cannot decrease the bandwidth of the IDT without limit by merely increasing the number of finger pairs. In practice, when N exceeds about 100, the losses associated with mass loading and scattering from the electrodes begin to neutralize any additional advantage associated with the increased number of electrodes; IDT impedance is affected by N as well. There are numerous other methods such as apodization and split-fingering that can be used to further enhance the performance of the IDT. These are beyond the scope of this discussion but are commonly employed in commercial SAW device designs. For SAW resonators (either one- or two-port), design criteria are very similar to those discussed above for delay lines, with an important caveat: the number of fingers utilized for the IDT must be significantly fewer than for delay lines in order to couple to the acoustic cavity (the ridge array) at the proper signal level, and simultaneously achieve the desired impedance. The result is that while

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the overall bandwidth of the resonator is very narrow due to the acoustic cavity, the bandwidth of a lone IDT is actually much wider than for a delay line IDT. The Q of a SAW resonator often exceeds 10,000, providing improved oscillator stability. The interdigital transducers of the FPW device differ in one significant way from those of SAW and APM devices: the FPW device typically has a conducting ground plane opposite and close to the transducers, and so the transverse electric fields set up by the voltages between adjacent transducer fingers play essentially no role in transduction. This is because the piezoelectric film t h i c k n e s s - typically about one /xm m is much smaller than the distance between the transducer fingers, which ranges from five to perhaps 25/zm. Therefore (as mentioned in Section 6.2.1.2), there is typically a connection to the ground plane as well as the IDT(s). While unnecessary in principle, the ground plane connection improves stability in practice. For protective and other reasons, the IDTs are fabricated on the membrane prior to sputtering on the piezoelectric layer, and the ground plane is deposited as a last step.

6.2.4

MICROFABRICATION TECHNOLOGY

Interdigital transducers are fabricated utilizing photolithographic techniques. The relatively simpler, single-pad electrodes utilized for bulk oscillators are readily defined using less sophisticated techniques (shadow masking, for example), but they are often fabricated using photolithography as well if the technology is readily available. Because of the requirements for a very thin (a few/xm) membrane surrounded by a much thicker supporting substrate, the FPW device is considerably more complex to fabricate than other AW devices; fabrication details for the FPW are not included here, but can be found in the literature [3]. 6.2.4.1

Metal Selection and Deposition

The two "metallizations" most commonly used to fabricate transducers on AW devices are gold-on-chromium and aluminum. Au is often Chosen for chemical detection applications because of its inertness and resistance to corrosion; a layer 100-200 nm thick is necessary to provide adequate electrical conductivity. Unfortunately, the inertness of Au also prevents its adhesion to quartz and other oxides utilized for AW device substrates. Therefore, an underlayer of Cr (2-10 nm thick) is utilized to promote the adhesion of Au to the substrate: the electropositive (reactive) nature of Cr allows it to form strong bonds with oxide surfaces, while alloying between the Cr and Au chemically binds the two metal layers

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tightly together. Care must be taken not to expose a freshly deposited Cr layer to oxygen (air) before the Au is deposited, as a chromium oxide layer will form instantaneously, preventing adhesion of the Au to the Cr. At elevated temperatures (ca. 300~ and above), Cr and Au interdiffuse; the unfortunate result of this is that the conductivity of the Au layer decreases significantly, eventually rendering the metallization too resistive for use. This problem can be partially circumvented by substitution of Ti for Cr as an adhesion layer, although Ti is more difficult to deposit (see below). Aluminum has the advantage that it adheres well to common oxide substrates, is easy to deposit, is only 17% less conductive (for an equivalent thickness) than Au, and is far less dense. The lower density is significant because reflections of AWs from Au IDT fingers in delay-line applications can cause appreciable passband tipple in the IDT frequency response. Al's main disadvantage is the relative ease with which it corrodes; this problem is sometimes addressed, particulady for (non-sensor) commercial applications of SAW devices, by passivating the A1 using a relatively impermeable layer of a material such as Si3N4 or A1N. Although it is not yet common for AW devices, other areas of microelectronics have demonstrated the utility of more exotic metallizations, such as Pton-Pd-on-Ti, for demanding, high-temperature applications; this combination would also be very corrosion resistant, though the relatively high density and poor conductivity of Pt are less than optimal for AW devices. Deposition of metals can be accomplished in one of several ways. The simplest is by thermal evaporation in a high-vacuum system (base pressure < 1 x 10 -6 Torr); Au and AI, contained in or distributed over a tungsten basket or filament, melt and deposit by evaporation from the liquid phase. Cr sublimes from the solid when heated, typically in a W basket. Ti cannot be deposited thermally, which may be why it does not replace Cr altogether. Electron-beam-induced evaporation, in which a stream of electrons is emitted from a hot filament and accelerated into a target of the material to be deposited, is an effective means to deposit AI, Au, Cr, Ti, and most any other metal, again in a high-vacuum system. The added complexity of e-beam systems makes them considerably more expensive than comparable thermal deposition apparatus. A third technique suitable for the deposition of virtually any metal, and a large number of metal oxides and other dielectrics as well, is sputtering. An inert-gas (often Ar) plasma is formed in contact with a target of the material to be deposited; excitation is provided by a DC or RF electric field. Magnetron sputtering.utilizes a strong magnetic field to limit the trajectories of the electrons associated with the plasma, preventing electron bombardment of the sample being coated; the magnetron also lowers the impedance of the sputtering structure. En-

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ergetic species in the plasma knock atoms loose from the target material; the dislodged atoms become part of the plasma and deposit onto nearby surfaces. Because gas pressure is relatively high (a significant fraction of 1 Torr), sputtering typically results in conformal coverage (over/around steps, edges, etc.), in contrast to the two evaporation techniques discussed previously, which result in lineof-sight coverage. Less commonly used techniques include inductive heating of the metal and deposition via the decomposition of a gas-phase metal complex, known as chemical vapor deposition.

6.2.4.2

Photolithographic Patterning

There are two similar but distinct photolithographically-based procedures for defining IDTs from a uniform metal layer. Each of these procedures in turn has two variations, depending upon the polarity of photoresist (negative or positive 6) and mask (clear- or dark-field). An etching procedure utilizing positive photoresist requires use of a lithographic mask that is opaque in the regions where metal is to be retained----this is called a clear-field mask. The completely metallized AW substrate is overcoated with a layer of photoresist (typically 1 /xm or so thick) by flooding the substrate surface with a solution of the resist, then spinning it at high speed (100(O4000 rpm), producing a very uniform resist layer. This layer is heated to drive off solvents, then exposed to UV light with the mask in direct contact or extremely close to the substrate. Exposure is typically provided by an expensive mask aligner, which can hold the substrate and mask in close, uniform alignment. In addition to providing illumination for a precisely controlled time interval, the aligner allows the fabrication of devices requiring multiple mask levels: a microscope permits simultaneous viewing of the mask pattern and the wafer being processed. Most AW devices require only a single mask level, but it is often very important to align the IDT patterns so that the AW will propagate in the intended crystallographic direction. Round substrate wafers are typically provided with a "fiat" oriented normal to the propagation direction for this purpose. 6Positive photoresist is based on resins containing photosensitizing molecules that become soluble in the developer, an aqueous solution of base, upon exposure to ultraviolet light. Negative photoresist is typically based on partially cyclized polyisoprene containing a few percent-by-weight of a photocrosslinking agent, such as a bis-azide. Absorption of UV light by such species causes them to link two adjacent polymer chains to o n e another, diminishing solubility in an organically based developer.

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A crude but inexpensive alternative to the mask aligner is to physically clamp the substrate to the mask, then use a UV "light box," which contains several black-light fluorescent tubes, for the exposure process. With care, this procedure can produce features in the vicinity of 5/xm and larger, making it possible to fabricate 150 MHz SAW devices on quartz, for example. Developing the exposed resist with a selected mixture of solvents removes the resist where it was exposed to light. The metal is then dissolved, in the regions unprotected by photoresist, by an appropriate etchant. Stripping away the remaining photoresist leaves the finished devices. The etching procedure using a negative photoresist is identical except that the lithographic mask must be opaque in the regions where metal is to be removed this is known as a dark-field mask. Exposure of negative resist to UV light makes it insoluble in its developer. A lift-off procedure is somewhat different. A layer of photoresist is deposited on the bare AW substrate, then exposed and developed prior to metallization. The appropriate combination of photoresist and mask are utilized so that, after developing, a polymer layer remains in the regions that are ultimately to be devoid of metal. Metallization is then carried out using a line-of-site technique (thermal or electron-beam evaporation), so that the sidewalls of the photoresist features, which must be considerably taller than the thickness of the metal, are not significantly covered by metal. The photoresist and the metal on top of it are "lifted off" by agitating the sample in a solvent for the resist. For this technique to work, the bond between the metal and the substrate must be significantly stronger than any ties between the metal resting atop the polymer and metal directly on the substrate. The foregoing discussion assumes one has a lithographic mask in hand; the mask is the "blueprint" for the IDTs of either a single or a wafer full of AW devices. Masks are typically purchased from a commercial "mask house." The mask is a (square) piece of soda-lime glass, initially coated with an opaque layer of chromium (or iron oxide). The opaque material is patterned using a lithographic process identical to that described previously, except the UV exposure is made in controlled areas using a complex and expensive instrument known as a pattern generator. The pattern generator controls a set of mechanical apertures to provide flashes of UV light in the locations dictated by the design and layout of the desired features; the design is typically transferred to the pattern generator from a computer-aided design system. The question of which fabrication procedures to use depends on a number of factors, not least among them being the availability of the appropriate tools and experienced colleagues nearby. Positive photoresist offers higher resolution, and

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6. Practical Aspects of Acoustic-Wave Sensors

the chemicals required for stripping and developing are easier to handle than those for negative resist; although positive resist requires longer exposure times than negative resist, high throughput is often low on the list of priorities for smallscale operations. Other factors being equal, clear-field masks are preferable to dark-field masks, since it is possible to see through them, and thus easily align the IDT patterns with the intended direction of wave propagation on the wafer. E-beam deposition systems are often the most free of contamination and can deposit most any metal, but they tend to be relatively expensive. A thermal or sputtering system can be cheaply assembled, but care should be exercised so that a poor vacuum system does not lead to poor quality, high resistivity metal films; this is more of a problem with AI than Au.

6.2.4.3

Preparation for Packaging

Following successful metallization, devices must be prepared for use. When a number of devices are fabricated on a single wafer of the substrate material, the first step is to dice (cut up) the wafer. In the case of quartz and many other substrates, this is best done using a high-speed (ca. 30,000 rpm) diamond-coated saw blade specifically designed for wafer dicing. If the devices are to be a specific size, allowance must be made when laying out lithographic masks for the thickness of material that is lost as a result of the saw kerf; this can be as little as 100 ,u.m. When the substrate is single crystalline and has major crystallographic planes running parallel and perpendicular to the direction of AW propagation, it is possible to scribe and cleanly break the wafer into individual die. This is typically not possible for the specially rotated cuts of quartz chosen for their low temperature coefficients. For delay-line-based devices, reflections of AWs from the crystal ends can adversely affect device stability and frequency response (see triple-transit echoes in the Glossary). There are two strategies to avoid this problem. One is to cut the ends of the substrate at an angle, rather than making them exactly perpendicular to the direction of wave propagation; the consequence of this is that waves reflected from the crystal ends travel off at some angle and thus are incoherent when they reach the output transducer. The second strategy is to absorb the wave energy that reaches the crystal ends. This is typically accomplished by applying a small amount of an acoustically absorbent material---room-temperature vulcanizing (RTV) silicone rubber and vacuum grease are two materials that work quite well - - to the face of the substrate near each end. Though the second method is less elegant than the first, it is simpler to implement and often works better. The topic of packaging itself is covered in detail in Section 6.4.4.

6.2 Basics of Acoustic-Wave Sensor Design and Fabrication

6.2.5

6.2.5.1

347

CHEMICALLY SELECTIVE COATINGS: REQUIREMENTS AND METHODS OF APPLICATION General Coating Requirements

An attractive feature of acoustic-wave-based chemical sensors is that they impose relatively few constraints on the materials that can be used as chemically selective coatings. In brief, the film must be uniform, adherent, thin, chemically and physically stable when in contact with its working medium (gas or liquid), and it must not electrically short-circuit the IDTs. Typically, uniformity in film thickness is not crucial, but can be important in some circumstances. Assuming all parts of the film fall within the acceptable thickness limits discussed in the following, and that the particular film being examined has been calibrated, then under conditions of equilibrium between the analyte in the ambient phase and the film, variations in film thickness are unimportant. If, however, transient measurements are of interest ~ one means of identifying a chemical species is its rate of permeation through a given material then uniformity becomes very important: non-uniformities in thickness will "smear out" the transient response, making identification difficult. Also, if device-to-device reproducibility is important, then the film must be quite uniform, unless all films can be fabricated with the same set of non-uniformities. Uniform coverage of the AW path is of some importance as well. In the case of a SAW, FPW, or APM delay line, the propagating wavefront is typically fairly linear; a film that covers some parts of the wave path to a greater extent than others causes parts of the wavefront to be delayed relative to others. The consequent loss of coherence of the propagating wavefront adversely affects the signal-to-noise ratio. The selected material must adhere to the device surface in such a manner that it moves synchronously with the AW, and must maintain this adhesion in the presence of expected analytes and interferants. The adhesion of thin films to many types of surfaces, including those that are chemically very dissimilar to the coating material, is a much-studied topic outside the sensor field. Often, adhesionpromoting interlayers have been developed for general classes of problems, such as securing a highly nonpolar polymer film to a very polar substrate. Anyone attempting to construct a reliable sensor would do well to examine the relevant literature [12]. Highly conductive coatings (i.e., all metals and most semiconductors) must, of course, be electrically insulated from IDT electrodes in order to prevent shorting; this is not a concern with the planar electrodes of TSM quartz resonators. This is readily accomplished by either deposition using a line-of-sight technique,

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e.g., vacuum evaporation, with a protective stencil interposed between the device and the source; or depositing over the entire surface, and then chemically removing the conductive film from the IDTs (the film's chemical nature must differ considerably from that of the IDT material in this case). A final constraint is that the coating be acoustically thin: many of the derivations of sensitivities to various perturbations given in Chapter 3 assumed any surface layer was thin compared to one acoustic wavelength. A somewhat standard rule of thumb is that thicknesses less than 1% of the acoustic wavelength are appropriate. In fact, whether or not a particular coating thickness is acoustically thin depends critically upon the acoustic properties of that material under the particular set of conditions (temperature, nature and concentration of contacting gaseous species, etc.) being evaluated. In other words, it is the acoustic wavelength in the coating film that is relevant; this can differ appreciably from the acoustic wavelength in the device substrate, particularly in materials such as rubbery polymers, which have vastly different sound velocities than, for example, quartz. In practice, coating thickness from a few A to several/xm have been utilized in sensing applications. In a number of cases, polymer films that are most certainly not acoustically thin have been studied; the viscoelastic nature of some polymeric materials makes them "acoustically thick" even at thicknesses well below 1% of a wavelength. Because other relationships that contribute to the overall response are often nonlinear (e.g., the solubility of organic vapor in the polymer, particularly at high concentrations), the additional nonlinearity introduced by an acoustically thick polymer film does not invariably cause difficulty, provided calibration is carried out over the entire concentration range of interest. There are some situations, however, where an acoustically thick film can cause confusion, such as when (counterintuitive) positive frequency shifts occur as a result of an increase in the concentration of species sorbed by the film due to viscoelastic effects [13]; in such cases, the frequency change vs concentration plot can be multivalued, i.e., two or more very different concentrations of an analyte give an identical frequency shift [14]. 6.2.5.2

Solution-Phase Methods of Application

Numerous methods have been described in the literature for depositing coatings onto piezoelectric acoustic sensors. They generally fall into three categories: solvent casting techniques, vacuum deposition techniques, and vapor-phase deposition techniques.

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Solvent casting is perhaps the simplest coating method. It requires that the coating material be soluble in a solvent that does not chemically attack the piezoelectric sensor device and its transducers. Once the coating material is dissolved, the solution can be spread over the device and the solvent evaporated to leave the desired coating material. Popular techniques in this category include syringe deposition, painting with small brushes or Q-tips, dipping, spraying, and spin casting. The coating reproducibility that is achievable with syringe deposition and painting can range from poor to good depending on the material used and the skill of the person applying the coating. In any of the solvent casting techniques, less than a few micrograms of coating material are sufficient to completely coat the sensor device with a film of the appropriate thickness. Thus, the solutions used are usually quite dilute, the consequence of which is that solvent purity and equipment cleanliness must be carefully considered. Three of the techniques discussed in detail in the following alleviate this concern to some extent: spin coating removes all but a very thin layer of the solution prior to solvent evaporation, allowing higher concentrations of the coating material to be utilized; Langmuir-Blodgett and self-assembled monolayers rely on molecules with very specific physicochemical properties, so many impurities remain behind in the deposition solution rather than codepositing on the device surface. Spray coating is performed by aspirating a dilute solution of the coating through an atomizing nozzle using a compressed-gas propellant (an inexpensive tool available at art supply stores, the air brush, is often utilized for this process). The fine, atomized mist of solution droplets is propelled toward the device where they impact, stick, and evaporate, thereby leaving the non-volatile coating. Like the syringe- and paint-brush-deposited films, the coatings formed by this procedure often have somewhat irregular texture and coverage, but good reproducibility in thickness is possible, particularly if the acoustic sensor is operating during the deposition process: monitoring the sensor output signal during deposition allows the apparent thickness of the coating to be measured in real time. Spin casting generally offers the highest degree of film uniformity and the greatest film-to-film thickness reproducibility. A commercially available "spinner" of the type used in the deposition of photoresist films for lithographic patteming (Section 6.2.4.2) holds the substrate face-up on a motor-driven vacuum chuck that can be spun at hundreds to several thousand rpm. The surface of the device is then "flooded" with a viscous solution of the coating. When the motor is turned on, centrifugal and aerodynamic forces cause all but a thin layer of the solution to "fly" off the device surface; spinning continues long enough

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6. Practical Aspects of Acoustic.Wave Sensors

(10--60 s) for the vast majority of the solvent to evaporate, inhibiting recoalescence of film droplets. The uniformity and thickness reproducibility of the resulting film are often excellent. Film thickness is controlled by varying spinning speed and the solution viscosity (through choice of solvent and concentration of coating material). Dip coating, particularly using the Langmuir-Blodgett (LB) technique [15], can be very reproducible. However, this method does require that the coating have ambiphilic properties (i.e., the individual molecules must possess a polar end and a nonpolar end separated by an intervening chain or body of at least a few atoms) and be somewhat water insoluble in order to form a stable monolayer at the air/water interface of the LB deposition trough. The required trough is commercially available but relatively expensive. For coating materials that do form stable monolayers, the LB deposition technique affords exquisite control of film thickness, since only a single monolayer of coating molecules is transferred to the device surface with each dip through the air/water interface. LB films have the advantage over other materials that they are highly ordered in two dimensions, a result of the alignment of all the molecules at the air/liquid interface prior to film deposition. The consequence of this is more predictable, precisely controlled chemical and physical properties than is available with the molecularly disordered materials produced with many other deposition techniques. A technique closely related to LB film deposition is based on self-assembling monolayers (SAMs) [16]. This class of materials spontaneously forms highly ordered monolayers by simple immersion of an appropriate substrate into a solution of the coating molecule, due to a combination of two chemical interactions. A strong chemical interaction between the "head group" of the coating molecule and the surface orients all the molecules "head down" on the surface. Next, the bodies of the coating molecules order themselves in two dimensions as a result of the cumulative energy of van der Waals interactions between the "backbones" of adjacent molecules. An example is the assembly of a monolayer of nhexadecane thiol on a single crystalline gold surface, shown schematically in Figure 6.5. The tilting of the chains away from the surface normal occurs because the spacing of the three-fold hollow sites on the Au (111) surface, into which the ---SH head groups fit, is slightly larger than the optimal van der Waals distance between adjacent hydrocarbon chains: by tilting at an angle of 20-25 degrees, the chains adjust their spacing to optimize the van der Waals interaction. To build films exceeding a single monolayer in thickness, the first layer must terminate in a reactive group onto which a second monolayer can self assemble [17].

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Figure 6.5 Schematicdepiction of a self-assembled monolayer (SAM) of n-hexadecane thiol (the "tail group" depicted in the figure is a methyl group in this case) on a single crystalline gold surface. Note the ordered nature of the SAM and the tilt of the chains, which accommodates the optimal van der Waals spacing of the hydrocarbon chains while allowing the thiol head groups to sit in regularly spaced sites on the crystalline gold surface.

SAMs have the advantage of providing highly ordered films without the need for a complex LB trough, but the disadvantage that they must be assembled on an ordered surface. Fortunately, the grain size of the polycrystalline gold surface that is produced by thermal or electron-beam evaporation is sufficient to produce high-quality thiol-based SAMs. Though the quartz from which many AW devices are fabricated is also a single crystal and thus might be expected to serve as a suitable SAM platform by itself, the combination of the surface damage inflicted by polishing and the fact that the quartz surface is covered b y - OH groups that are generally n o t in precise registry with the underlying structure precludes the sort of self-assembly process used for alkane thiols on Au. For materials that are neither ambiphilic nor suited to SAM formation, dip coating can still be quite effective, albeit with far less accurate control over film

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6. Practical Aspects of Acoustic-Wave Sensors

thickness and without the advantages of two-dimensional molecular ordering. In this case, a viscous solution of the coating in a solvent is prepared and the device is immersed in the solution. The device is then slowly withdrawn from the solution, leaving a thin film coating the device. Film thickness is controlled by adjusting the viscosity and the withdrawal rate from the solution; a motorized withdrawal system can enhance film thickness reproducibility considerably when compared to manual removal of the substrate. A technique that combines some aspects of SAM formation and "ordinary" (nonoLB) dip coating is solution-phase surface chemical derivatization [18,19]. This method relies upon formation of a strong chemical bond between the surface of the AW device and one functional group of the dissolved coating material. 7 A simple example is the reaction of chlorotrimethylsilane with an ordinary quartz surface, depicted in Figure 6.6(a). A very strong Si-O bond forms between the silane and the quartz surface; the result in this case is the conversion of the hydrophilic, w OH-covered quartz surface to a highly hydrophobic, methylgroup-covered surface. While such a coating is not suitable for absorbing analyte, the altered surface chemistry can be important in studies of interfacial adsorption-related effects. If formation of a thicker layer is the goal, there are two options: (1) a chemically derivatized surface can be used merely to enhance the adhesion of a subsequently deposited film of polymer or other material, formed by one of the many other techniques discussed in this section; (2) a "double-ended" molecule, which can react both with the device surface and with itself to form either a linear or a cross-linked polymer network, can be selected. An example of the latter case is depicted in Figure 6.6b. 6.2.5.3

Vapor-Phase Methods of Application

Coating materials that are not readily soluble can sometimes be deposited using vacuum-based techniques such as vacuum evaporation (thermal or electron-beaminduced) and vacuum sputtering (RF or DC, with or without a magnetic field). Both of these methods rely on the breaking of the coating material's intermolecular bonds, either by thermal means or by the physical impact of energetic gas particles. The liberated coating molecules are then free to travel through the vacuum until they redeposit onto a cool surface. With the materials for which these methods are suitable (see the following), extremely reproducible thin films typically result. Often, a commercially available TSM resonator-based system, as shown in Figure 1.5, is utilized as a monitor of coating thickness, in many cases providing resolution of a few A. 7Note that such films do not possess the two-dimensionalordering that characterizes SAM and LB films.

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353

354

6. Practical Aspects of Acoustic-Wave Sensors

Sputtering, in particular RF-magnetron sputtering (in which a strong magnetic field enhances the coupling of RF power into the gaseous plasma and shields the sample from electron bombardment), is suitable for the deposition of virtually every material, with some important qualifications. Metals generally all deposit quite well, but the resulting films may not have the extremely high purity obtainable with evaporative techniques. A large number of inorganic dielectric materials, including many metal oxides and nitrides, can also be deposited, provided the chemical bonding between metal and oxygen or nitrogen is very strong. When the metal-oxide (or -nitride) bonding is less rugged (e.g., RuO2, ZnO), the addition of some gaseous oxygen (or nitrogen or ammonia) to the plasma-forming gas, which is most often argon, helps keep the stoichiometry of the resulting coating "correct," rather than deficient in o~r or nitrogen. In the case of organic and/or polymeric materials, which typically lack the stability needed to retain their molecular structure during the sputtering process, complex molecules and polymer chains are broken apart into relatively small, reactive fragments, then reassembled on any available surface with little regard for the previous arrangement of bonds and atoms. The resulting films are typically highly crosslinked, one result of which is a marked reduction in permeability to would-be analytes. Thus, except for the possible retention of some basic chemical functionalities, the properties of sputtered organic/polymer films may bear little semblance to the starting materials. A little-explored but very promising method for depositing coatings onto acoustic-wave chemical sensor devices is chemical vapor deposition. A broad spectrum of materials including polymers, metals, semiconductors, metal oxides, and diamond film can be synthesized under reduced pressures in the presence of suitable reactant gases and/or energetic plasma excitation. In the case of polymers, film formation can be a simple matter of introducing a low pressure (a few Ton') of the monomer into a vacuum system, then forming a plasma from the gas in proximity to the surface to be coated. An example is the formation of a Teflon| coating via the plasma polymerization of C2F4 [20], The resulting material, like most polymeric materials made by plasma techniques, is more highly crosslinked than comparable materials made using conventional methods, but is still permeable enough for a number of sensor applications. In general, chemical vapor deposition is capable of producing coatings that are unobtainable by more conventional means. Two additional special cases that can be termed chemical vapor deposition are worthy of mention, since they are the vapor-phase analogues of solution techniques discussed above. These are self-assembling monolayer formation and vapor-phase surface chemical derivatization. In the former, it is necessary only to

6.3 Acoustic-WaveMeasurement Technology

355

expose the appropriate surface to a vapor of the appropriate coating molecule (which must, of course, be volatile), and the ordered film forms spontaneously; the example given in Figure 6.5 works equally well in solution or gas phase. In the case of chemical derivatization, the procedure is identical to that given previously for solution reactions, except that the (volatile) coating molecule is carded in a stream of inert gas; the reaction of Figure 6.6(a) is equally appropriate for gas- or solution-phase deposition.

6.3

Acoustic-Wave M e a s u r e m e n t Technology

6.3.1 I N S T R U M E N T A T I O N

AND COMPONENTS

Before embarking on descriptions of how the various acoustic-wave devices are connected to the equipment necessary to make basic measurements, an introduction to some of the components and instrumentation used to make measurements on these systems is warranted.

Active/passive device:

Active devices require input of power, most often low-level (5-24 V) DC, to achieve their specified function, with the consequence that their output RF power level can exceed RF input power. Passive devices, on the other hand, effect some transformation of the input signal without use of any external power source, so that the output power is always less than or equal to the input power. In the following, simple components are specified as active or passive (note that the addition of an electronic control system, e.g., a motor drive to set the value of a variable attenuator, is not considered grounds for calling a component active). The active/passive distinction is made only for circuit components having an input and output, not for measurement instrumentation (e.g., a frequency counter), the output of which is a visual indication or computer bus-compatible signal.

Amplifier (active):

The amplitude of the output signal is equal to the gain times the amplitude of the input signal. The gain may be positive (non-inverting) or negative (inverting). When an amplifier is operated in saturation, its output power level and/or amplitude s remains constant for small variations in the input signal level; thus, in saturation, the greater the amplitude of the

SBecause all the instrumentation discussed, as well as the devices (with the addition of appropriate tuning components) can be chosen to operate at a single impedance, Z = 50 fI, the relationship between signal amplitude (i.e., voltage, V) and average power (P) is always the same, P = V2/(2• 50 ft).

356

6. Practical Aspects of Acoustic.Wave Sensors

input signal, the smaller the gain. The bandwidth of an amplifier is the range of frequencies over which the gain is at least l/N/-2 of its specified value. Typically, the product of gain and bandwidth is approximately constant for any given amplifier circuit, so amplifiers with larger bandwidth tend to have less gain.

Attenuator (passive):

In many senses the opposite of an amplifier, this device diminishes the amplitude of an input signal by a specified fraction. Variable and step attenuators have a knob or electronic means of varying the extent of attenuation.

Balun transformer (passive):

This high-frequency transformer provides a means for "balancing" (about ground potential) the signal to or from an IDT, i.e., it converts an AC signal varying from + V to ground potential to a signal varying from + V/2 to -V/2.

Directional coupler (passive):

A device having three or more ports that passes the majority of an input signal straight through to its output while splitting off a small, specified fraction of the signal to send to another device (e.g., a frequency counter). The device is directional because any power returning to the "split-off port" from the external circuit is diverted either to a fourth port or to an internal load where it is dissipated.

Filter (passive):

A device that passes only a particular range of frequencies. A bandpass filter passes a specified band of frequencies (its bandwidth is often expressed as a percentage of the Center of the pass band); a notch filter removes a narrow band of frequencies; high- and low-pass filters pass signals higher or lower than a specified cut-off frequency, respectively.

Frequency counter:

Measures frequency by counting the number of cycles in an accurately known time period. The accuracy of the counter's internal time base is therefore critical, making "ovenized" (temperature-controlled) AW devices a common internal timing element of these instruments. The greater the accuracy required, the longer the counter must sample the signal; interpolation techniques allow some counters to report frequencies to accuracies 0.1% of the reciprocal of the sampling time, e.g., a one-second sampling time can give resolution of 0.001 Hz.

Impedance-matching network (passive):

An interconnected arrangement of components, the most important of which is an inductor (often tunable), that matches the impedance of a device (e.g., one transducer of an AW sensor) to the impedance of the instrumentation (e.g., an amplifier) to which it is to be connected. This maximizes the power that can be transferred.

Network analyzer:

An instrument that provides a controlled-amplitude signal to the input of a test device or circuit over a range of frequencies, then

6.3 Acoustic-Wave Measurement Technology

357

records and displays the output of the device/circuit in terms of its magnitude and phase relative to the input as a function of frequency. The network analyzer is the most powerful single tool for the characterization of AW devices. Some of the important features found on many models include a wide range of different display options, the ability to simultaneously measure both reflected and transmitted power, and the capability to Fourier transform frequency-domain responses into the time domain. An ersatz network analyzer can be constructed using a synthesized source and a vector voltmeter (see the following) to measure frequency-dependent response.

Phase shifter (passive): A device that shifts the phase of the output signal by a specified (knob or voltage-selectable) number of degrees relative to its input. Phase shifters function over a specified frequency range, and excessive attenuation of the signal typically results outside this range. Power meter: An instrument that measures RF power, typically utilizing a sensor that converts incident power to heat and measuring the resulting temperature increase.

RF Detector (passive): A device that converts an RF signal into a DC signal, with the DC magnitude being proportional to the RF power. Synthesized oscillator: An instrument that digitally synthesizes a controlledamplitude, controlled-frequency signal. The source is typically computer controllable, allowing a sweep (in discrete steps) of frequency. Vector voltmeter: An instrument that measures the amplitude (voltage) and relative phase angle of two signals, one of which serves as its reference. Typically, the phase difference as well as the ratio, difference, or individual values of the amplitudes of the two signals can be output in analog, digital, or visual display form.

6.3.2

MEASUREMENT OF ACOUSTIC-WAVE DEVICE FREQUENCY RESPONSE

Measurement of frequency response is important for several reasons. The response of an acoustic-wave device to an external perturbation, for example in a chemical sensing application, can be better understood if the device's frequency response is known in advance. Measurement of the frequency response is also important if the most stable and accurate measurement system is to be designed for a particular device. Finally, the change in the frequency response of a device that results from some significant modification of its "surface environment," such as the deposition of a polymer layer or immersion of the surface in a liquid, can

358

6. Practical Aspects of Acoustic.Wave Sensors

provide more information about the effect of that modification, in terms of the physical properties of the contacting layer or phase, than measurement of, say, oscillation frequency alone. In general terms, the frequency response of a device is the magnitude and phase of its "output signal" as a function of the frequency of a (constant amplitude) input signal. 9 The nature of the output signal varies from one type of device to the next, as discussed in detail in the following. The two related variations on the instrumentation that can be used to measure frequency response are discussed next as well. 6.3.2.1

One.Port Devices

One-port devices include TSM resonators, other bulk resonators [ 1,21 ], one-port SAW resonators, and one-port FPW devices (used to measure transducer impedance; see Section 6.3.3.2). Since these devices have only a single (coaxial) electrical connection, the only output that can be measured is the reflected signal, 1~ which travels back from the device along the same signal cable used to transmit the input signal. When a network analyzer is used to measure one-port frequency response, as depicted in Figure 6.7(a), the directional couplers (required to measure reflected power at the same terminal used to apply the input signal) are contained within the instrument and are appropriately switched by configuring the instrument for reflection measurements. Modern network analyzers often have self-contained means of storing, displaying, manipulating, and transferring the resulting response data. Frequency response can also be measured using a (synthesized) oscillator together with a vector voltmeter (VVM), as shown in Figure 6.7b. In this case, a pair of three-port directional couplers is required to provide the reference signal for the VVM and to send the reflected signal from the AW device to the measurement channel of the VVM rather than back into the source. This sort of setup is most conveniently controlled by a computer that sets the synthesized oscillator to a given frequency, records the re-

9An alternate means of expressing the response data, which is sometimes chosen for ease of mathematical manipulation, is in terms of the real and imaginary component of a vector in phase space. For such a response vector, expressed S = a + jb, the magnitude of the signal is given by S = (a 2 + b2) 1/2 and its phase angle is ~ = tan-~(b/a). 1~ reflected signal is also known as S ~ . S~j are "scattering parameters," (S parameters) where i denotes the device port upon which the signal is incident and j denotes the port of measurement. An S-parameter test set, which routes signals to/from the appropriate terminals, can be interposed between the network analyzer and the device under test, allowing all four S parameters to be determined without changes in connections.

Figure 6.7 (a) Diagram of the use of a network analyzer as used to measure one-port frequency response for a TSM resonator. (b) Measurement of one-port frequency response using a synthesized oscillator source together with a vector voltmeter and a pair of directional couplers. suiting magnitude and phase signals from the VVM, then steps to the next frequency, records the response, and so on. Figure 6.8 is an example of the frequency response of a TSM resonator, showing both the magnitude (solid) and phase (dashed) of the reflected signal as a function of the excitation frequency. The various features that appear in this re359

6. Practical Aspects of Acoustic-Wave Sensors

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sponse are explained in detail in Chapter 3. Note that there are two frequencies in Figure 6.8 where the phase angle crosses zero. These are referred to, from left to right, as the series and parallel resonances. The presence of two resonant frequencies, which correspond (from left to right) to minimum and maximum impedance, is best explained in the context of the equivalent-circuit model presented in Chapter 3 for the TSM resonator. Briefly, the equivalent circuit is such that there is one frequency where a parallel capacitor/inductor combination has its maximum impedance, and there is a second frequency where a series capacitor/inductor combination attains its minimum impedance, hence the names of these two resonances.

6.3 Acoustic-Wave Measurement Technology 6.3.2.2

361

Two-Port Devices

Two-port devices include SAW, FPW, and APM delay lines and the two-portresonator variations of these devices. For all the delay lines, the transmitted signal $12 (between ports) is most importand 1. Just as in one-port measurements, a network analyzer is the instrument of choice to measure frequency response; the setup is depicted in Figure 6.9(a) (page 362). Frequency response can also be measured using the synthesized oscillator/VVM combination shown in Figure 6.9(b). As for the one-port measurements, this setup is most convenient when computer controlled. Figure 6.10 (page 363) is an example of the frequency response of a SAW delay line, showing both the magnitude (solid) and phase (dashed) of the transmitted signal as a function of excitation frequency. While the concepts of magnitude and phase are probably familiar in a general sense, their meaning in the context of building a stable oscillator circuit will be discussed in Section 6.3.3.3. The general form of the insertion loss curve of Figure 6.10 is explained in detail in Chapter 3. For comparison, the frequency response of a two-port SAW resonator is shown in Figure 6.11 (page 364). Note that it resembles the response of the delay line, with the addition of a sharp "spike," where the insertion loss is considerably lower, at the center of the pass band. The similarity of the delay line and resonator frequency responses is a consequence of both devices using the same transducer pattern, while the spiked region of much lower insertion loss is a result of the ridge-reflector array utilized to set up a standing wave. Unlike the highest point of the delay-line spectrum, there is no 6-dB theoretical insertion loss limit for the peak of the resonator spectrum - - loss can approach 0 dB. 6.3.3

REAL-TIME MONITORING OF ACOUSTIC-WAVE DEVICES FOR SENSING AND CHARACTERIZATION APPLICATIONS

The most complete and unambiguous characterization of the response of an AW device is always obtained from a complete frequency response spectrum, including all four S parameters. In addition, there are cases, particularly for fairly complex interactions between the AW and a surface film, in which the nature of the response might never be understood without this important tool. There are several important reasons, however, not to attempt the measurement of an entire IIThough not especially useful for sensor measurements, reflected signals (Sit or $22) can be of considerable help in diagnosing IDT problems or in matching IDT impedance.

362

6. Practical Aspects of Acoustic-Wave Sensors

Figure 6.9 (a) Use of a network analyzer to measure two-port-device frequency response. (b) Setup for measuring two-port frequency response using the synthesized oscillator/VVM combination.

frequency response spectrum as a routine means to monitor the real-time response of an AW sensor. First, the amount of time required to obtain and store a frequency response spectrum is in the range of one to several minutes, depending upon the frequency resolution and noise level desired; this should be compared

6.3 Acoustic-Wave Measurement Technology

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to a fraction of one second to obtain, for example, the oscillation frequency and insertion loss from a SAW delay line. Second, the accuracy with which the center of the frequency-response peak can be determined is limited by the resolution of the network analyzer, unless curve fitting is used; even then, the asymmetry of typical response peaks, as well as other variables, makes it difficult to match the fraction-of-one-hertz accuracy available with a carefully designed oscillator circuit. Finally, the expense, complexity, and lack of portability of a network analyzer make it impractical for field applications. An important general distinction can be drawn between one- and two-port devices that applies to all the measurement schemes discussed throughout this chapter: perturbations of one-port devices result in significant changes in device impedance, without major changes in phase; for two-port devices, perturbations

364

6. Practical Aspects of Acoustic-Wave Sensors

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alter the phase difference and, in many cases, amplitude measured between input and output transducers, without major effects on the device impedance. It will prove helpful to keep this major difference in mind throughout the descriptions of various measurement systems. It is not the goal of the following subsections to provide all the information necessary to build various oscillator and control circuits "from scratch," although appropriate references are provided for such an undertaking. Instead, the general principles and the generic components utilized for such circuitry will be described.

6.3 Acoustic-Wave Measurement Technology 6.3.3.1

365

Simultaneous Measurement of Acoustic-Wave Velocity and Attenuation

Though a network analyzer may not be ideal for field use or even routine laboratory measurements of real-time perturbations, it is realistic and, in many cases, very important to monitor both the velocity and attenuation simultaneously. To date, the majority of AW sensor research has relied solely on measurements of velocity perturbations (typically via frequency shifts for an oscillator circuit). Such an approach is adequate if it is knov~n in advance that all perturbations will affect AW velocity alone; such perturbations include mass changes and purely elastic changes in mechanical properties. The great power of measuring attenuation changes is that they give a very clear indication when "something else is going on," providing a clear indication of whether or not it is safe to interpret a response in terms of a mass change alone. Such measurements require the use of either a vector voltmeter, one or two RF detectors, or the analog output from the automatic gain control (AGC) circuit of an AGC amplifier.

6.3.3.2

One-Port Devices

Because TSM oscillators have "been around" for over 50 years, quite a number of circuits to measure their response have been proposed, fabricated, and tested. The frequency of operation of TSM resonators (typically < 20 MHz) allows circuits to be constructed using "ordinary" components and printed circuit boards. Instruments and fixtures are commercially available from a number of vendors (see Appendix D) that utilize fairly simple oscillator circuits incorporating the TSM resonator as the principal frequency-control element. These systems are sold primarily for monitoring the deposition of metal films via evaporation or sputtering in a vacuum environment. The "operator" must typically input the density and acoustic impedance of the metal to be deposited, and the instrument then displays film thickness as deposition proceeds. These systems can also be utilized for gas-phase sensing applications, provided the TSM device is not coated with any particularly lossy materials: these can cause so much damping that oscillation ceases. The systems provide information derived only from the resonant frequency; there is no indication of damping except in the instance that oscillation ceases entirely. As discussed in Chapter 5, a number of researchers in the field of electrochemistry have utilized TSM resonators for the characterization of a wide range of electrochemical processes. Several practical problems had to be solved before

366

6. Practical Aspects of Acoustic-Wave Sensors

such measurements could be made. First, the conductive electrolytes that must be used in electrochemical experiments short-circuit the two electrodes (located on opposite faces of the TSM resonator) of a fully immersed device, so fixtures that expose only one face of the device to the liquid were devised. Second, the oscillator circuits discussed in the previous paragraph are generally unable to maintain crystal oscillation in the presence of liquid (a result of damping), so a number of circuits that can tolerate the greater amount of damping associated with liquid contact were devised [22-28]. Finally, the simultaneous use of the immersed electrode as part of the RF transducer and as the electrochemical working electrode created some complications. 12 Circuits that overcome all three of these obstacles to varying degrees have been described in detail by several authors [24,25,28], and a number of these circuits have been critiqued by Barnes [22], who has suggested two new and improved circuits for this application. Instrumentation designed specifically for making electrochemical measurements using TSM resonators is now available from at least two commercial vendors as well (Appendix D). As in the case of the vacuum/gas-phase circuits and instruments, the resonant frequency is typically the only measured parameter. In addition to commercial systems, there are quite a number of oscillator circuits that can be built from relatively inexpensive components to perform the essential measurements without the functions and convenience of a packaged instrument [22-28]. Both the commercial systems and most of these home-built oscillator circuits yield just one piece of information: the resonant frequency of the TSM device. While this is sufficient for mass-loading-only applications like vacuum deposition of metal films, for some electrochemical processes, and even for appropriately selected chemically sensitive films, it can fall short when changes in the mechanical properties of a surface layer or contacting medium are significant [29]. For both damped (liquid) and undamped environments, the ideal oscillator circuit should precisely track either the series or parallel resonance (see Section 6.3.2.1); there is some evidence that tracking the series resonance is advantageous [29]. In practice, however, oscillator circuits track one of these two frequencies only approximately - - some circuits actually do this job quite poorly --with the extent of deviation from true resonance increasing with damping. Recently, new circuits have been designed that provide closer tracking of true 12Fortunately, the working electrode is typically near ground potential (often at virtual ground) in electrochemical instrumentation, with the variation in potential (relative to earth ground) occurring at the reference and/or counter electrodes; modificationof the electrochemical instrumentation to put the workingelectrode at true earth ground potential makesconnection to the RF circuitry more straightforward.

6.3 Acoustic-Wave Measurement Technology

367

series resonance, even in damped environments, and provide output signals for both resonant frequency and oscillator damping [29]. A schematic of one such circuit is given in Figure 6.12. Conceptually, one-port SAW oscillator circuits are very similar to those described for one-port TSM resonators, the principal difference being a significantly higher frequency of operation (100s of MHz rather than a few MHz). Just as for TSM resonators, an external circuit is required that is capable of driving the device at resonance and tracking changes in the frequency of resonance as the device impedance is perturbed.

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368

6. Practical Aspects of Acoustic.Wave Sensors

One-port FPW measurements, typically using a network analyzer, yield the input impedance of the transducer, the real and imaginary components of which can be used to determine the density and viscosity of a fluid contacting the device. 6.3.3.3

Two-Port Devices in Oscillator Circuits

The most common of the three systems for making real-time measurements using two-port AW delay-line-based devices is the oscillator loop, shown schematically in Figure 6.13a. Note that only two components are shown in the schematic" the AW delay line and an amplifier. The AW device provides a feedback path for the amplifier. For stable oscillation to occur, i.e., for the signal to add coherently to itself after having traversed the loop, the signal must return to its starting point (1) having equal amplitude and (2) being shifted in phase by an integral multiple of 2~r radians. These two conditions are easiest to understand when viewed graphically. Figure 6.10, the frequency response of a 98-MHz SAW delay line, shows curves for both the insertion loss and the phase shift of the device. Conditions (1) and (2) above are simultaneously satisfied at the frequencies where the gain of the particular amplifier chosen is greater than or equal to the insertion loss (solid curve) a n d the phase shift (dashed curve) is zero. For the sake of argument, assume that the gain of the amplifier being used is 25 dB. From Figure 6.10, there are three points, at approximately 96.1, 96.5, and 96.9 MHz, where conditions (1) and (2) are both satisfied and oscillation can occur. 13 To create a high-stability AW delay line-based oscillator circuit and acquire real-time data from it, several additional components are required, as shown schematically in Figure 6.13(b). The components and their functions include: an amplifier; 14 a band-pass filter to prevent spurious oscillation at unwanted frequencies; one or more variable attenuators to adjust the total gain of the circuit; a tunable phase shifter to adjust the round-trip phase shift of the circuit; several directional couplers to send fractions of the loop signal to measurement instrumentation; a frequency counter; a vector voltmeter or other means to determine insertion loss by comparing AW device input and output amplitudes; an impedance-matching network for each IDT; and a computer for data acquisition. 13Althoughit may be clear how the amplifier and AW device produce a stable oscillator, the initial source of the signal that starts the oscillation is not as obvious. The answer lies in ever-present noise, small in amplitude though it may be, that is invariably picked up and amplified by the amplifier/AW device combination. 14Depending upon amplifier gain and a variety of factors pertaining to the device, its coating, and their application, it may be necessary to cascade (connect in series)more than one amplifier.

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Figure 6.13 (a) Two-port AW delay line-based oscillator loop. (b) Delay-line-based loop of part (a), showing additional components necessary to create a high-stability circuit and acquire real-time data from it.

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6. Practical Aspects of Acoustic-Wave Sensors

A few points regarding the circuit of Figure 6.13(b) warrant additional discussion. The order in which the various components are arranged can be varied somewhat, but the arrangement shown has proven to yield the highest stability. For example, placing the bandpass filter immediately after the amplifier removes any amplifier-generated harmonics that might "confuse" the frequency counter. Although stable oscillation can be achieved without the use of impedancematching networks for the IDTs, impedance matching typically eliminates 10-20 dB of insertion loss, requiting less amplifier gain. 15 The importance of both the phase shifter and the attenuator can best be clarified by referring to Figure 6.10: adjustment of the phase shifter causes the phase response (dashed curve) to move left or right along the frequency axis, permitting a zero-phase point to be made to coincide precisely with the frequency of minimum insertion loss; adjustment of the attenuator shifts the insertion loss curve downward along its vertical axis, the eventual consequence of which is to leave one, unique frequency where the gain of the amplifier is sufficient for oscillation and the round-trip phase shift is simultaneously zero. The presence of the vector voltmeter is not at all necessary for stable loop oscillation, but it makes possible the measurement of AW attenuation. Recall that a VVM measures both the amplitude and phase difference of the two input signals. In the present configuration, the phase information is superfluous, since phase changes are directly proportional to frequency shifts, which can be measured with greater accuracy. To eliminate the VVM altogether (without losing the ability to measure attenuation changes), it can be replaced either by a pair of RF detectors (one attached to the coupler for each IDT), the DC signals from which indicate the magnitudes of the input and output signals; or by a single RF detector at the device output if it is known with certainty that the amplifier driving the device is in saturation (constant power output) at all times; or by using the analog output from an AGC amplifier used to drive the device. Note that the sort of oscillator circuit shown in Figure 6.13(b) can be constructed by the interconnection of line-powered modular instrumentation [30], by the use of printed-circuit board-mounted, DC-powered components [31], by the use of surface-mount devices on a suitably metallized substrate, or even on a sin~Note that the theoretical minimuminsertion loss that can be obtained for a delay line employing simple di-directional IDTs is 6 dB, meaning the output signal has at most 25% of the amplitude of the input. This is a consequence of the bidirectionality of the IDTs, which causes half the input signal to go in the "wrong" direction (away from the output IDT) and, for reasons of reciprocity, means that at most half the acoustic power incident on the output IDT can be transduced to electrical power. In practice, some of the authors have obtained best-case insertion losses of approximately 8 dB with aluminum IDTs and about 11 dB with Au-on-Cr IDTs.

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gle Si integrated circuit, with ZnO-on-Si technology utilized for the AW delay line [32]. Relative to SAW and APM devices, the low frequency of operation of the FPW and TSM devices, typically between one and ten MHz, permits the use of inexpensive integrated amplifiers and other electronic components, as well as low-cost RF cable fittings. The general configuration of the oscillator circuit shown in Figure 6.13(b) can be used for SAW, APM, and FPW delay lines, as well as two-port SAW resonators. In many cases, the bandpass filter plays a crucial role, since different acoustic modes can propagate through the same substrate; the bandpass filter allows selection of one mode or the other. For example, the SH-APM propagates at 1.6 times the frequency of the SAW in ST-cut, X-propagating quartz. In addition, some acoustic waves (e.g., the APM) have multiple modes that propagate at different frequencies and may have differing sensitivities to mass loading and other perturbations; the bandpass filter allows selection of a particular mode. Note that in the presence of a contacting liquid, the SAW is highly damped; nevertheless, the filter is still necessary owing to the presence of several other, less mass-sensitive plate modes just above the SH-APM in the frequency spectrum. Although the instrumentation outlined above is most often used for SAW delay line-based circuits, it is also suitable for use with two-port SAW resonators. Recalling from the previous section that SAW resonators can be configured with only one port, the function of the second (or output) port deserves explanation. It is instructive to think of the input IDT as the driving transducer that provides the energy for the standing wave, just as in the one-port case. The function of the output IDT, then, is to "sample" this acoustic mode, providing a signal to the amplifier, which in turn drives the input IDT. Thus, a sensor response occurs when perturbation of the acoustic cavity (i.e., the ridge-covered surface of the device) changes its resonant frequency. The relationship between perturbations occurring over a limited fraction K of the total wavepath and the fractional changes in velocity and frequency has been given in Chapters 4 and 5: Af

Av "-

fo

K

......

vo

,

(6.1)

It is appropriate to point out here that there is more to this relationship than meets the eye. Referring again to the frequency response spectrum of Figure 6.10, the effect of a perturbation that is confined to the region between IDTs (but does not affect the region of the substrate underlying the IDTs themselves) is to shift the phase spectrum along the frequency axis without affecting the insertion loss curve. Note that if the magnitude of such a perturbation is sufficient, the circuit be-

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6. Practical Aspects of Acoustic-Wave Sensors

comes "detuned," in the sense that the zero-phase point no longer coincides with the point of minimum insertion loss. The consequence can be mode hopping, in which the frequency of oscillation hops (as much as several MHz) from one zerophase point to the next, effectively retuning the circuit to a frequency of lower insertion loss, but also creating much havoc for the person trying to interpret the results of the perturbation. Conversely, if only the region underlying the IDTs is perturbed, the consequence is to move the insertion loss curve of Figure 6.10 horizontally without moving the phase curve. Clearly, the method of choice is to simultaneously perturb the entire wavepath (r = 1). The result of a perturbation will then be that both curves in Figure 6. l0 move in unison along the frequency axis and the oscillator self tunes as the perturbation progresses. In some cases, notably when conductive films are utilized for sensing, this is not possible, in which case the perturbation must be small or mode hopping must be anticipated. Note that the argument for perturbation of the entire wavepath applies not only to SAW devices, but especially to APM devices, for which there are typically a large number of insertion loss peaks, similar in magnitude and closely spaced in frequency, enhancing the tendency for mode hopping. Even when the perturbation occurs on the face of the APM substrate opposite the IDTs, it is still desirable to perturb the entire length of the wavepath, including the region directly opposite the IDTs. Finally, a short discussion of attenuation measurements is appropriate. The circuit of Figure 6.13(b) shows the use of a vector voltmeter to monitor the insertion loss of the AW device. Insertion loss is readily converted to attenuation, a, normalized for wavenumber, k, using Ate k

_

_

~

ALt 54.6 Nx

(6.2)

in which ALt is the change in insertion loss expressed in dB and Nx is the center-to-center IDT spacing expressed in acoustic wavelengths.

6.3.3.4

Two-Port Devices: Propagation Measurements

In propagation measurements, a signal of fixed frequency and amplitude is input to one IDT using an external oscillator, while a vector voltmeter monitors changes in AW amplitude and phase shift between transducers; this is illustrated schematically in Figure 6.9(b). At constant frequency, changes in wave velocity are proportional to changes in phase according to

6.3 Acoustic-Wave Measurement Technology

Av V0

=

A~

.....

~

'

373

(6.3)

in which th0 = 21rNx + thr, where t~r is the phase difference (in radians) displayed by the VVM; A~b is the change in thr as a result of the perturbation. Although small phase shifts typically cannot be measured with sufficient accuracy to provide the same sensitivity as oscillator loop-based measurements, propagation measurements are not subject to the mode hopping that can afflict an AW oscillator circuit under certain circumstances. This is fortunate because sudden, large shifts in phase (>2~r radians) are likely to result in additive errors of factors of +_2nlr (n = integer) in the measurement of A4~ (phase is measured to +_It). In contrast to the discussion in the last few paragraphs of the preceding section on oscillator circuits, note that perturbation measurements are best made when the region underlying the IDTs is not at all perturbed, so that the fixed-frequency source continues to match the frequency of least insertion loss of the IDTs as the perturbation progresses. Thus, perturbation measurements are best made when: (1) highest accuracy is not necessary; and (2) a substantial perturbation only to the region between IDTs is anticipated; or (3) such a large perturbation is anticipated that it would be difficult to differentiate between a mode hop and the perturbation itself (e.g., the transition from a dry surface to one covered with liquid); or (4) such a large change in insertion loss is anticipated over the course of the measurement (e.g., a viscoelastic transition in a polymer layer) that it is not possible to set up and maintain a stable oscillator circuit.

6.3.3.5

Two-Port Devices: Phase-Locked Loops

A phase-locked loop is a bit of a hybrid of the oscillator circuit and the propagation measurement system discussed in the previous two sections. The instrumentation setup, shown in Figure 6.14 (page 374), closely resembles that used for propagation measurements. The phase is locked, or rather maintained at a constant value, in the following manner: initially, before any perturbation occurs, the phase difference between the two IDTs of the AW device is recorded; when a perturbation affects this phase difference, the frequency of the signal from the source is adjusted to return the phase to its initial value. In this way, the source frequency is constantly "retuned" to the extent dictated by the perturbation, and the phase difference between the two transducers remains "locked." The setup shown in Figure 6.14 utilizes a computer to monitor the phase difference, compute the change in frequency required to maintain the phase at its

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6. Practical Aspects of Acoustic-Wave Sensors

Figure 6.14 Computer-controlled phase-locked loop configuration for two-port AW device measurements. The computer adjusts the output frequency of the synthesized frequency source to keep the phase delay between transducers, as measured by the vector voltmeter, constant. initial value, then send an appropriate signal to the synthesized source. Thus, this system is known as a computer-controlled phase-locked loop [8]. For the appropriate calculation to be made for setting the new frequency, the phase slope (change in phase per unit change in frequency) must be measured initially, before any perturbation. In practice, the phase slope may vary somewhat as a function of changes in the AW device surface, its coating, and the environment. It is therefore helpful for the computer program to iteratively adjust the source frequency in progressively smaller steps to fine tune the phase difference, and also to redetermine the phase slope when three or four iterations fail to properly tune the phase. Like oscillator circuits but unlike the perturbation setup, it is best for the area of the substrate underlying the transducers to be perturbed along with the rest of the wavepath. The reason is that the constant retuning of the source frequency to track the perturbation eventually leads to detuning relative to the point of minimum insertion loss of the IDTs. The main advantage of the computer-controlled phase-locked loop configuration is that it is nearly as "rugged" as the fixed-frequency perturbation measurement system in terms of continuing to function during large changes in at-

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tenuation, with the difference that it is suited to the use of films that cover the entire AW substrate, including the region beneath the IDTs.

6.4

Controlling the Sensor E n v i r o n m e n t

Acoustic-wave devices are sensitive to a large number of physical and chemical measurands. These include such parameters as temperature, pressure, acceleration, stress, and the adjacent medium's density, viscoelastic properties, and electrical conductivity. Indeed, it is this wide range of measurand sensitivities that makes AW devices attractive for a wide variety of sensor applications. However, since one is interested in exploiting only one of these sensitivities for a particular application, all other responses become undesirable interferences. Thus, it is essential that the sensor environment be carefully controlled to eliminate the effects of sensor cross-sensitivities. 6.4.1

TEMPERATURE EFFECTS AND THE NEED FOR TEMPERATURE CONTROL

Temperature has a direct effect on the operation of all acoustic-wave devices. Changes in temperature produce changes in the density of the substrate, which changes the velocity of the AW. Since wave velocity is the most commonly used of the two fundamental AW responses, there is a temperature-dependent component to the sensor output signal. While efforts to identify piezoelectric substrate materials that have a zero temperature coefficient have yielded a significant reduction of temperature sensitivities, no substrate materials that have negligible temperature coefficients are available in practice. In addition, the physical properties of the chemically sensitive coating material are often temperature dependent. Finally, the fact that whatever material is chosen to package the sensor will, in general, have a different coefficient of expansion than the device substrate compounds the problem. There are three main methods by which the effects of temperature on AW sensors can be minimized: (1) selection of low-temperature-coefficient materials; (2) incorporation of a temperature sensor and compensation circuitry or software; and (3) active control of the sensor temperature. High-precision sensor applications frequently demand that all three techniques be used. Several low temperature-coefficient materials have been characterized for AW applications. The ST and AT cuts of quartz provide nominal zero temperature coefficients near room temperature for SAW and TSM resonator devices, re-

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6. Practical Aspects of Acoustic-Wave Sensors

spectively. For thin-film-based devices, careful balancing of the thickness of the piezoelectric layer and an underlying layer having a temperature coefficient of stiffness with opposing sign results in a very small temperature coefficient at a selected temperature. An excellent example of this is the ZnO-on-Si devices fabricated by Martin, for which an interlayer of SiO2 with the appropriate thickness provided a second-order temperature coefficient of - 5 2 ppb/(~ 2 at room temperature [2]. To place the problem of temperature drift into perspective, consider the following practical example. One low-temperature-coefficient piezoelectric substrate, ST-quartz, has a temperature coefficient that exhibits a parabolic dependence on temperature with a maximum "turnover" temperature around 20~ That is, the SAW velocity is not affected by temperature at 20~ Of course, it is quite difficult to run a SAW device at exactly 20.00~ since it is heated by the power used to excite the AW and by the nearby circuitry. At a more realistic operating temperature of 30~ the ST-quartz typically exhibits a temperature coefficient of about 4 ppm/~ Thus, at 30~ a 158-MHz SAW delay-line oscillator would experience a resonant frequency shift of about 632 Hz/~ (with a coatinginduced temperature effect, this value could be many times larger). Depending on the design of the remainder of the oscillator circuit, the same device could produce short-term frequency "noise" of less than 10 Hz, which suggests that the temperature must be controlled to _+0.016~ if the temperature drift is not to exceed the frequency noise. This is a challenging requirement, particularly for portable instrumentation. The need for stringent temperature control can be relaxed somewhat by either using a second SAW device as a temperature reference or by correcting the SAW frequency data numerically using data from a nearby temperature sensor [33]. By using another nearby SAW oscillator as a reference and taking the difference of the two SAW oscillator frequencies, it is possible to reduce the magnitude of the observed temperature drift by a factor of 10 or slightly better. 16 The resulting temperature sensitivity would then be about 60 Hz/~ which still demands temperature control of about _+0.2~ if temperature effects are to be eliminated. Thus, considerable attention to temperature control is essential unless the anticipated signals are so large as to make the temperature drift insignificant.

16A second advantage of mixing the signals from sample and reference SAW devices, and then using a low-pass filter to select the difference frequency, is that the resulting signal, rather than being in the 100 MHz-and-up range, will be between a few kHz and a few MHz, allowing it to be counted using simpler, less expensive instrumentation.

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Temperature variations can also produce drift due to stresses imposed on the acoustic device by packaging that has a different coefficient of expansion than the substrate material. If the acoustic device is rigidly mounted onto a material that expands at a different rate with temperature, then bending stress will be applied to the device, perturbing the AW velocity. This problem is discussed in more detail in Section 6.4.4. Changes in the physical properties of the coating material itself can also worsen the effects of temperature variation. At the very least, all organic materials have larger temperature coefficients of expansion (near room temperature) than do quartz and similar substrate materials, so the dependence of AW velocity upon temperature is greater m in some cases m a n y times greater ~ for a device coated with such a film than for a bare device. An even more severe perturbation occurs when a polymeric material undergoes a significant viscoelastic change near the temperature of operation, such as a glass-to-rubber transition, melting, or a long-chain-related relaxation (see Chapter 4). Finally, at a temperature where the density and sound velocity in the film are such that the film thickness corresponds to an integral multiple of one-quarter of the acoustic wavelength in the f i l m , resonant energy transfer occurs, the result of which is a major perturbation of AW velocity and attenuation (see Chapter 3) [14]. Temperature control may also be required to control the sensitivity of the coating to the analyte. Apart from the aforementioned temperature sensitivity of coating physical parameters, the partition coefficient between analyte in the ambient gas or liquid phase and that sorbed by the coating is typically exponentially dependent on absolute temperature. For simple physical interactions, such as an organic solvent being sorbed by a polymer film, the largest contribution to this effect is the strong temperature dependence of the solvent's vapor pressure. The sensitivity of the coated device is thus temperature dependent [34]. Finally, the rate of response of a coated sensor is temperature dependent. When measurements are made under conditions of equilibrium between free and sorbed analyte, changes in kinetics present no problem unless the response becomes too slow for a chosen application. In some cases, however, the rate of response can be used to identify the species being detected; an example is the molecular sizedependent diffusion of organic solvents into some polymer films [35]. In this case, failure to accurately measure and/or control temperature could lead to misidentification of the analyte. Clearly, temperature has a significant effect on the performance of AW devices. To achieve the highest levels of sensor performance, practical devices require incorporation of temperature sensing and compensation circuitry, active

378

6. Practical Aspects of Acoustic-Wave Sensors

control of the device temperature, and selection of low-temperature-coefficient materials, both for the device substrate and for the chemically sensitive coating. 6.4.2

PRESSURE EFFECTS

Ambient pressure can affect AW devices primarily in two ways: it can hydrostatically compress the device, resulting in small perturbations in the wave velocity and length of the AW path; and it can affect the density of the fluid medium in contact with the device. Generally, the sensitivity of AW devices to hydrostatic pressure fluctuations is so slight (e.g., 0.1 ppm/atmosphere variation in wave velocity for a quartz SAW device) that it can be neglected in most situations. On the other hand, changes in the density of the fluid medium adjacent to the acoustic device surface caused by pressure variations can result in significant changes in the wave amplitude and velocity [36]. In this regard, AW devices that have primarily in-plane (e.g., shear horizontal) wave displacements are less affected than those having longitudinal or vertical shear wave displacement components. Like temperature effects, pressure-related wave velocity changes can be at least partially compensated by use of a reference sensor and signal subtraction. The ambient pressure can also affect the baseline signal of an AW device through two rather indirect means. In the first, ambient pressure affects the rate at which heat is dissipated from the device, which in turn affects the device temperature, hence the AW velocity. This effect is usually small, because power dissipation in devices is typically in the mW range and also because conduction is often the dominant means of heat transfer. The second effect has to do with adsorption, desorption, and condensation. A major pressure change can perturb the equilibrium concentration of sorbed species (e.g., water) on the sensor/coating surface. This gives the impression of a pressure-related transient, although it is actually a result of a change in the partial pressure of the sorbed species in the contacting vapor phase. 6.4.3

FLOW-RATE EFFECTS

In chemical vapor sensor applications, it is often necessary to flow the vapors to be monitored over the AW sensor. Air-flow rate can affect both the sensor baseline signal and the apparent response time of the sensor. The baseline signal is affected because air flow over the device can cause cooling, which results in a small shift in the device temperature and, therefore, wave velocity. This effect has been exploited to construct an AW-based flow-rate sensor by heating a SAW device and using the device frequency as a measure of its temperature [37]. For

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chemical sensors, this is not much of a problem when flow rate is low or can be held fairly constant (i.e., within +_20% of its mean value). The flow rate affects the apparent response time in three ways. First, in order to have flow, the sensor must be contained in a cell having a finite volume, as well as inlet and outlet ports. If the flow rate through the cell volume is small compared to its volume, then it will take a long time before a change in vapor concentration outside the cell can be accurately represented in the cell. This is only a problem if the cell volume is large (e.g., 10 cm 3) and the flow rate is low (e.g., 10 cm3/min). In practice, the equivalent of four or more cell volumes of sample are required to thoroughly flush the cell. In the preceding example, it would take four minutes before the sensor would be exposed to a representative sample. The second way that flow rate affects the response time of the sensor is by controlling the rate at which vapor molecules can strike the surface of the coating. At low flow rates, and with appropriate cell design, the flow over the sensor surface can be laminar. This may actually increase the apparent response time of the sensor because the vapor molecules will need additional time to diffuse through the boundary layer immediately above the coating. Turbulent flow, which is encountered at higher flow rates and/or particular cell geometries (e.g., flow impinging directly on the device surface) can result in faster response since the boundary layer thickness is reduced. Finally, the nature of the vapor/coating interaction may result in a dependence on the rate at which vapor molecules are delivered to the coating. This is particularly true for reactive coatings that essentially integrate the dose (i.e., concentration-time product) of vapor to which they are exposed. Low flow rates deliver small amounts of vapor molecules per unit time and produce correspondingly small rates of signal change per second. Flow-rate effects are also possible if the transient response of the sensor is utilized to differentiate chemical species [35].

6.4.4

SENSOR PACKAGING CONSIDERATIONS

All acoustic-wave sensor devices must be packaged in order to be used, and the best packaging method is highly dependent on the application planned for the sensor. The package performs several critical functions including: providing a mechanical mounting point for the device; providing an electrical interface to the device; providing access to the measurand; and providing a heat sink and/or temperature-controlled platform for the sensor. Optimizing a package for one of these criteria may adversely affect one of the other concerns. Thus, it is often the case that designing a suitable package for a given application requires as much

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6. Practical Aspects of Acoustic-Wave Sensors

or more effort than designing the AW sensor itself. Packaging should be considered at the earliest stages of any new device development program. In the case of AW chemical sensors, the package often defines the "cell" volume around the device. As discussed previously, it is desirable that the so-called "dead-volume" of the cell be minimized in order to provide improved sensor response times. The sensor package must be constructed of materials that are able to withstand the environment in which the sensor must function. Conventional integrated circuit packages that are plated with gold or nickel are quite suitable for many applications; however, materials for associated tubing, seals, and adhesives must be selected carefully. Many plastics, while chemically inert, have significant permeability and/or porosity, which can result in easy contamination as well as slow and inaccurate responses. Many adhesives emit vapors during cure that can form thin films on the package and sensor or, worse, react with coatings applied to the sensor. The main electrical requirement of the package design is optimization of the signal-to-background ratio, which requires that stray capacitance, direct electromagnetic feedthrough, and electromagnetic interference be minimized. Metal packaging, though expensive, is desirable because it affords improved electromagnetic shielding of the sensor device; the shielding advantage of metal is especially important when multiple sensors will be placed in close proximity to one another or when electromagnetic interference (either to or from) the sensor is a concern. Stray capacitance, typically contributed by inappropriately shielded connecting leads, is most troublesome for one-port and for relatively highfrequency (> 200 MHz) two-port devices. Stray capacitance is minimized by utilizing appropriate impedance (50 I~) cable and connections from the instrumentation right up to the AW device or test fixture; a few mm of bare, unshielded wire can cause significant degradation in the signal-to-background ratio. The test fixture must be well shielded and grounded, typically by connection of the metal body of the fixture to the shield of the coaxial cable. Such test fixtures are commercially available for quartz TSM resonators for use in the gas phase and in liquids (see Appendix D). Direct electromagnetic feedthrough occurs when the leads to the input transducer act as transmitting antennas and the leads from the output transducer act as receiving antennas, thus providing a signal path that circumvents the AW device itself; this is only a problem for two-port devices. Like stray capacitance, this problem is avoided by using appropriately designed cables and connectors from the test instrumentation right up to the device itself; short lengths of unshielded connecting leads can be isolated from one another by intervening regions of metal that are well grounded.

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The sensor package also plays a critical role in thermal management of the sensor device. Heat generated by the sensor must be discharged through the package. Likewise, thermal contact between reference sensors and active temperature-control hardware is usually established directly with the package and, thus, only indirectly with the sensor device itself. Metal packaging also performs well in this application due to its high thermal conductivity. The physical means of attaching the device depends on a number of factors, including the nature of the acoustic mode and the sort of environment with which the device is to interact. An often-neglected aspect of acoustic sensor packaging is the thermally-induced stresses that can be imposed on the acoustic device as a result of mismatched thermal expansion coefficients between the sensor device and the package. Such stresses can contribute greatly to observed sensor baseline drift with temperature. Selection of packaging materials whose thermal expansion coefficients are similar to that of the device is effective, as are "singlepoint" sensor mounting schemes that rigidly fix only a single edge or comer of a device, preventing thermal stress. Compliant adhesives are normally favored over rigid materials, since they can mediate some of the mismatch between device and package. Possible chemical and physical degradation of the adhesive material as a result of contact with the environment must be considered as well. A second packaging scheme that minimizes thermal stress is to physically constrain the device without any rigid attachment. This can be accomplished by locating the device in a slightly oversized well and holding it down using springloaded pins that also serve as electrical contacts to the IDTs. Mounting is more complicated for all those modes that cause motion of both faces of the substrate m TSMs, FPWs, and SH-APMs. These devices must typically be attached by their edges, outside the region of appreciable surface movement. When detection in a liquid environment is planned, the means of mounting and packaging must also include provisions for introducing the liquid to the active region of the device and, if the liquid is at all conductive, means to prevent the solution from short-circuiting the transducers [4]. The actual package or substrate in/on which an AW device is contained/mounted has many forms. These include flatpacks--small, metal containers having a bottom and four sides through which multiple, hermetically sealed electrical leads pass; electronic device headers w metal platforms, with leads attached, that are used to mount electronic components of all types; printed circuit (PC) boards; coplanar w a v e g u i d e s - a subset of PC boards that have signal-carrying traces and surrounding ground planes carefully designed with widths and spacings to maintain a desired impedance; and custom fixtures, machined according to a design that minimizes stray capacitance and direct

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6. Practical Aspects of Acoustic-Wave Sensors

feedthrough. Of these variations, flatpacks, coplanar waveguides, and custom fixtures are best suited to higher frequencies. Flatpacks and headers typically have mating lids or covers that can be welded or soldered on, providing protection from electromagnetic interference, while the other platforms may require customized closures. It is tempting to leave an appropriately supported sensor "out in the open" to provide access for the environment to be monitored, but better stability and immunity to noise are provided by covering the device with a tightfitting, well-grounded metal cover equipped with the minimum practical size openings necessary to introduce the test gas or liquid. Once a device is physically mounted in/on an appropriate substrate or fixture, electrical contact must be made to the transducers. The lithographic layout for each IDT typically includes a metal area on the device substrate to which appropriate leads can be attached, called a bonding pad. One of three general techniques is typically utilized to make the connection between external wiring and the transducer's bonding pads. Wire bonding utilizes a specially designed commercial instrument to literally weld the ends of a fine wire (15-75/xm in diameter) from the device bonding pad to the contact pin/pad on the support or package. One or a combination of highly localized heating and ultrasonic energy is used to form the tiny weld; bond wire is typically made from Au or AI. Conductive epoxy can be used to manually attach wires to device electrodes; silverloaded, polyimide-based epoxy is one such material. The third technique involves the use of pressure-based contacts, including spring clips and "pogo pins," tiny spring-loaded cylindrical metal pins. Of these three methods, wire bonding requires the most complex apparatus but produces the most reliable, low-resistance, noise-free contacts; conductive epoxy is the easiest and cheapest, and can work very well if the epoxy is properly cured to make the contact resistance low; spring contacts allow the most rapid exchange of devices and can be used as part of a low-stress packaging scheme, but require careful engineering to implement a reliable, noise-free contact.

6.4.5

REMOTE SENSOR LOCATION SCHEMES

Some applications require that sensing be performed in a location that precludes the presence of RF electronic circuitry. For example, the location may be subjected to extreme temperatures or pressures, or it may simply not be large enough to allow room for the circuitry. In all of these situations, mounting of the sensor remote from the RF electronics is necessary. For two-port devices (e.g., SAW delay lines), separation of the sensor from the electronics can be accomplished by simply connecting a transmission line m

6.4 Controlling the Sensor Environment

383

a coaxial c a b l e - between the AW sensor and the electronics. In general terms, this is possible because the number of wavelengths comprising the delay line, typic~illy over 100, is large compared to the number of wavelengths contained in the cables. 17 The impedance of both the sensor and the RF electronics must match that of the transmission line, which requires additional hardware but poses no fundamental problems; for a SAW delay line, impedance can be matched reasonably well by the addition of an inductor in series with one comb of the IDT, with the second comb kept at ground potential. Although appropriately chosen commercially available coaxial cable can have losses of only a few dB over tens of meters, physical movement of flexible cables is to be avoided, as it perturbs the phase shift in the cable slightly, causing noise. In this regard, rigid coaxial line is superior to flexible line; for electrically noisy environments, rigid line is also superior in terms of immunity to interference. Remote location of sensor from electronics is extremely difficult for one-port devices such as the TSM resonator, even though they operate at lower frequencies than SAWs. This is because the oscillator circuits used with one-port devices rely on rapid impedance variation with frequency to locate the point of resonance, and transmission line length and stray capacitances affect impedance significantly. In fact, it can become impossible for the circuit to "find" a zerophase point at all if the external phase shift is large compared to the small phase shift associated with a resonator. In contrast, two-port devices rely only on the large phase shift (100-200 wavelengths) associated with the acoustic delay line, which is many times that of a few tens of meters of transmission line. A second fundamental problem with one-port devices is distinguishing the response from the background. Because the acoustically reflected signal must be separated from the incident signal, the response to be measured is typically no more than 30 dB above the background. Again, two-port devices have a decided advantage, owing in this case to the measurement of a transmitted signal, which can be as much as 100 dB above the transmitted background. Thus, depending on the particular oscillator circuit used with a one-port resonator, cable lengths in excess of a few centimeters to a meter or two are problematic. Fortunately, a few small, inexpensive components can be combined to build a DC-powered oscillator that can often be located in close proximity to the device, and the frequency signal from this oscillator can then be sent over long distances.

17The velocity of the electrical signal in the cable is nearly 105 times faster than the acoustic signal in the delay line, hence the wavelength is nearly 105 times as long in the electrical cables as it is in the acoustic delay line.

384

6. Practical Aspects of Acoustic-Wave Sensors

6.5 Enhancing Sensor Performance by System Design The ultimate performance of any sensor can be gauged by the signal-to-noise ratio that it produces when challenged by a known amount of the appropriate analyte. In the case of chemical-vapor sensor devices, improved (i.e., lower concentration) detection limits can be achieved either by increasing the signal or decreasing the noise. In either case, the signal-to-noise ratio is enhanced and the detection limit is enhanced. Considerable attention has been focussed on increasing the signal by using sample-enrichment techniques, improved chemically sensitive coatings, alternative AW probe device designs, digital signal processing, or in some cases, by the selection of different AW frequencies. Less attention has been given to reducing the noise produced by the sensor system in order to improve detection performance. Sensor noise can be broadly defined as any output signal that is not related to the desired analyte. It arises from a large number of sources, including the well-known mechanisms of Johnson noise, shot noise, and flicker or 1/f noise. It can come from the AW device, the coating applied to the device, the sampling system used to introduce the analyte to the sensor, the ambient environment around the sensor device, and even from digital signal-processing algorithms used to process the sensor signal. Ordinarily, these noise sources are only a problem if their frequency characteristics fall within the same bandwidth as those exhibited by the phenomenon being observed. Prudent system design often focuses on reducing the sources of noise and drift by controlling the temporal properties of the measurement. For example, high-frequency noise can be substantially reduced by averaging the sensor signal for a period that is long compared to the periodicity of the noise. Low-frequency drift can be compensated by modulating the exposure of the analyte to the sensor with a period that is short compared to the periodicity of the drift. This section will broadly describe some of the practical system design strategies that are being used to minimize problems that sometimes plague all types of chemical vapor sensors such as baseline drift, inadequate sensitivity, and inadequate selectivity. While special emphasis will be given to acoustic sensors, the approaches described here are generally applicable to any vapor sensing device. 6.5.1

BASELINE-DRIFT COMPENSATION STRATEGIES

Sensor drift is often a very difficult problem to solve. Under ideal conditions, a sensor produces an output signal that is related only to the analyte of interest. When presented with a constant reference state, the so-called baseline signal

6.5 Enhancing Sensor Perfomance by System Design

385

should also be constant. In reality, acoustic sensors are often sensitive to many more than one measurand (e.g., temperature, pressure, stress, fluid density, acceleration, gravitational force, etc.) or they may be constructed of materials whose physical properties change slowly with time. These imperfections result in a baseline signal that varies even though the reference state remains unchanged. In the simplest cases, the source of drift can be traced to one other measurand (e.g., temperature or pressure) that is not being defined by the reference state (e.g., constant vapor concentration). By independent measurement of this interfering measurand, a compensating signal can be derived that can be used to correct the measured signal. Indeed, this is one of the reasons that AW sensors are often used in a dual configuration, with one "sample" device configured to respond strongly to the analyte and another "reference" device that is intended to respond to the remaining "common-mode" interfering measurands. Ideally, simple subtraction of these two signals results in an output signal that is independent of the common-mode interferences. In practice, this scheme is good but not 100% effective [38]. The fact that the sample and reference devices are located in physically different places (although they may be very close - - e v e n on the same substrate) and are configured slightly differently (e.g., sample device coated and reference device uncoated) introduces enough of a difference to cause degradation of the matching between the sample and reference sensors, giving rise to a corresponding uncompensated response to common-mode i n t e r f e r e n c e s - i.e., drift. Usually, the remaining signal pattern of drift is stochastic, exhibiting temporal variations that are often indistinguishable from those of the analyte. Without a system to distinguish between the signal and the drift, precise measurement of small variations in the analyte is extremely difficult. The most common way to deal with the problem of stochastic drift is to modulate the exposure of the analyte to the sensor and to synchronously detect the sensor response. When the analyte is "off" (i.e., the sensor is "zeroed"), the sensor signal can be recorded as the baseline value. Drift-corrected signals can be obtained by subtracting the baseline signal from that recorded when the analyte is "on." If the frequency of the on/off modulation is much higher than the frequency of the baseline drift, then this scheme results in dramatically improved stability in the measured data. An implicit requirement in this measurement strategy is that the response kinetics of the sensitive film/analyte combination be sufficiently fast to allow on/off modulation at the desired frequency. Baseline drift compensation using this synchronous modulation/detection strategy requires a significant amount of additional hardware to be built around the sensor. Consider, for example, a vapor-measurement instrument. In this case, the modulator could consist of a valve that can alternately expose the sensor to

386

6. Practical Aspects of Acoustic-Wave Sensors

a stream of air that is known to be free of all contaminants, then to a stream that contains the contaminant to be measured. Some means would then be required to synchronize the switching of the valve, the recording of the sensor signal at the appropriate times, and the numerical subtraction of signal values. One common embodiment of this strategy is outlined in Figure 6.15. Here, a microcomputer is used to sequence the operation of a solenoid valve, read the sensor signals, and perfoma the baseline subtraction. Activated charcoal serves to provide reference air that is free of organic vapor contaminants. Re-zeroing schemes such as this are essential when high precision measurements are desired. 6.5.2

VAPOR CONCENTRATION ENRICHMENT

Occasionally, one needs to measure vapor concentrations that are below the detection limit of the sensor. In these situations, enrichment of the vapor concentration can provide substantial increases in the sensor's apparent sensitivity. Vapor-enrichment schemes for sensors based on sorbent trapping and thermal

~

'

"

AIR

~ERO" AIR

SCRUBBER

_

,

,,

SENSOR VAPOR INLET ii

,

,,.._ v

SAMPLEAIR SAW SIGNAL SOLENOIDVALVE POWER I

H

i

PUMP POWER ,i

,

i

,

i i

i

I

,i

i,,i,

i

DATA ACQUISITION & CONTROL M I C R O C O M P U T E R

,,

,,

,,,,

,,

,

,

,

,

,

Figure 6.15 Typical baseline-drift compensation strategy: a periodic "re-zeroing" is provided using the air scrubber and three-way valve.

6.5 Enhancing Sensor Perfomance by System Design

387

desorption have been reported by numerous investigators [39--42]. Indeed, such techniques are in widespread use by analytical laboratories that perform environmental monitoring. Thermally desorbed vapor concentrators are conceptually quite simple. They rely on a pump to pull a large quantity of ambient air (presumably contaminated with the vapor-phase analyte) over a polymeric sorbent that traps the vapors onto the large surface area of the polymer. These vapors are then released from the trap by applying heat and backflushing additional air over the hot sorbent to remove the vapors. Vapor concentration is enriched by virtue of the fact that the volume of air required to absorb the vapor sample onto the cool trap is much larger than the volume of air required to remove the vapor sample from the hot trap. Vapor concentrators can give impressive increases in sensitivity (e.g., a factor of 1000). There are many challenges to fabricating a practical vapor-concentrator device. First, the thermal mass must be kept small in order to minimize the energy required to heat the trap rapidly. Second, the geometry must be selected so that the device offers a low resistance to airflow while providing enough sorbent bed depth to prevent break-through of the vapor to be detected. Third, the sorbent material must be able to efficiently trap and release the target vapors over the operating temperature range of the device. Porous polymers such as Tenax TM, Chromosorb TM, Porapak TM, and Carbotrap TM, all commonly used by gas chromatographers, are especially attractive for this application. A typical commercial vapor-concentrator design is illustrated in Figure 6.16 (page 388). A 1/8-in internal-diameter tube is filled with a 1/4-in-long plug of Tenax GC TM weighing approximately 25 mg. Ambient air is pulled through the trap at room temperature for about 30 s by a small pump at a high flow rate (e.g., 600 mL/min). After pulling in a sample, the pump is stopped and a resistive heater is energized to heat the sorbent trap to a temperature in the range of 120~ to 220~ Once heated, air is flowed in the reverse direction through the trap at a lower flow rate (e.g., 12 mL/min) for a short period (e.g., 15 s). Assuming that the vapor is quantitatively absorbed and released under these conditions, one can readily calculate the enrichment factor by simply noting the ratio of the volume of air sampled to the volume of air utilized for desorption. In the case cited, the volume of air sampled is 300 mL and the volume of air used for desorption was 3 mL. The resuiting enrichment factor is 100. Besides offering enhanced sensitivity, the vapor concentrator can also act as a sample modulator for baseline drift compensation. As illustrated in Figure 6.17 (page 389), the enriched vapor concentration discharged from the concentrator exhibits a characteristic maximum at a predictable time after the desorption cy-

388

6. Practical Aspects of Acoustic-Wave Sensors

Figure 6.16

Configuration of a typical thermally desorbed vapor concentrator.

6.5 Enhancing Sensor Perfomance by System Design

389

Figure 6.17 Vapor concentrator operational sequence.

cle is initiated. Thus, the sensor signal can be recorded before heating the trap and again at the expected time of the concentration maximum in order to obtain a properly zeroed sensor response. A final advantage of the vapor concentrator is that it can enhance the selectivity of the sensor. Clearly, the method is only effective for compounds that can be trapped on a sorbent polymer. Low molecular weight vapors such as methane, ethane, and propane are not readily trapped and thus will not be enriched. Likewise, very high molecular weight vapors will not be easily desorbed from the trap and thus will actually be diminished in concentration. Overall, the addition of a vapor-concentrator device to a chemical vapor sensor can produce dramatic enhancements in performance. Significantly lower vapor concentrations can be reliably detected from the combined effects of source concentration enrichment, which increases the apparent sensor signal, and baseline drift compensation, which reduces the apparent noise produced by the sensor. Unfortunately, these performance enhancements come with a fairly heavy price in the form of additional pumps, valves, traps, and increased energy consumption requirements.

390

6.5.3

6. Practical Aspects of Acoustic-Wave Sensors

ARRAY ,SENSORS AND PATTERN RECOGNITION

Arrays of sensors have received a great deal of interest for many reasons. In the case of physical sensor devices, an array of sensors can provide vastly improved spatial resolution of the phenomenon being measured. By combining sensors of different types, a more comprehensive measurement can be made, perhaps over a much wider dynamic range of measurand values. In the case of chemical sen.sors, arrays have grown in popularity as a means to enhance selectivity and versatility. Indeed, preliminary efforts in this direction have proved the concept of building an "electronic nose" based on the acoustic array sensor/pattern recognition approach [43,44]. Experience with AW chemical sensors has demonstrated that the selectivity of a particular coating for a particular gas or vapor can be quite good under ideal conditions. However, for many analytes adequate selectivity is difficult to obtain without the time-consuming development of a coating specifically for the analyte. In addition, many applications demand that a number of vapors or mixtures of vapors be detectable. Chemical sensor arrays are intended to address these challenges. The strategy is to use a limited number of sensors, each having a different coating with preferential (but not unique) selectivity; the coated sensors are exposed simultaneously to the vapor analyte. Each sensor responds to a differing degree depending on the type of vapor. In a very simple approach, 18 the resulting pattern of responses can then be normalized to eliminate the effect of vapor concentration and this normalized pattern can be stored in a library or identified using a variety of pattern-recognition algorithms. A key advantage of an array sensor is that it can usually identify a number of vapors far greater than the number of sensors in the array. In addition, since the array responds to a large number of vapors, the identification of new vapors can often be accomplished with pattern-recognition software modification rather than replacement of sensor coatings. While the concept is quite simple, the physical construction of array sensors is less straightforward. In the interest of maintaining a minimal "dead-volume" in the detector cells, the sensors must be located in close proximity to one another. This objective is at odds with the need for electrical isolation between sensors. The RF electronic circuitry associated with AW sensors can give rise to electromagnetic fields that cause interference between adjacent sensors. Thus, careful consideration must be given to the system layout, packaging materials, and electromagnetic shielding. ~SThis simple case will be accurate only to the extent that the responses of each of the coated sensors is linearly proportional to the analyte concentration over the range of interest.

6.5 Enhancing Sensor Perfomance by System Design

391

Another problem associated with array sensors is the sheer volume of data they can produce. Consider a very modest one-minute measurement using a foursensor array whose AW-oscillator frequency signals are read once every second with a digital frequency counter, the results being stored in memory. Assuming that each frequency measurement is contained in 4 bytes, then this simple "sniff" would fill almost 1 kbyte of memory. A more ambitious system that had 8 sensors measured at 0.1-second intervals for 5 minutes would fill almost 100 kbyte per "sniff". A 4800-baud RS-232 serial communications line would have to run almost continuously just to move these data to another processor in real time. Clearly, the processing, storing, and archiving of these array sensor data are tasks that deserve more than casual attention. The selection of appropriate sensors for the array is also an important task. To obtain the most information from an array of sensors, it is desirable that their responses be as orthogonal as possible; that is, the response of each sensor should be unique and should not be similar to other sensors in the array. Generally, it is reasonable to select sensor coatings that respond strongly to the target vapors to be measured, together with some "different" coatings that respond strongly to known interferences. An example of some response patterns obtained from a four-SAW-device array sensor are provided in Figure 6.18 (page 392). Four 158-MHz SAW sensors were coated with films of poly(ethyleneimine), fluoropolyol, ethyl cellulose, and Tenax GC TM. The sensor array was then exposed to a variety of vapors. Each sensor responded to each vapor to a different extent. The magnitude of the signal obtained from each sensor (i.e., channel A, B, C, and D) is plotted in histogram form. The resulting response patterns are significantly different from each other, thereby permitting easy "fingerprinting" of the vapor analytes. As expected, chemically similar compounds produced patterns that are similar, though often different enough to permit identification. The array responds to mixtures of vapors and can "fingerprint" them, but determining the individual components of the mixture is a task beyond the capability of present instruments. The development of sophisticated pattern-recognition algorithms to process array-sensor data is an area of active research. Statistical pattern recognition techniques as well as neural network techniques have been applied to the problem of classifying the vapors introduced to a sensor array (e.g., hazardous vapor or nonhazardous vapor). Impressive results have been obtained by such patternrecognition techniques when the sensor array is adequately "trained" [43]. In the case of an array sensor for hazardous vapor detection, training is normally accomplished by recording the responses of the array to exposures to a large number of non-hazardous as well as hazardous vapor combinations that could be en-

392

6. Practical Aspects of Acoustic-Wave Sensors

Figure 6.18 Typical response pattems obtained from a four-SAW-device array sensor; the magnitude of each response is given by the height of the bar and numerically as a percentage at the top of each panel. countered in practice. These data are then used to develop an effective patternrecognition algorithm. This training and algorithm development process can be very time consuming and expensive. As a result, it is extremely important for the sensors that are used in the array to exhibit very stable sensitivity characteristics with time and to be manufacturable with highly repeatable characteristics. To minimize cost, it is very desirable that the algorithm developed for the training array be transferrable with no re-training to other arrays made with the same types of sensor.

6.6 System Design Challenges

393

Overall, the prospects for development of practical "electronic noses" based on AW sensor arrays and computerized pattern recognition are very good. A current design for such an instrument consists of an array of four 250-MHz SAW resonators along with RF electronics, frequency counters, interface circuitry, and neural-network pattern-recognition computer. The complete instrument occupies a volume of 500 cm 3 (i.e., 11.4 • 11.4 • 3.8 cm) and uses less than 2 W of power. Improvements in the near future should allow the volume to shrink to less than 160 cm 3 with a power consumption of about 0.7 W. While this is still a rather large "nose," further improvements in size and performance are quite likely. Thus, the quest for a small instrument having a volume of a few cubic centimeters and the ability to detect and identify vapors at the part-per-million concentration level (i.e., a truly versatile electronic nose) appears to be achievable.

6.6 System Design Challenges One can imagine that the ultimate acoustic-wave sensor device might be a monolithic "chip" consisting simply of the coated piezoelectric sensor and its associated RF electronic circuitry. This naked device would, of course, have insignificant cost, power consumption, and size, while affording awesome sensitivity, selectivity, ruggedness, and speed of response. While such an ideal device may one day exist, a vast amount of additional development will be required. The continuing investigation of AW sensor devices has provided a greater appreciation for the limitations of existing technology and has highlighted areas where improvements might produce substantial performance gains. A litany of major challenges have emerged. Big payoffs can be expected from continued research and development in the area of materials science for improved chemically sensitive/selective coatings and piezoelectric substrate materials; in the area of microfabrication technology for novel device structures having higher sensitivity to specific measurands; in the area of microelectronics for monolithic, low-power AW sensor-drive and signal-processing electronics; in the area of pattern recognition algorithms for array-sensor signal processing; in the area of system architecture to optimize the sensitivity to the measurand and reduce sensitivity to sources of noise and drift; and in the areas of device packaging, thermal management, and sample handling. Research on these AW sensors over the last two decades has clearly elucidated their important capabilities and has unequivocally established the importance of trying to meet the challenge to develop improved AW sensors for the future. During the period from 1982 to 1995, practical SAW vapor sensor instrumentation has evolved from a typical 31-MHz delay-line sys-

394

6. Practical Aspects of Acoustic-Wave Sensors

tem that occupied a volume of nearly 6000 cm 3, consumed nearly 10 watts of power, and could detect about 10 nanograms of mass change, to a 400-MHz dualresonator system that occupies a volume less than 15 cm 3, consumes less than 120 mW of power, and can detect about 10 picograms of mass change. Thus, the efforts to develop AW sensor technology in the preceding decade have resulted in more than a hundredfold reduction in size, power consumption, and absolute mass detection limit. It is likely that continued efforts during the next decade will yield yet another hundredfold improvement in performance, thereby establishing AW sensors as the method of choice for solving a wide variety of physical, chemical, and biochemical measurement problems.

References 1. Lakin, K. M.; Wang, J. S.; Landin, A. R. Proc. 36th Ann. Symp. Freq. Contr., pp. 517-524 (1982). 2. Gunshor, R. L.; Martin, S. J.; Peirret, R. F. Jap. J. Appl. Phys. 22, Suppl. 22-1, 37 (1982). 3. White, R. M.; Wenzel, S. W. Appl. Phys. Lett. 52, 1653 (1988). 4. Martin, S. J.; Ricco, A. J.; Niemczyk, T. M.; Frye, G. C. Sensors & Actuators 20, 253 (1990). 5. Bowers, W. D.; Chuan, R. L.; Duong, T. M. Proc. 178th Mtg. Electrochem. Soc. 902, The Electrochemical Society: Pennington, NJ, pp. l 116-1117 (1990). 6. White, R. M.; Voltmer, F. W. Appl. Phys. Lett. 7, 314 (1965). 7. Morgan, D. P. Ultrasonics 11, 121 (1973). 8. Ricco, A. J.; Martin, S. J. Sensors & Actuators, BI0, 123 (1992). 9. Kepley, L. J.; Crooks, R. M.; Ricco, A. J., Anal. Chem. 64, 3191 (1992). 10. Frye, G. C.; Martin, S. J.; Ricco, A. J. in Chemical Sensors and Microinstrumentation, ACS Symposium Series No. 403, American Chemical Society: Washington, DC, Ch. 14 (1989). 11. Smith, W. R. Physical Acoustics Vol. XV, Academic Press: New York, pp. 99-189 (1981). 12. Lee, L.-H. Fundamentals of Adhesion, Plenum Press: New York (1991). 13. Martin, S. J.; Frye, G. C. Appl. Phys. Lett. 57, 1867 (1990). 14. Martin, S. J.; Frye, G.C.; Senturia, S. D.; Anal. Chem. 66, 2201 (1994). 15. Langmuir-Blodgett Films, Roberts, G. Ed., Plenum Press: New York (1990). 16. Swalen, J. D.; AUara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelachvili, J.; McCarthy, T. J.; Murray, R. W.; Pease, R. F. Langmuir, 3, 932 (1987). 17. Evans, S. D.; Ulman, A.; Goppert-Berarducci, K. E.; Gerenser, L. J. J. Am. Chem. Soc., 113, 5866 (1991 ).

References

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18. Leyden, D. E.; Collins, W. Silylated Surfaces, Gordon and Breach Science: New York, (1980). 19. Arkles, B. Chemtech, 7, 766 (1977). 20. Butler, M. A.; Ricco, A. J.; Buss, R. J. Electrochem. Soc., 137, 1325 (1990). 21. O'Toole, R. P.; Bums, S. G.; Bastiaans, G. J.; Porter, M. D. Anal. Chem., 64, 1289 (1992). 22. Barnes, C. Sensors & Actuators A 29, 59 (1991). 23. Nomura, T.; Okuhara, M. Anal. Chim. Acta, 142, 281 (1982). 24. Bruckenstein, S.; Shay, M. Electrochim. Acta, 30, 1295 (1985). 25. Schumacher, R. Angew. Chem., 29, 329 (1990). 26. Thompson, M.; Dhaliwahl, G. K.; Arthur, C. L.; Calabrese, G. C. IEEE Trans. Ultrasonics, Ferroelectrics, Freq. Contr. UFFC-34, 127 (1987). 27. O'Dell, T. H. Electron. Wireless World 94, Appendix A (1988). 28. Melroy, O.; Kanazawa, K.; Gordon, J.; Buttry, D. Langmuir 2, 697 (1986). 29. Wessendorf, K. O. Proc. 1993 IEEE Int'l. Freq. Control Symp., IEEE, New York, pp. 711-717 (1993). 30. Ricco, A. J.; Martin, S. J. Thin Solid Films, 206, 94 (1992). 31. Frye, G. C.; Martin, S. J.; Cemosek, R. W.; Pfeifer, K. B. Intl. J. Envir. Conscious Manf. 1, 37 (1992). 32. Vellekoop, M. J.; Nieuwkoop, E.; Haartsen, J. C.; Venema, A. Proc. 1987 Ultrasonics Sympos. IEEE: New York, pp. 641-644 (1987). 33. Alder, J. F.; Fox, C. G.; Przybylko, A. R. M.; Rezgui, N. D. D.; Snook, R. D. Analyst 114, 1163 (1989). 34. Wohltjen, H.; Ballantine, D. S. Jr., Jarvis, N. L. Chemical Sensors and Microinstrumentation: ACS Symp. Series 403, ACS: Washington, DC, pp. 157-175 (1989). 35. Frye, G. C.; Martin, S. J.; and Ricco, A. J. Sensors & Materials, 1, 335 (1989). 36. Wohltjen, H.; Dessy, R. E. Anal. Chem. 51, 1458 (1979). 37. Joshi, S. G. IEEE Trans. lnstrum. Meas. 38, 824 (1989). 38. Alder, J. F.; Fox, C. G.; Przybylko, A. R. M.; Rezgui, N. D.; Snook, R. D. Analyst (Communication) 114 (1989). 39. Kindlund, A.; Lundstrtim, I. Sensors & Actuators 6, 1 (1984) 40. Sides, G. D.; Miller, H. C.; Lishawa, C. R.; Kuhn, K. A. Proc. lnt'l Symp. on Protection Against Chemical Warfare Agents, Stockholm, suppl, pp. 39-46 (June 6, 1983). 41. Sherman, R. W.; Collard, E. S.; Solecki, M. F.; McKinney, T. H.; Grande, L. H.; Overton, E. B. Proc. 1st lnt' l Symp. on Field Screening Methods for Hazardous Waste Site Investigations, US EPA EMSL" Las Vegas, pp. 279-282 (October 1988). 42. Wohltjen, H. U.S. Patent No. 4,759,210 (1988). 43. Rose-Pehrsson, S. L.; Grate, J. W.; Ballantine, D. S.; Jurs, P. C. Anal. Chem. 60, 2801 (1988). 44. Schmautz, A. Sensors & Actuators B 6, 38 (1992).

Appendix A

Lists of Symbols by Chapter

Chapter 1

No symbols

Chapter 2 wave attenuation factor area of ith face of elemental cube

Ol

Ai s

b~

ij th component of inverse permittivity at constant strain E.

19.

Cq; C ij, C q, ciykt

ij th component of elastic stiffness in reduced notation; ij th component of elastic stiffness in reduced notation at constant electric field; ij th component of elastic stiffness in reduced notation at constant electric displacement; ijkl th component of elastic stiffness tensor

Kroenecker delta equal to 1 when i = j = k and 0 otherwise ij th component of piezoelectric strain constant

D; D~

electric displacement vector; tah component of electric displacement vector

396

Chapter 2 T eq; e U

397

ij th component of piezoelectric stress constant; ij th

component of piezoelectric stress constant at constant stress Eq; Es

/jth component of permittivity; /jth component of permittivity at constant strain

eijk

/Jk th component of piezoelectric tensor

E; E; Ei

electric field vector; electric field; /th component of electric field

f

frequency

F; Fi

force vector; /th component of force electric potential function

T; AT; AT'

complex propagation factor; change of complex propagation factor; change of complex propagation factor normalized to k0, the real part of unperturbed propagation factor

~qq

ij th component of shear viscosity tensor

hij

ij th component of piezoelectric constant

J

(--1) 1/2

k

wavenumber

K

electromechanical coupling coefficient

A

wavelength

li

ith direction cosine

m

mass of elemental volume

p; Ap; po

density; change of density; initial (unperturbed) density

P; Pd; PT

acoustic power; power dissipated per unit volume; complex power transfer from wave

E sij; s q

ij th component of elastic compliance tensor; ij th component of elastic compliance tensor at constant electric field

S', S'~ Sift S i

strain tensor; strain; ij th component of strain tensor; ith component of strain in reduced (or engineering) notation

398

Appendix A Lists of Symbols by Chapter

T

transit time

t

time

r; r; rij

stress tensor; stress; ij th component of stress

u(x, y, z, t)

particle displacement vector

U l, //2, //3

x-, y-, and z-components of displacement

U; A U; Uo; UE;

energy density; change of stored energy density; unperturbed stored energy density; electric energy density; kinetic energy density; strain energy density

Uk; Us v; v; vi; Av; v0

phase velocity vector; phase velocity; ith component of phase velocity; perturbation of phase velocity; unperturbed phase velocity

x; x

unit vector in x-direction; rectangular position coordinate

Y; Y

unit vector in y-direction; rectangular position coordinate

tO

angular frequency (= 27rf)

z; z

unit vector in z-direction; rectangular position coordinate

Chapter 3 wave attenuation factor a

radius of cylindrical rod

Ai

ith

B

frequency interval between adjacent nulls of interdigital transducer response; bending stiffness of plate

ciy; cij

component of elastic stiffness in reduced (or engineering) notation; piezoelectrically stiffened stiffness component

Cm; Cs

mass sensitivity factor; capacitance/length along surface (c~ = Eo + ~)

c; Co; Co*; Cp

capacitance; static capacitance of crystal; sum of static and parasitic capacitance; parasitic capacitance

antisymmetric plate wave

Chapter 3

399

~; Be; 8v

viscous decay length; evanescent decay length (for FPW); viscous decay length (for FPW)

d; ds

periodicity of interdigital transducer; thickness of sorptive film (for FPW)

~; ~ij; Co; Es

permittivity; component of permittivity; permittivity of vacuum; permittivity of SAW substrate

e~jk

piezoelectric tensor components

E

electric field; Young's modulus

E'

effective Young's modulus, E' = E/(1 - v 2) (for FPW)

f; A~ Afmin;fN; A; fo

frequency; change in resonant frequency; minimum detectable change of resonant frequency; resonant frequency associated with N th mode; series resonant frequency of crystal; synchronous frequency of interdigital transducer phase shift, and electric potential function for SAW; phase of SAW component with respect to ui; electric potential function for rightward propagating SAW; electric potential function for leftward propagating SAW

Y; TN

complex propagation factor; propagation factor of Nth APM mode shear viscosity

h; hf ; hs

thickness of APM crystal; thickness of conductive film on SAW substrate; thickness of shear mode crystal angular displacement along semicircle in Aodk vs Av/v plot

J

current; SAW-generated current per unit area ( - l)It 2

JN

APM parameter (Jo = I/2; JN = I, N >- I)

k; kN; kt

wavenumber; wavenumber corresponding to resonant frequency fN; wavenumber for bulk transverse waves

K

electromechanical coupling coefficient

A; At

wavelength; wavelength of bulk transverse waves

I; I0

400

AppendixA Lists of Symbols by Chapter

inductance; also path length (center-to-center distance) between pair of interdigital transducers /z;/xs

shear modulus; substrate-dependent constant relating electric wave potential to applied transducer voltage (for SAW)

m' ; mso,.ptive; Am; Ammin

added mass per unit area (for FPW); mass per unit area of sorptive layer (for FPW); change in added mass per unit area due to change of fluid density (for FPW); minimum detectable added mass per unit area due to change of fluid density (for FPW)

M

mass per unit area of plate (for FPW)

1)

Poisson's ratio

N; N: Np

integer associated with resonant mode; number of transducer fingers; number of transducer periods perturbation factor

P; Pr; PTl; PT2 Pq; PF; Pq; P~

Ap;/~;

acoustic power; also complex power flow (see definitions p. 27) mass per unit volume (mass density) of quartz; density of fluid (for FPW); change of density of fluid (for FPW); mass per unit volume (mass density) of liquid; mass per unit area of surface layer (areal mass density)

R

resistance; mode resolution parameter (for APM)

Rm

mass resolution of sensor

o'; trc; trl; trs

bulk conductivity; critical sheet conductivity; liquid (solution) conductivity; sheet conductivity of film

S; Si; am

sensor sensitivity to added mass; ith symmetric plate mode; mass sensitivity of sensor (for FPW)

z; Zxy

relaxation time; component of tensile stress in plate

t

time

r; ri: r~

stress tensor; ij th component of stress; x-component of in-plane tension (for FPW)

lax, Uy, Uz

x-, y-, and z-components of displacement

vk; up

kinetic energy density; potential energy density

Chapter 4 ve; VN; Vp; Vs; Vx; VxO; VxO, VyO, VzO; VO

401

speed of sound in fluid; phase velocity of Nth mode (for APM); phase velocity of plate wave; phase velocity of shear wave; x-component of particle velocity in liquid; value of Vx at surface of crystal; three particle velocity components at surface (for SAW); propagation velocity (for SAW)

v; v~; Vo

voltage; excitation voltage of nth transducer finger (for SAW); magnitude of transducer excitation voltage (for SAW)

to; too; ~s

angular frequency (= 2"nf); unperturbed resonant angular frequency; series resonant angular frequency

x; X

rectangular position coordinate; detuning parameter for interdigital transducer, and reference to crystal cut

y; Y

rectangular position coordinate, and distance into substrate (for SAW); reference to crystal cut

Y(~o); Ym.x

admittance; maximum admittance

Z; Z

rectangular position coordinate; reference to crystal cut

Ze; Z~; Zq; Z,; Z0

impedance appearing in equivalent circuit for shear resonator; motional impedance; equivalent shear-wave mechanical impedance for quartz; equivalent shearwave mechanical impedance of surface film; (for Z0 see Equation 3.17 and following)

Chapter 4 /3

defined variable for BET equation (Equation (4.5))

C

concentration of analyte in film

Co C(x,0

equilibrium concentration of analyte in film

D

diffusion coefficient

f;Af

frequency; change in frequency

concentration of analyte in film at depth x at time t

402

Appendix A Lists of Symbols by Chapter

f.

fractional porosity of porous film

G'

storage modulus

G"

loss modulus

rl

viscosity (not kinematic)

hi /(,%)

film thickness

Ao

incident optical wavelength

Ix

modulus (stiffness)

ml

film mass per unit area

M(t)

total mass of sorbed analyte in film at time t

Mmax

incremental change in mass of sorbed analyte

n; nm

number of adsorbed molecules; number of adsorbed molecules in a monolayer

P; Po

partial pressure of vapor; saturated vapor pressure

Pr

partial pressure of vapor at which capillary condensation occurs

spectral density (intensity) of source at wavelength A0

film density Ps

surface mass density of film

psk

skeletal density of porous coating matrix

rc

radius of hemispherical meniscus gas constant

n(~)

rate of change in APM velocity due to film crosslinking at wavelength A0

O"

surface tension polymer relaxation time

T

absolute temperature (Kelvin)

r~

liquid crystal phase transition temperature

r~

polymer glass transition temperature

Tm V~

melting temperature

Y

admittance

molar volume of gas, analyte

Chapter 5 tO

angular frequency

Ze

film impedance element

403

Chapter 5 a; aa

chemical activity of a species in the ambient phase, and adsorbed on a substrate, respectively

a2; a~

solvation parameter for hydrogen bond donor acidity of the solute; complementary solvent coefficient (i.e., solvent H-bond acceptor basicity)

f12; bl

solvation parameter for hydrogen bond acceptor basicity of the solute; complementary solvent coefficient (i.e., solvent H-bond donor acidity).

~t~ , x

activity coefficient of solute i in phase x

r

stiffness (Section 5.2)

Ca

ambient concentration of analyte

Cs

analyte concentration sorbed into film (Section 5.4.2), film surface capacitance (Section 5.2.3)

Cth

threshold concentration for human detection (toxicity limit) Hildebrand solubility parameters for solute i; and for solvent phases x, y permittivity

Ea; Ec, Ed

activation energy of bond formation; chemical bond strength; energy barrier for breaking of a chemical bond

AE; AEv; AEm

energy of solute transfer; energy of vaporization; energy of mixing

fa

attempt frequency for desorption of an adsorbate (Equation 5.15)

fo; Af; AL; Afe; Afs; Afm

initial (unperturbed) frequency; change in frequency change in frequency due to application of a coating; change in frequency shift due to elastic changes;

404

Appendix A Lists of Symbols by Chapter

change in frequency due to sorption of analyte; change in frequency due to mass loading

F

reaction rate/adsorption constant (Equation 5.20)

AGa; AG~

Gibb's free energy change associated with adsorption, and absorption/solvation, respectively

o; o~

fraction of adsorption sites filled by analyte, fraction filled by species i

h

sensor coating/film thickness

AHm; AH~o,,d

enthalpy of adsorption, solution, condensation, mixing, and condensation, respectively

K

geometric factor for fraction of active device area being perturbed (Equation 5.1)

k; ka; ka; ke

reaction rate constant; adsorption rate constant; desorption rate constant; empirical constant for Freundlich adsorption (Equation 5.12)

kl; k2

material constants for piezoelectric substrate (Wohltjen equation)

K

material constant for piezoelectric substrate (Saurbrey equation)

g2

electromechanical coupling coefficient

Ka

distribution coefficient for adsorption

KI2; K34

equilibrium constant(s) for stepwise formation of coordination complexes, where the subscript(s) refers to the number of ligands added to the complex in a given step equilibrium partition coefficient

L216; II

solvation parameter, Ostwald's partition coefficient of solute in hexadecane; complementary solvent coefficient (dispersion interactions) film Lam6 constant

/z

film shear modulus

m; Am; Am,,

mass; change in mass; change in mass per unit area

mA; mML

mass of adsorbate/area, adsorbed mass/area at monolayer coverage

Chapter 5

M; M~ ma; mm;

405

molecular weight, or molar mass of species x (analyte, adsorbate) mc; ms

mass of adsorbed analyte; mass of a monolayer of adsorbed analyte; mass of coating; mass of analyte sorbed into coating

NA N; No

Avogadro's number (6.02 x 1023)

ni ; nF

number of moles of species I, empirical constant for Freundlich adsorption (Equation 5.12)

r/

viscosity

p; pi

partial pressure; partial pressure of species i

p; pc

film density or coating density

71"2; S 1

solvation parameter for dipolarity/polarizability interactions; complementary solvent coefficient

R2; r~

solvation parameter for excess molar refractivity; complementary solvent coefficient (i.e., electron pair interactions)

r

rate of reaction

R

Ideal Gas Law constant

or

conductivity

SP

solubility property of interest for LSER application (i.e., K, Vg)

So

"sticking coefficient," indicates probability of collision with an empty site resulting in adsorption (Equation 5.14)

Se; Sm

device specific constants relating frequency shifts to changes in elastic and mass loading effects, respectively

ASa; ASm

entropy of adsorption; entropy of mixing

(for Langmuir adsorption isotherms) number of fill sites/area; total number of sites/area

relaxation time (shear) T

absolute temperature (Kelvin)

Tb"~ Tg'~ T m

boiling point (temperature in Kelvin); (for polymers) glass transition temperature; temperature of melting

406

AppendixA Lists of Symbols by Chapter

Y, Vo

acoustic wave velocity, unperturbed (initial) acoustic wave velocity

m

vi; vc; Vvap; Vx

molar volume of solute i; volume of sorbent coating, volume of vapor phase; volume of condensed phase x specific retention volume of solute (in gas chromatography)

Xi

mole fraction of species i

o.)

angular frequency

Chapter 6 Ol

attenuation

BW

bandwidth

Co

static capacitance

d

periodicity of an interdigital transducer

~s

dielectric permittivity of a substrate

f0; af; fR

IDT center frequency; change in frequency; resonant frequency

~; A,k; 4,.

unperturbed total phase difference; change in phase difference; instrumentally measured phase difference (-~r < tkr < ~')

k

wavenumber

K

acoustic path fraction

K

electromechanical coupling coefficient

t,i

insertion loss (expressed in dB)

Lr

tuning inductance wavelength

N

number of finger pairs in an interdigital transducer

n,~

number of acoustic wavelengths

N,~

number of acoustic wavelengths between centers of input and output IDTs

Pa

power dissipated

Chapter 6

407

quality factor (see discussion in Section 6.2.1.1) peak total energy unperturbed acoustic wave velocity; change in acoustic wave velocity angular frequency

Appendix B

absorption (absorb) acoustic aperture

Glossary of Terms

the process of a species present in a contacting gas or liquid phase penetrating into the bulk of a solid material the width of a plane-parallel acoustic wavefront, typically as defined by the overlapping finger length of an interdigital transducer launching the wave

acoustic path fraction

the fraction of the center-to-center distance between input and output transducers of a delay-line-based acoustic wave device that is perturbed by a stimulus and/or covered by a thin film that confers chemical or other sensitivity to the device

acoustic plate mode (APM)

a mode comprised of acoustic waves that are reflected periodically at the planes bounding the surfaces of a thin plate, which thus acts as an acoustic waveguide

acoustically thin

describing a film whose thickness is small compared to the effective acoustic wavelength in that material

active device

a device, such as an amplifier, that requires the input of power, most typically at a voltage of from 5 to 24 volts (DC), to accomplish a desired signal transformation or other function

adsorption (adsorb) AGC

the process of a species present in a contacting gas or liquid phase "adhering" to molecules at the surface of a solid

alcohol

an organic compound having a hydroxyl functional group bonded to a carbon atom, - C - O H

aldehyde

a class of organic chemical compounds characterized by a carbonyl group in one terminal position of a carbon chain, e.g., formaldehyde, HCHO

see

automatic gain control

408

Appendix B Glossary of Terms

409

aliphatic

describing an organic compound in which the carbon atoms are joined in chains, rather than rings (compare aromatic)

alkane

a hydrocarbon compound in which all carbons are joined by single bonds, i.e., - C - C -

alkene

a hydrocarbon compound in which two or more carbons are joined by double bonds, i.e., - C = C -

alkyne

a hydrocarbon compound in which two or more carbons are joined by triple bonds, i.e., - C ~ C -

amalgam amorphous

an alloy of a metal, often gold or silver, with mercury having little or no organized chemical structure (compare crys-

talline) amplifier

a device that produces an output signal whose amplitude is equal to the amplifier gain times the amplitude of the input signal

analyte

a chemical species that is to be analyzed, in terms of its identity and/or concentration

antibody

a protein, usually produced in vivo, that engages in specific chemical interactions with an antigen

antigen

a toxin or other substance that elicits the formation of specific antibodies in vivo

APM

see acoustic plate mode

aromatic

a class of chemical compound characterized by the presence of one or more ring structure in which electronic resonance effects play a major role in bonding (e.g., benzene rings)

AT-cut quartz

quartz crystal that generates shear waves when placed in a timeperiodic electric field; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

attenuator

a device that diminishes the amplitude of a signal by a specified fraction

automatic gain control (AGC)

a feature of an amplifier that automatically adjusts the amplification to maintain a constant output signal level; changes in the gain of such a device are a measure of changes in wave attenuation in an acoustic wave device

balun

a circuit that converts a voltage, such as that applied to an interdigital transducer, from being balanced with respect to ground to being unbalanced with respect to ground, or vice versa (most electrical test equipment has an output that is unbalanced with respect to ground)

410

Appendix B Glossary of Terms

bandwidth (BW)

for resonant systems, the range of frequencies over which the reflected power is within 3 dB (a factor of two) of its minimum value, attained at fR; for non-resonant systems such as delay lines, the range of frequencies over which the transmitted power is within a factor of two of its maximum value

baseline drift

an often gradual change in the output signal (from a sensor) in the absence of a change of the quantity being measured; for example, baseline drift can be caused by a gradual changes in ambient temperature or gradual changes in the physical properties of a sensor coating material

bidentate

referring to a ligand that can bind to a metal atom or other moiety at two sites in the ligand structure, e.g., ethylene diamine, oxalate anion

bonding p a d

a metal region on a silicon chip, sensor, or other device, provided as a place to make off-chip electrical contact using wire bonding (see)

BT-cut quartz

quartz crystal that generates shear waves when placed in a timeperiodic electric field; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

BW

see

carbonyl

a chemical functionality consisting of an oxygen atom attached to a carbon atom by a double bond, i.e., - C =O

chemisorption (chemisorb)

an adsorption process in which strong interactions, including covalent or ionic bond formation, occur between an adsorbate and a solid surface; such strong interactions often make the adsorption process irreversible

clear-field mask

a lithographic mask that is opaque in the regions where metal is to be retained, and clear elsewhere (the "field")

common-mode

in a two-wire circuit, a signal that appears on both wires; often, a so-called differential amplifier is used to minimize the disturbing effect of common-mode signals

signal

bandwidth

coordination

referring to complex compounds in which ligands (see) are bonded to a central metal atom by a shared pair of electrons supplied by the ligand

crosslinking

the process of forming chemical bonds between polymer chains, resulting in a three-dimensional polymer network that is typically insoluble

Appendix B Glossary of Terms

411

crystalline

having highly ordered, long-range structure in which atoms, molecules, or ions are arranged in regularly spaced and repeating patterns

damping

a colloquial term for a decrease of wave amplitude (attenuation) caused by the dissipation of wave energy, as in propagation through a viscous fluid

dark-field mask

a lithographic mask that is clear in the regions where metal is to be retained, and opaque elsewhere (the "field")

dB DC decibel (dB)

see decibel see direct current a logarithmic measure of the ratio of a variable to its reference value: relative power (dB) = 101oglo (P/Pref), where P,'efis the reference power; because of their square-law relationship to power, relative voltage, V, and pressure, p, expressed in dB are given respectively by 201ogl0 (V/Vref) and 201oglo(p/pref), where V,.ef = reference voltage and Prey= reference pressure

delay line

a device for which an electrical signal incident on the input port arrives, after some finite time delay, at the output port; for example, propagation of a Rayleigh wave from one transducer of a SAW delay line to the other typically causes a time delay ranging from a fraction of one to several ~s

device header

a package upon which an electronic device is mounted to permit making electrical connections via a socket and, in some cases, gas or liquid connections via tubing to introduce samples for measurement

diffusion

the process whereby chemical species intermingle, moving from a region of high concentration to a region of low concentration

diffusion coefficient

a parameter that quantifies the rate of diffusion of one species through a gas, liquid, or solid material (the amount of the species diffusing through a unit of cross section per unit time when the volume-concentration gradient is unity)

DIP direct current

see dual in-line package

(DC) direct electromagnetic

feedthrough directional coupler

colloquially, a steady quantity, such as a current or voltage, whose value is independent of time spurious electromagnetic signal coupling between input and output transducers that is independent of the properties of the acoustic path, and therefore not an accurate indication of the value of the intended measurand a device having three or more ports that passes the majority of an input signal straight through to its output port while splitting

412

Appendix B Glossary of Terms off a small, specified fraction of the signal to send to another device or instrument

dosimeter

a sensor or device that provides a measure of the total dose or exposure to a substance over a given period of time

drift

a gradual, often monotonic, change with time in the value of some parameter; often referring to such changes in the sensitivity of, or signal from, a device (compare noise)

dual in-line package (DIP)

a commonly used ceramic or plastic package for physically mounting and making electrical connections to an integrated circuit

elasticity (elastic)

the ability of a material to return to its original shape after it has been stressed; elastic behavior implies a linear relationship between stress and strain

elastomer

a polymeric material that exhibits elastic properties, e.g., rubber

electrochemistry

chemical processes and reactions induced by imposed electrical potentials

ele ctro ne gati vity

the tendency or ability of an atom to attract electrons, especially through a chemical bond

endothermic

designating a chemical reaction or process in which heat is absorbed

enthalpy

a thermodynamic measure of the (thermal) energy content of a chemical system

entropy

a thermodynamic measure of the amount of energy in a chemical system that is not available for work; a measure of the degree of disorder in a system

enzyme

a protein or protein-like substance that acts as a catalyst, speeding up specific chemical reactions

ester

a class of chemical compounds formed by the reaction of an organic acid with an alcohol, e.g., - R - C O O R ' or - R - SO3 - R'

ether

a class of organic compounds characterized by an oxygen atom bonded to two carbon atoms, i.e., - C - O - C -

exothermic

designating a chemical reaction or process in which heat is produced

external phase

the phase shift of a sensor signal that occurs outside the acoustic measurement path, e.g., the phase shift in an electronic amplifier and connecting cables

shift filter

a device that passes signals only within a specified range of frequencies

ftatpack

a metal version of the dual in-line package (see)

Appendix B

Glossary of Terms

413

flexural plate wave (FPW) FPW frequency response

a flexural ultrasonic wave propagating in a thin membrane, formed typically in a silicon chip

frequency counter

an instrument that measures frequency by counting the number of cycles in an accurately known time period

glass transition temperature (Tg)

the temperature at which the relaxation, or second-order transition, from the glassy to the elastomeric state occurs in a polymer; this transition exhibits a time (frequency) dependence

halogens; halides

reactive, non-metallic elements of the VIIb family; compounds containing these elements, e.g., chlorine, C12; hydrogen chloride, HCI

heterocycle

a compound that contains a ring system made up of more than one kind of atom; typical heterocycles consist of carbon plus nitrogen, oxygen, or sulfur

heterogeneous homologous

see flexural plate wave the frequency-dependent characteristics of a device expressed as a function of the excitation frequency, either in terms of insertion loss and phase shift, complex impedance (or admittance), or S parameters

consisting of more than one substance designating a series of chemical compounds whose structural formulas differ in a regular fashion, often by the addition of one or more - C H 2 - groups, e.g., CH3OH, CH3CH2OH, CH3CH2 CH2OH

hydrocarbon

a chemical compound consisting only of carbon and hydrogen atoms, e.g., methane, CH4; benzene, C6H6

hydrophilic hydrophobic hydroxide

having an affinity for water; highly soluble in water

hygroscopic

designating compounds or substances that readily absorb moisture

hysteresis

a dependence of the physical state or response of a substance or system upon its previous history, often manifested as the lagging of an effect behind its cause

IDT immunoassay impedancematching network

having an aversion to water; insoluble in water a chemical compound, usually inorganic, containing the hydroxide ion, OH-, in combination with a cation, e.g., sodium hydroxide, NaOH

see

interdigital transducer

an analytical test for, or derived from, immunological reagents or materials such as antigens or antibodies an interconnected arrangement of components that matches the impedance of a device to that of the instrumentation (or another device) to which it is connected

414

Appendix B Glossary of Terms

insertion loss

the extent of attenuation of a signal, typically expressed in dB, due to its traversal of a device

interdigital transducer (IDT)

a pair of interpenetrating comb-like structures, typically made from a lithographically patterned thin metal film that has been deposited onto the surface of a piezoelectric substrate; the IDT excites (or detects) acoustic waves when driven (or monitored) at the appropriate frequency

intermolecular

relating to interactions or processes occurring between or among different molecules

intramolecular

relating to interactions or processes occurring between or among the atoms or groups of atoms within a molecule

ionization potential

a measure of the energy required to remove an electron from an atom to infinity, forming an ion

ketone

a class of organic chemical compounds characterized by a carbonyl group in a non-terminal position of a carbon chain, e.g., acetone, C H a - C O - C H 3

kinetics, reaction kinetics

the study of molecular motion; specifically, the factors that determine the rates of chemical reaction, including their dependencies upon chemical concentrations and temperature

Langmuir-B lodgett film

a molecular monolayer film produced by passing a substrate through a water-surface-supported, compressed layer of molecules possessing polar and nonpolar ends (separated by an intervening chain or body of at least a few atoms), conferring a very regular alignment of the molecules; such films are typically produced using a commercial Langmuir-Blodgett trough to control the compression of the molecular layer and dipping of the substrate

lift-off procedure

a lithographic process for patterning thin films in which a layer of photoresist is coated on a substrate, then exposed to light through a mask, and developed prior to deposition of the layer of material to be patterned; following ,thin film deposition, the remaining photoresist is dissolved "out from under" the film in those regions where it is to be removed

ligand

an atom, ion, or molecule that can engage in coordinate bonding with a central (often metal) atom or ion (see coordination)

limit of detection (LOD)

the smallest value of some parameter to which a device responds that can be reliably detected; "reliably" is often taken to mean

Appendix B Glossary of Terms

415

that the signal measured is no smaller than three times the rootmean-square noise level

linear dynamic range a sensor in which linear proportionality between concentration and response is maintained (LDR) the general class of organic compounds consisting of fats, or lipid having properties similar to fats, e.g., hydrophobicity

lithographic mask

a radiation-transparent (often glass) plate bearing an opaque pattern that is the image (or negative image) of a pattern to be produced using photoresist-based patterning techniques

macropores mask aligner

pores with diameters greater than 50 nm

masking

referring to the action of a chemical reagent that renders an atom, ion, or molecule unreactive toward another chemical reagent

measurand

a quantity to be measured, such as temperature or the chemical concentration of a substance

melting temperature (Tin)

the temperature corresponding to (1) a physical change from the solid to the liquid phase, or, (2) in the case of polymers, a first-order transition from a crystalline to an amorphous state (the melting temperature is independent of frequency)

mesopores micropores microwave modulus

pores with diameters between 3 and 50 nm

molecular permeation

molecular transport of chemical species through a film of material such as a polymer

negative photoresist

photoresist that is rendered insoluble in a chemical developer, typically by photoinduced crosslinking of polymer chains, in

a device that holds a photoresist-coated substrate and lithographic mask in close, uniform proximity, providing uniform, controlled-duration irradiation of the substrate through the mask

pores with diameters less than 2 nm an electromagnetic wave in the 1-100 GHz regime a measure of the stiffness (or elasticity) of a substance, defined as the stress associated with a unit strain and having units of force/unit area (dynes/cm2); for polymers, it is the complex shear modulus that can be effectively probed with AW devices. Shear modulus can be represented by G = G' + jG", where G', the storage modulus, is associated with energy storage and release during the periodic deformation associated with the oscillating stress, and G", the loss modulus, is associated with the dissipation of energy, usually as heat

416

Appendix B Glossary of Terms those regions where it is exposed to (typically ultraviolet) irradiation

network analyzer

an instrument that provides a controlled-amplitude signal to the input of a test device or circuit over a range of frequencies, then records and displays the frequency response (see) of the device/circuit; both transmitted and reflected signals can be measured

noise

in a sensor or other device, irregular, often random variations in output signal resulting from conditions unrelated to the intended measurand, examples being temperature-induced variations of electrical resistance and random particle motions in a solid or fluid

olefin

any of a series of unsaturated, open-chain hydrocarbons containing one carbon-carbon double bond, e.g., propylene, CH3-CH2=CH2

oxidation

a chemical reaction or process that involves the removal of one or more electrons from an atom, ion or molecule (compare

reduction) parallel resonant frequency

for an electrical resonator (particularly one that represents a resonant mechanical system), the frequency at which the magnitude of the electrical admittance is minimum and the phase angle of the admittance is zero; the equivalent circuit model for such a system is characterized by a parallel combination of an inductor and capacitor, the square root of the product of whose values is equal to the reciprocal of the angular resonant frequency

partial pressure

the pressure of one gas or vapor that independently contributes to the total pressure in a gas and/or vapor mixture

partitioning

the process by which a chemical substance distributes between two or more media (phases) based on its affinity for the respective media; at equilibrium, the ratio of the concentrations of a substance in the two phases is equal to the partition coefficient, Kc

passive device

a device that effects some transformation of an input signal without use of any external power source; hence, the output power from a passive device is always less than or equal to its input power

phase shifter

a device that shifts the phase angle of the output signal by a specified (knob- or voltage-selectable) number of degrees relative to its input

Appendix B Glossary of Terms

417

slope

in an electrical system, the change of phase of a signal per unit change of frequency

phase-locked loop

a circuit in which feedback is used to adjust some parameter so as to maintain the phase difference between two discrete points in the circuit at a constant value

photoresist

photosensitive polymeric film used in photolithographic device fabrication (see lift-offprocedure)

physisorption (physisorb)

an adsorption process characterized by relatively weak interactions, such as those typical of van der Waals forces; because such weak forces occur between all molecules, physisorption is typically reversible and can occur on any surface

piezoelectric

referring to the property exhibited by certain crystals, whereby a polarization charge or voltage is generated upon the application of a mechanical stress; conversely, the tendency to undergo mechanical strain when subjected to an electric field

piezoelectric stiffening pogo pins

the effective increase of elastic modulus of a crystal owing to the presence of piezoelectricity

phase

spring-loaded pins for making electrical contact to a silicon chip, electroded crystal, or other electrical contact

polarizability

the tendency of a molecule's electron cloud to deform under the influence of an external charge or dipole

polynuclear

referring to organic compounds containing more than one aromatic ring, e.g., naphthalene, anthracene

port

an electrical connection to a device or instrument, typically comprised of a ground contact and a signal contact

positive photoresist

photoresist that is made (more) soluble in a chemical developer in those regions where it is exposed to (typically ultraviolet) irradiation

p o w e r meter

an instrument that measures RF power, typically utilizing a sensor that converts incident power to heat and measures the resulting temperature increase

propagating propagation

wave

measurement

see

traveling wave

in a delay-line acoustic sensor, determining the value of the measurand from the measured acoustic wave speed and/or attenuation

protein

one of a class of biologically important, high-molecular-weight compounds consisting of a complex sequence of amino acid units

pyroelectric

relating to the property exhibited by certain crystals, whereby a change of polarization charge (or voltage) results from a change of temperature

418

Appendix B Glossary of Terms

Q QCM quality factor (Q)

see qualityfactor see quartz crystal microbalance in the context of resonant acoustic devices, Q -fR/BW, where fR is the resonant frequency and BW is the bandwidth; Q can equivalently be defined as toUplPd., where to is the angular frequency, Up is the peak total energy present in the device, and Pd is the power dissipated by the device

quartz crystal microbalance (QCM)

a colloquial term for a thickness-shear mode (see) resonator

radio frequency (RE) receptor

the range of frequencies useful for radio transmission (but below the microwave range); typically in the range 10 kHz-1 GHz

redox

relating to a chemical reaction or process involving the transfer of an electron from one species to another (see oxidation and reduction)

reduction

a chemical reaction or process involving the addition of one or more electrons to an atom, ion, or molecule (compare oxida-

in biochemistry, that portion of a molecule (antibody, enzyme) that engages in specific binding interactions with another molecule (antigen, substrate)

tion) relative humidity (RH)

the partial pressure of water vapor contained in the air compared to that in air, at the same temperature, that is saturated in water vapor

resonance

a condition in which, at a particular frequency, energy in an electrical or mechanical system alternates stably between kinetic and potential energy forms

resonator

in acoustics, a device that supports a standing mechanical wave when excited at the appropriate frequency

RF RF detector

see radiofrequency a device that converts an RF signal into a DC signal, with the DC magnitude being proportional to the RF power

RH

see relative humidity

saturated

in electronics, referring to an amplifier operating at the limit of its output power and therefore unable to produce an increase in output signal amplitude as a result of an increase in input signal amplitude; in chemistry, referring to organic chemical compounds in which there are no double or triple bonds

Appendix B Glossary of Terms

419

saturation vapor pressure SAW self-assembled monolayer

the partial pressure of the vapor of a liquid that exists in the gas phase in equilibrium with an excess of that liquid

sensitivity

the change in signal of a device (e.g., a chemical sensor) per unit change in the parameter to which the device is sensitive (e.g., the concentration of a chemical species)

series resonant

for an electrical resonator (particularly one that represents a resonaat mechanical system), the frequency at which the magnitude of the electrical admittance is maximum and the phase angle of the admittance is zero; the equivalent-circuit model for such a system is characterized by a series combination of an inductor and capacitor, the square root of the product of whose values is equal to the reciprocal of the angular resonant frequency

frequency

SH.APM shear.horizontal acoustic plate mode (SH-APM) sorption (sorb) ST-cut quartz

see surface acoustic wave an ordered molecular monolayer film produced when a substrate with a crystallographically ordered surface is exposed to a dilute solution or vapor of the coating molecule, which must be capable of two chemical interactions: a strong chemical interaction between the "head group" of the molecule and the surface to orient all molecules similarly, and cumulative Van der Waals interactions between the "backbones" of adjacent molecules that confer regular alignment of the chainlike molecules

see shear-horizontal acoustic plate mode an acoustic plate mode (see) with particle displacement polarized perpendicular to the direction of wave propagation and parallel to the planes defined by the plate's surfaces a term that includes both absorption and adsorption (see) quartz crystal that generates a surface acoustic wave (see) when subjected to a time-periodic electric field typically produced by excitation of an interdigital transducer at the proper frequency; the crystal is cut at a specified angle to the crystallographic axes so that it has a small or vanishing dependence of wave velocity upon temperature at room temperature

stray capacitance

incidental capacitance, usually introduced by connecting wires, that reduces the amplitudes of transducer input or output voltages

substrate

in biochemistry, a substance acted upon by an enzyme and/or consumed in a biochemical reaction; in electronics, a physical platform upon which a device is constructed or fastened

surface acoustic wave (SAW)

a propagating or standing acoustic wave that is confined to the planar surface of a solid plate

420

Appendix B Glossary of Terms

surface chemical derivatization

the reaction and chemical binding of a chemical species to the surface of a material or device in order to (often permanently) alter the physical and/or chemical characteristics of that surface

synthesized oscillator

an instrument that digitally synthesizes a controlled-amplitude, controlled-frequency signal

thickness-shear mode (TSM)

an acoustic mode propagating in the direction normal to the plane surfaces of a crystalline plate, characterized by particle motion in the crystal that is parallel to the plate surfaces, and displacement maxima at both surfaces; the most familiar example of a TSM-based sensor is the quartz-crystal microbalance (QCM), more properly denoted as a TSM resonator

transmission line triple-transit echoes

an electrical or acoustical wave-guiding structure for delay-line-based devices, traveling acoustic waves that are launched by the input IDT, reflected backwards from the output IDT, reflected back again from the input IDT, and finally received by the output IDT

TSM

see thickness-shear mode

vector voltmeter

an instrument that measures the amplitude (voltage) and relative phase angle of two signals, one of which serves as its reference

viscoelasticity (viscoelastic)

the property of responding with a combination of elastic and viscous responses to a mechanical stimulus; many polymers exhibit viscoelastic behavior as a direct consequence of their chain structure

viscosity (viscous)

a measure of the flow resistance of a substance such as a liquid, polymer, or polymer solution; viscous behavior implies a linear relationship between shear stress and the rate of strain

wave path

the region of an acoustic wave device traversed or occupied, respectively, by a traveling or standing acoustic wave

wire bonding

the process of attaching fine connecting wires between metal bonding pads (see) on a silicon chip (or piezoelectric crystal) and the pins on a sensor device package, such as a device header or DIP (see); some combination of heat, compression, and ultrasonic energy is utilized to form a weld between a soft metal wire (gold or aluminum) and the bonding pad, often formed from a like material

Polymer

Density Solubility (g/cm3) Parameter, 8 (20-25 ~ (cal/cm3)1/2

Monomer Structure

Butyl Rubber (poly(isobutene-coisoprene)) Cellulose polymers: (structure is for unmodified cellulose)

0.925

[-CH2C(CH3)2-]n plus

7"= (*c)

-63

1.5

Re.t: 4:53 5:18

Imle

CH2OH O O

l

cellulose acetate butyrate cellulose triacetate ethyl cellulose Fluoropolyol

O ,,<

,

OH

1.3

10.9

240

(17% ........ butyrated)

1.25

9.5

235

1.14 1.65

10.3 11.0

(100% ........ acetylated) (48% ........ ethoxylated)

OH I

CF3 I ~

CF3 I

OH I

t~

n

(40% of hydroxyls acetylated)

CF3 I

~F31

43 10

165

4:100 5:206 4:92 4:100 5:90,257 4:52,71 5:55,56,207

CH2CHCH2OC--~/ ~--- COCH2CHCH2OCCH2CH--CHCOT (see Figure 5.10) phthalocyanine (polymerized) Pluronic L64

"O

[-- CH2CH= C(CH3)CH2- In

cellulose acetate

~

7.8

r~ (*c)

5:70 H - [OCH2CH2]m- [OCH2CH(CH3)]n-OH (m ~ 40; n ~ 30)

5:215

g~

1o

Polymer polyamidoxime

poly(aniline) polybutadiene polybutadiene (-OH terminated) poly(butadiene acrylonitrile) (nitrile rubber) poly(butadiene) methacrylate) poly(butadiene)/ polystyrene poly(1-butene) poly(tert-butyl acrylate) poly(caprolactone) poly(caprolactone)-triol polycarbonate3

Monomer Structure

[-BD-].55- [-AC-].38[-CH2CH(C(NH2)(NOH))-].07 (see end note6) electrochemically polymerized from aniline (C6H5NH2) monomer [ - CH2CH = CHCH2- ]n cis: .36 cis/.55 trans: H O - [-CH2=CHCH2-]n-OH

Density Solubility (g/cm3) Parameter, 8 (20-25*) (cai/cm3)z/z 9.7

r~ (*c)

1". (*c)

19

4~ I'bO ,O

Kef. 5:168,207 m~

4:203,231 1.01

6.3

- 102

0.90

8.38

-95

5:18,137 257 5:257

10.4

[-CH2CH=CHCH2-].55 [CH(CN)CH2-].45 (see end note6) [--CH2CH = CHCH2CH2CH(CO2CH3)- ]n

5:207,257

5:257

[ - S T - ] m [ - B D - ] n [ - S T - ] p Kraton Dl102 (see end note6) 0.28 ST/0.72 BD 0.91 [-CH2CH(C2H5)- ]n [-CH2CH(CO2C (CH3)3)-]n

4:62 -24 43

[-O(CH2)5CO-]n MW: 300 9OO

1.08

[-- (C6I'~)C(CH3)2(C6H4)OCO2- ]n

1.20

1.07

150

125

5:257 4:55,56

60

5:257 4:52 5:257

10 30 267

4:50,51,68 5:52

m

r

Density Solubility (g/cm~) Parameter, 8 Polymer polyepichlorohydrin polyethylene poly(ethylene glycol) trade names: Carbowax Pluronics* (*mixed with poly(propylene glycol)) poly(ethylene glycol methyl ether) poly(ethyleneimine) poly(ethylene m a l e a t e )

poly(ethylene oxide) poly(ethylene terephthalate) 3 poly(hexamethylene adipamide) (Nylon 6/6)

Monomer Structure

(20-25 ~ (cal/cmZ) 1/z

[-CH(CH2C1)CH20- ]n low MW (37000) high MW (150000) H - [-OCH2CH2-]n-OH MW: 200

(Carbowax 20M) CH3-[-OCH2CH2-]n-OH

T ,,,

(*C)

1.36

[-CH2CHE-]n

(Carbowax 1000) (Carbowax 1540)

Tg (~

0.90 0.98 1.13

1000 1500 3400 20000

1.10 1.09 1.20

MW: 350

1.08

7.9

( - 130,-30)

85 130 -65 39 45 55

(9.5)

~ef. 4:71 5:55,90,207 5:18 5:118,I52 5:211 5:213 5:43,215

-8

5:257

"O r gI,

[-CH2CH2NH- ]n [-CH2CH202CCH =CHCO2- ]n

[- CH2CH20-]n (see polyethylene glycol) [ - OCH2CH2OE(~(C6H4)CO-]n

[- NH(CHE)6NHCO(CH2)4CO-]n

1.35

9.7

- 10

1.13

-67

1.38

81

1.09

13.6

5:90,205 4:52 5:35,90, 136,207

45

r

I'D

66

267

4:50 5:90,247, 251 4:100

"I m

4~

Polymer

Monomer Structure

polyimide

Density Solubility (g/cm3) Parameter, 8 (20-25*) (cal/cm3)l/z

r~ (*c)

1.40

T,,,

(*C) 310

4~ bO 4~

Sef. 4:10,68-70, 76,85,86 92,100

u .

polyisobutylene

polyisoprene poly(methyl methacrylate) poly(phenyl ether) (six rings) poly(pyrroles)

Ar and Ar' can be various aromatic structures (see refs. 4:76,92) [-CH2C(CH3)2-]n

[-CH2CH=C(CH3)CH2- ]n cis: trans: [ - CH2C(CH3)(CO2CH3)- ]n

5:52 o_ 0.92

7.7

0.91 0.904 1.19

7.9 9.3

1.22

9.4

-76

-67 -68 114

1.5

36 60 180

4:55,56 61,64-66,71 5:55,57, 90,108 4:195 5:35,207 4:51,86, 154,168 5:18,35,257

[-- ( C 6 H 4 ) O - ] 6

electrochemically polymerized from pyrrole (R = H), N-methyl pyrrole (R = CH3) and b i p y r r o ~ e ref 4:230)

%7 I

R

5:166 4:78, 101-103, 228-230

~o

-I

ml, m

Polymer poly(siloxanes)

polystyrene

polysulfone3

Monomer Structure

Density Solubility (g/cm3) Parameter, 8 (20-25 ~ (callcm3fl/z

r~ (.c)

T., (*C)

4:80,81, 86,96

Basic unit: Si(CH3)3 - O - [ - S i(CH3)2- O - ]nSi(CH3)3 SE-30; OV-1 CH3 groups replaced with: 50% -(C6H5) DC-710 75% -- (C6H5) OV-25 50% -CHECH2CF3 OV-210; OV-202 25% -(C6H5); 25% -CH2CH2CHECN OV-225 5% -CH2CHECHECN OV-105; 25 % - CH2CHECH2CN XE-60 100% -CH=CHCHECN OV-275 5% (C6H5); 1% -CH=CH2 SE-54 [-CH2CH(C6Hs)-]n MW: 45000 250000

[ - ( c 6 a 4)C(CH3)2(C6H4)O (C6H4)SO2(C6H4)O- ]n

Ref.

7.3-7.5

- 130

5:251 5:166 5:207 5:213, 247,251 5:213

-86

1.10 1.15 1.28 1.096

-80

g~ gl. ~o

1.00 0.98 1.05

1.24

9.1

60--93 100

190

238

5:166 5:251 4:47,51, 53,86, 168 5:18,21, 257 4:50,51, 151

mo

t~

m, ,

4~ tO

Polymer

polysulfonic acid

poly(vinyl a c e t a t e ) poly(vinyl butyral)

Monomer Structure

(CH2= C(CH3)CO2CH2CH2OH) co-polymerized with (CH2=CHCONHC(CH3)2SO3H) [-CH2CH(O2CCH3)-]n ~F ~ ]/

Density Solubility (g/cmJ) Parameter, 8 (20--25~ (callcmZ)1/2

Tg (*C)

Tm (*C)

Ref.

5:206 iiio

1.19 1.083

9.35 9.9

30 51

4:55,56 5:257

oi H iI io

0~/0

l=

2.

C3H7

poly(vinyl carbazole)

poly(vinyl chloride) poly(vinyl ferrocene)

i-f L

ID iiii

~HCH2.... i

[-CH2CHC1-]n electrochemically polymerized from vinyl ferrocene monomer

~

CH~ CH2 Fe

1.2

1.39

200

9.53

85

>300

285

4:78 5:257

5:18,257 4:198,202, 222-224

Polymer poly(vinyl isobutyl ether) poly(p-vinyl phenol) poly(vinyl propionate) poly(vinyl pyrrolidone)

Monomer Structure

Density Solubility (g/cm3) Parameter, 8 (20-25 ~ (cal/cmJ)1/z

[ - CH2CH(OCH2CH(CH3)2) - - ]n

Tg (*C)

8.5

-- 75 to -20

8.85

10

Tm (*C)

5:257

[ - C H 2 C H ( C 6 / ~ O H ) - ]n

~

[ - CH2CH(O2CCH2CH3)- ]n

Ref.

5:257 1.02

4:56 5:90,207

CI-I 2 - - - C H

t~

poly(vinyl stearate)

[-CH2CH(O2C(CH2)16CH3)-]n

52

5:257

l. The references listed in the last column are references from Chapters 4 and 5 which used the polymer coating for sensor applications or for characterization of the polymer properties. 2. The data listed in the above table were compiled from various sources, including: a. the 1994-1995 Aldrich Catalog Handbook of Fine Chemicals b. the Polymer Handbook (3rd Ed.), J. Brandup and E. H. Immergut, Eds.; Wiley: New York (1989). c. (in some cases) the references listed in the last column. 3. The phenyl groups shown by (C6I-I4) are bonded in the 1 and 4 positions (para orientation) in these polymer chains. 4. In most cases, groups in parentheses in the formulas are side chains attached to the main polymer backbone. Some exceptions to this rule are phenyl groups in the main chain, shown by (C6H4), and long hydrocarbon chains, shown by (CH2). Keeping track of the number of bonds to each atom can allow the structure to be determined unambiguously. 5. The formula 02C represents - O - C O - while CO2 is - C O - O - where CO is C=O. 6. AC is -CH(CN)CH2-; BD is -CH2CH=CHCH2-; ST is -CHCH(C6I-Is).

~. mo

r "~ g-

~"

bO --0

Appendix D

Commercial Sources for Acoustic-Wave Substrates, Devices, and Systems

,m

Company Name

i ,i

,,

i

,,

,,

i

Address

,,,,,

,

,

,

,

,,

j

,,

,

,

Products Available

Valpey-Fisher

75 South St. Hopkinton, MA 01748

Piezoelectric substrates

Crystal Technology

1035 East Meadow Circle Palo Alto, CA 94303

Piezoelectric substrates

P. R. Hoffman Materials Processing

321 Cherry St. Carlisle, PA 17013

Piezoelectric substrates

RF Monolithics

4441 Sigma Rd. Dallas, TX 75244

SAW devices

SAWTEK

PO Box 609501 Orlando, FL 32860

SAW devices

GTE Electronic Components

2401 Reach Rd. Williamsport, PA 17701

SAW devices

Phonon Corp.

7 Herman Dr. Simsbury, CT 06070

SAW devices

Plessey Semiconductor

Cheney Manor Swindon Wiltshire SN2 2QW UK

SAW devices

Andersen Electronics

310 Penn St. Hollidaysburg, PA 16648

TSM devices

Colorado Crystal

2302 W. 8th St. Loveland, CO 80537

TSM devices

Standard Crystal Corp.

9940 E. Baldwin PI. El Monte, CA 91734

TSM devices

Bliley Electric

2545 W. Grandview Blvd. Erie, PA 16508

TSM devices

McCoy Electronics Co.

100 Watts St. Mt. Holly Springs, PA 17065

TSM devices

CTS-Knights Div.

400 Reimann Ave. Sandwich, IL 60548

TSM devices continued

428

Appendix D Commercial Sources for Acoustic-Wave Products

Appendix D ,

continued

,

|

,

Address

Company Name

429

Products Available

Piezo-Technology

2525 Shader Rd. Orlando, FL 32804

TSM devices

International Crystal Mfg.

701 W. Sheridan Oklahoma City, OK 73126

TSM devices

Kristall-Verarbeitung

Neckarbishofsheim Germany

TSM devices

Amerasia, Inc.

2301 Townsgate Rd. Westlake Village, CA 91361

SAW systems

Andersen Laboratories

45 Old Iron Ore Rd. Bloomfield, CT 06002

SAW devices and instrumentation

Berkeley Microlnstruments

1301 S. 46th St. Richmond, CA 94804

FPW devices and instrumentation

Femtometrics

17252 Armstrong Ave. Irvine, CA 92714

SAW devices and systems

Integrated Chemical Sensors Corp.

90 Oak St. Newton, MA 02164

SAW systems

Microsensor Systems

62 Corporate Court Bowling Green, KY 42103

SAW devices and systems; gas-flow systems

Royal Melbourne Institute of Technology

Dept. of Communication & Electronic Engineering 124 LaTrobe St. Melbourne, Victoria 3000 Australia

SAW and bulk-wave systems

Xensor Integration bv

Shoemakerstraat 97 P.O. Box 3233 2601 Delft The Netherlands

FPW devices and systems

Elchema

P.O. Box 5067 Potsdam, NY 13676

TSM systems for electrochemical applications

Leybold Inficon

6500 Fly Rd. East Syracuse, NY 13057-9714

TSM devices and systems for vacuum deposition

Maxtek

2908 Oregon Ct., Bldg. G3 Torrance, CA 90503

TSM devices and systems for monitoring electroplating

Universal Sensors

5258 Veterans Blvd. Metairie, LA 70006

TSM systems

,

,

,

,

,,, . . . . . . .

INDEX

1% rule, 232, 348 Absorption, 68-69, 99, 129, 152, 164-171, 175-176, 178, 210, 228, 230, 247, 251, 288-300, 387; defined, 408 -based sensors, 300-306 Absorbance, optical, 3, 203-204, 344 Acoustic absorber, 154, 346 path fraction; defined, 408 plate mode. See APM spectroscopy, 158 streaming, 136 Acoustically thick film, 91-92 96-99, 348 inertial deformation, 96 Acoustically thin film, 43, 91-92, 94-97, 161, 232, 348; defined, 408 Acoustoelectric interaction, 78, 83-90, 103, 109-Ill, 153, 210, 234-237, 311,372 Activated charcoal, 274, 276-278, 289, 386 Active device, 355; defined, 408 Admittance, 46, 58 Adsorption, 152, 179-191,210, 225, 247, 251,257-258, 266-270, 378; defined, 4O8 at liquid/solid interface, 193-197 kinetics of, 266-272 nonspecific, 272, 279, 312 Adsorption isotherm, 179-180, t 82, 190, 211, 256, 258-265 BET, 182, 187, 189, 263 Freundlich, 262-263, 269 Langmuir, 193, 259-262 Adsorption-based sensors, 272-281 Aging, 188, 385 Air-brushing. See Coating methods Alumina, 277 gel, 274 porous, 275 Aluminum nitride (AIN), 140, 226-227, 247, 334, 337-338, 343 Amalgam, 282, 286-287; defined, 409 Amplifier, 355, 370; defined, 409 Antibody, 3, 306; defined, 409 Antigen, 3, 306; defined, 409 Antoine equation, 265 APM, 4, 36-37, 39, 99-111, 117, 120-121, 141-145, 152-153, 195-196, 199-204, 222, 224, 226-227, 233, 311,332, 334, 336, 342, 347, 361,371-372, 381; defined, 408 Areal mass density, 68, 223 Array, sensor, 145, 248, 313-320, 302-303, 306, 314, 390-394 classification criteria, 319-320 cluster classification of coatings, 317 data interpretation, 315-320

430

Arrhenius relation, 248, 272 Attachment, rate of, 312 Attenuation, 21-22, 33, 107, 152, 237, 244, 302. See also Insertion loss; Damping Attenuator, 356, 370; defined, 409 AW. See specific acoustic-wave device Bacterial growth, rate of, 312 Balun, 335, 356; defined, 409 Bandwidth, 77, 340, 342, 356, 384; defined, 334, 410 transducer, 103, 341-342 BET adsorption model, 263-265 Biological sensor; biosensor. See Sensor, biochemical Bond strength, chemical, 256-257 Bovine serum albumin, 195-196 Brillouin scattering, 2 l0 Bubble evolution, 208 trapped in surface voids, 63--64 Capillaries, 258, 265 Capillary condensation, 183-184, 265, 291 force, 63, 259 pressure, 63, 187 Cells, 112, 129, 140, 174, 200, 307-308 Characterization of material properties. See specific property Charge-transfer bonding, 257 complex, 255 electrode processes, 207 interaction, 282 Chemical activity, 257 Chemical surface modification, 151 Chemical vapor deposition, 115, 117, 150, 344, 354 Chemiresistor, 237 Chemisorption (chemical adsorption), 191-194, 210, 251-252, 256, 261,263, 266-267, 271,277; defined, 410 -based sensors, 279-287 Chromatography, 99, 165, 230-231,237, 270, 292-293, 297-299, 306, 387 Cluster; cluster analysis, 316, 319 Coating, 6 passivating, 182 protective, 182 selection criteria, 347-355 temperature effects, 377 Coating material, selection of, 272-279, 302, 314-315 Coating methods air brushing, 224 chemical vapor deposition, 354

Index dip coating, 150, 224, 350-351 evaporation, 117, 150, 197-198, 343-345, 348-354, 365 electron-beam-induced evaporation, 343, 345-346, 351-353 painting, 224 solution-phase, 348-352 surface chemical derivatization, 106, 275, 352-355; defined, 420 solvent casting, 349 spin casting, 150, 224, 349 spray coating, 150, 224, 349 sputtering, 150, 198, 343, 354 sublimation, 224, 235, 343, 353 vapor-phase, 352-354 Coating-analyte interactions, 248, 250--313 Coaxial cable, rigid, 383 Compensation, sensor, 234, 238, 246-247, 375-378, 384-387, 389 Complexation, 254-255, 257, 285 Compressional mode or wave, 14, 19-21, 25, 39, 59, 71-72, 91, 94, 96-97, 99, 140, 153, 200, 233 Condensation, 179-180, 182-184, 258-259, 261,263, 265, 294, 378 Conducting polymer, 176, 235,237, 208-209 Conductive epoxy, 382 Conductivity, 151,153-154, 210, 212, 223, 234-235, 237 Constitutive relation, 16-18, 21, 24 Coordination, 254-255, 257, 282; defined, 410 Coplanar waveguide, 381-382 Corrosion, 150-152, 191,205-207, 211-212, 343-344 Cosmic dust, 199 Crosslinking; defined, 410 in polymers, 154, 157, 165, 200-203, 212, 275, 289, 352, 354 photo-induced, 201-203, 344 Crystallography, 24 CVD. See Chemical vapor deposition Damping, 21-22, 38-39, 67, 70-71,153, 233, 366-367; defined, 411 Deactivation, 272 Decay length evanescent, 109, 127, 174 viscous, 54, 56-57, 60, 62, 124, 132 Deformation, 12 Delay line, 118, 226-227, 334-336, 361,363, 368-369, 371,382; defined, 411 Dendrogram, 315-316 Density, 6, 16, 18, 33, 151, 153-154, 212, 378 Depletion layer effects, 207 Deposition, 6, 211-212 electroless, 199 from liquid, 199-200 Desorption, 266-270, 378 thermal, 387-388 Detector, RF, 357, 370; defined, 418 Detuning parameter, 76 Dielectric constant, 154, 212

431

Dielectric loading, 57 Diels-Alder adduct, 279 Diffusion, 151-152, 155, 159-160, 167-178, 211-212, 247-248, 251,270-272; defined, 411 Fickian, 168-170, 175-176, 247, 270-271 non-Fickian, 175 hindered, 270 Dilatation, 25 Dip coating. See Coating methods Dipolar interactions, 297 Debye, 252 dipole-dipole, 155, 252 dipole-induced dipole, 252 dispersion, 252, 276 hydrogen bonding, 252-253 Keesom, 252 London, 252-253 Direct electromagnetic feedthrough, 380, 382; defined, 411 Directional coupler, 356; defined, 411 Dispersion diagram, 116 Dispersion forces, 297 London, 155 Dispersion relation, 20 Displacement chemical, 284 electrical, 27 mechanical, 12, 28 Dissolution, 199-200 DNA, 132, 140, 196, 210, 313 Dosimeter, 242, 279; defined, 412. See also Reversibility defined, 412 Draize test, 210 Drift, 245, 332, 376, 384-387, 389; defined, 412 Dubinin/Radushkevich isotherm equation, 265 Dynamic range, sensor, 238, 244-245 Elastic, defined, 412 behavior, 155 loading, 89, 97 moduli, 40, 156. See also Storage modulus, Loss modulus moduli, shear, 201,229. See also Lam6 constants Elastomer, 156, 159, 165, 247; defined, 412. See also Polymer, rubbery Electrical loading. See Acoustoelectric interaction Electrical properties, 152 Electrochemical cell, 136-138 Electrochemistry, 207-209, 366; defined, 412 Electrochromic materials, 208 Electromechanical coupling coefficient, 27-28, 31, 46, 83, 110-111,234, 338, 340 Electronic nose, 309, 390-391,393 Electroplating, 200 Electropolymerization, 237 Electrostatic forces, in analyte-coating interactions, 254 ELISA immunoassay, 140 Elongation, 155

432

Index

Energy, 28-34 Engineering notation, 16--17 Enzyme, 238, 306, 311-312; defined, 412 Equation of motion, 15-16 Equivalent circuit, 45, 48--62, 68, 71, 83-84, 163, 224, 313, 360 distributed model, 45 lumped-element model, 46 Mason, 45 transmission-line model, 45 Etching, 106, 115, 117, 140, 199, 211, 345 plasma, 198 Euler's identity, 20 Evanescent field distribution, 83, 125 Evaporation. See Coating methods Fick's Laws. See Diffusion, Fickian Film deposition, 151-152, 197-200. See also Coating methods growth, 181 growth, biological, 200 removal, 197. See also Etching; Dissolution resonance. See Resonance, film Filter electrical, 72, 76, 140, 340, 356, 368, 370-371; defined, 412 physical size, 174 SAW, 72, 76 Fixture, custom, 381-382 Flatpack, 381-382; defined, 412 Flexural plate wave. See FPW Flory-Huggins theory, 298 Flow cell, 130, 135, 137, 379 Flow-rate effects, 332, 378-379 Fluid flow, 181 Fourier transform, discrete, 76 FPW, 4, 5, 36-37, 39, 111-145, 152-153, 160, 174-175, 195, 199-200, 222, 224, 227, 230, 233, 277, 311,332, 334, 336-337, 342, 347, 358, 361,371,381; defined, 413 Frequency, 12 counter, 356; defined, 413 response, 357-361,363-364; defined, 413 spectrum, acoustic, 4 Gallium arsenide (GaAs), 24-25, 74, 87, 140, 338 Gel, 134, 174, 309 Gibb's free energy, 192, 257, 293, 295 Glass transition, 156-163, 165, 168, 209, 212, 244, 288, 377 temperature of, 156-163, 288; defined, 413 Glue, 274 Hacskaylo-Levan equation, 265 Harmonics, 12, 40-41, 76, 99, 161, 163, 370 Header, 381; defined, 411 Henry's Law, 263, 290 Hildebrand solubility parameter, 295-300 Hooke's Law, 113 Hydration, of polymer layers, 207

Hydrogel, 275 Hydrogen bonding, 155, 252-253, 273, 275 Hydrophilic, 62--63, 195,352; defined, 413 Hydrophobic, 62-63, 195, 278, 291,352; defined, 413 Ideal Gas Law, 296 constant, 257 IDT, 72-78, 102, 117, 226, 335-337, 339-342, 347, 361,368, 370-375, 381,383; defined, 414 designing, 339-342 Immobilization, 225, 230, 273-274, 306, 309, 312 lmmunoassay, 140, 306-308, 311-313; defined, 413 Impedance matching, 370, 383 network, 356; defined, 414 Impurity scattering, 21 Inelasticity, 233 Insertion loss, 361,368, 371-373, 383; defined, 414 Insonication, 139-140 Instrumentation, 355-375 Interdigital transducer. See IDT Interference, 75, 96 common-mode, 385, 410 Interferences, sensor, 239, 284, 320 lntermolecular forces, 154 Inversion symmetry, 22 Irreversibility (chemical), 191,241-245, 248, 252, 256, 259, 269, 273, 279, 285-287, 289 Kelvin equation, 184, 265 Kinetic diameter (of molecules), 273 Kinetic effects (mixing, pumping), 113, 134-140 Kinetics, chemical, 191, 193, 195, 207, 241, 244-247, 251,266--272, 288, 342, 377, 385; defined, 414 Knudsen effusion, 270 Lamb wave, 113. See also FPW Lam6 constants, 17-18, 94-95. See also Elastic moduli, shear Langmuir-Blodgett film, 197, 209-210, 224, 235, 312, 349-350; defined, 414 Langmuir-Hinshelwood model, 269-270 Laser ablation, 199 Levenspiel unreacted-core model, 271 Lewis acid, 283 Lift-off process, 345; defined, 414 Limit of detection (LOD), 243-244; defined, 414 Linear dynamic range (LDR), 245; defined, 415 Linear-regression analysis, 299 Lipid bilayer, 209 film, 160, 209-210, 309 Liquid crystals, 209, 314 Liquid loading, 38-39, 54, 59, 102-103, 106-109, 112, 124-131,145, 226, 233, 366, 381

Index Lithium niobate (LiNbO3), 18, 24-25, 74, 80, 85, 87, 110, 234-238, 338 Lithium tantalate (LiTaO3), 238 London forces. See Dipolar interactions; Dispersion forces Loss modulus, 66, 68, 91,156, 163, 201,203 Loss. See Attenuation; Insertion loss; Damping Love wave, 153 sensor, 141 LPCVD (Low-pressure chemical vapor deposition). See Chemical vapor deposition Lysis, 140 Mass flow rate, 154, 242 loading, 5, 52, 80, 104-106, 119-123, 151-152, 155, 169, 181,198, 200, 209-210, 225, 230, 232, 234-237, 285, 292, 302, 366 Mass sensitivity, 152, 225-226, 235, 243 APM device, 104-107, 109, 111 FPW device, 120-122 SAW device, 79-82 Table of, 227 TSM device, 43--45, 193, 207, 226 Material properties acoustoelectric, 87 adsorbent materials, 274 adsorption on activated charcoal, 276 density, 18 elastic moduli, 94 piezoelectric, 24 quartz. See Quartz SAW propagation, ST-quartz, 95 sorption in natural rubber, 289 stiffness, 18 wave velocities, 20 Materials modification, 152 MaxweUian fluid, 106-107 Meat freshness sensor, 210 Mechanical impedance, 45, 51, 69, 96 Mechanical properties density, 18 stiffness, 18 Melting (of polymers), 157, 160, 244, 377 temperature of, 157-163, 289; defined, 415 Membrane biomaterial, 192, 306-308, 309, 311, 314 mechanical, 111, 115, 117, 119, 121,128, 131-132, 137, 140, 174, 342 separation, 150, 167, 178, 182 Metallization, 342-345 Microbalance, 4, 6, 39, 44, 66-67, 89, 106, 191,207, 210, 222 Microfabrication, 222, 342-346 Microflow, 139 Micromachining, 113-115, 336 Microsensor, 3 Mixing acoustic modes, 227 analyte/coating, 288, 294, 295 fluids or gases, 113, 134, 139-140 frequencies, 134, 376 Mixtures, 153, 297, 309, 319-320, 345, 390-391

433

Mode hopping, 372-373 Molecular sieve(s), 270, 274-275, 277-278 Molecular size, of adsorbate, 171 Monitoring chemical processes. See specific process material processes. See specific process Monitoring, real-time, 361-375 Monolithic, 393 Monomer, 154, 288-289, 354 Motional impedance, 46-57, 59, 63, 69-70 Nanotribology, 181 Network analyzer, 313, 356, 358-359, 362; defined, 416 Newton's First Law, 16, 113 Newtonian fluid, 39, 54, 56, 59, 106-109 Noise, 121-122, 145, 226, 244-245, 302-303, 337, 341,347, 362, 376, 382-384, 389; defined, 416 Non-slip boundary condition. See Slip, interracial Normal boiling-point model, 293-295 One-port device, 36, 333-334, 336, 358-360, 363, 365-368, 380, 383 Organo-clays, 278 Oscillator, 5, 27, 29, 77, 109, 127, 142, 245, 342, 391 circuit (loop) 4, 36, 39, 44, 81, 109, 118, 121,311,335, 341,361,363-374, 376, 383 Oscillator, synthesized, 357, 362, 372, 374; defined, 420 Ozone, 241,279, 286-287 Packaging, 346, 377, 379-382 Packed bed, 274 Palladium (Pd), 282, 286-287, 343 Parallel resonant frequency, 48, 360, 366; defined, 416 Parametric representation attenuation and velocity, 34-35 SAW response, acoustoelectric, 89-90, 305 SAW response, polymeric coating, 165, 305 Particle deposition and removal 197-200 formation, 210 sizing, 199 Partition coefficient, 160, 164, 176, 210-211, 230-231,248, 291-300, 309, 315, 377 Partitioning, 242, 279, 288, 293; defined, 416 Passive device, 355; defined, 416 Pattern recognition, 248, 313-320, 390-394 Permeability, 288, 354, 380 Permeation, 155, 167, 178-179, 247 Permittivity, 24, 110, 223 Perturbation, 22, 31, 34 FPW, 119, 133-134 SAW, 78 Pharmaco-chemical animal tests, 210 Phase shift, 368 shifter, 357, 370; defined, 416 slope, 374; defined, 417

434

Index

Phase transition, 181,209-210, 373 first-order, 157, 160. See also Melting second-order, 157, 160. See also Glass transition Phase velocity, 20, 30-31, 33, 115, 117 Phase-locked loop, 373-374; defined, 417 Phonon scattering, 21 Photolithography, 342, 344-346 Photoresist, 198, 200-203, 344-345, 349; defined, 417 Phthalocyanines, 235-237, 248, 282, 284, 353 Physisorption (physical adsorption), 179-191, 193, 251-252, 266-267, 270, 274; defined, 417 materials for 274-276 -based sensors, 277-279 Piezoelectric, defined, 417 constitutive relations, 24 coupling coefficient. See Electromechanical coupling coefficient material, 10, 45, 71-72, 74, 78, 83, 87, 110, 117, 222, 225, 234, 238, 331,333, 337-340, 375-376 material, thin film, 115, 117, 121,140, 247, 277, 337-339, 342, 376 point groups, 24 stiffening, 28, 30; defined, 417 stress constants, 24-25 transduction, 36, 39, 48, 74, 102, 117, 121, 277, 337 Piezoelectricity, 4, 10, 22-31,109, 117, 225, 234, 238, 247, 277, 306, 337-338, 375 Piezoresistivity, 338 Plasticization, 68, 99, 155, 164-167, 171,244, 291,302 Platinum (Pt), 136, 248, 278, 282, 284, 286-287, 343 Pogo pin, 382; defined, 417 Poisson's ratio, 17, 117 Polanyi adsorption potential concept, 265 Polarity, 273, 275 Polarization electrical, 22 mechanical wave, 19-20, 30 Polymer, defined, 154 glassy, 92, 97, 156-159, 176, 232, 247, 288-289 porous, 176, 274 properties. See Ch. 4.2, or specific property rubbery, 69, 92, 97, 122, 247, 288-289, 291, 300, 348 table of materials, 421-427 Polymer sorption isotherm, 290-293 BET, 290-291 FIory-Huggins, 290-291 Henry's Law, 290-291 Langmuir/Freundlich, 290-291 Polymerization, 151,200-204, 212, 275 photo-induced, 151 Pore size, 152, 181-191,259, 273-275 distribution, 152, 181-184, 188, 259, 273 Porosity, 63, 66, 178-179, 182-184, 187-188, 258-259, 265, 270, 273-275, 380

Powders, 274 Power, 28, 31-34 consumption, sensor system, 394 meter, 357; defined, 417 Power-law model, 269-270 Preconcentration; preconcentrator, 248, 386-389 Pressure, 224 effects, 63, 112, 127-128, 153, 156, 181, 224, 245, 267, 270, 290, 332, 334, 375, 378, 382, 385 Pressure, partial, 168-171, 179-184, 193, 257-263, 267, 269, 296, 378; defined, 416 Pressure, saturation vapor, 179, 182, 187, 258, 265, 273-274, 296, 314, 377; defined, 419 sensing, 128, 233 Principal-component analysis (PCA), 319 Printed-circuit board, 381 Process characterization, 209 monitoring, 197-212 Propagation factor, complex, 34, 71, 85 Pumping in sensor systems, 387, 389 with acoustic waves, 113, 134-140 Pure-mode direction, 20-21, 72 Pyroelectricity, 238; defined, 417 Q. See Quality factor QCM. See TSM; defined, 418 Quality factor, 181,334, 342; defined, 418 Quartz, 4, 18, 24, 39, 43, 46, 48, 101, 110, 227, 234, 247, 333, 33%338, 346, 348, 371,375, 378 AT-cut, 39, 40, 102, 227, 334, 338, 375; defined, 409 BT-cut, 338; defined, 410 fundamental properties of 18, 24, 40, 44, 49, 57, 74, 87, 91, 95, 227, 234, 341,376, 378 ST-cut, 74, 81, 87, 89, 91-92, 95, 97, 102, 161,227, 234, 238, 247, 338, 340-341, 375-376; defined, 419 surface adsorption/chemistry of, 87, 106, 111, 181, 196, 199, 237, 279, 309, 342, 351,352 Quasi-modes, 21

Raoult's Law, 263, 290, 296 Rayleigh principle, 30, 43 wave, 71-72, 340. See also SAW Rayleigh, Lord, 71 Receptor-protein pair, 306 Reciprocity, 74 Redox (oxidation/reduction) reactions, 193, 208, 237, 285-287; defined, 418 Reduced notation, 16-17, 24 Regeneration, 284 Regular solution theory, 295-300 Relative humidity, 205, 237, 239, 245-246, 248, 276-277, 285, 312; defined, 418 Relaxation effect; response, 85, 156-157, 175-176, 209, 289, 377 time, 106-107, 110, 131-132, 156-157

Index Reliability, 238, 245-246, 320 Remote sensor operation, 382-383 Repeatability, 245-246, 392 Reproducibility, 245-246, 277, 311,347, 349-350, 352 Resolution, 2 frequency, 356, 362-363 mass, 44, 81,106, 193 mode, 101 spatial, 345, 352, 390 Resonance, 39-43, 45--46, 57, 101; defined, 418 film, 67, 69-71, 99, 161-163, 167, 232, 377 Resonator, 226-227, 333-335, 347, 367; defined, 418 bulk wave, 333 SAW, 334, 336-337, 342, 361,364, 371, 393-394 TSM, 39. See also TSM Response time, 238, 246-247. See also Kinetics, chemical Reversibility (chemical), 38, 179, 209, 229, 238, 241-243, 245-246, 248, 251-252, 255, 274, 279, 282, 284-287, 307-308, 311,314 Rheology, 233-234 Saturation vapor pressure, defined, 419. See also Pressure, saturation vapor Sauerbrey equation, 44, 52 SAW, 4-5, 7, 36-37, 39, 71-99, 100, 117, 141-145, 152-154, 165, 168, 170-171, 174-175, 178, 181, 185-187, 191-194, 197-199, 205-206, 210, 222, 224-227, 229-230, 232-234, 236-237, 240, 248-250, 270, 277-282, 284-285, 294, 297, 299-302, 304-305, 311, 318, 320, 332-338, 341-342, 347, 358, 361, 363-364, 367, 371-372, 375, 378, 382-383, 391-392; defined, 419 resonator, 198, 227, 333-338, 341-342, 358-359, 361,364, 371,393 Scattering parameters (S parameters), 358, 361 Scholte wave, 126 Selectivity, 2-3, 38, 129, 145, 167, 182, 223, 228, 232, 237-241,243, 248, 251, 255-256, 273, 275, 278-279, 284-287, 289, 299, 302-303, 307-308, 309, 311-320, 347-355, 389-390 Self-assembled monolayer (SAM), 192-193, 208, 224, 285, 349-351,354; defined, 419 Sensitivity, 2, 38, 200, 223, 230, 238-239, 243, 377; defined, 419 adsorption-based sensors, 278 biochemically based sensors, 307-308 chemisorption-based sensors, 286-287 gravimetric, 81, 104, 120, 122, 151, 225-227. See also Mass sensitivity gravimetric and density to, 127-129 gravimetric, comparison, 141-145 pressure, 128 sorptive polymer-based sensors, 303 to elastic modulus changes, 232 to stiffness changes, 230 to temperature changes, 232, 234

435

Sensor, defined, 1 amperometric, 3 biochemical, 2-3, 112, 117, 200, 230, 234, 238-239, 246, 251-252, 254, 299, 306-313 chemical, 2, 4, 38, 165, 234, 25 l, 299, 318 enthalpimetric, 238 force, 112 humidity, 232 Love wave, 14 l optical, 3 pH, 311 potentiometric, 3 SH-SAW, 311 surface transverse wave (STW), 141 Taguchi, 2 thin-film compressional wave, 140 thin-rod, flexural-wave, 141 vapor (chemical vapor), 4, 68, 121-123, 139, 222, 229-230, 232, 235, 277, 318, 378, 384, 389, 393 viscosity, 107, 132, 145 Sensor array. See Array, sensor Series resonant frequency, 46-48, 51-52, 56-57, 360, 366-367; defined, 419 SH-APM. See APM; defined, 419 Shear, 14 deformation, 156 wave, 39, 41, 71 Signal-to-background ratio, 380 Signal-to-noise ratio, 121-122, 140, 244, 337, 347, 384 Silanization, 272-273, 275-276, 278, 307-308, 352 Silica, 277 gel, 274-275 porous, 278 Silicon (Si), 115, 277, 338, 371,376 Silicon nitride (Si3N4), 115, 117, 119, 134 Simultaneous measurement acoustoelectric and mass-loading effects, 89 electrochemical current and surface mass change, 207, 366 of multiple analytes, 314 reflected and transmitted RF power, 357 static and dynamic glass transition temperature, 160 velocity and attenuation, 107, 200-201,306, 314, 365 SiO2. See Quartz; Silica Slip, interfacial, 62, 181, 196, 209 Sol gel, 184, 187-188, 275, 277-278 Solubility, 164, 288 parameters. See Hildebrand solubility parameters Solvation, 293 parameters, 299 Solvatochromic parameters, 298 Solvent casting, See Coating methods Solvent effects, 207 Sorption, 159; defined, 419 polymer, 288-300 isotherm, 245. See also Polymer sorption isotherm

436

Index

Spin casting. See Coating methods coating. See Coating methods Spraying. See Coating methods Sputtering. See Coating methods Stability, 200, 238, 245-246, 334, 369 thermal, 145 Standing wave, 41,333, 336 Stationary phase, 297 Stiffened elastic constant, 30 Stiffness, 16-18, 28, 223, 230 Storage modulus, 66, 68, 91,156, 163, 201, 203 Strain, 12-18, 22, 25 Stress, 12-18, 212 Sublimation. See Coating methods Superconductivity, 209-210 Superlattices, 209-210 Surface acoustic wave, defined, 419. See also SAW Surface area, 152, 197, 243-244, 247, 258, 263-265, 271-274, 387 of film, 181-191,211 Surface chemical derivatization (functionalization), defined, 420. See also Coating methods Surfactant, 195-196, 208, 21 l Swelling, 164-165, 176, 297 Symmetry, 23, 25 Synchronous frequency, 74 modulation and detection, 385 System design 384-393 system sensor, 394 Temperature coefficient, 133, 234, 238, 247, 337-338, 346, 375-377 control, 233-234, 238, 375-378 effects, 232, 238, 247-250, 272, 332, 338, 375-378, 385 Tension, 18 Texture, surface, 59-66, 153, 198, 212 Thermal expansion, 377, 381 Thermal management, 381 Thermoelasticity, 21 Thickness shear mode. See TSM Thin-film interference, 69 Time-temperature superposition principle, 156 Transduction, 1 Transition metal, 235, 237, 241,254-255, 275, 277, 278, 282-287, 353 Transmission line, 383 Transport phenomena, 113, 134, 139, 208, 275 through films, 247, 270-272, 288 Triple-transit echo/reflection, 346 Trouton's Rule, 294

TSM, 4, 7, 36--37, 39-71, 54, 121,141-145, 153, 160, 176--177, 179-181, 187, 191, 193, 195-201,205, 207, 209-211,222, 224-227, 230, 232, 237, 277-279, 282, 285, 294, 302, 309, 311,332-333, 338, 347, 352, 358-360, 365, 367, 371,375, 381,383; defined, 420 Turbulence, 154, 379 Two-port device, 36-37, 334-338, 341,361, 363, 368---375, 380, 382-383 Vacuum deposition. See Coating methods, evaporation; Electron-beam-induced evaporation; Sputtering; Sublimation Valve(s), 170, 385-386, 389 Van der Waals equation, 17 l interactions, 179, 192-193, 251-252, 257, 35O Vanadium oxide, 238 Vapor sensing. See Sensor, vapor Velocity, phase, 40 Virus, 200, 307-309 Herpes, 309 Viscoelastic loading, 66, 68, 89, 152 Viscoelasticity, 151-152, 155, 157-158, 164-165, 200, 209, 212, 223, 228-234, 244, 302, 373; defined, 420 Viscosity, 6, 21-22, 153-155, 201,209, 223, 230, 271,309, 31 l; defined, 420 Viscous loading, 60, 107-108, 131-133 Volcanic eruptions, 199 Voltmeter, vector, 357, 362, 370, 372; defined, 420 Wave equation, 18-21, 25-28 excitation, 22, 27, 40, 69, 71-72, 74, 117 path; defined, 420 propagation, 10-35 velocity, 6 velocity in liquid, 153 Wavelength, 12 Wavenumber, 12, 34 Waves in solids bulk, lO, 21-22 compressional, 20 plate, lO shear, 22, 27, 30 surface, 10 Wire bonding, 382; defined, 420 Young's modulus, 17, I 17 Zeolite, 274-275, 277 Zinc oxide (ZnO), 18, 24-25, 27-28, 117, 119, 121,134, 227, 238, 247, 277-278, 337-338, 371,376 Zinc oxide-on-silicon, 235, 277, 371,376

Series Preface

Modern Applications of Acoustics is a series, that will, in the hopes of the editors, present the most exciting developments in the applications of acoustics that have emerged in the past few decades. This first seven-author volume, which was already nearing publication when the series was conceived, is an auspicious beginning. It can be argued that all living entities have their own built-in biological acoustic sensors, be they aural or tactile, whose sensitivity, in some instances, is at the optimum signal-to-noise level. For instance, it is known that if the human ear were any more sensitive, Brownian noise would mask the intelligibility of perceived sound. It is possible that the sound emitted by crackling dry leaves and twigs may be the first artificial sensors devised by humans for detecting game or intruders. The sensors described in this volume avail themselves of the most modem microphotolithographic techniques, and use sophisticated signal processing techniques that could not be achieved without the use of the formidable power of modem computers. But, the germinal ideas are the product of human ingenuity. The editors envision that future volumes will be authored by scientists and engineers who are internationally recognized in their fields as experts and who have made major contributions to the advancement of their areas. The series will include volumes that may be prepared by a single author, a few co-authors, or in the instance of emerging fields, the required expertise may best be harnessed by a guest editor who then will solicit contributions from many experts in narrower subfields. At present the editors are actively pursuing the publication of volumes in ther-

xi

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Series Preface

moacoustic engines, resonant ultrasonic spectroscopy, modem architectural design, active noise suppression, biological and industrial flow detection, nondestructive evaluation, underwater detection, acoustic tissue characterization, sonoluminescense, and more. The editors dedicate this series to their thesis advisor and mentor, Professor Isadore Rudnick.

Richard Stern Moises Levy