Advances in Electronics and Electron Physics, Volume 31

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 31

CONTRIBUTORS TO THISVOLUME P. L. Bargellini P. H. Dawson W. J. Fleming G. H. Kimbell Sherman K. Poultney E. S. Rittner J. E. Rowe Richard 0. Rowlands Edward S. Yang

Advances in

Electronics and Electron Physics EDITED BY L. MARTON Sniithsoniun Inst it u tion, Washington, D. C. Assistant Editor CLAIRE MARTON

BOARD EDITORIAL E. R. Piore T. E. Allibone M. Ponte H . B. G. Casimir W. G . Dow A. Rose L. P. Smith A. 0. C . Nier F. K. Willenbrock

VOLUME 31

1972

ACADEMIC PRESS

New York and London

COPYRIGHT 0 1972, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. N O PART OF THlS PUBLlCATlON MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION I N WRITING FROM T H E PUBLISHER.

ACADEMIC PRESS, INC.

1 1 1 Fifth Avenue, New York. New York 10003

United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/24 Oval Road, L o n d o n N W 1

LIBRARY OF

CONGRESS CATALOG CARD

NUMBER: 49-7504

PRINTED IN T H E UNITED STATES OF AMERICA

CONTENTS CONTRIBUTORS TO

FOREWORD . .

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Vii

ix

Chemical Lasers P . H . DAWSONA N D G . H . KIMBELL

I . Introduction .

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11. General Conditions for Lasing Action . 111. The Vibrational Transition . . . . 1V . The Pumping Reaction . . . . . . V . Relaxation of the Excited State . . . V1. Characteristics Favorable to Chemical Laser

VII . Some Laser Systems . VIII . Conclusion . . . . . . References

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3 5 9 16 26 29 35 36

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Single Photon Detection and Timing: Experimentsand Techniques SHERMAN K . POULTNEY I . Introduction . . . . I1 . Single Photon Detection

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. . . . . . . . . . . . . . 111. Fast Timing with Single Photons . . . . . . . . . 1V. Single Photon Detection with Moderate Timing Requirements . Appendix: Summary of Photomultiplier Notation . . . . References . . . . . . . . . . . . . . .

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39 42 69

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Advances in Satellite Communications P. L . BARGELLINI AND E . S . RITTNER

I . Introduction .

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11. The INTELSAT System 111. The Orbita System . .

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1V . Systems Considerations .

V. V I.

VII .

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. . . . . . Spectrum and Orbit Utilization . . . . Modulation, Multiplexing. and Multiple Access Electron Devices . . . . . . . . . Materials Technology . . . . . . . . . . . . . . . . Future Trends References . . . . . . . . . . . . V

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119 123 . . . . . . . . . 127 . . . . . . . . . 128 . . . . . . . . . 130 . . . . . . . . . 134 . . . . . . . . . 137 . . . . . . . . . 155 . . . . . . . . . 157 . . . . . . . . 158 .

vi

CONTENTS

AcoustoelectricInteractions in In-V Compound Semiconductors AND J . E . ROWE W J FLEMING

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I . Introduction . . . . . . . . . . . . . . . . . . . I1 General Theory of Off-Axis Acoustoelectric Interactions . . . . . . 111. Exact Solution of the Acoustoelectric Interaction for Collinear Static Fields IV . Solution of the Acoustoelectric Interaction for Arbitrarily Oriented Static Fields and On-Axis Acoustic-Wave Propagation . . . . . . . . . V . Solution of the Acoustoelectric Interaction for Arbitrarily Oriented Static Fields and Off-Axis Acoustic-Wave Propagation . . . . . . . . . VI . Solution of the Acoustoelectric Interaction for Electron-Hole Carrier Transport and Off-Axis Acoustic-Wave Propagation . . . . . . . . . VII . Summary . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

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i62 166 I76

185 206 234 242 244

Current Saturation Mechanisms in Junction Field-Effect Transistors EDWARD S . YANG

1. I1. 111. IV . V. VI . VII . VIII .

Introduction . . . . . . Review of the Literature . . . Governing Equations . . . Gradual Channel Approximation Saturation Models . . . . Numerical Calculation . . . Current Saturation in MOSFETs Conclusion . . . . . . References . . . . . .

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249

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Electronic Engineering in River and Ocean Technology RICHARD 0. ROWLANDS I . Introduction . . . . . I1. Water Quality Measurement 111. Surface Waves . . . . 1V. Tides . . . . . . . V . Ocean Currents . . . . VI . Navigation . . . . . VII . Sonar Application . . . VIII . Fishing . . . . . . . IX . Helium Speech Processing . X . Data Transmission . . . References . . . . . AUTHORINDEX . . . . SUBJECTINDEX . . . .

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261 268 214 216 217 280 283 293 295 295 299

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CONTRIBUTORS TO VOLUME 31 P. L. BARGELLINI, COMSAT Laboratories, Clarksburg, Maryland P. H. DAWSON,Centre de Recherches sur les Atomes et les Molecules, Universite Laval, Quebec, Canada W. J. FLEMING,* Electron Physics Laboratory, Department of Electrical and Computer Engineering, The University of Michigan, Ann Arbor, Michigan

G . H. KIMBELL, Defence Research Establishment Valcartier, Courcelette, QuCbec, Canada SHERMAN K. POULTNEY, Department of Physics and Astronomy, University of Maryland, College Park, Maryland

E. S. RITTNER, COMSAT Laboratories, Clarksburg, Maryland J. E. ROWE,Electron Physics Laboratory, Department of Electrical and Computer Engineering, The University of Michigan, Ann Arbor, Michigan RICHARD 0. ROWLANDS, Ordnance Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania

EDWARDS. YANG,Department of Electrical Engineering and Computer Science, Columbia University. New York, New York

* Present address: Research Laboratories, General Motors Corporation, General Motors Technical Center, Warren, Michigan 48090. vii

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FOREWORD The present volume encompasses a greater variety of subjects than some of its predecessors. The phenomenal growth of laser research and development is reflected in Dawson and Kimbell’s review of chemical lasers. Parallel, however, to the development of more sophisticated light sources, work proceeds toward the detection of fainter and fainter sources of light. Thus it is very timely to review single photon detection experiments ; Poultney’s review covers techniques as well as the experimental results. The review of Bargellini and Rittner tackles an important aspect of the problem of communication. The use of satellites for communication is a relatively new field, but sufficiently advanced to warrant a review of its present stat us. The next two contributions take us into semiconductor technology. First, there is a discussion, by Fleming and Rowe, of acoustoelectric interactions as they appear in 111-V compound semiconductors. A different aspect is treated in Yang’s review of current saturation mechanisms in junction fieldeffect transistors. The final contribution, by Rowlands, covers a field which we have not treated for several years: oceanography. The title of the review, Electronic Engineering in River and Ocean Technology, is indicative of the scope of the discussion. In our next few volumes we expect to publish reviews on the following subjects : Galactic and Extragalactic Radio Astronomy Image Formation in the Electron Microscope Recent Advances in the Field Emission Microscopy of Metals Multiple Scattering and Transport of Microwaves in Turbulent Plasmas Microfabrication Using Electron Beams The Effects of Radiation in MIS Structures Small Angle Deflection Fields for Cathode Ray Tubes Sputtering Interpretation of Electron Microscope Images of Defects in Crystals Optical Communication through Scattering Channels Wave Interactions in Solids ix

Wrn. C. Erickson and F. J.

Kerr D. L. Misell L. W. Swanson and A. E. Bell V. L. Granatstein and D. L. Feinstein A. N . Broers Karl Zaininger R. G. E. Hutter and H. Dressel M. W. Thompson

M. J. Whelan Robert S . Kennedy Morris Ettenberg and Vural

B.

X

FOREWORD

Hollow Cathode Arcs Channelling in Solids Physics and Applications of MIS-Varactors Ion lmplantation in Semiconductors Self-Scanned Solid State Image Sensors Quantum Magneto-optical Studies of Semiconductors in the Infrared Gas Discharge Displays Photodetectors for the i p to 0.11” Spectral Region High Resolution Nuclear Magnetic Resonance in High Superconducting Fields The Photovoltaic Effect Application of Single Photon Techniques

The Future Possibilities for Neural Control Electron Bombardment Ion Sources for Space Propulsion Recent Advances in Hall-Effect Research and Development Semiconductor Microwave Power Devices The Gyrator Electrophotography Microwave Device Technology Assessment The Excitation and Ionization of Ions by Electron Impact Whistlers and Echos Experimental Studies of Acoustic Waves in Plasmas

J. L. Delcroix R. Sizmann and Constantin Varelas W. Harth and H. G. Unger S. Namba and Kohzoh Masuda Paul K. Weimer Bruce D . McCombe and Robert J. Wagner R. N. Jackson and K. E. Johnson David H. Seib and L. W. Aukerman

H. Sauzade Joseph J . Loferski Sergio Cova, Mario Bertolaccini, and Camillo Bussolati Karl Frank and Frederick T. Hambrecht Harold R. Kaufman D. Midgley S. Teszner K. M. Adams, E. Deprettere, and J. 0. Voorman M. D. Tabak and T. L. Thourson Jeffrey Frey and Raymond Bowers John W. Hooper and R. K. Feeney Robert A. Helliwell J. L. Hirshfield

We would like to express our pleasure that the request for suggestions on subjects and authors, voiced at the end of the forewords of previous volumes, has borne fruit. A number of valuable suggestions and proposals were received; this volume, as well as earlier volumes, reflects those results. We would like to repeat our request and amplify it by saying that inquiries from potential authors are most welcome. L. MARTON CLAIRE MARTON

Chemical Lasers P. H . DAWSON Centre de Recherches sur les Atonies et les Molecules, Universite Laval, QuPbec, Canada

AND

G. H. KIMBELL Defence Research Establishment Valcartier, Courcelette, Quebec, Canada

Ill. The Vibrational Transition. .....................

...........

V. Relaxation of the Excited State . . . . . . . . . . 16 V1. Characteristics Favorable to Ch VII. Some Laser Systems. . . . . . . . . . . . . . . . . . . . 29 A . A True Chemical Laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. A Flame Laser.. . . .

I.

INTRODUCTION

Gas lasers (I) can be characterized according to the means by which the necessary population inversion is achieved. This mechanism may be, for example, excitation by energetic collisions-such as electron bombardment in a gas discharge, by photoh impact, or by the direct production of excited species in chemical reactions (chemical lasers). Chemical lasers were the last type to be realized but represent a rapidly evolving technology. 1

2

P. H. DAWSON AND G . H. KIMBELL

In 1958, Schawlow and Townes (2) made the first proposal for an “optical maser ” using population inversion in a gas. This was to utilize optical pumping. However, the first practical device was the result of work by Javan et al. (3) in 1961 and used a gas discharge. The following ten years have resulted in the development of a large number of these “physical” lasers. The carbon dioxide system, in particular, is capable of high power (up to 60 kW cw has been realized using gas dynamic principles) and, i n certain cases, operation at atmospheric pressure (4). The electrical efficiency (power out/power in) is generally of the order of 5 The possibility of a chemical laser was recognized in the early days of the gas laser ( 5 ) and in 1964 a symposium was organized on this subject (6); at about the same time the first chemical laser was devised by Kasper and Pimentel (7) using the reaction between atomic chlorine and molecular hydrogen to form vibrationally excited HCI. The reaction was initiated by the production of chlorine atoms in flash photolysis. The laser action, of course, only occurred as a short duration pulse. The use of pulsed electrical discharges to produce reactive atoms was a subsequent development (8) and the first continuously operating lasers (cw) were only reported late in 1969 (9,ZO). Since this breakthrough, there has been a rapid advance in the development of chemical laser systems although the chemical reactions utilized for cw lasers have been largely limited to the formation of hydrogen halides and to the formation of CO in a reaction between oxygen atoms and carbon disulphide (11). One system has been found (J2) which is a true chemical laser and requires no external energy input to create the reacting atoms, i.e. to initiate reactions. Scientifically,chemical lasers are of importance as tools which give deeper knowledge of chemical reactions. They are of potential technological importance because of the possibilities of high efficiency and freedom from the dependence on an external power source. Much development work is still required to increase power, and, more especially, efficiency. Ultimately it is hoped to achieve efficient operation at atmospheric pressure or in flames without external power input. The art of chemical lasers is, nevertheless, still in its infancy. In this article we discuss first the necessary conditions for the achievement of chemical lasing action and then describe, in turn, the important processes involved in lasing systems such as (a) the vibrational transition which gives the emitted radiation, (b) the production of vibrationally excited species by reaction, and (c) the vibrational-vibrational and vibrational-translational energy exchanges which can cause depopulation of the excited levels. The aim is to elucidate the kind of characteristics one must look for in the search for new and improved chemical lasers. Finally we describe some typical examples of chemical lasers to illustrate the progress achieved. Since the

x.

3

CHEMICAL LASERS

field of chemical lasers is evolving so rapidly, there is no attempt at comprehensive coverage of the achievements. Such a review would be outdated before its publication. Rather, the intent is provide a general view of the field and to illustrate present experimental trends. 11. GENERAL COND~TIONS FOR LASING ACTION

The laser is based (13) on the fact that a molecule i n an excited state can be stimulated to emit some or all of its excitation energy by an incoming photon that has exactly the right energy. The incoming photon may therefore be amplified as it passes through the lasing medium. If the incoming photon meets a molecule in the lower (less excited or ground) state, it may be absorbed. Therefore a necessary condition for overall amplification is that there is a large population of molecules in the excited state. This provides the lasing medium (analagous to a negative resistance). Since, in many systems, the amplification or gain per meter of path length is not very large, the cascade process is increased by having the lasing medium within an optical resonance cavity. The cavity consists of a pair of aligned mirrors which reflect the laser radiation. Figure 1 illustrates a simple geometrical arrangement which is frequently used. More details of experimental systems are given in Section VI. Let us look in more detail at the conditions which are favorable for lasing action. Consider a simple two-level system. The absorption coefficient cq, in a medium, for radiation at the center of the transition (when natural line broadening is small in comparison with Doppler broadening), is given by (14)

'I

TO -2450Mc

~

EX HA U ST

MICROWAVE

FLAT FRONT-SURFACED MIRROR Se ON Ca FE 2%TRANSMISSION ~~~

E"

120CM

~

4 M RADIUS ALUMINIZED MIRROR ~

-

~

~-~-

FIG.I . The geometrical arrangenientsof a longitudinal flow, continuous wave, chemical laser.

4

P. H. DAWSON AND G. H. KIMBELL

where e is the electron charge, rn the electron mass, f21 the oscillator strength of the transition from state 2 to state 1, N, the population density of molecules in the lower level (state l), N, the population density in the upper laser level, g1 and g2 are the statistical weights of the two states, and A v D is the Doppler width of the transition and can be expressed as AvD =

(2vo/c)[(2KT/M) In 2I1l2,

(2)

where vo is the center frequency of the transition, K the Boltzmann constant, T the absolute temperature, and M the atomic mass. For optical gain, a0 must be negative. That is, g1lg2 . N , > N , .

(3)

To satisfy this condition, one must have an appreciable excitation rate to the upper level and it is desirable that the lifetime of the upper level (due to radiation and other deexcitation) be much greater than that of the lower level. For laser oscillation there must be a net gain in the system. For a medium of length I, the gain is exp( -uo I ) - 1 where a0 is now negative. For small gain, this can be approximated by - uo 1. For a net gain in the system -u,I > L, where L represents the total of diffraction and reflection losses involved in the single pass through the optical cavity.

Laser action is therefore favored for transitions with small line widths and large oscillator strengths. Obviously optically allowed transitions are desirable. By chemical reaction, it is possible to form species in rotationally, vibrationally, or electronically excited states. Rotational energy is rapidly thermalized since only a few molecular collisions are required to sec at 1 Torr of a molecular gas). Vibrational level lifetimes are of the order of 10-2-10-3 sec. Most electronically excited levels have shorter lifetimes and it is difficult to form these excited states, by chemical means, at a high enough rate to obtain a population inversion. As expected, laser action on vibrationally excited levels has proved to be the easiest to achieve. Use of purely rotational transitions has been reported (15) but, so far, chemical lasers do not employ electronically excited levels. An intriguing idea for the latter involves molecules which are only stable in the excited state, the lower (or ground) level then always having a very low population.

5

CHEMICAL LASERS

The characteristics of the vibrationally excited levels and the associated transitions are now examined in more detail.

111. THEVIBRATIONAL TRANSITION We consider the transitions of diatomic molecules for simplicity and because present chemical lasers involve mainly such molecules. The simplest model for a vibrating molecule is a harmonic oscillator (16) for which the energy levels are equidistant. The levels are separated by hvo .

E(v) = hvo(u

+ 9,

where v is the vibrational quantum number and can have integral values 0, 1 , 2 etc. and vo

= (1/2Zl(WP)>

where p is the reduced mass and k is the force constant. A much better approximation is the anharmonic oscillator of which the energy values are given by E(u) = hv,(v

+ +) - hv,x,(u + *)’ + hv,y,(v +

4)3

...,

(5)

where ye 4 x, 6 1. Figure 2 gives an example (16) of an anharmonic potential curve and the associated vibrational levels. Each vibrational level is actually made up of a number of closely spaced rotational levels. A suitable model is the nonrigid rotor (two mass points connected by a massless spring) of which the rotational energy levels are given by

E,.(J) = hc[BJ(J

+ 1)

-

DJ’(J

+ l)’],

(6)

where J is the rotational quantum number and B is a rotational constant (in cm-’) which is inversely proportional to the moment of inertia. D is much smaller than B but is larger the smaller the vibrational frequency (i.e. the less rigid the rotor). Energy levels of a vibrating rotator are illustrated (16) in Fig. 2b. The constants B and D vary a little according to the vibrational level. The selection rule for transitions between the rotational levels of different vibrational levels is AJ= + I (provided that A = 0; the Q branch, AJ = 0, can be seen for molecules such as NO and OH). Furthermore, although 2’ can change by any integral amount since the oscillator is anharmonic, Ao = 1 (the fundamental) still gives far

6

P. H. DAWSON AND G. H. KIMBELL

la)

V"

(L

W W

z

-0

INTERNUCLEAR DISTANCE (b)

4 "'I

I

3 2 '0

ENERGY LEVELS 4 v

=o

3 2 '0

IIII.illlI P

R

SPECTRUM Y

FIG.2. (a) An anharmonic potential energy curve for a diatomic molecule, showing schematically the positions of the vibrational levels. (b) Rotation-vibration energy levels showing the allowed transitions, AJ = & 1, and the resulting P and R bands of the spectrum.

more intense transitions than the overtones (I Avl > 1). As indicated in Fig. 2b, those transitions for which the rotational level is highest in the lower vibrational level are known as the P branch and vice versa as the R branch. Now consider the population of the various levels. The rotational and vibrational temperatures will only be identical under equilibriuni conditions. For a temperature T,,, the distribution between the vibrational levels is given by the Maxwell-Boltzman law Nu e - E v l K T v . (7) However, for the rotational levels each level has a (25 + ])-fold degeneracy (the levels coinciding in the absence of a magnetic field) and therefore

N J K (25 + I ) e - E J / K T r as in Fig. 3.

7

CHEMICAL LASERS b

02-

J

FIG.3. Illustration of the population distribution among rotational levels, expressed as N J / x N J as a function of J , where N J = N J U l ) - ‘ h c ’ K T ” B ~ J ( J’ +) . The rotational temperature T, is 300°K. Curve A represents HCI with B equal to 10.59 and curve B represents N 2 0 for which B = 0.41.

+

Let us compare two adjacent vibrational levels and the conditions for which a population inversion between appropriate rotational levels will occur. If the vibrational temperature is negative (i.e. > N , ) and the rotational temperature is positive (the rotational energy will in fact be thermal in most cases), then there will be a population inversion for all P branch transitions and for some R branch transitions. For the P branch transitions the population distribution within the rotational levels provides a “natural assistance towards the inversion. For the R branch transitions the population distribution works against the inversion. Figure 4 illustrates some calculated gains for various conditions. The condition > N u has become known as a “ total population inversion.” When T, is positive, but T, > T , , a population inversion can exist between certain rotational levels of adjacent vibrational levels. This is called a “partiaI population inversion.” Owing to the rapid redistribution of energy between vibrational levels, many diatomic gas lasers operate under conditions of partial inversion. The inversion is again the result of the shape of the distribution curve for the rotational levels. ”

8

P. H. DAWSON AND G . H. KIMBELL

0

I

1

I

I

I

I

4

8

12

16

20

24

Upper level

*

J

FIG.4. Normalized gain curves calculated by Patel (33) for the P and R branches of the 7-6 transitions of CO, plotted as a function of the upper level J for T = 300°K and population ratios between the 7 and 6 levels given by N,,/Nu,= 0.8,0.9, 1.0, 1.1, and 1.2.

Consider the necessary conditions for the population of the level ( u + I , J - I) to be greater than that of ( v , J ) (i.e. P branch transition), with the simple approximation that the rotational constant B is the same for both levels and that the vibrational populations are represented by a vibrational temperature T, and the rotational level populations by a temperature T , . For inversion Nv+l,J-l

or

'Nu,

J ,

CHEMICAL LASERS

9

Tv/Tr> vo/2JBc.

(1 1)

If J is large, this simplifies to

This condition can obviously be satisfied if T, > T , and if J is sufficiently large [a situation exploited in gas dynamic lasers (17)]. The inversion is favored for molecules with a large B ; that is, a small moment of inertia. In such a case it tends to occur at smaller J values where the absolute population densities are higher and laser gain will also be higher. The condition (11) can be more accurately expressed

TJT, > vo/c[2JB,+ aJ(J - I)],

(12)

where a = B, is the constant of interaction between rotation and vibration. The derivation of a condition analagous to (11) but for an R branch transition N u + , , , + , > shows that an inversion can only occur if the vibrational temperature is negative. As shown in Fig. 4, even for total inversion the P branch transitions tend to dominate. However, R branch transitions have been observed in many cases and can be isolated by the use of selective tuning of the appropriate wavelength using a grating within the optical cavity (18).

IV. THEPUMPING REACTION The pumping reaction must, of course, be exothermic, must lead to product molecules in an inverted population, and must be sufficiently fast to maintain an appreciable inversion in the system. Measurement of product energy distributions have generally been made by studying infrared chemiluminescence, as will be described later, or by molecular beam techniques. Theoretical approaches to predicting the factors favorable to vibrational excitation will be considered first. A . Theoretical Approaches

The main effort has been in the use of classical trajectory calculations of reaction dynamics, especially by Polanyi and co-workers (19-21). We will give a qualitative account of such calculations. Consider the three-body exchange reaction A-tBC

-

ABIC,

Assumption of a suitable potential energy hypersurface is the starting point of the calculation, since ab iniiio calculations of these surfaces are only just beginning to be carried out. Figure 5 shows some simplified schematic

10

P. H. DAWSON AND G. H. KIMBELL

‘E

rAB

‘AS

FIG.5 . A schematic representation of three types of potential energy surfaces for the collinear reaction A BC + AB C. (a) A repulsive surface, the energy barrier is in the retreat coordinate; (b) an intermediate case; (c) an attractive surface, the energy barrier is in the approach coordinate. The broken lines represent possible trajectories giving rise to varying degrees of vibrational excitation of the products.

+

+

examples for collinear reaction. Three-dimensional computations have also been carried out (22,23). The classical Hamiltonian equations of motion are integrated numerically for motion on the potential energy hypersurface, involving 12 simultaneous differential equations. Different choices of initial conditions can be made and generally “ batches” of trajectories (perhaps 300) are calculated and the results averaged to simulate the normal Boltzmann distributions of translational and vibrational energy in the reactants. The examples of Fig. 5 show surfaces which differ in the location of the saddle point ; the energy barrier being located in the retreat coordinate (a) (called a repulsive surface), in an intermediate position (b), or in the entry valley or approach coordinate (c) (called an attractive surface). Although the families of trajectories are necessary to obtain quantitative results, the qualitative trends are readily discernable in examining individual trajectories. For example, in the figure the dotted lines show trajectories for cases where reactants have a translational energy only slightly in excess of that necessary to pass over the saddle point and a small initial vibrational energy. Figure 5a shows little of the released energy appearing as vibration; Fig. 5c shows much of the energy appearing as vibration and Fig. 5b is intermediate. That is, the location of the energy barrier in the approach coordinate favors vibrational excitation of the reaction product. One can perhaps better understand

CHEMICAL LASERS

11

this by considering a rolling ball on an analogous potential surface. Other interesting results are that initial translational energy is effective in increasing the reaction cross section on the Fig. 5c attractive ” potential surface but the fraction of the energy appearing as vibration tends to decrease. Initial vibrational energy does not help in this type of reaction. For the “repulsive” case Fig. 5a, the opposite situation applies. Initial vibrational energy enhances the cross section and increases the small fraction of energy appearing as vibrational excitation of the products. To increase the value of these results, Mok and Polanyi (21) have attempted (for some related families of reactions) to correlate the barrier location with other better known properties of reaction. They conclude that for substantially exothermic reactions the barrier is in the entry valley. For decreasing barrier height the barrier moves to successively earlier positions along this valley. It has also be found (19) that the most probable trajectory depends on the relative masses of the particles involved and this is important particularly for the intermediate case (Fig. 5b). The optimum situation for the release of energy as vibrational excitation of AB occurs when M A N M , 4 M c . The case of M A 6 M , N M , is unfavorable. Polanyi has recently produced movies derived from the computed trajectories, vividly illustrating the collision dynamics. Quantum mechanical solutions for collinear reactive systems have also been obtained (24,2.5) and these include the possibility of “ tunneling ” through the potential barrier. The degree of vibrational excitation predicted was quite low but the quallitative features outlined above were confirmed. At low energies (just sufficient to overcome the barrier) quantum tunneling increases the reaction cross section if the barrier is narrow and more of the available energy becomes vibrational excitation. This is more likely to be important for the H atom; for example, with H + C1, tunneling would be effective below about 500°K. “

8. Experimental Studies

Of concern in the experimental investigations is the measurement of the initial vibrational energy distributions; that is, the rate constants for reactions into levels L’ = I , v = 2, . . . , etc., before any relaxation has occurred. The relaxation processes can then be studied as a separate factor (Section IV). Two methods of approach have been developed-the method of arrested relaxation and the method of measured relaxation (26). As the name suggests the principle of the first method is to prevent relaxation from influencing the observations while directly observing the vibrational energy distributions by means of the emitted infrared radiation. It may also permit the observation of initial, rotational energy distributions.

12

P. H. DAWSON AND G. H. KIMBELL

The second method consists of making observations of vibrational distributions at known times after mixing and deducing the initial distribution, often by a simple extrapolation. Figure 6a shows a reaction vessel used by Polanyi and co-workers in the method of arrested relaxation. It is a large chamber with internal mirrors and walls that can be liquid nitrogen cooled. Experiments are carried out at pressures in the l o w 4Torr range so that the mean free paths are comparable to the cell diameter. Product molecules should be removed from the vessel by capture at the walls before significant gas phase relaxation can occur. The cold walls appear to work quite efficiently for the hydrogen halides (26) but in removing vibrationally excited OH, room temperature walls coated with silica gel (27) were found to be more effective. The population of the vibrationally excited products can be determined by recording the fundamental or first overtone regions of the infrared luminescence. The first overtone is frequently used, because of the sensitivity of lead sulphide detectors in that region. Conventional infrared grating spectrometers have been used but Fourier transform spectroscopy (27) has been recently applied to the H + 0, reaction as illustrated in Fig. 6a. The latter gives advantages in efficiency which can be important in low pressure studies. Figure 7 shows the results obtained by Polanyi et al. for OH formed in the reaction H O 3 OH* 0 2 ,the populations being given relative to u = 9. At 3 x Torr the distribution of products is quite different from that at 5 x low4Torr suggesting that gas phase relaxation became important. That the spectra of Fig. 8 at 5 x Torr represent initial distributions is supported by observation of the rotational energy distributions (Fig. 8) for which the populations of the higher levels are very much in excess of room temperature values and where the distributions are clearly nonBoltzmann. The method of arrested relaxation has also been applied to the reactions H CI, HCI* C1(26), H + Br, -+ HBr* + Br (26), CI + HI --t HCI* + I (28), and H SCI, HCI* SCI (29). A mean fraction of the available energy in the vibrational mode as great as 6 5 % has been observed. In favorable cases contours of equal detailed rate constant as a function of vibrational and rotational energy of the products [and therefore also of the translational plus internal energy ( E ’ ) ] can be determined. Figure 9 shows an example for H SCI, -+ HCI + SCI. Figure 6b shows a reaction vessel for the method of measured relaxation, as described by Polanyi et al. An analagous system has also been used by Jonathan, Melliar-Smith, and Slater (30). Measurements are made of infrared emission at successive points along the line of flow; that is, at different times after mixing and reaction. Extrapolation to zero time may give indications of the initial distribution. Polanyi’s vessel has three circular bands of highly reflecting gold (shaded in the figure) which sharply delineate the

+

+

-+

+

+

-+

+

-+

+

+

FIG.6a. Apparatus of Polanyi et al. (27) for the study of the initial distribution of vibrational states of OH formed by H O3 + O H O2 by the method of arrested relaxation. A Fourier transform spectrometer was used to give greater sensitivity and the ability to work at very low pressures.

+

”,

+

-+J I cm

TOP

MIDDLE

BOTTOM

FIG.6b. Flow tube (31) used in the method of measured relaxation. a, Wood’s discharge tube; b, CI2 inlet; c, wire screen; d, pressure probe; e , lateral wall of vessel; f, slide valve; g, liquid nitrogen trap.

14

P. H. DAWSON AND G . H. KIMBELL

o,2

0

1

5x

Torr

3

4

5

6

7

8

9

U

FIG.7. Distribution of vibrational levels of OH (formed by H i '03) relative to it = 9, observed by Polanyi ef a / . (27) by the method of arrested relaxation at 3 x lo-' Torr and 5 x Torr. The latter represents the initial vibrational energy distribution.

volumes viewed via the corresponding windows. The distance between adjacent windows corresponds to a time difference of about I . 1 msec. Pacey and Polanyi (31) have made a detailed computer analysis of the diffusion, flow, radiation and deactivation occurring in their flow tube, and find that the K, obtained by detailed calculation are fairly close to those obtained by simple extrapolation, but the latter does tend to give rate constants for the lower vibrational levels which are too large. Obviously, the details of gas mixing and flow will be different in different systems and simple extrapolation

15

CHEMICAL LASERS

v = ?

-.._ ---__

0

I

0

10

1

I

I

I

1

1

1

1

1

1

20 3.0 40 50 60 ROTATIONAL ENERGY (kcol m o l d )

1

1

7.0

I

.

8.0

FIG.8. Relative rotational populations within vibrational levels u = 7, 8, and 9 for the experiment at 5 >: Ton shown in Fig. 7. The A curves refer to t h e n J i t substate; the B curves to the HI,* substate. The dashed curves are Boltzniann distributions drawn on the assumption that the lowest rotational levels have been thernialized to correspond to the wall temperature.

to zero time, unsupported by detailed calculation, may be misleading. According to Pacey and Polanyi, their corrections for relaxation are not very sensitive to the relaxation model, suggesting that their flow tube is not suited to the determination of relative relaxation rates. For H + CI, -+ HCI C1 vibrational distributions are in quite good agreement with those measured by the method of arrested relaxation as shown in Fig. 10.

+

16

P. H. DAWSON AND G . H. KIMBELL

,

60

~

0,4

,

0,8

,

1,2 H+SC12

,

1,6

-

,

2,o

,

HCI(V'J')+SCI

2,4 e l

eV 24

EXOHERMIC

50

,

v ' = 6 lkf=OOO)

20

R' (kcal mole-')-

+

FIG.9. Contours of equal detailed rate constant (29) for the reaction H SCI2+ HCI SC1 plotted versus product (HCI) vibrational energy V', rotational energy R', and translational energy plus 'internal energy of SCI, symbolized E', the latter being given by the diagonal dashed lines. The total energy available is 48 kcal mole-'. The rate constants are given relative to a total rate of 1.OO into the u' = 3 level (the most populated level).

+

V. RELAXATION OF THE EXCITED STATE We have considered the formation of vibrationally and rotationally excited states by chemical means. In the laser, we are concerned with the subsequent evolution of the excited population after the initial excitation. This requires, firstly, an evaluation of the individual processes of relaxation of the excited state and, secondly, studies of the combined effect of such processes. As stated previously, rotational relaxation, at least for heavy molecules, is completed within a few collisions because the energy changes involved are small compared with the average translational energy. Since a partial population inversion occurs when the rotational temperature is less than the vibrational temperature, chemical lasers generally have provision to encourage rotational relaxation, such as by cooling the walls and adding sufficient helium to the gas mixture to ensure efficient heat transfer. For molecules with small

17

CHEMICAL LASERS

0

02

06

04

08

10

f",

FIG.10. Semilogarithmic plots of the relative rate constants K ( d ) for the reaction H CI2 --f HCL,. GI versus f"', the fraction of the available energy which goes into product vibration. The curves were obtained ( 3 1 ) by the methods of measured relaxation (MR) and of arrested! relaxation (AR).

+

+

moments of inertia, relaxation may require numerous collisions; for example, 300 for H, (32) unless the dipole moment is large (HCI requires an average of about seven collisions). Relaxation of vibrationally excited levels can occur through spontaneous emission of radiation, through vibrational-translational energy transfer in molecular collisions, or through vibrational-vibrational relaxation, that is to say, by transfer of vibrational quanta between molecules of the excited species and other acceptor molecules which may be present. We have already described the nature of the emission processes for vibrationally excited states. It is perhaps sufficient to give some examples of the speed of the processes for some molecules of interest i n chemical lasers. Table I (38) shows lifetimes calculated by Pate1 for CO using the relation

18

P. H. DAWSON AND G . H. KIMBELL TABLE I CALCULATED EMISSION COEFFICIENTS AND LIFETIMES (33) OF THE v = 1 TO v = 10 VIBRATIONAL LEVELSOF CO ( x ' C + ) V

1 2 3 4 5 6 7 8 9

A"-"-, (sec-')

(sec-')

30.30 59.33 89.66 111.2 134.8 157.7 178.5 197.8 215.2

0.55 1.62 3.21 5.20 7.66 10.50 13.72 17.25

r, = l/CA,

A,+,-2

(

4

33 x 16.7 x 11.0 x 8.7 x 7.1 x 6.0 x 5.3 x 4.7 x 4.3 x 4.0 x

10

10-3 10-3

10-3 10-3 10-3

10-3 10-3 10-3

10-3 10-3

and values of the ratios of the matrix elements for vibrational transitions (R) as obtained by Cashion (34). The probability of decay by emission of a single is always much greater than that for two quanta quantum although less so at higher u. Also A,-,,.-l is approximately proportional to u, so that the lifetimes of highly excited states become quite short. The shorter lifetime of the more excited level tends to be unfavorable to laser action (see Section 11) except that the stimulated emission coefficients are also larger. TABLE 11 RADIATIVELIFETIMES OF THE v = 1 VIBRATIONAL LEVELSOF SOMESIMPLE MOLECULES

(msec)

co NO HCI HF H Br

33 145 29 5 I39

vt-lo (cm-')

2143 1876 2886 3958 2559

Table I1 gives a comparison of the lifetimes of the u = 1 level for several molecules. The rate of stimulated emission is given by ZB, where Z is the appropriate radiation density and B, @hestimulated emission coefficient. The ratio A J B , is proportional to l / v 3 so that laser action is harder to achieve the lower the frequency of the transition involved.

CHEMICAL LASERS

19

Vibrational relaxation by collision has been determined by a variety of methods; ultrasonic absorption (35,36), flash spectroscopy (37), and the quenching of fluorescence (38). However most of the data only apply to the lowest vibrational level. Recently, detailed measurements applying to several levels have begun lo be obtained by chemiluminescence studies (39,40).Rapid progress may therefore be expected i n both experiment and theory. Some theories were developed many years ago because of the importance of thermal relaxation in sound absorption. From the viewpoint of classical mechanics, considering the collinear approach of a " billiard ball " atom A to a spring BC, energy transfer is most likely when the interaction time is small compared with the vibrational period ( 4 / ) ;that is, when Iv/s is small, where v is the frequency of vibration, s is the velocity of A, and I is a measure of the range of the interaction. It seems, then, that short range forces between the molecules would be the most important. The quantum mechanical approach derived by Schwartz, Slawsky, and Herzfeld (34,4/,42)-widely known as the SSH t heory-considered as an approximation only the short range forces which are, in fact, repulsive forces. For example, in a V-T (vibration to translation) exchange between A and BC, if x is the separation of A from the center of gravity of BC and X is the separation between B and C (during vibration), then, for a collinear collision, the distance between A and B is

The repulsive interaction energy can therefore be expressed as ~ = ~ ~ e x p [ (ll7g x -f

1 7 7 ~

where V, and 1 are the interaction parameters. The SSH theory assumes that the probability of inelastic scattering is small compared with the probability of elastic scattering, thus providing a basis for the distorted wave approxiniation in which the interaction causing the energy transfer is treated as a perturbation. It may only be valid, therefore, when the probability of energy transfer per collision, is not too large. This probability is found to be a product of three factors. Pi+f(P)= P o x Pf!+,(s)x P;yf,

(15)

where Po is called the steric factor. P;LFis the translational part, and P;Zf is the oscillator part.

20

P. H. DAWSON AND G. H. KIMBELL

The Oscillator Part P?fc is s independent and is given by

This is normally integrated by an approximation of the exponential expression in terms of a Taylor expansion. That is, it is assumed that the amplitude of oscillation is small compared with 1. For a single quantum transition in the collision A + BC, the integral gives

where p B c is the reduced mass of BC and ui is the initial vibrational quantum number of BC. For two quantum transitions PoSc(Au= 2 ) ‘V [ P o s c ( A=~l)j2/2,

(18)

so that the probability is much reduced. Since A is just as likely to collide with A close to C instead of B, Eq. (17) should be modified to

The Translational Part The integral for the translational part can be evaluated to give

where q = 4np1/1z and p is the momentum. Note that this expression is.independent of V,, so that I remains the only parameter required. The remaining problem is to average PI; over the range of velocities wherein collisions occur in the gas. For a Maxwellian velocity distribution, an analytical expression can be derived, provided that the energy exchange is fairly large (1.e. the process is not close to “resonance,” A&= 0). The resulting expression is

( )’

p!r= ( 2~)”~ AE [(Ac)’ If nKTo K

where

-1

TTo

[

exp - -3 [(A&)’ 1 2 K T T ,

1”’

--A & ]

2KT ’

21

CHEMICAL LASERS

The Steric Factor The steric factor takes into account the three-dimensional nature of real encounters (not one-dimensional as in the above theory) and the fact that the probability of interaction of the incoming A with the molecular vibration will be reduced for other than collinear approaches. For a diatomic molecule BC, Po has been calculated to be about 1/3. The above discussion has concerned a V-T energy exchange and the general usefulness of the theory in calculating orders of magnitude is shown by the data assembled by Herzfeld and Litovitz (35), with the exception of dipolar molecules or molecules likely to form chemical complexes during collisions. For V-V exchange between two molecules AD and BC, the same approach can be employed. The oscillator part becomes

*

v1(vz

+ 11,

(22)

where the v1 level of AD and the v 2 level of BC become (ul - 1) and (u2 + l), respectively. The oscillator part is less than for a V-T exchange but the translational part is much larger because AE,the energy which must be converted to the translational form, is greatly reduced. Equation (21) applies with

AE = h( v’& - VZ;

I)

- h( ~2~ - v::

’).

The sign of the second term of Eq. (21) then depends on whether the process is endothermic or exothermic. For two diatomic molecules Po N 1/9. Although only the short range repulsive potential is considered in the theory, some account of other forces can be made through the choice of the parameter I to best fit a known potential (such as the Lennard-Jones 6-12 intermolecular function). Although the choice of I is important, (dp/p N -EM//), a value of 0.2 8, is frequently used for order of magnitude calculations. Figure 11 shows some calculated and experimental values for the process (43) CO(u = 0 )

+ CO(u

=

u’)

-

CO(u = 1)

+ CO(u =

1” -

1).

Curve D is derived from the above SSH theory using I = 0.2 A. Curve E is a modification of the SSH theory, removing the approximation in integrating Eq. (16) by performing a direct integration and numerically averaging the translational part over all velocities to avoid the divergence close to resonance (v = 1). The agreement with the experimental results (curves A and B, to be discussed later) is much improved. Figure 12 compares interaction of several different vibrational levels calculated in the same manner.

22

P. H. DAWSON AND G . H. KIMBELL

10-2

P

lo-:

lo-’

lo-!

5

10 V’

FIG.1 1 . Calculated and experimental probabilities for vibration exchange per collision for the processes CO(u = 0)

+ CO(u

=

u’)

-

CO(u = 1 )

+ CO(u = u‘

-

1).

Curves A and B are experimental values by different workers (39,40).Curve D is given by SSH theory, which considers short-range forces, curve E by a modified SSH theory (43). and curve C by a modified Sharnia theory (39) which considers long-range forces.

The weaknesses of the SSH theory lie in the neglect of the rotational energy mode and the neglect of long range forces. Attempts have been made to consider these factors by other methods. Cottrell and Matheson (44) suggested that rotation to vibration transfer can be significant in the excitation of hydrogen containing molecules which tend to have very fast excitation and relaxation (45) (“the light atom anomaly”). Mahan (46) postulated that for

23

CHEMICAL LASERS

P

c

I

,

I

0

5

10 "I

FIG.12. Probabilities of some vibration-vibration energy exchanges of the type

CO(0 = n,) i-CO(0 = n 2 )

_3

CO(v = 12, - 1)

+ CO(0 = nz i -1)

calculated by a modified SSH theory (43).

infrared active vibrations and near-resonant vibrational exchange the interaction could occur by means of long range dipole-dipole coupling. This was developed further by Sharma and Brau (47,48) in calculations for N, and the asymmetric stretching mode of CO,. At temperatures below 1000°K the long range interactions dominated. It was necessary to also include the rotational transitions because of the strong angular dependance of the dipolequadrupole interaction. The agreement with experiment was good below about 1000°K but above this probabilities increased with temperature, as predicted by SSH theory, and it seems that the short range forces again become important. A modified version of Sharma's theory has been applied to the CO V-V exchange problem by Hancock and Smith (39) again taking into account simultaneous rotational transitions (AJ = ? 1 for dipole-dipole coupling). As shown by curve C in Fig. 12, the agreement with experiment is excellent close to resonance but rapidly deteriorates at high u numbers. Yardley (49) has extended the long range interaction theory to nonresonant exchanges. Further attempts to better approximate the full interaction between colliding vibrationally excited species, perhaps including both long

24

P. H. DAWSON AND G. H. KIMBELL

and short range forces are to be expected, especially now that experimental data are becoming available. Hancock and Smith (39) have recently determined rates of energy transfer between CO in u = 4 to 13 with ground state CO, OCS, NO, N,,N 2 0 , and CO, . Suart, Arnold, and Kimbell (40) have made similar measurements for CO, OCS, and N,O. There is a disagreement over the absolute values, Suart et al.’s values being five to ten times lower (for example, curves A and B, Fig. 11) and showing less dependence on the u level of the CO. However the general trends are clear. Table 111 shows some of the results of Hancock and Smith. The experimental method is to observe the infrared chemiluminescence of CO formed in the reaction between 0 and CS with and without the presence of the added gases. The experiments are best carried out at low reactant pressures or extrapolated to low reactant pressures to allow for self-quenching effects. Wall effects are a problem in interpreting the measurements but can be minimized by the presence of a large excess of buffer gas such as argon. However, the interpretation in terms of rate constants is based on an assumption of homogeneity within the observed reaction volume, and it may be the evident violation of this assumption which gives rise to the differences between different experimenters. The simplest way to examine the kind of effects that are caused by relaxation in a laser flow is to carry out computer simulations of the evolution of the populations of the various vibrationally excited states. The CO formed in the CS,-0, laser is a good example because levels up to u = 14 may be initially populated by the reaction. Figure 13 shows (43) how an initial population (arbitrarily assumed) evolves with time when (a) CO-CO vibrational exchange is considered and (b) when 1 Torr of CO in the ground vibrational state (i.e. “cold” CO) is added to the mixture. The theoretical values such as those in Fig. 13 were used in these computations. In these simulations, stimulated emission, which would considerably modify the distributions, has not been included. However, one can clearly see the importance of the relaxation processes in three factors: ( I ) strong interactions between neighboring levels which quickly smooth out any fine structure in the initial population distribution, (2) the time for which the population inversion can be maintained and therefore, perhaps, the upper pressure limit for lasing action, and (3) the modification of the distribution and the enhancement of population inversion by the selective relaxation of the lower levels such as by the addition of “cold” CO. In fact, in the CS,-0, laser, an excess of oxygen is usually also present. The oxygen tends to de-excite levels above u = 12 and, with the added CO de-exciting those below u = 5, this gives an enhancement of lasing action in the intermediate region. This double use of relaxation effects may be of more general value in lasing systems.

TABLE I11 VALUESOF P ","- l a

v1 , d c n i - ')

V

4 5 6 7 8 9 10 11

12 13

FOR

DE-EXCITATION OF CO, BY He, CO, NO, 0, , N z , OCS, NzO, AND C02'

2143.3

1876

1556.2

6.7 ( - 3 y 4.3 (-3) 2.1 (-3) 1.1 (-3) 5.9 (-4) 3.8 (-4) 2.0 (-4) I .53( - 4) 1.1 3( -4) -

1.9 (-3) 2.9 ( - 3) 4.0 ( - 3) 7.2 (-3) 1.47(- 2) 2.1 (-2) 2.7 (-2) 3.0 (-2) 3.2 (-2) 2.8 (-2)

-

2330.7

v,(cm-')

2062

2224

2349

v,.,,,-,(cni-') 2064.0 2037.7 201 1.5 1985.4 1959.3 1933.6 1907.2 1882.7 1856.1 1829.9

c, -

-

4.2 (-7) 6.2 (-7) 9.1 (-7) 1.4 (-6) 1.67(-6)

f'E,v-l is the probability of de-exciting CO, According to Hancock and Smith (39). '6.7(-3)~6.7 X

--f

-

7.1 (-5) 1.5 (-4)

CO,-l per collision.

7.9 (-6) 5.6 (-6) 3.7 (-6) 2.9 (-6) 2.4 (-6) 1.7 (-6) 1.3 (-6) 7. (-7)

1.1 (-1) ~ 1 . 5(-1) 1.4 (-1) 9.0 (-2) 3.6 (-2) 1.79(-2) 9.9 (-3) 7.8 (-3) 4.8 (- 3) 2.5 (-3)

1.6 7.7 4.3 2.9 2.6 2.6 2.9 3.2 3.0 2.7

(-3) (-4) (-4) (-4) (-4) (-4) (-4) (-4) (-4) (-4)

1.0 (-4) 5.6 ( - 5 ) 5.4 (-5) 5.1 (-5) 5.4 (-5) 7.0 (-5) 1.12(-4) 1.75(-4) 2.9 (-4) 4.0 (-4)

8

i>3 r

r

ii

z

P. H. DAWSON AND G . H. KIMBELL

A = 0 I msec

8 = 0 5 m sec

C = I 0 msec \

0 : 2 5 msec E

:4 0

msec

I

V

(a)

FIG. 13(a) FIG. 13. (a) Computer simulation (43) of the evolution of the vibrational energy distribution of CO molecules. Allowance has been made for spontaneous mission and for the presence of 1.25 Torr of oxygen (as is likely in a CS2-02 laser system). The main process of interest is the V-V energy exchange and values calculated as in Fig. 12 were used. An initial distribution was arbitrarily assumed. (b) The same conditions as in (a) but with the addition of 1 Torr of "cold" ( u = 0) CO which undergoes V-V exchange more rapidly with the lower vibrational levels than the upper.

Detailed computer simulations of chemical laser systems including rates of reaction and V-T and V-V processes have been reported for the H,-CI, (50) and the CS,-02 (51) systems. VI. CHARACTERISTICS FAVORABLE TO CHEMICAL LASERACTION Before considering some of the particular achievements in obtaining laser action, it is valuable to summarize the sometimes conflicting requirements for systems favorable to chemical laser action as they have emerged from the earlier discussion. 1. The reaction must be exothermic.

27

CHEMICAL LASERS

A

= 0 I rnsec

8 = 0 5 rnsec C = IOrnsec

D = 25rnsec E = 4 0 rn sec F = 7 0 rnsec I n i t i a l distilbullon

,4--A --,

\

-

I I

\

I

5

"

I0

(bi

FIG.l3(b). See Fig. 13(a) for legend.

2. The reaction must be fast enough to maintain an inversion. It must have a low energy barrier and low steric factors. Atom abstraction reactions A - I BC

-

ABt C

are particularly likely to be useful. 3 . (a) Vibrational excitation of the products is favored if the energy barrier ir i n the approach coordinate (the most exothermic reaction in a related family of reactions), i.e. A is strongly attracted to BC. (b) Energy is more likely to be in the vibrational form if M*

=M,

% M,.

28

P. H. DAWSON AND G . H. KIMBELL

4. The excited levels must not be too rapidly relaxed, e.g. the vibrational levels of diatomic and triatomic molecules are good. 5 . The oscillator strength of the transition should be high. 6. Lasing is easier in conditions of partial inversion for molecules with small moments of inertia. This is important in diatomics where the energy tends to equilibrate over the available vibrational levels (rapid V-V transfer). The rotational temperature must also be kept low. 7. Concentration of the vibrational excitation into a few Ievels, e.g. the use of energy transfer to, or chemical production of, linear triatomic molecules may improve the chemical efficiency. 8. The presence of a chain reaction is useful. Even with a small external energy, output may then be large. 9. Suitable selective vibrational exchange reactions with added species can enhance the population inversion. 10. The high vibrational levels have larger stimulated emission coefficients and will give a greater gain for a given population inversion. The aim, of course, is to produce lasing systems of high chemical and electrical efficiency, operating at useful power levels at pressures near atmospheric to obviate the need for bulky pumping systems. Many of the characteristics listed above (fast exothermic reactions, chain reactions) seem most likely to be found in gas mixtures which are self-igniting under certain pressures and temperatures. Indeed lasing action has been recently observed in a freeburning flame (see below). One conflicting requirement is then the desirability of maintaining a low rotational temperature. Some of the reactions so far employed in chemical lasers are listed in SOMEOF

THE

Reaction mixture

csz + 0

2

csoz + 0

+

2

C1tO Ht Br2 RH Clz RH

+ +

TABLE IV REACTION MIXTURES USEDIN CHEMICAL LASERS Output

Pulsed Pulsed cw cw Pulsed Pulsed cw cw Pulsed Pulsed cw Pulsed Pulsed Pulsed Pulsed

Initiation

Power

Transverse discharge ca. 1 kW hv Low 3w Discharge Flame ca.1 mW hv Low Discharge High (>1 MW) Discharge Low > I kW hv Low hv Low Discharge Low Discharge Low hv Low Discharge Low Discharge Low

29

CHEMICAL LASERS

Table I V together with the nature of the output (pulsed or cw), the means of reaction initiation (photolysis, discharge), and in significant cases the power output. Photodissmociation and photoelimination lasers are not included in the table.

V11. SOMELASERSYSTEMS The following examples have been chosen to cover a broad spectrum of the experiments to date, emphasizing particular acievements in power output, various methods of initiation, and novel features such as spontaneity of reaction and use of energy transfer. A . A True Chernical Laser

Cool and Stephens have achieved cw chemical laser operation merely by fluid mixing (52). Figure 1 shows the type of apparatus. A source of fluorine atoms was provided by mixing NO with a flow of F, and helium by using the reaction Fz -t NO

-

NOF t- F.

This reaction is fairly rapid at ambient temperature. The combined flow is rapidly mixed with deuterium and carbon dioxide to produce vibrationally excited DF by the chain reaction F f Dz D+Fz

-

___*

DF*$ D, DF*+F.

These reactions aire capable of populating vibrational levels of D F up to u = 4. There is a subsequent intermolecular transfer of energy to the CO,. That is, DF(u

= n)

+ CO,(OO"O)

-

DF(u = n - 1 )

+ C02(Oo"1),

and this is followed by the "classical" CO, laser operation at 10.6 p between the (00O1) and (lOO0) levels. A power of 8 W (53)has been achieved with flow rates of He = 3800 pm/sec, CO, = 1550 pM/sec, D, = 370 pM/sec, F, = 365 pM/sec, and N O = 24 ,uM/sec and a chemical efficiency (coefficient of conversion of chemical energy to laser radiation) of 4 % .The reaction tube of the type shown in Fig. 1 was a 21 cm long, 9 mm bore Teflon tube. All interior wall surfaces of the laser were coated with H,BO, (54) to minimize atom recombination. Figure 14 shows how the laser output was related to the flow rates of the various components, the flow rates having been normalized by the optimum value for each gas. Detailed kinetic analysis of these results is not presently available.

30

P. H. DAWSON AND G . H. KIMBELL

FLOW RATE IN RELATION TO ITS OPTIMUM

+

FIG. 14. Power output (52) of the pure chemical laser: NO F 2 + N O F + F, F + D2+ DF* t D, D -tFZ+ DF* -1 F, DF(u = n) COz(OOoO)-+ DF(u = n - 1) COz(OOol),as a function of partial flow rates of each gas.

+

+

B. A Flame Laser It was recently reported (55) that, in a free-burning flame of CS2 and 0 , at low pressures (of the order of 1 Torr), population inversions occurred on vibrational-rotational bands of CO. This was shown by measuring the distribution of energy in the first overtone region of CO. Thus these workers predicted the use of this system in the establishment of a true free-burning flame laser.

31

CHEMICAL LASERS

In a recent communication workers at N R L (56) have succeeded in achieving laser action from this system. The burner consisted of a horizontal array of 24 parallel tubes. Each tube was 60 cm long, 6 nim o.d., and had 50 evenly spaced 1 mm holes along the top. A low loss cavity was formed by two dielectrically coated mirrors mounted internally within the vacuum system. Continuous wave laser action was observed at 5.216 11, u = 8 + u = 7 P(11); 5.297 p , u = 9 -+r = 8 P(12); and 5.421 p , u = 1 1 -+zi = 10 P(10). Total output power was on the order of ImW.

C. A

CIV

Carbon Monoxide Laser

The cw CO chemical laser depends on initiation of reaction by production of oxygen atoms in a microwave discharge and a subsequent series of reactions with CS, . A longitudinal gas flow apparatus, similar to that of Fig. 1, has given a power output of 2.3 W (57) with a chemical efficiency of at least 1 and an electrical efficiency of about 0.65 %. The gas mixing, accomplished here by admitting the CS, through a radial array of 12 holes each 0.5 mm diameter downstream of the O,/He inlet, has to be rapid to obtain high power. The 2.3 W was only obtained with the addition of vibrationally “cold” CO to enhance the population inversion as discussed in Section VI. The analysis of the spectral output showed the complete inversion of several vibrational levels. The observed transitions were the P(8) to P(11) bands of the 7 + 6 transition, P(13) to P(7) of the 8 - + 7 transition, P(13) to P(8) of the 9 -+8 transition, P(13) to P(7) of the 10 - + 9transition and P(11) to P(7) of the 11 -+ 10 transition. The strongest line in the presence of the added CO was the P(8) branch of the 8 + 7 transition. At maximum power output the gas flow rates were 67 liters/min for He, 6.8 liters/niin for O,, 1.1 liters/min for CS,, and 3.4 liter,s/min for added CO giving a total pressure of 9 Torr. The helium helps in the oxygen dissociation by the microwave discharge and serves to maintain a thermalized rotational distribution (Section 111). The mechanism of reaction has been analyzed in some detail (57). The essential steps are as follows: Rate constants

o+csz -+ cs -1- so 0-I-cs -+ CO*-tS S t - 0 , - so + o O,+CS -+ co +so so I-so szo2

2.1 x 2.1 x

S 2 0 - t 0,

--b

-

SO+SOZ

1013

1.2 x 10’2

-b

--b

(cm3 mole-’ sec-’)

109

s2o+soz

32

P. H. DAWSON AND G. H. KIMBELL

The reaction between 0, and CS has been suggested as an alternative pumping step but the evidence from analysis of flash photolysis experiments makes this seem unlikely. The reaction

so+o2

soz+o

__*

gives the possibility of a chain reaction but it seems that this only becomes important at temperatures above 500°K. The oxygen atoms are competed for by the CS radicals formed in the first step and by CS,. If CS, is in excess, some of the oxygen atoms are used to create CS which can no longer be converted to CO except by the slow reaction with 0,. The conversion efficiency is reduced by the excess CS,. Figure 15 shows relative power as a function

I N I T I A L 0 ATOM CONCENTRATION

OL 0

t 1

1

I

I

I

2

[CSz]

I

4 X I 0 - O ADDED

I

6

FIG.15. [CO] formed or relative power as function of [CS,] added. Curves (a) and (b) show the result of varying the rate constant for the pumping reaction 0 $- CS + CO I- S; curve (c) the relative power (58); curve (d) the relative power (59); curve (e) neglects the SO. above reaction and assumes a rate constant for CS O2 +CS

+

+

of the CS, present as observed by Jeffers and Wiswall (58) and by Suart, Kimbell, and Arnold (59). Also shown is a prediction of the extent of formation of CO in a lasing condition given by a computer simulation of the chemically reacting system (57). D . A Transversely Sparked HF Laser

The use of transverse multiple-spark discharges to initiate lasing action was developed for the CO, “physical” laser and later applied to CS,/O,/He

33

CHEMICAL LASERS

mixtures (60,6/). A similar electrically pulsed laser operating with niixtures of CF,, C2F6, C4Fe, or SF, and H,, CH,. C2H6, C,H,, or C4H,, will function even at atmospheric pressure (62). Figure 16 shows the apparatus. The discharge cavity was a 5 cm diam pyrex tube. Premixed gases enter at one end of the tube and are exhausted at the other. The electrodes were parallel monel rods (1.3 cm diam and 1.2 m long) and the high tension electrode had 200 monel pins oriented to form a transverse electrode array with an interlectrode gap of 1.3 cm. The spark discharges were obtained from a 0.01 pF capacitor charged to 30 kV by a dc power supply, the initiation being triggered by a spark gap.

RESISTANCE CHAIN INITIATING SPARK GAP RGlNG VOLTAGE CAPACITANCE CROSS -SECTION OF T U B E

FIG.16. A transverse discharge laser apparatus.

At pressures less than 50 Torr, the addition of helium did not greatly affect performance but it was necessary at higher pressures to obtain lasing action. The maximum observed powers were greater than 0.5 MW. The maximum pulse energy was 40 mJ for a SF,/C,H,/He mixture in the ratio 6.4/1/78 at a pressure of 115 Torr and using a cavity formed by a concave mirror and a 35 7,;reffecting flat. This gas combination was superradiant (no mirrors on the cavity) at pressures between 20 and 760 Torr. At atmospheric pressure the optimum peak power was about 30 kW. The greatest number of the observed transitions were in the L' = 2 + r = 1 series although the I -0 and 3 + 2 transitions were also present. The pumping reaction is F

+ RH+

HF* + R

1 HF 2.8 pm laser radiation

The maximum gain was for J = 4 indicating that the gain (and population inversion) was very high.

34

P. H. DAWSON AND

G . H. KIMBELL

E. A Flash-Induced OH Laser The formation of OH(u s 2) in the flash photolysis of O,, H,, and N, mixtures was reported by Basco and Norrish (63). Photolysis of ozone in the ultraviolet produces O(’D) atoms which react as follows : O(’D)+H,

-

-

OH*+H.

There is then a possible further reaction H+01

OH*+02.

The latter reaction has been studied at low pressure Torr) by infrared chemiluminescence by Polanyi et al. (27), who find that the OH is formed predominantly in the u = 8 and u = 9 levels (Fig. 7) but that even at Torr there is a rapid relaxation by vibrational exchange or chemical reaction (see Section 111). However, levels up to u = 9 have recently been observed by EPR at higher pressures (64), so that the possibility of using this reaction remains open. Recently Callear and Van Den Bergh (65) have observed stimulated emission from OJH, mixtures in the ratio of 1 :10 and at pressures of 1 to 10 Torr. Flash energies were in the range of 400-2000 J. The peak power output was quite low. Emission was observed from the 3 +2, 2 + 1, and even the 1 4 0 fundamentals. The observed frequencies are about 3200 cm-’. Flash photolysis laser studies, such as this, are particularly important in studying new potential lasing systems.

F. Transverse Flow Lasers The emphasis in cw lasers has now switched to transverse flow systems instead of the longitudinal flow described in Section VII, A and C above. That is, the gas flow is made transverse to the optical axis. Such systems have been described by Jeffers and Wiswall(58) and by Cool, Shirley, and Stephens (66). A recent design by Foster and Kimbell (67) is shown in Fig. 17. In this device oxygen atoms from a microwave discharge are mixed rapidly with carbon disulphide which is injected into the flow through a series of tiny teflon tubes. Combustion then occurs, rapidly producing CO, the laser medium. The two rows of tubes are inserted to allow for the possibility of the addition of a vibrationally “cool” gas to enhance the inversion as described earlier. The advantage of the transverse flow is that the “spent” gases are rapidly removed from the optical field of view, avoiding undesirable absorption effects, and measured output powers can be several times greater than equivalent longitudinal flow systems. In suitable cases, the normal cavity volume can be extended by the use of a multiple reflecting system of mirrors (66). A fivefold

35

CHEMICAL LASERS

PURGE

I

A

BREWSTER WINDOWS

OPTICAL AXIS

.................... .................... csz 7

"TOTAL" REFLECTOR (1.3m r o d of curvature)

ADDED GAS --I'

iDISCHARGED

Ge FLAT

(98% reflecting 05 . 2 ~ )

He, 0, MIXTURE

FIG.17. A transverse flow laser system.

configuration has been used with two plane mirrors of 99.4% reflectivity, one 10 m radius of curvature niirror with 99.4'j, reflectivity, and, for decoupling, a partially transmitting mirror of 10 ni radius of curvature. This device using the DF-CO, chemical system has produced 167 W with a chemical efficiency of 4.6 %. The transverse flow system should also provide a useful diagnostic technique since the cavity can be moved to different positions along the flow (different times after mixing), and used to examine the relaxation processes that are occurring.

VIII. CONCLUSION The chemical laser represents a method of obtaining new laser frequencies; in conventional molecular gas lasers one is restricted to molecular gas mixes wherein population inversions of the parent molecules can be sustained during electrical discharge. In a very short time, rapid progress has been made, as is demonstrated by the development of the purely chemical laser (no external power source), the free-burning flame laser, and several cw lasers. All this despite an evident lack of fundamental knowledge of many of the processes involved. These lasers exploit the chemical nature of the excitation process and hold the promise (or dream?) of portable, efficient, laser sources. Further progress, i n the direction of higher efficiencies and operation at higher pressures, will undoubtedly be slower and may involve the exploration and utilization of more complex chemical systems.

36

P. H. DAWSON AND G. H. KIMBELL

There is, however, considerable promise in the exploitation of what might be termed “hybrid” systems such as the transversely sparked H F laser described above which already gives high peak power and atmospheric pressure operation. Another possibility is integration of the flame chemical laser in a gas dynamic type of laser system. In any case, the technology is unlikely to progress without further advances in our knowledge of the chemical creation of excited species and the subsequent loss and exchange of the excitation energy.

REFERENCES 1. C. K. W. Patel, “Lasers” (A. K. Levine, ed.), Vol. 2,p. 1. Dekker, New York, 1968. 2. A. L.Schawlow and C . H. Townes, Phys. Rev. 112,1940(1958). 3. A. Javan, W. R. Bennett, and D. R. Hehiot, Phys. Rev. Lett. 6 , 106 (1961). 4. A. J. Beaulieu, Appl. Phys. Lett. 16,504 (1970). 5. J. C.Polanyi, J . Chem. Phys. 34, 347 (1961). 6. Appl. Opt. Chem. Laser Suppl. 2 (1965). 7. J. V. V. Kasper and G . C . Pimentel, Phys. Rev. Lett. 14, 352 (1965). 8. T.F.Deutsch, AppL Phys, L e f t . 11, 18(1967). 9. D. J. Spencer, T. A. Jacobs, H. Mirels, and R. F. Gross, Int. J . Chem. Kinetics 1, 493

(1969). 10. T. A. Cool, R. R. Stephens, and T. J. Falk, Int. J . Chem. Kinetics 1,495(1969). 11. R. D.Suart, G . H. Kinibell, and S. J. Arnold, Chem. Phys. Lett. 5, 519 (1970). 12. T.A. Cool and R. R . Stephens, J . Chem. Phys. 51, 5175 (1969). 13. G. C.Pimentel, Sci. Amer. 214, 32 (1966). 14. A. C.G . Mitchell and M. W. Zernansky, “ Resonance Radiation and Excited Atoms.” Macmillan, New York, 1962. 15. T. F. Deutsch, Appl.Phys. Lett. 11, 18 (1967). 16. G. Herzberg, “Spectra of Diatomic Molecules.” Van Nostrand, Princeton, New Jersey, 1950. 17. E. A. Gerry, BuIl. Amer. Phys. SOC. 15, 563 (1970). 18. D . W. Gregg and S . J. Thomas, J . Appl. Phys. 39, 4399 (1968). 19. P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner, and C . E. Young, J . Chem. Phjx 44, 1168 (1966). 20. J. C . Polanyi and W. H. Wong, J..Chem. Phys. 51, 1439 (1969). 21. M. H. Mok and J. C . Polanyi, J . Chem. P ~ J J51, S . 1451 (1969). 22. D.L. Bunker and N. C. Blais, J . Chem. Phy~..41,2367 (1964). 23. M. Karplus and E. M. Raff, J . Chem. Phys. 41, 1267 (1964). 24. C. C.Rankin and J. C . Light, J . Chert. Phjlv. 51, 1701 (1969). 25. D. Russell and J. C . Light, J . Chem. Phys. 51, 1720 (1969). 26. K. G. Anlauf, P. J. Kuntz, D. H. Maylotte, P. D. Pacey, and J. C . Polanyi., Disc. FaradaySoc.44,183(1967). 27. P. E. Charters, R. G . Macdonald, and J. C . Polanyi, Appl. Opt. 10,1747(1971). 28. K.G.Anlauf, J. C. Polanyi, W. H. Wong, and K. B. Woodall., J . Chem.Phys. 49, 5189 (1968). 29. H. Heydtmann and J. C . Polanyi, Appl. Opt. 10, 1738 (1971). 30. N.Jonathan, C. M. Melliar-Smith, and D . H . Slater, Mol. Phys. 20, 93 (1971). 31. P. D. Pacey and J. C . Polanyi. To be published.

CHEMICAL LASERS

37

32. M. S . Dzhidzhoev, V. T. Platonenko, and R. V. Khokhlov, Sou. Phys.-Usp. 13, 247 (1970). 33. C. K. W. Patel, Phys. Rev. 141, 71 (1966). 34. K. Cashion, J . Mol. Spectrosc. 10, 182 (1963). 35. K. F. Herzfield and T. A. Litovitz, “Absorption and Dispersion of Ultrasonic Waves,” Academic Press, New York, 1959. 36. J. D. Lanibert, Quart. Rev. Chern. Soc. 21, 67 (1967). 37. A. B. Callear, ‘’ Photochemistry and Reaction Kinetics,” Chapter 7. Cambridge Univ. Press, London and New York, 1967. 38. R. C. Millikan, J . Chem. Phys. 38, 2855 (1963); 43. 1439 (1965). 39. G. Hancock and I . W. M. Smith, Chem. Phys. Lett. 3, 573 (1969); Appl. Opt. 10, 1827 (1971). 40. S . J. Arnold, R . D. Suart, and G. H. Kimbell, private communication. 41. A. B. Bhatia, ‘‘ Ultrasonic Absorption.” Oxford Univ. Press (Clarendon), London and New York, 1967. 42. R. N. Schwartz.. Z. I . Slawsky, and K . F. Herzfield, J . Chem. Phys. 20, 1591 (1952). 43. P. H. Dawson and W. G. Tam, Can. J . Phys. 50, 889 (1972). 44. T. L. Cottrell and A. J. Matheson, Trans. Faraday Soc. 59, 824 (1963). 45. M. G. Ferguson and H . W. Read, Trans. Faruday Soc. 63, 61 (1967). 46. B. H. Mahan, J . Chem. Phys. 46, 98 (1967). 47. R. D . Sharma and C . H. Brau, Phys. Reo. Lett. 19, 1273 (1967). 48. R. D. Sharnia and C. H. Brau, J . Chem. Phys. 50, 924 (1969). 49. J. T. Yardley, J . Chem. Phys. 50, 2464 (1969). 50. N. Cohen, T. A . Jacobs, G. Emanuel, and R. L. Wilkins, Znr. J . Chem. Kinetics 1, 555 (1 969). 51. B. R . Bronfin, Conf. Mol. Energy Transfer, Cambridge, England, 1971. 52. T. A. Cool and R. R. Stephens,J. Chem. Phys. 51, 5175 (1969). 53. T. A. Cool and R. R. Stephens, Appl. Phys. Lett. 16, 55 (1970). 54. E. A. Ogryzlo, C a n . J . Chem. 39,2556 (1961). 55. K . D. Foster and G . H. Kimbell. J . Chem. Phys. 53, 2539 (1970). 56. H . S. Pilloff, S. K. Searles, and N. Djeu, Appl. Phys. Lett. 19, 9 (1971). 57. R. D. Suart, P. H. Dawson. and G. H . Kimbell, J . Appl. Phys. 43. 1022 (1972). 58. N. Q. Jeffers and C. E. Wiswall, Appl. Phys. Lett. 17, 67 (1970). 59. R. D. Suart, G. H. Kimbell, and S . J. Arnold, Chem. Phys. Lett. 7, 337 (1970). 60. T. V. Jacobson and G . H . Kimbell,J. Appl. Ph.vs. 41, 5210 (1970). 61. M. C. Lin and W. H . Green, J . Chem. Phys. 53. 3383 (19701. 62. T. V. Jacobson and G. H. Kimbell. J . Appl. P h j 42, ~ 3402 (1971). 63. N. Basco and R . G. W. Norrish, Proc. Roy. Soc. Ser. A , 254, 317 (1960). 64. K. P. Lee, W. G. Tam, R. Larouche, and G . A. Woonton, Can. J . Phys. 49, 2207 (1971). 65. A. B. Callear and H. E. Van Den Bergh, Chern. Phys. Lett. 8, 17 (1971). 66. T. A . Cool, J. A . Shirley, and R. R. Stephens, Appl. Phys. Lett. 17, 278 (1970). 67. K. D. Foster and G. H . Kimbell, to be published.

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Single Photon Detection and Timing: Experiments and Techniques SHERMAN K. POULTNEY Departnient of Physics and Astronomy, University of Maryland, College Park, Maryland

I. Introduction

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

. . . . . . . . . . . . . . . . . . . 39

11. Single Photon

C . Photodevice and Background Noise and Their Reduction D. Practical Photodevice Techniques and Photon Detection

C. Single Photon Timing Methods.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Single Photon Precise Timing Experiments. . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

114

I. INTRODUCTION Single photon detection and timing means essentially the detection and timing of a single photoelectron released by light from a photosensitve surface of a photomultiplier, channel multiplier, avalanche multiplier photodiode, or other photodevice. An electron released by a particle or photon bombardment of a windowless multiplier is also thus included. Single photoelectron detection requires sufficient low noise amplification to overcome the Johnson noise in the first resistor of the eventual electronic circuit plus additional amplification to operate standard discriminator detection circuits. The time response is usually quite fast due to the desire to count at both low and high rates, to time closely spaced events, or to time intervals to highest precision, 39

40

SHERMAN K. POULTNEY

and so most of the gain usually comes before the electronic circuits. This gain is obtained by secondary electron emission processes or their equivalent down a chain of electrodes or a continuous channel and is subject to statistical fluctuations. The resultant fluctuations in the output charge can affect timing with single photoelectron pulses, the length of time needed to achieve a light flux measurement to a given precision, the efficiency of single photoelectron detection, and the discrimination against some types of device noise. The major type of device noise has a similar output charge distribution, however, and this dark noise must be reduced by cooling the photodevice or by other techniques in most weak light applications. Background light noise also has a similar distribution and must be reduced when present by narrow spectral and spatial filters. Correct technique can help minimize device noise, but is often neglected. It is important to have standard experimental tests to evaluate the single photon counting performance and the noise performance of photodevices. Use of certain photoemissive materials and reduced photosurface size can also reduce device noise. However, for single photon counting, the choice of material is usually dictated by quantum efficiency considerations at the wavelength of interest. A number of opaque, reflection-mode photosurfaces are now available which extend the spectral range of high sensitivity. The older transmission-type photosurfaces show worthwhile increases in sensitivity by means of external and internal quantum efficiency enhancement techniques. The total quantum counting efficiency of a photodevice can often be lower than the photosurface quantum efficiency. The discrepancy may be caused by those photoelectrons that fail to get collected by the multiplier or by those anode pulses that fail to exceed the discriminator threshold due to the multiplication statistics. A low counting efficiency is just as serious as a low photosurface quantum efficiency and should be evaluated for any photodevice under consideration. Experiments involving single photon detection are usually photometric or spectrophotometric measurements of a weak light beam. The weak intensity may be due to scattering with small cross sections as in laboratory studies of Raman and Brillouin lineshifts or due to weak astronomical sources being viewed directly or through a many-channel spectrophotometer. The length of time needed to obtain a given precision is limited by background noise, device noise, or signal shot noise depending on which cannot be reduced. Digital storage of standardized discriminator pulses has both theoretical and practical advantages over other storage and detection methods. If the light source can be effectively modulated, digital synchronous detection can be used at least for convenience and stability in much the same manner as analog synchronous detection. If photometry over a wide range of intensities is required, the single photon counting method will be limited by photodevice or circuit time responses or dead times.

SINGLE PHOTON DETECTION AND TIMING

41

A second class of experiments requires both single photon detection and precise (nanosecond or better) timing. Timing of this precision depends on both the photodevice and the arrival time detection circuit. The photodevice must be designed to minimize electron transit time spreads; especially between the photosurface a.nd multiplier and in the first stages of the multiplier. The timing capabilities and limitations of some representative photomultipliers are examined closely in order to understand the timing capabilities and limitations of improved photomultipliers and other new photodevices. The arrival time detection circuit should be of the constant-fraction-of-pulse-height type or its equivalent to minimize any timing spread due to the multiplication fluctuations of tht: photodevice output signal. A photodevice which itself reduces these fluctuations in some manner also helps to minimize this time walk. A short time interval between two events of interest is best measured by sending the now standard timing pulses to a time-to-pulse-height converter which can be interrogated by a suitable analog-to-digital converter. The time distribution of intervals between repeatable physical events can be stored in a multichannel pulse height analyzer for on-line or later use. If the time interval becomes too long 10 obtain the desired resolution with a time-to-pulse-height converter, either the time-to-pulse-height converter has to be used in conjunction with a suitable digital time-interval meter or another timing method must be used. Methods for measuring the timing precision and accuracy of photodevices with single photons are outlined with special emphasis on the necessary fast light pulses. Methods of calibrating and monitoring the stability of the ti.ming circuits are also outlined. Typical photon timing experiments are the measurement of atomic and molecular fast fluorescence decay times and the lunar ranging experiment. The former measurement often has plenty of light signal, but this signal is attenuated to single photon levels in order to measure the fast decay time statistically so that it is limited only by the photodevice transit time spread. The width of any short light pulse can similarly be examined. Reference to the large body of work at higher light levels with scintillators is made since this work sets the basis for the terminology, theory, and past performance of photodevices for fast timing. In the lunar ranging experiment, the very low signal cannot be significantly increased. In spite of the high signal attenuation, high background noise, and difficult pointing problem, nanosecond timing of a 2.5 sec interval is now being done at the single photon level with current nanosecond laser transmitters. Ultra:short pulse lasers will leave the photodevice as the limiting factor in achieving the goals of that experiment. A third class ol' experiments requires single photon detection in addition to moderate timing capabilities. The time information may be added to the light signal by effectively modulating it in order to employ synchronous detection to aid in the separation of signal from noise. Optical radar is a

42

SHERMAN K. POULTNEY

pulsed version of this modulation and can be used for probing of the structure of the atmosphere, for example. The measurement of the arrival time distribution of photons in a light beam can characterize the statistical properties of that light beam. If the beam properties are known, this measurement on scattered light can yield information about the internal behavior of a scattering medium undergoing statistical fluctuations in some property. These fluctuations may be due to particles undergoing Brownian movement in a liquid or to driven or spontaneous excitations of the medium. The spontaneous thermal excitations can be either propagating as in the case of optical and acoustic phonons which yield Raman and Brillouin scattering, respectively, or nonpropagating as in the case of density fluctuations at constant pressure which yield Rayleigh scattering. The measurement of photon arrival time is thus a valuable complement to spectroscopic studies of the above phenomena in that it is able to resolve the narrow linewidths. Typical experiments considered are the study of particles in Brownian motion and the measurement of the statistical properties of a narrowband thermal light source. The question of time-correlated photodevice noise can be studied with these same techniques. All of the above topics about single photon detection and timing cannot be treated in detail here. Wherever possible, reference is made to current reviews in the literature about individual topics. It is hoped that the following introduction will allow new workers to use these techniques in their fields of interest and will provide old hands with a current survey of the field which integrates many loose ends. 11. SINGLE PHOTONDETECTION

A . Necessary Photodevice Gain and Detection Circuits Consider an electron produced by photoemission from the photosurface of a photodevice (e.g. Fig. 1). This electron must be detected by electronic circuits in order to be of further use. It constitutes a charge pulse of 1.6 x C . Such a charge pulse is often collected on an RC network between photodevice anode and detection circuit. To be detected, the corresponding voltage pulse must exceed some preset level in the integral pulse height discriminator or single channel pulse height analyzer which then generates a standard counting pulse (I). If the time constant of the RC network can be much greater than the photodevice impulse response time, then the peak of the corresponding voltage pulse Vp = elC

43

SINGLE PHOTON DETECTION AND TIMING

t PHOTCl

TIMING CIRCUIT

.ECTRON

COUNTER

STOP

START

L

I MULTIPLIER GAIN G,

SLOW

FAST

SYNC 'IGNAL

DISCRIMINATOR

NOD*

t AMPLIFIER

REGULATED HIGH VOLTAGE

FIG.I . Schematic of single photon detection and timing with a photomultiplier. Diagram is not to scale. Co is bypass capacitor used when anode is at high potential.

which is a measure of the total charge of the charge pulse. In this case, V, wouldequal 25 nV if C is taken be the stray capacitance 40/2n p F and certainly needs amplification1 to be detected. The amplification must be of a special kind because charg,e fluctuations in the output resistance, R, of the photodevice due to Johnson noise will be the basic limitation to detection. These spontaneous charge fluctuations in R at a temperature T yield a voltage fluctuation for the RC network given by

wrm5(kT/e)(r/C)

(2) where k = 1.38 x J/"K. In order for the emitted photoelectron to be detected above Johnson noise during the observation time, it must be amplified without the use of it resistance by a charge gain G1 such that it is larger than the fluctuation charge. The necessary G, is thus given by (

=

'

GI 2 ( C / e M Tie),

(3)

where kT/e equals 0.025 V at 300°K. In the present case, G, must be greater than lo4 which yields a voltage pulse with a peak of 0.25 mV. An additional gain G, of at least 200 is needed to activate the discriminator. This gain can be provided by an amplifier for slow counting applications. Kowalski (I) discusses the many aspects of amplification, pulse-shaping, and detection. Both the RC integration method and slow electronics were developed for precise measurements of the total charge contained in the anode pulse and for operation with counting dead times of about 1 psec.

44

SHERMAN K. POULTNEY

The need to count at higher rates or to time short intervals makes it necessary to treat the photodevice anode pulse in a different manner. Neither single photon detection nor timing requires a precise measurement of charge. The RC time constant of the output circuit can then be made less than or equal to the pulse width or circuit resolution time whichever is longer. If the device is already being operated to minimize C, the time constant can only be lowered by decreasing R. The peak of the voltage pulse across RC now becomes lower than that given by (1) because it corresponds to less than the total charge. The gain of the device G1 must be raised to overcome the Johnson noise. For example, a good approximation for the anode current pulse of a photomultiplier is given by i(t) = i, exp [- ( t - h)2/21’] = (Gle/@A)

exp[-(t - h)2/21Z1, (4)

where the full width of the current pulse at half-maximum is given by 2.36 A and where h is the average transit time in the device. The voltage pulse across R of the network of Fig. 1 can be obtained with some reinterpretation from the work of Lewis and Wells (2). Ge 2c

[

V ( t ) = - exp - ( t - h )

If

RC

+

-1

(erf

2RC

[% J-

- ___ A ,RC]

v(t)is expressed as v(t>= (G,e/C)Wt, h, 1,RC),

(6)

one can display the solutions as in Fig. 2 for several 1/RC ratios. Note well the units along the abscissa. This unorthodox scale allows either A or RC to 1.21

,

I

I

,

,

I

,

,

,

-1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 t-h RC

-

FIG.2. Voltage waveform from RC network of Fig. 1 corresponding to a Gaussian current pulse from photomultiplier anode. Parameter is d2 / \ / R C . Figure after Fig. 7.3 of Lewis and Wells (2). (Courtesy of Pergamon Press.)

SINGLE PHOTON DETECTION AND TIMING

45

be varied. For RC = ,/i A, the peak voltage is 0.4 of that in (1) and GI must be 2.5 x lo4 for detection above Johnson noise. A typical 1for a fast photomultiplier is about 1 nsec (i.e. full width of 2.4nsec) so that if RC = ,/2 A the R equals 220 R for the above stray capacitance C. Standard fast detection circuitry is usually lbased on 50R so that G,must be lo5 or greater for fast detection of single photoelectrons above the Johnson noise. The standard fast integral discriminators or timing discriminators typically have thresholds of 50 mV so that the additional G, of at least 200 is still needed. For fast counting .(e.g. lOOMHz), this G, may be provided by a fast amplifier. For precise timing, it is essential that the whole gain be provided by G, of the photodevice, which here must be 2 x lo7. Discussion of the necessary fast circuits can be found in Kowalslti (I), Meiling and Stary (3), or the product literature. Precise timing with photodevices is considered in Section 111. Other constraints on single photodetection and photometric measurements are discussed here in Section 11. The above gain considerations are important when examining the suitability of new photodevices for single photon detection. They are also important as a guide to the redesign of present devices. In trying to improve count rates and timing capabilities of photomultipliers, designers now try to reduce A and, concomitantly, the stray capacitance C since R is probably fixed. The former is done by electrode and field design. The latter is accomplished by the use of a coaxial structure for the anode output which also reduces pulse distortion by eliminating electrical discontinuities (4). These reductions lead to a corresponding decrease in the necessary gain by (4) as long as the detection circuits are fast enough. Some photodevices may be subject to cooling along with the resistance R and so would also have a lower gain requirement since the Johnson noise is lowered by ( 2 ) . Operation of many photomultipliers at high gain can lead to noise problems as discussed in Section II,C. Some photodevices are subject to gain nonlinearities under certain conditions. In a photomultiplier, the gain is subject to saturation caused by the basic limitation of spacechargeeffectsin the final stages (5,6).This gain saturation limits the peak anode current. Am increase in the applied high voltage then increases the total charge gain and so broadens the pulse width. If gain saturation is reached before the level of single photon detection, one can sacrifice speed for gain by using an amplifier G, in conjunction with a lower G , or by using a larger RC. If sufficient gain G, is available and maximum count rates are not required, saturation may have a beneficial effect on timing precision as mentioned in Section II1,B. At high gains thcre is also the danger that the high peak or average currents can damage the electrodes of the photomultiplier. The above and other photomultiplier nonlinearities as well as corrective procedures are discussed by Kowalski (I), Pietri and Nussli (5), and RCA Staff ( 4 ) .

46

SHERMAN K. POULTNEY

B. Mechanisms and Statistics of Photodevice Gain 1. Introduction

Photodevice gains up to lo9 can be attained without the use of a resistance by means of secondary electron emission. If a photoelectron from the photosurface in Fig. 3 is given sufficient kinetic energy before striking an electrode, INCIDENT RADIATION SEMITRANSPARENT PHOTOCATHODE

PHOTOCATHODE TO DYNODE No 1 ELECTRON OPTICS

TYPICAL PHOTOELECTRON TRAJECTORIES

VACUUM ENCLOSURE ELECTRON MULTIPLIER

FIG.3. Schematic of 4 typical photomultiplier employing a focused multiplier. Electrodes 1-1 2 are dynodes, 13 is anode, 14 are focusing electrodes, and 15 is the photocathode. Some electron trajectories are shown. RCA Staff (4). (Courtesy of RCA.)

a number g of electrons will be emitted from that electrode. A chain of these multiplications can be arranged at separate electrodes as in Fig. 3 for a photomultiplier or along the continuous surface of a curved channel as for a channel multiplier if the cascading charge packet is suitably directed. The time response of the photodevice depends on the secondary electron trajectories, their energy distribution, and their spatial distribution ; the multiplication at each electrode; and the number of multiplication steps. These limitations to time responses in the nanosecond region are discussed in Section II1,A. A solid-state analog of the secondary gain of a multiplier is being developed in

SINGLE PHOTON DETECTION AND TIMING

47

the form of a carrier avalanche process in semiconductor diodes (7). Gains of 10’ to lo4 have been reached in small area diodes (8). If the electron multiplier were an ideal device, the anode output pulses resulting from single photoelectrons would have exactly the same charge. However, in a real device, not only might some of the photoelectrons go uncollected by the multiplier, but the secondary emission process is a statistical process. The inultiplier gain G , is an average gain and the multiplication factors g are average values. Output charge pulses therefore have a spectrum of sizes. These fluctuations in the output charge need not affect single photon detection as outlined in Fig. 1 as long as the spectrum is well-behaved at the lower end where the level of the integral discriminator would be set. Otherwise, a number of 1 he smaller single photon pulses would be lost and a number of small noise pulses may be added. The pulse height spectrum can also affect system time resolution as discussed in Section III,B. 2. Secondary Electron Emission

Within the last few years, important improvements have been made in secondary emission (and photoemission) from materials. In order to understand these improvements and their relation to multiplication fluctuations and fast timing, a description of the emission process is given in Section II,E,2 for photoemission and the differences for secondary emission are given here. Secondary emitters are either semiconductors or insulators with a band structure similar to that in Fig. 6 (9). An energetic electron incident upon a secondary emitter excites a number of electrons to the conduction band. Some of these electrons mlove towards the surface and escape if their energies are greater than the electron affinity energy of the surface. During the transport to the surface, the electrons lose energy as a result of phonon or electron collisions. In conventional secondary emitters, one thus expects and observes the multiplication factor g to increase with the energy of the primary. However, a more energetic primary excites electrons at greater depths in the material from which escape is much less probable. Consequently, g reaches a peak at some primary energy and then decreases. This peak value is typically from 6 to 10, but at primary electron energies somewhat higher than typical for photodevice electrode potentials. The distribution in energy and direction of the secondary electrons has an important bearing on the timeresolutionof the photodevice as discussed in Section III,A,l. Conventional emitters have quite large spreads in energy (i.e. 1 to 1OeV) (10). Improvement in secondary emission has been obtained by modifying the band structure with asurface layer of electropositive Cs on GaP as shown in Fig. 7 and as discussed in Section II,E,2. Under these conditions even the thermalized secondary electrons in the conduction band can escape the surface.

48

SHERMAN K. POULTNEY

Secondary electrons thus have a much greater escape depth and the multiplication at an electrode can be expected to be much larger than for the same primary energy incident on a conventional material. Multiplications of up to 50 have been observed in production photomultipliers for a single GaP dynode (IZ). These authors also point out the expectation that the energy distribution of secondary electrons will be quite narrow with the highest energy about l e v . Such an energy distribution would lead to an improvement in multiplier time resolution. However, this improvement is limited by the long diffusion times (e.g. 100psec) of excited electrons which are related to the greater escape depths.

3. Gain and Gain Statistics for Discrete Dynode Multipliers

A number of multipliers with high gain, well-focused structures (e.g. Fig. 3) have an output pulse height distribution for single photoelectrons that is peaked with a fairly narrow width. A typical single photoelectron distribution is shown in Fig. 4. These distributions can be obtained with the circuit

2i

20

CHANNEL NO. 5

leF

2e6

3e8

4e6

PULSE HEIGHT

FIG. 4. Single photoelectron integral and differential pulse height distributions. RCA type 4501 (similar to 8575). Photocathode K,CsSb. Counting time 10 min. Morton (7).

of Fig. 1 as discussed in Section II,D. By varying the level of the integral discriminator, one obtains the integral curve which intersects the ordinate at the total number of electrons entering the multiplier during the observation period. This integral curve allows one to calibrate the abscissa of the pulse height distribution curve in equivalent photoelectrons. Note that the spread of the distribution due to multiplication statistics causes some of the single photoelectrons to appear as doubles and others to be lost below a discriminator threshold. If the threshold could be set at the lower end of a very narrow

SINGLE PHOTON DETECTION AND TIMING

49

distribution without admitting any low amplitude device noise, one could expect stable single photon detection in spite of gain changes due to causes other than multiplication statistics. Theoretical derivations of single electron response (i.e. SER) amplitude distribution by a number of authors are summarized by Donati, Gatti, and Svelto (12) with particular emphasis on scintillation spectrometry. Various stochastic processes are used as models for secondary electron emission from an individual multiplier electrode. The SER distribution is obtained from an appropriate probability generating function which cascades the distribution successively down the electrode (or dynode) chain. The mean gain of the multiplier GI is then the product of the mean multiplication factor g of each dynode and results in an output pulse with mean amplitude A . If a Poisson process is assumed to describe the secondary emission at a dynode and if each dynode has equal mean gain, one can computean SERamplitude distribution that resembles Fig. 4 for a g of about 4. One can also calculate the percentage of single photoelectrons lost in the multiplication process for various g as in Table I (13). For g = 4, this loss is less than a few percent. It is often conTABLE I PERCENTAGE OF SINGLE PHOTOPULSESLOST I N A MULTIPLIERFOR DIFFERENT VALUES OF DYNODE GAIN9''

ELECTRON

9

Percent lost

1.5 2.0

42 20

2.5 3.0 5.0

11

Lombard

6 0.70

and

Martin

(13). (Courtesy of American

Institute of Physics.)

venient to use the ratio A of the full width of the SER amplitude distribution at half-maximum to the peak amplitude as a measure of the observed (or expected) width for a particular photomultiplier with dynode gain g. Here A is related to the relative variance by 2.35 E ~ The . relative variance is given by Morton (14) as 2 &A

= gEg2/(g-

=

l/(g - 1)

(7)

50

SHERMAN K. POULTNEY

for a Poisson process (cg2 = I/g) at each dynode and for a sufficiently long chain of dynodes, Much work has gone into trying to resolve the discrepancy of observations with theory for older photomultipliers. Relative variances larger than predicted by (7) are ascribed to non-Poissonian statistics in the secondary emission process itself or to a nonuniformity of gain on a dynode surface. In either case, the gain variance of a dynode is better expressed by t g 2= (bg + 1)/g where b expresses the deviation from Poisson behavior. The closer b is to 1, the larger the dynode variance, the amplitude variance and the A, Stable and efficient single photon detection requires a photomultiplier with a fairly narrow SER amplitude distribution (i.e. g 2 4). The width of the SER amplitude distribution can be decreased in several ways. With conventional dynode materials, one can increase dynode gain to its maximum value of 6 to 10 by raising electrode potentials. Fortunately, the first dynode has a dominant influence on the tA2as might be expected and only the first dynode or two need the high potentials. By regarding the first dynode as the source of the group of g1 electrons, one can compute the for a photomultiplier with remaining dynodes of gain g and for Poisson statistics using the results of Morton (14). &A2

=g/(g - l)gI.

(8)

The A for a photomultiplier with g1 = 10 and g = 5 would be 0.83 which is an improvement of 40% over a uniform gain photomultiplier. One can narrow the A much more dramatically by using the high gain dynode material on the first dynode. The A for a photomultiplier with g1 = 43 and g = 5 would be 0.40 which is close to that measured by Morton, Smith, and Krall(1.5). Such a photomultiplier is an excellent device for single photon detection. I t allows stable, efficient counting in addition to the capability of studying its noise behavior, as disccused in Section lI,C,l. Figure 5 shows the remarkably narrow peak of the distribution for single photoelectron noise (as well as other noise). Photomultipliers employing discrete dynodes and static, crossed electric and magnetic fields have been built to obtain fast time response as discussed in Section III,A,2. Their usefulness for single photon detection can be judged on the basis of their total gains which are 2 x lo4 to lo5 and of their dynode gains of 3 to 4. 4 . Gain and Gain Siatistics f o r Continuorrs Midtipliers Several varieties of continuous electron multipliers exist. Heroux (16) reviews the detection performance of a crossed-field continuous multiplier with respect to a discrete dynode multiplier. The crossed-field continuous multiplier uses a straight strip of high resistance dynode material. The electrons

SINGLE PHOTON DETECTION A N D TIMING

51

lo4 Small pulses

l-

a

I I : c I-

Single electron pulsrs

~

10

'

I

Large pulses I

I

PULSE

HEIGHT

FIG.5 . Diagrammatic noise pulse height distribution. RCA type C31000D (similar to 8575 but with GaP first dynode). Single electron noise represented by dotted line. Coates ( 2 1 ) . (Courtesy of The Institute of Physics.)

are guided between successive impacts on the dynode strip by means of an electric field between the dynode strip and a parallel (field) strip and by means of a crossed magnetic field. Gains high enough to detect single photoelectrons (e.g. G, = lo') can be obtained, but the SER amplitude distribution is very broad and lacks a well-defined peak. This distribution is attributed to a low value of dynode multiplication (e.g. g = 1.5) at the first impact and to an effective nonuniformity of the niultiplication factor due to photoelectrons striking the dynode strip at different positions. Moreover, the percentage of single photoelectron pulses lost in the multiplier would be expected tobehigh (e.g. 42). from Table I. Other impediments to the use of the crossed-field magnetic multiplier for single photon detection would be additional loss in efliciency due to photoelectron collection problems between photosurface and multiplier and a regeneration noise problem. The channel multiplier overcomes most of the above problems as described in a review by Wolber (17) and makes an attractive photodevice for single photon detection and timing. The channel multiplier is a hollow glass tube with a secondary-emitting coating deposited on its inner surface. Its length is relatively long compared to its inside diameter which is typically 1 mm. A voltage is applied to the ends of the channel to establish a uniform field along its axial length. An electron injected into the channel will be

52

SHERMAN K. POULTNEY

accelerated down the channel until it hits the wall to begin the multiplication process. The secondaries again are accelerated and collide with the wall due to their transverse energy components. Gains of lo7 are easily obtained. The SER amplitude distribution might be expected to be very broad from the discussion above. Such a behavior is found for moderate gains. However, at higher gains, SER amplitude distributions are obtained that are as narrow as the one in Fig. 5 for the high gain dynode photomultiplier. The cause of this narrowing is output pulse saturation. The mechanism for this saturation has been most recently studied by Harris (18). Stable single photon detection can thus be expected. Injection of the photoelectron into the multiplier is usually done by an accelerating potential of about 200V so that the first multiplication factor is about 3 and only a small loss is present inside the multiplier. The channel is usually curved to minimize regeneration noise. Due to its small size, the channel multiplier has other advantages with respect to device noise and to fast timing as discussed below in Sections II,C,2 and 111,A,3, respectively. The saturated output pulse is typically 10 to 20 nsec long. For single photon detection, the considerations of Section II,A indicate that load resistances of 2000 R or greater are optimum. The channel multiplier is limited in maximum counting rate to about lo5 counts/sec by current limitations and not by the pulse width. However, maximum count rates up to lo7 counts/sec have been obtained by Zatzick (19) using an auxiliary amplifier. An elaboration of the channel multiplier is a bundle of channels called a wafer. One such michrochannel wafer photomultiplier is described by Boutot and Pietri (20). It consists of about 5 x lo4 microchannels with individual diameters of 40pm.The useful photocathode diameter was about I cm and the multiplier gain was about lo5. The mircochannel wafer thus retains many of the channel multiplier advantages with the addition of a larger photosurface which is a necessity for many workers. However, the SER amplitude distribution has not yet been reported.

C. Photodevice and Background Noise and Their Reduction It does no good to be able to detect single photons if they are obscured by background and/or photodevice noise. An ideal photodevice would probably be one in which the only noise source was thermionic emission of electrons from the photocathode. In such a case, noise photoelectrons would exhibit the same SER amplitude distribution as signal photoelectrons. The same would be true for background noise photoelectrons. The only way to separate signal from noise is then to reduce the noise to tolerable levels by an appropriate technique or by choice of an appropriate photodevice. Figure 5 shows the noise pulse height distribution of a photomultiplier. Its behavior is not ideal in that there are additional pulses both smaller and larger than the well-

SINGLE PHOTON DETECTION AND TIMING

53

defined peak of single thermal electron pulses. The narrow SER amplitude distribution here allows one to set the threshold of the integral discriminator of Fig. 1 so as to accept most of the single electron pulse and reject most of the small pulses. The causes and reduction of photodevice and background noise is discussed below. The limits that the various noise sources set to single photon detection are discussed in Sections II,G; ll,C,l; and IV, both ingeneral and for particular photodevices.

I . Device Noise in Photomultipliers and Its Reduction Noise in photomultipliers depends greatly on the type of photomultiplier, the type of photocathode, the operating gain, technique, and the history of the particular photomultiplier selected. Attention is directed here to a recent study by Coates (21) of the dark noise performance of the photomultiplier with the high gain dynode discussed in Section II,B,3. The narrow SER amplitude distribution allows one to separate, identify, and study its various noise sources. Figure 5 shows a diagrammatic pulse height distribution for this photomultiplier at gains of about lo7 when the photocathode is shielded from external light sources. The contribution from single noise electrons is indicated by the broken line. Subtraction leaves two other classes of noise; small pulses below 0.2 electrons and large pulses above 2 electrons which account for 5 to 10% of the total counts. The small pulses were attributed to three sources; thermal emission from the dynodes, internal ohmic leakage between anode and the dynodes, and electron emission from the dynodes as a result of bombardment by ions. The small pulses are of minimal importance here because they can be discriminated against with little loss in single photon detection. The large pulses were also divided into three groups; ion pulses, afterpulses, and pulses due to cosmic rays. Ion pulses are single large pulses occurring at random and are due to ion bombardment of the photocathode. They are the major source of large pulses in this photomultiplier and their count rate increases with both gain and temperature. Afterpulsesare due to ions formed i n the region between photocathode and first dynode by the collision of an electron with gaseous impurities in the photomultiplier. The event is characterized by correlations in time between single electron pulses and large pulses. A characteristic time for this photomultiplier was 0.4psec. In photonlultipliers of different design, afterpulses coming 40nsec later are seen and are due to feedback of light produced at the anode by charge pulses ( 4 ) . Cosmic ray pulses are due to the production of Cherenkov radiation in the photomultiplier window by the fast particles. These ultrashort pulses occur at the rate of about 0.3 counts/sec for this 5 cm diameter photomultiplier and appear to saturate the output at about the 15 photoelectron level for typical gains. The cosmic ray particles also excite fluorescence in the window with a decay

54

SHERMAN K. POULTNEY

time of the order of 20 to 50psec and so generate more correlated noise pulses. The large noise pulses do not have a particularly serious effect on single photon detection since they are each standardized to one count in the discriminator. At low signal rates with an otherwise quiet photomultiplier, the cosmic ray pulses or pulses due to radioactivity in the tube envelope can be serious. At low rates, however, one could use a single channel analyzer to eliminate both small and large noise pulses. The predominant photomultiplier noise is single electron noise. Its magnitude depends on both the particular photosurface and particular photomultiplier in use. Coates (21) studied photomultipliers with bialkali photosurfaces. A typical room temperature noise rate was 200 counts/sec. The single electron noise consisted of two parts: thermal emission from the photocathode and an excess noise apparently generated by field emission. The thermal emission could be eliminated by rooling the photomultiplier to 0°C or below where the excess noise became dominant at about 50 counts/sec. The excess noise shows a nonrandom behavior (approximately Ilf in character) and will affect single photon detection (Section II,G,I). It also usually increases greatly with photomultiplier gain and so may become serious if high gains are required. If the application allows, one might use an amplifier to lower the gain operating point of the photomultiplier. Red sensitive photosurfaces show much higher thermal dark noise so that selection and noise reduction become very important for single photon detection. Table 111 lists typical room temperature noise rates for various photocathodes. Cooling of the photodevice is a popular method of noise reduction. A rough rule of thumb is that the noise rate drops by a factor of ten for each 20°C drop until the excess single electron noise dominates. Such a rapid dependence of noise on temperature requires good temperature control for single photon detection of weak sources. Foord, Jones, Oliver, and Pike (22) give a recent review of noise reduction by cooling in a paper concerned with many aspects of photon counting. Cooling does have the disadvantages of condensations and of Cherenkov radiation produced in windows added to prevent condensation. The other noise reduction techniques require that the incoming light signal be collimated to a small spot or narrow beam. Oliver and Pike (23) studied a photomultiplier with an effective small photosurface which was also cooled. They obtained a dark noise rate of 0.459 counts/sec at -20°C which was excess noise, random, and ascribed to radioactivity in the tube window. Another method is to eliminate from the multiplier input optics the electrons from all but a small portion of a large photosurface by means of a magnetic or electrostatic lens. Manufacturers are now making these available. A clever use of a magnetic lens was made by Topp et al. (24) who combined it with a device to enhance the quantum efficiency of their photomultiplier. Even more serious than dark noise for many applications is noise genera-

SINGLE PHOTON DETECTION AND TIMING

55

ted by the light signal. If noise electrons can produce afterpulses, photoelectrons can do likewise. Coates (21) found about one afterpulse for every 100 photoelectron pulses. Foord et a/. (22) investigated signal afterpulsing for a number of photomultipliers and pointed out their effects on both photon counting and correlation experiments (see Section IV,B) and photometry of weak sources. In some photomultipliers, prepulsing has been observed as mentioned by Meiling and Stary (3, p. 25). The signal-correlated noise can be studied by either viewing a light source known to cause random emission of photoelectrons in ii series of photon counting intervals or viewing it with a multichannel time analyzer as outlined i n Section 1V,B,3.

2. Deuice Noise in Channel Photomultipliers The dark noise pulse height distribution of the channel photomultiplier is effectively the same as the single photoelectron distribution when the channel multiplier is operaied in the pulse saturation mode. However. the amount of noise is substantially lower compared lo a photomultiplier. Wolber (17) reports noise counts of from 1 to 10counts/sec for an S-20 photosurface at room temperature and attributes them to thermionic emission from the photosurface. The low noise rate is due primarily to the small size of the photosurface ( 1 tnm'). Again collimated light signals are required if a single channel is used. A reduction of 20 in the noise was observed upon cooling to -2O"C, but no further reduction was observed at lower temperatures. Replacement of the photocathode with a blank disk reduced the room temperature noise rate to 0.01 counts/sec and indicated the cosmic ray contribution. The discrepancy between the coolecl rate and the blank rate is probably due to excess noise although the smoothness and continuity of the channels should minimize that source. The conditions for ion noise and time-correlated afterpulses are much more restrictive in the small channels, but they may be present. Afterpulses would cause the same problems in applications as with photomultipliers and should be studied. 3. Background Noise

In some applications, single photoelectrons from a light background could obscure the signal photoelectron. Reduction is again the only alternative in the form of spatial filtering, spectral filtering, or time gating. An extreme example of the background limitation is the detection of a single photon against the combined background of bright moon and bright sky as in the Lunar Laser Experiment (see Section III,D,2). A 6 arcsec field of view and a 1 A wide filter still allowed about 300 kcounts/sec of noise using the 2.7 m diameter McDonald observatory telescope. The final reduction

56

SHERMAN K. POULTNEY

technique required the setting of a microsecond time gate about the expected time of arrival of the lunar return by electronic means. A number of repeated rangings were, of course, necessary to be certain of a signal return. It is also of interest to note here that the photomultiplier used had to be operated at very high gains and so was subject to excess noise. The ERMA photosurface which was used exhibited a noise rate of 30 kcounts/sec at room temperature and several kcounts per second when cooled to about 0°C.

D. Practical Photodevice Techniques and Photon Detection Performance Tests It is important to be able to measure the SER amplitude distributions of both single electron signals and noise in order to evaluate the single photon detection capabilities of a particular photodevice. These tests also enable one to be sure that correct photodevice techniques are being employed. Poor practices can greatly increase photodevice noise and may lead to destruction of either the photosurface or the device. Table I 1 gives a checklist of good TABLE II

CHECKLIST OF Goon PHOTONCOUNTING PRACTICE WITH PHOTOMULTIPLIERS Housing design a. Optical isolation b. Electrostatic, magnetostatic, and rfi shields c. Insulating material choice and plncement d. Stable, high frequency electrical components e. Dissipation of heat from divider resistors f. Stable cooling method free of electrical noise g. Cooling scheme free of condensation h. Tapered divider and charge-storage capacitors

Practice a. Test housing before inserting tube b. Ground photocathode (if at all possible) C. Never expose tube to strong light d. Keep clean of cloth fibers, moisture, etc. e. Use as low a gain as possible f. Allow device noise to stabilize g. Use stable, low noise high voltage supply h. Good high frequency wiring technique

practices; a number of which seem always to be ignored i n homemade and commercial photodevice units. Recent discussions of performance tests and good photodevice techniques have been given by Morton (7), Zatzick (19), and RCA staff ( 4 ) . If afterpulsing can seriously affect a particular single photon detection experiment, additional tests for time correlations should be made as discussed in Section 1V,B,3.

SINGLE PHOTON DETECTION AND TIMING

57

Morton (7) gives a concise summary of tests for single photon counting performance of photodevices based on Fig. I . First in importance is the determination of the location and shape of the single photoelectron peak. An approximate location of this peak can be found by setting the threshold of the integral discriminator at its lowest value and by examining the dark noise as a function of tube voltage. The presence of a peak in the single electron pulse height distribution will be recognized by the occurrence of aplateau in this integral voltage curve. If the noise rate on this plateau is sufficiently low, one can study the single photoelectron peak by illuminating the photosurface with a steady, weak light source which yields a count rate about ten times the noise rate and examining the count rate as a function of discriminator level. The result should be an integral curve similar to that in Fig. 4. To express the abscissa in terms of equivalent electrons, one sketches in the rectangle shown with height equal to the total number of electrons observed and whose area is the area under the integral curve. The intercept of this rectangle on the abscissa gives the height of one photoelectron. The slope of the integral curve gives the SER amplitude distribution. The use of a multichannel pulse height analyzer obtains the amplitude distribution directly and greatly reduces the time necessary for these tests. However, the tests should be done as close as possible to the operating conditions of a particular experiment which may preclude the use of an analyzer. I t is sometimes necessary to subtract the integral curve of the device noise in order to interpret the single photoelectron distribution. In any case, a careful study of the device noise amplitude spectrum (e.g. Fig. 5) is necessary in order to set a lower (and upper if used) discriminator level to optimize noise discrimination with a known loss of single photoelectromn pulses. If cooling is necessary, the tests should be done under these conditiions. SER amplitude distributions can be examined in the presence of high device noise by using the time-gating method discussed in Section lll,C, I . Fiinally, one should investigate the statistics of the counting process for device noise by repeated counting since this is one of the factors limiting detection measurements of weak sources. Deviations of the signal counting statistics from random behavior is discussed in Section IV,B.

E. Quantutn Eficienry of'Photosurfaces I . Introduction The photosurface of the photodevice converts incident signal photons into photoelectrons which enter the multiplier to be detected. The efficiency of this conversion, I], at the wavelength of interest, I , , is therefore very important for single photon detection. It is called the photosurface quantum efficiency and is usually quite a lot smaller than 100%. If one were simply

58

SHERMAN K. POULTNEY

trying to detect a signal photon in a gated interval in the absence of noise, it is obvious that the probability of detection increases directly with the quantum efficiency at the wavelength of interest. If a background photon noise rate, N B ,and a device noise rate, N , , are present, the probability of detection depends on the accumulated photoelectron signal, qn, , becoming larger than noise fluctuations in the expected interval after repeated trials. Assuming that both noise and signal fluctuations can be described by Poisson statistics, one can obtain the signal to noise ratio, SIN, as

SIN

=

qn,/(qn,

+ q N , T + Nd T ) ' / 2 ,

(9)

where it has been assumed that the noise has been measured in an equal time interval where the signal was hot present and T is the total time of observing both intervals. A similar result is obtained for photometry of weak sources in Section II,G,l. If device noise dominates and the photoelectron signal is written in the form of a rate, (9) reduces to the expression for the figure of merit of a photodevice for photon counting given by Morton (7). In this case, it is possible that one would select a photodevice with a lower noise to maximize this figure of merit rather than a higher q. In all other cases, the choice is the highest quantum efficiency. A history and description of most available photosurfaces is given by Sommer (25). A review to mid-I970 is given by Bell and Spicer (26).Table 111 is compiled from these sources plus RCA Staff ( 4 ) and includes the properties of some of the older photocathodes as well as those of the new photosurfaces TABLE I l l

TYPES A N D CHARACTERISTICS OF VARIOUS PHOTOSURFACES~

Cathode type

S-lb S-I1 S-20 Bialkali ERMA GaAs GaAsP GaInAs

Stoichiometry

Ag-0-Cs Cs3Sb-O Na,KSb(Cs) K,CsSb Na-K-Sb-Cs GaAs(Cs) GaAs, -xP, InCaAs-CsO

Wavelength of peak response

Peak quantum efficiency

Wavelength at I % peak quantum efficiency

(A)

( %)

(A)

8000 4000 4100 3800 5600 3400 3300 4000

0.5 15 19 30 10 12

12,000 6300 8300 6600 9300 9000 7400 10,500

17

22

Dark noise rate at 20°C (e/cm2/sec) 5 x lo6 100

400 30 I 03 104

I 04

Dark noise rates from Zatzick (19). Other data from Sonirner (25) and RCA staff (4. Above 4000 A.

SINGLE PHOTON DETECTION AND TIMING

59

that have been developed for use in the near infrared. The ultraviolet response of conventional photosurfaces is generally limited by the device window. New materials are sought for this region primarily for lack of sensitivity at longer wavelengths. Table I11 lists peak quantum efficiency, a measure of the span of the spectral response, and dark noise rates. Spectral response curves can be found in the references. The quantum efficiency at a given wavelength is related to the commonly used radiant spectral sensitivity, c, in mA/W by

where Al is in Angstrom units.

2. The Pliotoemiss,;onProcess A concise description of the photoemission process will be useful at this point for a number of reasons. It aids in the understanding of the improved yields of photoemission and secondary emission of the new materials, their effects on device time resolution (see Section IIl,A), and quantum efficiency enhancement in thle older photosurfaces. Even prior to the development of the new materials. a basic description of the efficient conventional photosurface was achievled on the basis that they were semiconductors (25). Figure 6 shows an energy model for a semiconductor photoemitter which includes the space dimension normal to the surface. The valence band is the highest filled energy band for electrons. Immediately above the valence band is an energy gap of width EG for which no energy states exist for electrons. Above this forbidden band, there is a band of permitted energy states (i.e. the conduction band) which at ordinary temperatures contains very few electrons. VACUUM LEVEL

CONDUCTION BAND

SOLID

7’, EA

-

I

---L

VACUUM

FIG.6. Energy band model for a semiconductor photoemitter. Distance from surface also shown. Threshold for photoemission is EPH= E, E G . EA is electron affinity

+

energy.

60

SHERMAN K. POULTNEY

An electron at the bottom of the conduction sees a potential barrier for emission to the vacuum represented by EA which is called the electron affinity energy. Photoemission from the semiconductor for a photon of energy E,, may then be viewed as a three-step process; absorption of the photon by the material and excitation of an electron from the valence band to the conduction band, movement of the excited electron to the vacuum interface, and escape of the electron over the potential barrier into the vacuum. Therefore, the minimum photon energy necessary to produce a photoelectron is the sum of EG and E A . This minimum sets the limit of red response. For example, the S-20 photosurface has an EG of I .OO eV and an EA of 0.55 eV. The absence of thermal electrons in the conduction band and the typical E A which are much smaller than impact ionization thresholds mean that the electron excited to the conduction band can escape from moderately large depths compared to a metal ; being limited only by energy loss through electron-phonon interactions. This large escape depth leads to high quantum efficiencies as long as the wavelength-dependent absorption coefficient is high enough. Typical escape depths for conventional photosurfaces are about 200A compared to ~ o Ain metals. The addition of the concept of negative electron affinity to the above description started a search for suitable photoemitters among the more familiar semiconductors. Negative electron affinity means that the energy bands near the surface of the semiconductor are bent in such a way that the bottom of the conduction band deeper inside the surface lies above the vacuum energy as shown in Fig. 7. This bending can be accomplished by the adsorption of electropositive metal atoms on the surface of a sufficiently p-type bulk semiconductor (such that its Fermi energy is at or near the edge of the valence band). The depth of the bent band region should be as small as possible. The great advantage of materials with negative electron affinity is

CONDUCTION BAND VACUUM L E V E L FORBIDDEN BAND

FERMl

SOLID +--

I

-VACUUM

Fro. 7. Energy band model of a semiconductor photoemitter with negative electron affinity. Distance from surface also shown.

SINGLE PHOTON DETECTION AND TIMING

61

that the majority of electrons excited to the conduction band and traveling slowly toward the surface can be emitted even though they lose energy in phonon collisions. Even those electrons excited deep within the material (up to 10,OOOA) have a reasonable probability of being emitted as photoelectrons into the vacuum. Consequently, the photosurface quantum efficiency is greatly enhanced, especially near the threshold. The limit of red response is approximately equal to the semiconductor band gap (e.g. 1.4 eV in GaAs-Cs). Scheer and van Laar (27) reported the first photosurface (GaAs-Cs) built on this concept in 1965. The practical utilization of these concepts had to await the development of high quality semiconductors with appropriate band gaps and doping levels and with good minority carrier transport properties. Most promising for practical and commercial applications are the 111-V compounds. The incorporation of the new photoemissive materials into photomultipliers is proceeding rapidly. Reports on the performance of these new photomultipliers have not yet reached the general literature although some numbers are available in Table 111. The energy distribution of photoelectrons may be narrowed as for secondary electron emission, at least for shorter wavelengths. A greater effect on time resolution could come from the long electron diffusion times (e.g. 100 psec) associated with the greater escape depths. This effect does not at present limit the time response of photodevices, but may if materials with greater escape depths are used to obtain higher quantum efficiencies. Cooling of a photosurface to reduce dark noise can affect the quantum efficiency of the phiotosurface. Boileau and Miller (28) report that a lowering of the temperature usually increases the short wavelength efficiency, but decreases the long wavelength sensitivity. The increase is minor while the decrease can be as much as 2% per "C near the photosurface threshold. If one is working in the long wavelength region and is cooling the photosurface, one should measure the quantum efficiency at the operating temperature. In any case, the temperature of the photosurface should be kept constant in in order to have a stable efficiency photomultiplier. It is best to assume that a given photosurfact: has a large temperature coefficient in the far red until proven otherwise. 3. Measurement of' Photocathode Quantum Eficiency It is often necessary to measure the quantum efficiency of a photosurface in order to check its uniformity over the surface, to check its relative spectral behavior, to examine its temperature dependence at a given wavelength, or to measure an absolute value at a certain wavelength. These and other basic tests of a photodevice are' described in the IRE Standards (29). The absolute measurement is difficult to carry out accurately. Relative measurements can

62

SHERMAN K. POULTNEY

be made more easily (30). The photodevice is connected as a diode if possible with all other electrodes at a potential of several hundred volts. The cathode current is then measured for a constant amount of light at the wavelength of interest as the conditions arevaried. If the wavelength is varied, a thermopile or some other secondarystandard is needed to monitor the light intensity. If a rough measure of the quantum efficiency is sufficient (i.e. to about 10 %) and the secondary standard is stable and previously calibrated, the quantum efficiency in electrons per photon can be calculated.

4. Quantum Eficiency Enhancement Quantum efficiency enhancement really consists of the reduction or elimination of losses which occur at the photocathode (25). Before the new materials, all photocathodes were deposited as thin layers on opaque or transparent substrates. Aside from the obvious reflection losses at the photocathode interfaces, there are two other types of losses: transmitted light and light absorbed beyond the escape depth. These losses are wavelength dependent because the absorption coefficient of the photosurface material usually varies with wavelength. One method of enhancement increases the light path (and absorption) without going beyond the escape depth by depositing the photosurface on a reflecting substrate. The enhancement is usually greatest in the red where the absorption coefficient is lowest. A further improvement is to make the photosurface part of a reflection interference filter which, however, limits the range of useful wavelengths. These techniques are not particularly useful with the new materials which are already near optimum absorption and escape depth and which are small bulk semiconductor crystals mounted as an integral part of the multiplier. In addition, most older photomultipliers were designed for use with diffuse light sources and so required large, transmission-type photosurfaces. These transmission-type photocathodes have thicknesses chosen to maximize their response toward the blue. Much of any incident red light is transmitted through the photosurface resulting in low quantum efficiencies. Thicker photosurfaces would help, but would soon be limited by the escape depth problem in addition to lowering the blue response. These photocathodes can have their red response enhanced by external optical techniques that prolong the light path inside the photocathode without causing it to move too far from the surface. Gunter, Grant, and Shaw (3f)give a good review of these techniques and practical results with several tube types. Enhancements of about two were obtained in the blue and up to six in the red and near-infrared. Optical enhancement requires narrow, collimated beams as do the photomultipliers with the new photosurfaces. Finally, Crowe and Gumnick (32) report enhancements with conventional photosurfaces as a result of the application of external electric

SINGLE PHOTON DETECTION AND TIMING

63

fields. This enhancement may be due to a lowering of the vacuum potential barrier shown in Fig. 6. Enhancements of 3 to 6 were observed near 9000A. The same enhancement technique may be applicable to the new photoemitting materials.

F. Total Quantum Counting Eficiency The photoelectrons released from the photosurface of a photodevice may not all be detected as counts at the discriminator for a variety of reasons. The total quantum counting efficiency o f the device will therefore show a discrepancy compared to the photosurface quantum efficiency. The discrepancy may occur due to inefficient collection of photoelectrons at the first multiplier surface, losses in the multiplication process, or rejection o f the smaller pulses o f the SER amplitude distribution by the discriminator. Pietri (33)measured the collection efficiency of an early high gain, focused photomultiplier to be 807; at 4200A for a 2 cm2 spot at the center of its photosurface. He was able to redesign the input optics in a later tube to raise the collection efficiency to near 100%. The collection efficiency was found to decrease with an increase in the area o f the photosurface used and to increase as the wavelength of the incident light was increased. The collection efficiency of most photodevices and its behavior with wavelength and position can be predicted by computer simulation o f electron trajectories in the photocathode-first dynode region ( 4 ) . Focused photomultipliers are designed to give collection efficiencies from 85 7”to 98 ”/, depeoding on the size of the photosurface used. Other geometry photodevices may have lower collection efficiencies. Wolber ( 1 7 ) quotes a lower bound of from 70 to 90 for a channel multiplier. Loss of counts in the multiplier would riot be expected to affect discrete dynode multipliers, as discussed in Section II,B,3. However, this loss might be expected to be more serious in devices which have low initial multiplication factors. The possible source of discrepancy most easily studied is the rejection of small pulses by the discriminator. Although it can be taken into account i n experiments by knowing the SER amplitude distribution and the setting of the integral discriminator, observing times still depend on the detected signal rate. The high gain, first dynode photomultiplier discussed in Section II,B,3 should enable one .to work on a counting plateau where a very large percentage of the single photoelectrons are detected and thereby to achieve a counting efficiency very close to the photocathode quantum efficiency. Lakes and Poultney (30) have made a direct measurement o f these two quantities for this photomultiplier arid find about a 25 %, discrepancy even though an excellent counting plateau was observed. Birenbaum and Scar1 (34) later found a 407; discrepancy, but with a plateau of significant slope at their operating gain. They attributed the discrepancy to an unexpected number of photoelectron

64

SHERMAN K. POULTNEY

pulses much smaller than the well-behaved single photoelectron peak. Figure 5 gives an indication of the deviation at small pulse heights. Coates (35) has studied such a deviation of the SER amplitude distribution from the predictions (Section II,B,3) for this particular photomultiplier and was forced to propose an edge effect after considering many other causes. The edge effect consists of a loss of electrons from a charge packet due to striking either the edge of a dynode or a macroscopic inhomogeneity on a dynode. Again this photomultiplier allows a very detailed investigation of its own behavior. It is not now clear whether this otherwise excellent photomultiplier has a unique problem or whether the poorer SER ampitude distributions of other photomultipliers manage to mask the effect. In any case, workers should be aware of the possibility that the total quantum counting efficiency of a photodevice may be lower than the photosurface quantum efficiency. The discrepancy can cause longer observing times, in the least, and unexpected systematic errors in photometric applications.

G . Typical Photon Detection Experiments 1. Introduction

There are a wide range of photometry and spectrophotometry experiments that require the measurement of a weak light intensity. The weak intensity may be due to a weak source, scattering with small cross sections, or many spectral channels viewing a stronger source. With the assumption that the photodevice has been selected for optimum quantum counting efficiency, qo , one can define weak light intensity as about 100 counts/sec or less. The photodevice is operated as shown in Fig. 1 for single photon detection which is also called photon counting. The anode charge pulse is detected at the discriminator, standardized, and recorded by a digital counter. If there are no correlated afterpulses and if the device and background noise rates are much smaller than the signal rate, the fractional precision of a measurement (i.e. the inverse of the signal to noise ratio) is given by (S{N)-’ = I/(qoNpT/2)1’2,

(1 1)

where N P is the signal photon rate and T/2 is the measurement period. The signal counts are Poisson distributed in time or shot noise limited, at least for coherent and broadband light. Alternate detection and recording methods do exist in which analog recording (i.e. a rate meter or current meter) can be used on either standardized or nonstandardized photodevice output pulses. Jones, Oliver, and Pike (36) show theoretically and experimentally that photon counting yields the best precision as given by (11) in a given observation

SINGLE PHOTON DETECTION AND TIMING

65

period. A rate meter (i.e. analog recording) viewing standardized counts is shown to yield a fractional precision lower by 4’2 and therefore requires twice the measurement period to obtain the same precision. This result can easily be obtained from Campbell’s theorem for the situation in which one observes for a period four times the integration time of the rate meter. An additional lowering of the fractional precision of a measurement in a given period enters if nonstandardized counts are recorded. For an SER amplitude distribution whic.h fits the theory outlined in Section II,B, the fractional ) 1 + ( A / 2 . 3 5 J 2where precision is lowered by the square root of ( I E ~ * = and A are defined in Section II,B. This factor becomes \/2 for a photodevice without a peak. The particular choice of detection method depends on the signal rate. Photon counting is superiof at very low signals rates, but does have a high signal limit. Near or above this limit one must switch to analog recording of nonstandardized pulses. At signal rates in between these two limits, the method is probably determined by past practice and simplicity of record keeping. One advantage of photon counting is that it allows one to make a detailed study of the photodevice being used. Further advantages of photon counting are discussed below for a number of typical experiments, The presence of ‘lo in (1 1) should also be noted. Assume now that the photodevice in use is being operated under optimum conditions as discussed previously so that a counting plateau exists and the dark noise and background rates have been reduced to about 1 count/sec. As the signal rate approaches 1 count/sec, the observation period needed to obtain a certain precision will increase over that predicted by ( I I ) . This increase can be obtained from

+

(SIN)-’

= (‘loN

,

+ 2q0 N , + 2Nd)”‘/q0 N P ( T / 2 ) ’ ” ,

where N , , N , , and Nd are the signal photon, background noise photon, and dark noise rates, respectively. The signal has been separated from the noise by effectively modula.ting the source with a square wave of period T and the noise is also assumed to be Poisson distributed in time. Again, any of the alternate detection methods can be used with the fractional precision ( 1 2 ) lowered as discussed above for the shot noise limited expression (1 I ) . It should be pointed out that synchronous analog detection has additional noise discrimination advantages over a straight current measurement (37), due to low frequency circuit noise not considered above. Synchronous digital detection has no such advantage over photon counting. Its advantage over all other methods beyond those already discussed is its low drift operation with time which allows very long observation periods (of the order of hours). Synchronous photon counting was first reported by Arecchi, Gatti, and Sona (38) and somewh,at later by Oliver and Pike (23). A more sophisticated

66

SHERMAN K . POULTWY

version with provisions for readouts of signal and noise as well as the difference and sum for assignment of statistical uncertainty was recently reported by Zatzick (19).Their results are consistent with the determination of a signal of 0.1 count/sec with a precision of 10% ( S I N = 10) in the presence of 1 count/sec Poisson-distributed noise using a counting period of one hour. Predictions for other signal and noise rates can be obtained from (12). Again note the advantage of the highest possible total counting efficiency. The high signal rate limit of photon counting is determined by the response times of photodevice, amplifier, discriminator, or digital counter. Usually, the dead time of either the discriminator or counter sets the limit. The recent version of the synchronous digital photon counter has a limit of 85MHz yielding a practical intensity range of about lo*. However, this upper limit may have to be lowered considerably if it corresponds to an anode current limitation of a photodevice or if afterpulses are present. One way to eliminate the effect of afterpulses is to gate the detector off until after the characteristic time of afterpulsing (e.g. 10psec). Rather than switch to other detection methods from photon counting, one has the final alternative of attenuating the incoming signal with calibrated filters. The deviation of the signal and noise rates from a Poisson behavior due to the photodevice will lower the precision of a measurement below (12) in a fixed observation time. The same is true for deviations due to fluctuations in the light intensity. However, here a study of the deviations in the counting statistics would reveal information as to the nature of the light source, or the scattering medium as discussed in Section IV,B. The deviations due to the photodevice which are discussed in Section II,C, 1 can also dictate the choice of detection method. For example, the residual noise component due to cosmic rays occurs at a very low rate, but yields very large pulses. If measurements are made on weak sources using nonstandardized pulses, the large pulses can cause serious systematic errors (39). In addition, afterpulsing can only be eliminated in the photon counting mode. The most serious deviation due to photodevice from a diagnostic viewpoint would be the presence of single electron afterpulses several microseconds after every dark or signal count. Neither pulse height spectra nor a cursory counting statistics study would uncover it and a systematic error in source intensity would result. Probably only a study of the arrival times of each count by the methods of Section II1,C would catch it. 2. Laboratory Photometry and Spectrophotometry

Weak source photometry in the laboratory includes measurements of the angular and polarization dependence of light scattered from either single particles (40) or from the cooperative effects of many particles (41). These

SINGLE PHOTON DETECTION AND TIMING

67

measurements can be used to study the sizes and other properties of individual particles and to study the correlation lengths for cooperative particle or density fluctuation effects. Low light level spectrophotometry includes the measurement to medium or high resolution of the spectra of any weak source or of any scattered light. The threefold advance of recent years in laser light sources, high resolution (and high background rejection) spectrometers, and photon counting has had a profound effect on the study of matter by light scattering. Smith (42) gives a brief review of the many different collective motions in matter now being studied by combinations of these techniques. Accessible with taindem monochromators are weak Raman-shifted frequencies (10” to 10l3 Hz) of light scattered from molecules and from various optical modes of excitation in matter as well as smaller frequency shifts previously obscured by conventional source linewidths. Accessible with high resolution, scanning Fabry-Perot interferometers are weak Brillouin-shifted frequencies ( lo9 to 10’ Hz). Chu (43) briefly reviews recent Raman and Brillouin scattering studies, discusses Rayleigh scattering studies using optical mixing spectroscopy, and recommends the photon counting statistics discussed in Section IV,B as an alternate to that new spectroscopy. Single photon detection is only used in these types of experiments for the weakest intensities. Reynolds (44) reviews an interesting series of photon detection experiments with interferometers and slit systems which demonstrate that the interference patterns are obtained as expected with very weak sources. Both photomultipliers and image tubes were used. Arecchi et al. (38) used their synchronous photon counter to measure the angular distribution of Raman scattered light from the 992 cni-’ vibrational frequency of benzene in a direction parallel to the polarization plane. A He-Ne laser at 6328A was used a.s the excitation source. Signals as low as IOcounts/sec were measured to 10% precision with observation times of 1 min in the presence of noise of 500counts/sec from the uncooled RCA 7265. An example of photon detection as applied to Brillouin scattering in gases is given by Greytak and Benedek ( 4 5 ) . They use an ITT FW 130 with 3 dark counts/sec and state that signal shot noise limited the precision. Their peak signal rate was 300 counts/sec. Lineshifts of about 10‘ Hz and linewidths of about 3 x lo7 Hz (nearly equal to instrumental width) were measured. Background scattered light had to be subtracted. Barrett and Adams ( 4 6 ) give an excellent description of the many related techniques used to improve signal to noise ratios in a study of Raman scattering from rotation-vibration lines in ultrasmall gas samples. These techniques include sample illumination, polarization discrimination against Rayleigh-scattered light, optimum collection of scattered light, and single photon detection. An EM1 62568 photomultiplierwas used at a peak signal rate of about 10 counts/sec resulting in a total of a few hundred pulses for a typical rotational line in the vibration band. The dark count was

68

SHERMAN K. POULTNEY

46 counts/sec at room temperature and one count every 5 sec when cooled to about -40°C. A rate meter-type recorder was also provided for viewing the standardized pulses. The monochromator was scanned at as low a rate as 1.8 cm-'/min for a total scan time of three hours in the case of the rotationvibration (1-0) band in nitrogen. An integration time of 10 sec was used for counting. The magnitude of the background was not mentioned. Mooradian (47) considers the elimination of unwanted excitation radiation as one of the most difficult experimental problems of laser light scattering spectroscopy and refers to several electronic and optical subtraction techniques that have been successfully employed. Most of these techniques are coupled with synchronous detection. The unwanted radiation becomes most troublesome in the spectral region near the laser line itself and even several monochromators in tandem cannot reject it sufficiently. The resolution, scan rates, and integration times of weak source spectroscopy will depend on the aims of the particular experiment as well as the signal to noise ratio. The decision to move to single photon detection and most likely to synchronous digital detection probably requires the recording and processing of the data in digital form. Commercial manufacturers of spectrometer systems now offer the whole range of detection and recording methods mentioned in Section II,G,I.

3. Photometry and Spectrophotometry in Astronomy Interest in the detection and measurement of faint astronomical sources has always constituted an impetus to single photon detection. An early review of this work can be found in the articles by Baum, Johnson, and Lallemand in the volume edited by Hiltner (48). Photometry and spectrophotometry in astronomy differ from those in the laboratory in that other natural phenomena affect the measurements and other workers are waiting to use the costly facilities. The natural phenomena include atmospheric " seeing," scintillation, and extinction. In addition, the night sky background may fluctuate due to physical processes. Background can be subtracted by means of a two-channel photometer with one detector viewing a nearby patch of dark sky or by means of a one-channel photometer synchronously switched from star to dark sky in conjunction with the synchronous digital detection mentioned in Section II,G,l. The switching can be done either in the telescope optics or in a photomultiplier designed for magnetic deflection of a viewing spot on the photosurface. Tull (49) describes a photon counting system for high resolution spectrophotometry and includes a discussion of the atmospheric and other noise limitations. Zatzick (19) briefly describes a 32channel photon counting spectrometer attached to the Mt. Palomar 5 m telescope. Each photomultiplier views a different region of the spectrum and is interfaced with a computer for data recording, background subtraction, and

SINGLE PHOTON DETECTION AND TIMING

69

limited data analysis. The typical light flux may be about 1 or 2 photons/sec so that spectral information from stars of 22nd magnitude can be obtained. The need to perform calibration measurements on bright stellar objects with known properties; requires the additional capability of fast counting devices and circuitry. Dennison (50) has recently described the philosophy and practice of electronic optical astronomy and includes therein new developments with single photon detection in astronomy. Rather than use 32 or 80 photomultipliers one would like to use a single image tube with an electronic readout of the image of a weak source or spectrum. At present, the image intensifier is used as the front end of such an image tube and its single electron detection properties determine those of the whole device. Methods of evaluating the single photon detection capabilitiesof imageintensifiertubes have been pioneered by Reynolds (51) and have many similarities to the evaluation of photomultipliers. 111. FASTTIMING WITH SINGLE PHOTONS

Fast timing with single photons means that the timing system consisting of a photodevice, timing circuits, and timing methods is capableof measuring the interval between single photon events to nanosecond or better accuracy. The capability of counting photons at high rates is closely related; especially if the interval between events being timed is very small. In addition to this timing capability, the fast system must possess all the single photon properties outlined in Section 11. In special cases such as background noise limited detection or a surplus of signal photons, this last requirement can be relaxed by allowing a high device noise or by allowing a poor counting efficiency respectively as noted in Section II1,D. A . Photodevice Timing Capabilities and Limitations

Photomultipliers with discrete linear dynodes and electrostatic focusing (see Fig. 3) have long held the lead in precision timing of intervals between single photon events or between a time marker and a photon event. Many of the properties which placed them foremost i n efficient single photon detection also aid in the attainment of this fast timing and counting. Efficient photon detection is not, however, a sufficient condition for fast timing. A review of the timing capabilities and limitations of this particular type of photomultiplier will establish a framework for the comparison of present devices and for the contemplation of new devices. Several of these new devices can be expected to yield an order of magnitude improvement over present photomultipliers.

70

SHERMAN K. POULTNEY

Most devices operating on the principle of external photoemision possess three basic elements; a photosurface with electron optics which directs the photoelectron into the electron multiplier, the electron multiplier which amplifies the single electron by secondary emission, and the anode which collects the charge packet to provide an external signal (see Fig. I). The time of travel from the photosurface to the external output lead is called the electron transit time, 11, of the device. It can be measured using a short light signal of single or multiple photon intensity which has a synchronous electrical pulse. The arrival time of the resultant charge pulse at the external output must be defined with respect to a characteristic of the pulse such as its centroid or a point part way up its leading edge. This arrival time will fluctuate from one measurement to another, especially for single photon signals. This fluctuation in device transit time will limit the timing precision for single photon events and will be assumed to consist of transit time fluctuations or spreads between photosurface and multiplier, e K M ,in the multiplier, eMS, and between multiplier and anode, These spreads originate both in the geometry of the device and in the distribution of initial velocities of photo and secondary electron emission. For example, the geometry may be such that all possible electron paths between two device elements are not isochronous for even the electrons emitted at rest. The individual spreads will be expressed as standard deviations and added as such with suitable weighting factors. Values for the individual transit time spreads and their dependence on photodevice design are discussed below. It might be expected that initial stages of a photodevice contribute with the greatest weight to the total transit time fluctuation. In the later stages, the growing number of electrons in a charge pulse provides many samples of the transit time of a stage and should reduce the transit time fluctuation of that stage in the manner of the standard error of a mean (i.e. the transit time variance of that stage divided by the number of electrons sampling the paths). With the assumptions that all transit time spreads after E K M are equal cSS, that all stage multiplications are equal (i.e. g), and that multiplication fluctuations do not have a significant effect on the spread weighting factors, one can express the total transit time fluctuation for a photomultiplier as & H ;

= & k M f &&/(g -

l),

(13)

Gatti and Svelto (52).The first stage or dynode often has a larger gain g, as well as a larger eSS as discussed below. In this case, the single photon transit fluctuation of the photomultiplier would be approximated by H ;‘

= &kM

+ &;1S2/g1 + &;S/(g

- lbl.

(14)

Thus the high multiplication factors that yield good SER amplitude distributions also yield better time resolution. Time resolution, R, is related to the

SINGLE PHOTON DETECTION AND TIMING

71

transit time fluctuation by 2.35 cpHand is the experimentally observed quantity (see Section 111,C). Single photon time resolutions of as low as 320psec have been measured for a particularly fast photomultiplier by Birk, Kerns, and Tusting (53). If the charge pulse collected at the anode is neither saturated nor ringing, the anode pulse width can also be estimated from the transit time spreads, but with different weighting factors. The anode pulse for a single photon is called the single electron time response and can often be approximated by (4). Its full width at half-maximum, P, is given by

where n is the number of identical multiplications and II is the width of the single electron response in terms of a standard deviation. The front stages no longer dominate so that a device with a very narrow anode pulse need not have exceptional time resolution. Gatti and Svelto (52) also show that the variance of II is much smaller than the total transit time fluctuation epHfor the usual case of a number of multiplications in a multiplier at moderate gains. This conclusion further supports the use of a standard shape for the single electron time response of a photomultiplier. Birk and co-workers (53) find a single electron response of roughly Gaussian shape with a full width P of 0.8 nsec for the fast photomultiplier. This response is best measured in real time with single (or multiple) photon light pulses of sufficiently short duration. This time response sets the limit to the counting rate at high levels and, through a Fourier transform, to the frequency response of the photodevice. Great care is necessary in the design of the anode to minimize ringing and saturation which will cause an additional decrease in counting rate and frequency response. Pietri (54) outlines a number of these precautions as well as raising the specter of a transit time fluctuation related to saturation of larger pulses. RCA staff ( 4 , pp. 24, 107) give some advice about preserving the device time resporise at the anode and at the external connection. Saturation and ringing tend to affect the falling portion of the time response and usually do not limit timing resolution. When these are present, connection with (15) can still be made flor a study of cSS by using the rise time of the pulse. A general theory of the statistical time behavior of a photodevice could be constructed as summarized by Donati et al. (12). The probability density functions of transit times in each element of the photodevice would have to be calculated or measured and then convoluted together. To calculate the probability density functions, one would need to know photodevice geometry, element potentials, element multiplication factors g, and the distribution of photoelectrons and secondary electrons in energy and angle of emission. This general theory would also necessarily include the amplitude fluctuations

72

SHERMAN K. POULTNEY

previously treated. However, there may be a correlation between the probability density functions of successive stages which would render even a numerical convolution inaccurate. The analysis of the electron trajectories and transit times in a device with given geometries and potentials is in practice done numerically by computer simulation [Krall and Persyk (55a)l. The assumption made above of the Gaussian behavior of individual spreads and the use of (13), (14), and (15) is an attempt to estimate and compare the timing capabilities of various photodevices without doing the detailed calculations.

1. Photomultipliers a . Conventional fast photomultipliers. Conventional fast photomultiplier here means the type in Fig. 3 with transmission-type photocathode, electrostatic focusing, and linear, discrete dynode multiplier. Typical single photoelectron transit time fluctuations cpHare about 0.5 nsec. Pietri (54) and Pietri and Nussli ( 5 ) give a particularly clear account of the design, characteristics, and improvement of a photomultiplier of this type. The large contributor to the cpHof this and many other types of photodevices is the transit time spread cKSl in the photocathode-first dynode transit time. This spread shows up of course only after repeated measurements with single photons and after allowance for later dynode compensation. In a photomultiplier, the cKSl depends on the geometry, electric fields, and the process of photoemission in the KSl region. The electrode geometry is usually adjusted so as to equalize the flight times to the first dynode of photoelectrons emitted at rest anywhere on the photocathode. In addition, the photocathode is curved, fields are made uniform in its vicinity, and some compensation is introduced in later dynodes. Any remaining difference for the larger photocathodes is quoted as a transit time difference across the photocathode (e.g. 0.8 nsec). Here it is assumed that only the central portion of the photocathode is used so that the transit time difference is zero. The central photoelectronscan, however, leave the photocathode with different velocities which depend on the process of photoemission as well as the wavelength of the incident light. The transverse velocity component (perpendicular to the mean path of the photoelectron) on average spreads out the target spot on the first dynode. The focusing fields must be configured so as to keep this spot smaller in size than the active part of the dynode for every point on the photocathode in order to achieve good collection efficiency. The transverse velocity spread need not cause a transit time spread except for the need to leave the axial symmetry of the KSl region and enter the planar symmetry of the multiplier. This change in symmetry means that the first dynode intercepts the electron paths at about an angle of 45"(Fig. 3). The deviation of the next two dynodes from

SINGLE PHOTON DETECTION AND TIMING

73

the linear multiplier geometry is introduced to compensate transit time differences due to transverse velocity spread. This compensation will be assumed sufficient to leave the spread in normal emission velocities as the prime contributor to &KS1. Assuming the electric field between K and S1 uniform and due to a potential cp over the distances sI and with the energy W, corresponding to the normal component of initial velocity small compared to ecp, one can esimate the transit time spread by

d t , / t , = - ( W,/ecp)"2. The KSI transit time t , is given by

t, =s,(3 x

lO-*)/q1'2,

where sI is in cm and cp in V. Large photocathode photomultipliers usually have s1equal to or larger than their diameters to aid in flight time equalization and collection efficiency maximization. 'Typical values of s,, cp, t , , W, might be 7cm, 300V, 12nsec, and 0.3eV. The eKSl is then about 3.5 o/, of the transit time or 0.42nsec. An increase in cp would decrease the eKSl in direct proportion, but the increase is finally limited by either photomultiplier construction or the need to be near the peak of the secondary emission curve. The transit time fluctuation in the multiplier also depends on the geometry, electric fields, and the process of electron emission. The linear cascade of opaque dynodes in Fig. 3 is used for good time response as well as minimizing ion and light feedback noise and providing a good SER amplitude distribution. It quickly becomes a regular array after the coupling region where the dynodes are shaped and positioned to compensate transit time differences. Additional focusing fields are provided near each dynode so that the cross section of the electron cloud becomes narrower and narrower as it travels down the multiplier. If it is assumed as above that the geometrical problem has been solved, the secondary emission velocities again determine the transit time fluctuations of each stage of the multiplier. These velocities correspond to energies W , about ten times greater than those of photoelectrons for conventional materials. An estimate for e,, can be obtained from ( I 6) and ( 17) slightly modified assuming that only the velocity spread along the path is important. Typical parameters are s, = 2cm, cp = 135V, and W,, = 3eV. The modifications consist of a substitution of 2cp for cp in (16) and a substitution of s,/2 for s, in ( 17). These modifications enter because of the effect of the n 2 dynode on the electrons traveling between n and n + I dynodes. For uniform potentials between dynodes, the field at the n dynode is doubled. Thus the transit time between dynodes is about 2.6nsec and the transit time fluctuation E,, is 10% or 0.28nsec. The transit time fluctuation in the first stage of the multiplier eSlS2 is much larger at about 0.90nsec, due no doubt to the extreme difficulty of making geometric compensation for this stage.

+

74

SHERMAN K. POULTNEY

The total transit time of a twelve-dynode conventional fast photomultiplier is 43 nsec and the total transit time fluctuation E , , ~is, by (14), equal to 0.60 nsec for a g1 = g = 4. The single electron time response by (1 5) is 3 nsec if the anode does not broaden it and if the center of the photosurface is used. Some manufacturers quote a pulse response for full illumination of the photosurface and so include the photosurface transit time difference. Table IV TABLE IV SINGLE PHOTON TIMING(AND DETECTION) CHARACTERISTICS OF SELECTED PHOTODEVICESa

Identification

Gain

A

Transit time

Time resolution R

Rise Pulse time width T, P

Amperex 56AVP Amperex XP1020 Amperex XPI 21 0 RCA 8575 RCA C31000E/F RCA 8850 RCA C3 I024 RCA C3 1OOOK C3 1034 RCA 31024B RCA C70045

10'

(1.5)

1.2 0.66 0.38 1.1 0.6/0.45

2 1.8

-

lo6

0.9 0.8 1 to(1.2) (0.6) (0.4) 0.5 1.5

41 28 20 31 34 31 -

0.47 0.60

lo6 5 x lo6

0.6 0.8

34

0.32

0.8 0.45

Static crossed field

Sylvania 502

2 x 104

1.5

0.1

-

0.1

Channel photomultiplier

Bendix RX 754 Amperex HR300

107

(0.4)

105

-

2 I

Photodevice tY Pe

____

Photomultiplier with linear focused multiplier of electrostatic type

lo8 107

10' 10'

lo9 lo6

-

-

<0.2

I

2.1 2.4 2.1 0.8

_

2.5 2.2 1.2 -

-

-

0.84 -

-

10

-

<0.3

a All times in nanoseconds. R is the experimental time resolution and is related to the theoretical E ~ by ~ 2.36 , E ~ , ,. P is the measured output pulse width and is related to h by 2.36h. A is the single photon pulse height resolution related to by 2.36 and is here usually theoretical unless noted by ( ). See text for references.

summarizes these time properties for the conventional fast photomultiplier as do Chevalier, Boutot, and Pietri (5%). A check of the ,/'p dependence of ( I 7) can be obtained by examining manufacturer data (e.g. 56) on transit times. The q~ dependence of the pulse width P (or the rise time) and hence the individual transit time spreads checks for only a few tubes with many being

SINGLE PHOTON DETECTION AND TIMING

75

closer to a \/cl, de:pendence. Discrepancies may be due to the method of measurement since the whole photosurface may have been illuminated or the rise time measured using a sampling scope triggered by the light pulser. Two popular examples of this fast conventional photomultiplier are the Amperex 56AVP and RCA 8575 listed in Table IV. 6. Improved fcwt photomultipliers. The conventional fast photomultiplier discussed above has been improved as is evident in Table IV. Reductions in transit time spreads of the larger photosurface tubes were made by redesigning the configuration of the input optics and raising the accelerating potential of each stage. Pietri and Nussli (5) and Pietri (3334) give a good view of the evolution of the three Amperex tubes in Table IV. Chevalier et a/. (556) give a concise tabulation of this evolution. The higher S1 potential and the new input optics created a much higher initial field at the photosurface (i.e. 5 to 6 x ) and better isochronism to SI for edge photoelectrons, leading to an E ~ of~ about , 0.07 nsec. The redesign of S 1 and S2 in addition to the higher potentials (e.g. 3 x ) and multiplication factor (e.g. 9) reduced the ESIS2/g1 contribution to ( 14) to 0.10 nsec. The cSS was reduced to about 0. I3 nsec by the higher potentials and its contribution to the total transit time spread reduced to 0.03 nsec. Straightforward improvements to conventional tubes thus result in transit time spreads of about 0.13nsec and experimental time resolutions R of as little as 0.38 nsec. The SER impulse response given by (1 5) was decreased to 1.2nsec. It had been reduced not only by the reduction in individual spreads but also by the reduction of the number of dynodes from 14 to 10 and the u:je of a coaxial output line. A contemporary tube by RCA (i.e. C70045) achieved comparable speeds with a unique multiplier design employing interdynode accelerating and decelerating grids and with a sidelooking large photosurface. This tube has been studied in detail experimentally by Birk et a/. (53).The SER amplitude distributions of these improved tubes probably corresponds to a A of 0.83 due to the higher gains at the first dynode (e.g. g, = 10). These time resolutions and responses probably represent a lower limit that can be achieved with conventional materials, large photocathodes, and linearly focused, electrostatic multipliers. A second approach to improving conventional large photocathode photomultipliers is to incorporate some of the new secondary emission material in them. The time resolution (14) should be improved by the higher gl, the higher potentials used to obtain the gl, and the lower velocity peak of the secondary electron distribution. RCA has placed such a high gain dynode in the first stage of the multiplier of the RCA 8575. This C31000E/F (or 8850) has been examined for time resolution by Present and Scar1 (57) who find an improvement of 40% to 0.64 nsec. The increase in g1 appears to account for the entire improvement. Lakes and Poultney (580) reported an R of 0.45nsec

76

SHERMAN K. POULTNEY

for the same tube using a different technique and a wavelength much closer to the wavelength threshold of the photosurface (i.e. 0.4 eV vs 1.4 eV). A larger gKSl due to a higher W , of photoemission in the former measurements may have masked the improvement in cSlS2due to the lower W,, of secondary emission. The latter measurement indicates the expected improvement for a lower W,, at the first dynode. The impulse response (15) would not be expected to change due to the initial stage improvements. To decrease this response in any multiplier and maintain the necessary gain, one could use a few number of high gain dynodes. RCA has reduced the number of conventional dynodes from 12 in the 8575 to 5 high gain ones in the C31024, increased the interdynode potentials by about a factor of 3, and added a coaxial output at the anode. This modification is reported to decrease the rise time of the impulse response from 2.1 nsec to 0.8 nsec. The corresponding P are 2.9 and 1.1 nsec if the output pulse is given by (4) since one can show that P equals 1.4 times the rise time. A decrease in P from (15), (16), and (17) to 0.9 nsec might have been expected for the potential increases and to 0.68nsec for a drop in W, to 1 eV. However, a rise time measurement with a fully illuminated photosurface may have masked the full decrease due to the transit time difference problem at the photosurface. Leskovar and Lo (5%) have just completed detailed studies of the RCA 8850 and C31024. They report time resolutions of 0.58 and 0.47nsec, respectively, which may indicate that a geometric limitation in the KSl region probably exists in these devices. The ultimate in time resolution and impulse reponse for large photosurface photomultipliers could probably be obtained by using high gain dynodes in the fastest conventional tubes discussed in the preceding paragraph. One might expect an E pH of 0.1 nsec and a 1 of 0.2 nsec. A third approach to improving the time resolution of conventional fast photomultipliers would be to give up the requirement of a large photosurface; which is quite feasible for many applications having narrow, collimated light signals. This relaxation can be done in a straightforward manner by placing one of the new photosurfaces on the “first ” dynode of an existing multiplier structure. The total gain G1 of the tube drops slightly and the tKSlno longer ~ tube now decreases (to contributes. The relatively large E ~ of , the~ original about 0.3nsec) by (16) and (17) since W, is now that of photoemission, but the high g1 is not present to allow a better sampling of that transit time fluctuation by (14). The author has found that the time resolution of such a tube (e.g. C31000K or C31034) based on the.8575 is quite close to the time resolution for the C31000E. A predicted time resolution of 0.35nsec is not approached perhaps due to geometrical problems in the first stages now‘without the long KSl stage. The additional use of high gain dynodes as in the RCA C31024B may or may not improve the time resolution depending on the

SINGLE PHOTON DETECTION AND TIMING

77

presence of the ge’ometry problem. The reported rise time of the C31024B is 0.8nsec which s h o w no improvement over the C31024 due to reduced spreads in the initial stages, but then Krall and Persyk ( 5 . 5 ~indicate ) an anode design limitation. Measurements are needed on these new material photomultipliers to answer the above questions. If the input stages of the multiplier do place a geometrical limit on time resolution and impulse response, it is probably more effective to place the small photosurface on one of the symmetric dynodes of the conventional multiplier (Fig. 3), replace the others with high gain dynodes, and inject the light from the side. The use of a small photosurface of the new materials allows one to consider other fast miultiplier structures. One such structure was developed for the RCA C70045CI by Morton, Matheson, and Greenblatt (59). The addition of a photosurface on its “first” dynode might be expected to lead to an .cpHof about 0.05nsec. With high gain dynodes, this c P Hmight be reduced to 0.02 nsec and the practical operation of the tube considerably simplified. These transit time fluctuations are already near the expected emission times of the photoelectrons and secondary electrons. Only experiment will resolve the question of what the time resolution is and what its limit is. A second multiplier design is described by Miller and Wittwer (60) who use a “cancellation-in-pairs geometry. They built and tested an eight stage version which exhibited performance comparable to the crossed-field photomultiplier discussed immedia.tely below. Their measurements were consistent with an cpH of 0.01 nsec and an impulse response P of 0.07nsec. It is not known whether the new materials would or would not improve this multiplier. ”

2. Crossed-Field Photomultipliers Miller and Wittwer (60) also designed and built a photomultiplier which employed crossed electric and magnetic fields in conjunction with a segmented strip multiplier. The photosurface occupied one segment of the strip. The orbits of all electrclns originating from rest on a given segment are congruent. These orbits are cycloids along the strip and strike where they will oii the next segment. The transit time fluctuations arise solely from the distributions in emission velocities and are independent of the initial position at all electrodes. These fluctuations can also be represented by (16) where cp is about 3000V for each stage. An eight-stage version was tested and achieved a gain of lo5 and a frequency response of 4GHz. These measurements were consistent with an cpk,of IOpsec and a A of 140psec. Meiling and Stary ( 3 ) on p. 32 mention a Russian crossed-field tube and a prediction that its e p Hcould

78

SHERMAN K . POULTNEY

be expected to be an order of magnitude better than conventional photomultiplier designs. The Sylvania 502 is a commercially available version with a gain of 2 x lo4, 9 stages, conventional materials, impulse response P of 0.3nsec, and an eSS of less than 10psec. The gain cannot be raised once the magnetic field is selected and incorporated and so present versions may not be able to detect single photons. The higher gain, continuous strip, crossedfield multiplier mentioned in Section 11,B,4 has also not been studied. The single photon detection and timing properties of crossed-field photodevices should be closely examined for they represent the ultimate in time resolution (e.g. epH= 10psec) and in impulse response (e.g. A = 70psec) among all the photodevices discussed in this review.

3. Channel Photomultipliers The excellent single photon detection properties of the channel photomultiplier have already been noted for the Bendix BX 754. Studies of the single photon time resolution of this channel photomultiplier are not yet available in the literature. Estimates of its time resolution and impulse response can be made using Eqs. ( 1 3) through ( I 7). A straight, electrostatic channel depends on the secondary emission velocity to cause the axiallyaccelerated electrons to hit the opposite side of the channel and multiply. For a W, of 3eV, a channel diameter of 1 mm, and a channel length of a few centimeters, one concludes that the transit time between multiplications is 0.9 nsec, the total transit time is about 9 nsec, and the eSS is 0.9 nsec. The eKSl and eA are separate problems. A typical qKS1is 200V and the ‘‘s, is I mm. E~~~ is then 4 % of t,, by (16), or about 0.02nsec. Additional transit time spreads may enter due to delay variations of about 0.2nsec which depend on the point of impact of the photoelectron and variations which depend on pulse saturation. Omitting these and any anode problem, one might expect an epH of 0.45 nsec and a A of 2.7 nsec. Boutot and Pietri (20) report that the microchannel wafer they studied would be expected to have eKSl less than 10psec and eSS less than 100psec. Careful design at the input and output was necessary to preserve its time resolution. Pulse responses less than 300 psec were expected (evidently nonsaturated operation), but the test light source allowed only the conclusions that it was less than 500psec. Total transit times of I nsec were expected. Gains of lo5 were achieved. Chevalier et al. (5%) measured a single photon time resolution of less than 0.2 nsec for this HR300 microchannel photomultiplier, but were probably limited by the method used. ”

SINGLE PHOTON DETECTION AND TIMING

79

B. Time Derication and Time Interval Measurement Circuits

I . Time Derivaiian Circuits In order to time intervals to high resolution, the arrival time of the single photon anode pulse must be determined by a suitable detection circuit, also called a time pickoff circuit or timing discriminator. This timing discriminator also acts as an integral pulse height discriminator but any simultaneous pulse height measurement or selection should be done in a separate slow channel. Its output is a standard fast pulse for further processing. A variety of timing discriminators have been developed for timing with fast scintillators and are described by Meiling and Stary (3)in Section 3.4.2, by Kowalski ( I ) on pp. 179 and 217, and by Gedcke and McDonald (61). Three of these techniques are leading edge timing, fast crossover timing, and constant-fraction-of-pulseheight timing. Leading edge timing gives excellent results for anode pulses within a narrow pulse height range. Miehe, Ostertag, and Coche (62)measured a time resolution of 76psec using the C70045 photomultiplier, a fast leading edge timing discriminator, and a fast light pulser producing a short, multiphoton signal. This time resolution probably represents the capability of the timing discriminator for a pulse height range of about 10% since the large signal (e.g. 400 photoelectrons) reduces the transit time fluctuation of the photomultiplier ( I 3) by about a factor of 20 through better sampling of the KS1 region. The leading edge timing discriminator produces an output pulse at a time (often called the machine time) related to the instant at which the anode pulse crosses a certain pulse height threshold, Fig. 8. Its time resolution can be limited by a number of factors. The most important is the walk effect. Pulses with the sa.me rise times but different amplitudes cross the threshold at different times as shown in Fig. 8. The walk effect becomes especially bad at the single photon level where the pulse height fluctuation is characterized by z A ' . The resultant timing uncertainty can be expressed as E , given by &,

= EA'/(dA(t)/dt),= T,

(18)

where the denominator is the slope of the average signal shape A ( ? ) as it equals A times the relative crosses the discriminator threshold at t = Tand variance cA previously used. An approximate E , for the walk of single photon timing can be obtained from (18) in terms of the width of the SER amplitude distribution A and rise time T, of the photomultiplier by considering the leading edge of thse anode pulse to have a linear rise. In this approximation, E,

=

eA T, = ATJ2.37.

For wider ranges of amplitudes, this approximation does not hold and the timing uncertainty increases more rapidly. The walk effect can be minimized

80

SHERMAN K. POULTNEY

FIG.8. The walk effect in leading edge timing discriminators due to variation in pulse height amplitudes. Walk due to charge sensitivity of the discriminator has been omitted. (Courtesy of Ortec, Inc.)

by using photomultipliers with fast rise times and narrow single photon pulse height distributions. For example, the RCA 8850 in Table I V would show an additional timing uncertainty E , due to walk in a leading edge discriminator of 0.35 nsec for a single electron counting efficiency of 84 %, and 1.6 nsec for about 97% efficiency. The general references for this section describe other methods for correcting this walk effect. The simplest is selection of a narrow range of pulse heights by means of a slow parallel channel (see SectionII,B,2), but this cannot be used if one requires high counting efficiencies. Fast crossover timing and constant-fraction-of-pulse-height timing were developed to overcome the serious walk effect in the wide dynamic range use of leading edge timing. In fast crossover timing, the anode pulse is clipped to produce a bipolar pulse with a zero crossing. A fast crossover discriminator is used as the timing discriminator. The zero crossing time represents the same phase point on all pulses and the walk effect is nearly cancelled. This method provides good walk characteristics over a wide range of pulse heights (e.g. less than l00psec for 100: 1 dynamic range) (61). For a narrow dynamic range, its time resolution is somewhat worse than with leading edge timing. In constant-fraction-of-pulse-height timing (61), an attenuationsubtraction shaping technique is used to produce the pulse with a zero crossing phase point. Its walk characteristics are typically less than 5- 120psec for a 100: 1 dynamic range and its time resolution is comparable to that of leading edge for narrow dynamic range. The zero crossing phase point was selected to be on the leading edge of the anode pulse because studies of leading edge timing with scintillators (e.g. 63) showed that the time resolution was a function of the fraction of the pulse height used as the threshold. The optimum triggering level varied between 10% and 20% depending on the light

SINGLE PHOTON DETECTION A N D TIMING

81

source. Constant-fraction-of-pulse-height timing has the advantage over fast crossover timing that these small fractions can be attained. Fast crossover timing is found to work best for fractions near 50 due mainly to noise and ringing on the tail of the anode pulse. The optimum fraction is thought to occur because of finite rise times of scintillator light pulses. The author has not found any clear evidence for an optimum fraction with single electron pulses. The above timing discriminators have a number of common problems. Electrical noise will cause a jitter in the timing, based on (18). The faster the rise time from the photodevice, the smaller the jitter will be. If a fast amplifier must be used due to total gain considerations, there will usually be an optimum rise time since circuit noise increases with amplifier bandwidth. Any time jitter in the anode pulse will be passed directly on to the processing circuit. An additional walk not shown on Fig. 8 is a walk due to the charge sensitivity of the timing discriminator. This finite charge threshold can be represented by equal areas under the anode pulse and therefore adds a different walk for each pulse height. Tests of commercial fast timing discriminators with electrical test pulses indicate that this walk is usually a much smaller effect than the walk discussed above. Finally, it has been assumed above that the anode pulse has a constant shape. If this assumption should not hold in a particular application, an additional walk due to varying rise times would enter in both leading edge and fast crossover timing. Constant-fraction-of-pulseheight timing has been shown by Chase ( 6 4 ) to be adjustable so as to cancel this rise time walk. The determination of the arrival time of the photodevice output pulse for further processing is one of the limitations to fast timing, especially for single photon pulses of varying amplitude. This range of pulse heights can be minimized by the choice of a photodevice with a narrow SER amplitude distribution A from Table IV. The promise of the channel multiplier is that operation in the saturation region might further narrow A below 0.4 so that only a leading edge discriminator need be used to realize its inherent timing precision. Tests of commercial fast discriminators with standard electrical pulses indicate that they are capable of precisions of IOpsec. In timing one need not preserve all the pulse height information as is most evident in the channel multiplier. It is worth the try to see if saturation can be used in photomultipliers to limit the range of pulse heights without introducing varying transit time delays due to the saturation. In most cases, however, constantfraction-of-pulse-height timing is the choice. This method has been used in most of the test methods described in Section 111,C,I. The measurements by Gedcke and McDonald (61) in their Fig. 4 give an idea of its precision over pulse height ranges smaller than 100: 1. For example, a selected 4: 1 range would probably yield f50psec or better. Leskovar and Lo (586), on the other hand, favor fast crossover methods for single photoelectron timing.

82

SHERMAN K. POULTNEY

2. Time Interval Measurement Circuits Now that a standard timing pulse is available for each event of interest, the time interval between two such events must be measured to the precision required. Kowalski (I) in Chapter 5 and Meiling and Stary (3)in Section 3.4 describe a wide variety of time interval measurement techniques. Only two techniques will be discussed in this review; a technique for intervals shorter than tens of microseconds here and a technique for intervals up to seconds in Section 111,D,2,The short interval measurement can be done using a time-topulse-height converter capable of 0.02% or better resolution in ranges as small as 50nsec. Typical circuits are shown in Figs. 9 and 10. During the interval between start and stop pulses a capacitor is charged from a constant current source. The amplitude of the voltage generated on the capacitor is linearly related to the time interval between these pulses and is read into the memory of a multichannel pulse height analyser for later use. The start and stop pulses can be obtained from the same photodevice if they occur far enough apart, from two photodevices, or from one photodevice and an electrical sync signal. Higher data rates could be obtained with a number of stop channels going to their own time-to-pulse-height converter which is started by a single sync pulse. However, the readout system quickly gets very sophisticated. All of the diagnostic work on photodevices and circuits and all of the applications involving short time intervals which are discussed below make use of the time-to-pulse-height converter technique. A typical processing delay in the time-to-pulse-height converter is one microsecond. If such a delay does not affect the application, the time-topulse-height converter can be used as a coincidence circuit to provide information that the events occurred within a certain interval of each other. This mode of operation requires a single channel pulse height analyzer with its window properly set. A second single channel analyzer can be set to monitor the random coincidence background. The narrower the window, the more inefficient the counting becomes. If fast information must be provided about the coincidence of two events, fast coincidence circuits must be used entirely as discussed in the general references above. An additional important application of slow single channel analyzers and coincidence circuits is their use to select either desired pulse height ranges in one or both time-to-pulse-height channels as outlined in Fig. 12. The single channel analyzers view a slow, linear pulse from one of the last dynodes when photomultipliers are used. If the pulse heights are in the desired range, the single channel outputs produce a slow coincidence signal in a coincidence circuit which gates the multichannel analyzer to view the time-to-pulse-height converter output. This fast/slow scheme can be used to select single photon events with photodevices possessing good pulse height resolution or to minimize the walk due to a wide range of anode pulses.

83

SINGLE PHOTON DETECTION AND TIMING

C. Single Photon Timing Methods I . Introduction Single photon precise timing experiments make use of all the time derivation and interval measurement circuits described above. It is very important to be able to carry out diagnostic studies on the time resolution of the photodevices used as well as on the stability, time resolution, and calibration of the timing circuits. The diagnostic studies will employ circuit configurations almost identical to those of the experiments themselves except for the introduction of ter;t light or electrical pulses at the appropriate points. These circuit configurations are of two general classes. The first class makes use of a low jitter electrical signal synchronous with a short light pulse as the start pulse as shown in Fig. 9. For a very weak light pulse with width much shorter than the photodevice transit time fluctuation, the result is a measurement of the single photon transit time fluctuation of the device. The second class of LIGHT

BOX

PHOTODEVICE

DIODE

I SLOW

LENS

LINEAR OUTPUT

El=

AMPLIFIER

TIMING

DARK

PULSER

CONVERTER STOPS

COUNTER

MULTICHANNEL AN ALY 2 ER

FIG.9. General block diagram of the electronics for single photoelectron time resolution measurements of a photodevice using an electrical start pulse. The light box had a shutter and an inner box with slots for various optical filters and attenuators. The lens was used to illuminate only a small portion of the photosurface. The counter was used to monitor photodevice dark count rates and the start and stop rates of the time-to-pulse-height converter.

84

SHERMAN K. POULTNEY

diagnostic studies of a photodevice makes use of photodevices in both channels as shown in Fig. 10. For a very short, weak fight pulse, the result is a measurement of the convolution of the transit time fluctuation of both photodevices. If the light source in Fig. 10 allows one of the photodevices to operate at high light levels or if one of the photodevices is much better than the other, the second class of diagnostic studies approaches the first in practice. The realization of light pulsers with the above properties (i.e. single photons within tenths of nanoseconds and an electrical sync pulse) is not an easy matter and is discussed first in Section 111,C,2. The electrical tests for circuit time resolution, calibration, and stability are a good deal easier and are discussed in Section III,C,3. A brief view of other diagnostic studies of a photodevice (e.g. impulse response) is given in Section 111,C,4.

CE R ENKOV /RADIATION /COLLIMATOR

TIMING DISCRIMINATOR

DISCRIMINATOR

TIME-HEIGHT CONVERTER

I

MULTICHANNEL ANALYZER

FIG.10. General block diagram of the electronics for single photoelectron time resolution measurements of a photodevice using two photodevices. The radioactive source eniits particles which radiate light in the Cerenkov radiator. Other light sources could be substituted. From Present and Scar1 (57). (Courtesy American Institute of Physics.)

SINGLE PHOTON DETECTION AND TIMING

85

Measurements of the single photon transit time fluctuation consist of viewing the pulsing light source with either the circuit in Fig. 9 or the one in Fig. 10 and of accumulating the distribution on the multichannel pulse height analyzer. Its full width at half-maximum in Fig. 1 1 is the R used above. Figure 9 also allows a measurement of the transit time of the photodevice. I t i s here assumed that the walk effect has been eliminated in a suitable

RELATIVE COUNTS

-Z 20 U--1t 5 - 1 0 - 0 5

0 0 5 10 1 5 2 0

TIME DIFFERENCE (ns)

FIG.1 1. Measured time difference distribution for pairs of photomultipliers responding to simultaneous single photons using the circuit of Fig. 10. The outer curve is for a pair of tubcs with CuBe first dynodes, the inner for a pair of tubes with GaP first dynodes. Present and Scad (57). (Courtesy American Institute of Physics.)

fashion and that the light pulser emits very short pulses consisting of single photons. Adjustment of the light pulser to give these single photon signals is closely related to the ability of the photodevice to detect single photons. To separate the two, one might repeat the procedure outlined in Section 11,D with a steady, weak source, but with no other changes in the circuits. One might rather choose to use the light pulser itself and look at the pulse height spectrum of linear pulses detected using Fig. 9, especially if a high device noise causes problems with the method of Section II,D. If the photodevice under study has excellent pulse height resolution, one merely attenuates the light pulse i n a suitable fashion until the niultielectron peaks go away and adjusts the system gain so that the single electrons are detected. For wide SER amplitude fluctuations or saturated pulses, an indirect technique must be employed. This technique was first used by Tusting, Kerns, and Knudsen

86

SHERMAN K. POULTNEY

(65) to ensure that only a single photoelectron is emitted for each light pulse. It will now be assumed that the light pulser generates a pulse constant in shape and intensity as well as being sufficiently short. It will be shown in Section IV,B that the probability of detecting Y photoelectrons, P,, in a single flash when m is the number expected on average is well described by a Poisson distribution for coherent or broadband light.

P, = mre- " / r !

(20)

The mean number of photoelectrons expected, m, can be shown to be just the mean number of photons multiplied by the total counting efficiency of the photodevice. The probability of detecting no electrons in a flash Po is then

Po = e-"

=

1 - 6,

(21)

where 6 is the probability of detecting an event. The probabilities PI,P,,etc. can be generated from Po by use of the relation

Pr+,IPr = mlir + 1).

(22)

If now the light pulse is attenuated until very few flashes are detected as stops (e.g. the fraction a), m approaches 6, PI approaches m, and the probability of detecting other than single electrons vanishes. Table V gives these probabilities for various fractions of the flashes detected. A 6 of 10% or less is typical in a totally blind situation and thus makes the technique quite inefficient unless a high pulse rate is available. Included in Table V are the probabilities of occurrence for higher 6. If one can resolve the multielectron pulses in an auxiliary channel and eliminate them from the analysis by gating off the multichannel analyzer, one can greatly increase the data rate of the measurement. The maximum occurrence of single electron pulses is 37% of the light pulse rate at a detection rate of 6 3 x . The use of a light pulser makes it possible to dispense with dark noise reduction techniques in many cases. One usually works on the 50nsec range of the time-to-pulse-height converter which only registers noise counts that are in coincidence with signal counts within this range. If a start rate of 700 Hz is available and a 6 of 10% used, a dark count rate of 30kcounts/sec will yield only one accidental count per second while the detected stop rate will be 70Hz. A final check of both photodevice and light pulser adjustments for single photon counting can be made in the totally blind version of Fig. 9. The optical attenuation can be varied in known steps and the stop rate checked to see if it is a linear function of that attenuation. This test follows directly from (21) for small m. If the test circuit of Fig. 10 is used where both photodevices must operate on single photons, it is probably best to locate the single electron counting plateau separately for each photodevice using the test circuit of Fig. 9. To

87

SINGLE PHOTON DETECTION AND TIMlNG

TABLE V

THEPROBABILITY O F OCCURRENCE OF SINGLE AND MULTIPLE PHOTOELECTRON PULSESW H E N T H E PHOTODIVICL I N FIG.9 DETECTS ONLY T H E FRACTION 6 OF THk LIGHT PULSE RATF" r

6

I71

0

1

0.01 0.05 0.10 0.20 0.40 0.60 0.80 0.90

0.01 0.05 0.10 0.16 0.51 0.91 1.6 2.3

0.99 0.95 0.90 0.80 0.60 0.40 0.20 0.10

0.01 0.05 0.094 0.18 0.30 0.37 0.32 0.23

3

2 0.0005 0.001 0.005 0.02 0.08 0.16 0.26 0.26

-

0.05 0.14 0.20

" Mean number of photoelectrons is also given for each 6

ensure that the short light pulse of Fig. 10 contains only a few photons, one can examine the pulse height spectrum of each photodevice and if they possess good resolution attenuate as necessary. Where pulse height discrimination is not possible, one must use the indirect method described above. At best, one photodevice can be strongly coupled to the light pulser in turn and the other one adjusted for single photon operation. To count single photons in both channels, the so determined optical attenuation is added to both channels at once. In practice, the count rates will be quite small (e.g. 1 count/sec) and accidental noise counts will become serious if the photodevices do not have noise reduction provisions. Surprisingly, it will be shown below that the circuit of Fig. 10 can be used with a filtered thermal light source to measure the transit time fluctuations of photodevices. 2. Light Pulsers f o r Testing Photodevices

Light pulse generators may be divided into two classes; those with light pulse widths much shorter than the photodevice transit time fluctuations under study and those with light pulse widths comparable to or larger than these fluctuations. The latter are very convenient to use and may in special circumstances allow a statement about transit time fluctuations. A third class of light source is the steady, filtered thermal source. a . Verji short light pulse generators (lU0psec or less). Light pulses with widths smaller than 100 psec are available from mode-locked, pulsed lasers either in a pulse train or a single pulse. DeMaria, Stetser, and Glenn (66)

88

SHERMAN K. POULTNEY

give a general review of this technique and Carman, Reintjes, and Furumoto (67) give a recent account of single pulse production, These single pulses typically occur at very low repetition rates, in the green if frequency-doubled Nd:YAG, and with about 10l6 photons. The pulse trains typically yield pulses too close together to be used in the manner of Fig. 9. These features make the use of this light generator for transit time fluctuation studies very inefficient and expensive. The real value of this light pulse generator for testing photodevices comes in other diagnostic studies such as measurements of impulse responses. Fortunately for the worker of modest means, there is a second means of producing these very short light pulses, which makes use of the Cerenkov radiation process. This weak radiation is emitted over a wide spectral range by a charged particle traversing a transparent medium above a threshold velocity. Scar1 (68) used a IOOpCi Sr9'Yg0 source to produce Cerenkov light in plexiglass as shown in Fig. 10. The electrons from the beta decay have a maximum energy of 2.2meV, a maximum range of about I cm, and are collimated to a narrow beam before entering the plexiglass. Each electron produces at most 50 photons in the wavelength interval between 3000 and 7000a. The radiator is designed so that these photons leave the plexiglass simultaneously limited only by dispersion in the plexiglass (e.g. 5 psec). With the photocathodes of the two PMT about 13 cm away from the radiator, most of the photons produced by each beta particle go undetected. However, two photons produced by one particle do hit the two cathodes often enough to give a coincidence rate of about one event per second. After a running time of hours, the time distribution on the multichannel pulse height analyzer looks like Fig. I 1 which shows the convoluted transit time fluctuations of two pairs of photomultipliers respectively. Time jitter in the electronics of Fig. 10 is believed to contribute less than 0.1 nsec to this time spread in the worst case. In addition, only the central 2.5 cm of each photocathode was illuminated to eliminate any photosurface transit time difference problems. Lami, D'Alessio, Zampach, Radicella, and Kesque (6Y) have recently constructed a clever modification of the Cerenkov light pulser in which one channel produces a low jitter start pulse. The Cerenkov radiator is modified so that the charged particle escapes from the radiator and produces a large light pulse in a fast scintillator attached to the start channel photodevice. Only the stop channel views the single photon Cerenkov signal. The resultant timing curve gives the transit time fluctuation directly. A resolution R of 1.61 nsec was quoted for an Amperex 56 UVP, but the walk effect may have been overlooked. These workers were involved in the study of the short decay times of fluorescence induced in scintillators by ionizing particles as discussed in Section III,D,I.

SINGLE PHOTON DETECTION AND TIMING

89

The data rates of the Cerenkov pulsers are quite low for avariety of reasons and require moderately long data runs. Practicality aside, perhaps the most useful Cerenkov pulser would consist of two radiators placed in a monoenergetic, collimated beam from an accelerator which consists of one particular type of particle at an optimum velocity. The start channel of the test circuit would be closely coupled to its radiator while the stop channel would be weakly coupled. 6. Short light pulse generation (0.5nsec and longer). Short light pulses of about the widthofthe transit time fluctuations under study can be conveniently produced in three basic ways. Either a short electrical pulse can feed a suitable lamp, an energetic charged particle can excite fast fluorescence in a suitable medium, or a coritinuous gas laser can be mode-locked. Kowalski (I) on p. 52 gives a list of references for a number of these light generators. Meiling and Stary (3) briefly review them in Sections 2.2 and 4.2 and on p. 377, as well as reviewing test methods with these light generators in Section 4.4. The mode-locked laser is again most useful for the other diagnostic studies. The use of fast scintillators is mentioned in conjunction with Section III,D, 1. The use of a pulsed lamp is especially convenient for testing preliminary to a precise measurement of transit time fluctuation in a photodevice. Here only the use of inexpensive, light-emitting semiconductor diodes will be described. The short pulser based on this device consists of two parts; an electrical pulser which produces the necessary short electrical pulse and the light diode which can follow the fast electrical pulse. The fast electrical pulser is itself a necessity for testing and calibrating the fast circuits and components discussed above. A well-known pulser for these purposes is the Tektronix 109 mercury reed pulser which has rise times less than 0.25 nsec, minimum full width at half-maximum of 0.5 nsec, repetition rate of about 600 Hz, and amplitudes up to 5OV. Lakes and Poultney (58a) used this pulser to drive a GaAs red light diode in their study of the transit time fluctuation of the RCA C31000E as sketched in Fig. 9. They also used a pulser built by a colleague which was triggera.ble, operated at higher repetition rates (e.g. IOkHz), and had a full width half-maximum of 0.3nsec. It consisted of a step recovery diode which shaped a relatively slow trigger pulse, an avalanche transistor fired by the shaped pulse, and an open-ended transmission line which was thereby discharged into the light emitting clode. The exact shape and width of the light pulse is not yet known, but the light pulse is fast enough t,o study transit time fluctuations greater than about 0.5 nsec. If the shape of the short light pulse is either known or can be measured, it is possible to unfold the photodevice time resolution from the observed distribution. Measurement of the shapes of weak short light pulses is discussed in Section JII,D,I and presupposes the availability of a photodevice

90

SHERMAN K. POULTNEY

with a transit time fluctuation shorter than the one under study. The shapes of strong short light pulses can be measured using fast semiconductor diodes, streak cameras, and nonlinear optical techniques. The mercury switch pulser used by Birk et al. (53) probably fits into the category of a known light pulse in that it behaved as if it were exponential decay of 300 psec with a much shorter rise time. Koechlin (70)was probably the first one to use the method of Fig. 9 to measure the single photon transit time fluctuation of a photomultiplier. Koechlin and Raviart (71) review this method and show that their result for a 56TVP is compatible with an unfolding from the observed shape of a fast scintillator decay which is assumed to be exponential. They used a mercury switch with similar time characteristics to the above one, but obtained a single photon time resolution R of 0.6 nsec for the 56TVP which is at least a factor of two shorter than observed by other workers. Birk, Kerns, and Tusting (53)were, of course, measuring a faster photomultiplier and used the unfolding technique on the light pulse shape itself. One other known light pulse shape that should be considered for these measurements is the nearly square wave shape of the injection-laser diode mentioned in Section ITI,C,4. c. Filtered, thermal light source. The intensity of a filtered, thermal light source fluctuates on a time scale of the order of magnitude of the inverse of the spectral frequency width as discussed in Section IV,B. Given the spectral width, one can compute the correlations in the photon arrival times. For example, a 1.6 GHz mercury line would yield a distribution 0.17 nsec wide. Scarl (68) measured this distribution using a circuit similar to that in Fig. 10. The distribution is significantly affected by the transit time fluctuations of the photomultipliers. Scarl built the Cerenkov light source in order to take these fluctuations into account. Now that the phenomenon is understood, his experiment can be turned around and used to measure the transit time fluctuations of a pair of photomultipliers. The experiment is quite difficult, though, as discussed in Section IV,B,3 and takes an order of magnitude longer than the measurement with the Cerenkov source. 3. Calibration and Stability of Timing Circuits

It is important for fast timing to use stable, low jitter circuits and components and to be able to calibrate and monitor these at will. The key to the precise measurement of short time intervals discussed here is the time-topulse-height converter which includes the multichannel analyzer as one unit. It should be carefully calibrated and monitored. Measurement of its differential and integral nonlinearities is mentioned by Kowalski (1) in Section 5.5 and Meiling and Stary ( 3 ) in Section 4.4.6. Differential nonlinearity is the deviation of channel widths from a nominal value and is measured by feeding

SINGLE PHOTON DETECTION AND TIMING

91

the start and stop channels with uncorrelated pulses. Integral linearity is the correspondence of each channel to the time difference of the events and is often measured with delay lines and pulse generator. Probably the most sophisticated calibration and monitoring scheme has been used for the Lunar Ranging Experiment in which a 2.5sec interval must be known precisely and accurately to 1 nsec or better as discussed in Section IIl,D,2. This scheme, capable of an accuracy of 0.1 nstx, has been described by C. Steggerda of the University of Maryland in an unpublished report. One part of it is based on the precision crystal oscillator i n the timekeeping system of the experiment. The oscillator output is multiplit:d to 20 MHz and sent to a fast leading edge discriminator to produce standard timing logic pulses to operate the time-to-pulse-height converter or other circuit components. If these timing pulses are sent to both start and stop channels, the multichannel pulse height analyzer would show a peak on its time axis at 50nsec. The remaining time axis interval of 0 to 100 nsec is calibrated using a family of delay cables specially constructed for this application. As a first approximation, the delay cables can be cut to appropriate lengths calculated from the advertised propagation speed. Precise adjustments can be made based on extensive intercomparisons of the cable family using the 20 MHz pulse rate and a fast oscilloscope as a null detector. Meiling and Stary ( 3 ) ,in Section 4.4.5. and Taylor (72) discuss other methods of cable calibration. Members of this delay family (e.g. a 10 nsec one) can then be alternately added first to the start channel and then to the stop channel to determine a time point below and above the 50nsec point (e.g. 40 and 60 nsec). I n the Lunar RangingExperiment,thecalibrationof the timeto-pulse-height converter system is semiautomatic with data readout done by an on-line computer which also can calculate the best fit calibration curve. Longer time intervals can be calibrated to the same accuracy by using a time delay generator in conjunction with a dual coincidence unit to gate any two clock pulses out of the clock pulse train. One thus has standard timing pulses available Rith a separation of 50 nsec up to a maximum of 2.5 sec. These standard pulses in conjunction with the calibrated time-to-pulse-height converter can be used for all other electronic diagnostic studies. In the lunar ranging system, moreover, these timing pulses can each drive a light emitting diode at the start photomultiplier and the stop photomultiplier for an integral system check in both precision and accuracy. Needless to say, most workers use simpler schemes such as displacing their timing peak along the time axis by a delay cable of 2 or 4 nsec. 4 . Other Diagnostic Techniques Fast counting with photodevices depends on the impulse response of the photodevice and the absence of correlated afterpulses. Neither of these

92

SHERMAN K. POULTNEY

factors has a serious effect on short time interval measurements unless the same photodevice is used to provide both start and stop channels as in one class of photon statistics experiments discussed in Section IV,B. Due to this close relation, measurements of time correlated signals and noise in a photodevice are outlined there. Minor effects on time interval measurements have been reported due to the prepulsing in some photodevices mentioned in Section II,C and to a late peak observed in photodevice time resolution measurements. Yates and Crandall (73) mention one 25 nsec after the main peak. A possible cause could be prompt afterpulsing following a single photoelectron that was not detected by the stop channel. Three methods of measuring impulse response deserve to be mentioned. Birk et al. (53) use a multiphoton Cerenkov light pulse to illuminate the photodevice and measure the impulse response in real time with a fast oscilloscope. Boutot and Pietri (20) used the pulse train from a mode-locked laser to measure the impulse response of their microchannel photodevice in real time with a fast oscilloscope. Miller and Wittwer (60) set an upper limit on the impulse response of their fast device using a mode-locked continuous gas laser in conjunction with a sampling oscilloscope. The single pulse modelocked laser holds considerable promise for studying the transit time spreads in the stages of a photodevice in a step-by-step analysis. Most dynode materials are also photoemissive so that the laser can be used to inject an electron into a multiplier chain at a particular dynode. Finally, for those workers who like to measure the rise time of a device, at least one company is offering semiconductor laser diodes with a square shaped pulse of rise time less than 0.2 nsec. Many of the above diagnostic techniques are described in a recent supplement to the ZEEE Standards [i.e. Adelman (29)].

D. Single Photon Precise Timing Experiments Two basic types of single photon precise timing experiments will be discussed. The first type measures a fast decay time of an excited state by the single decay particle statistical technique outlined in Section III,D,l. The second type measures the time of flight of a light pulse to a distant target and back. Both types make use of the circuits discussed in Section III,B with the addition of a digital time interval measurement in the second case. 1. The Measurement of Lifetimes of Excited States

The fast decay time of an excited state can be measured by timing the appearance of a decay product after the excitation occurs in a statistical fashion. The excited state can be prepared by particle bombardment, flash lamp excitation, or decay of another excited state. The excited state under

93

SINGLE PHOTON DETECTION AND TIMING

study can be that of a nucleus, atom, ion, or molecule. The timing circuits are essentially those of Figs. 9 and 10 with sophistications added as shown in Fig. 12. The initial use of these circuits was made in the measurement of the decay times, schemes, and energies of excited nuclear states. The decay products were detected by converting all or part of their energies into fluorescent light in scintillators viewed by photomultipliers. The photomultipliers were operated at high light levels and the circuit time resolutions were complicated by the energy transfer process in the scintillator. These nuclear experiments would not be disclussed (as they are briefly in Section IIl,D,l,d) if it were not for the fact that tlhey have set the terminology, the theory, and some applicable results for single photon timing. I n the nuclear and atomic applications of these techniques, the number of decay products is very small after each excitation. The observed time distribution after a large number of repeated excitations would be expected to mirror the decay curve of the excited state. If more than one decay product is detected per excitation, this distribution would become skewed toward apparent shorter decay times. Bollinger and Thomas (74) were the first to apply this single ‘decay product statistical technique to bright light flashes by attenuating the light signal until less than one photoelectron was detected in the stop channel per excitation. in much the same manner as described in Section III,C,I. Tlhey used slow timing circuits to measure scintillator decay

ri

EXCITATION -ALTERNATE START

m Po

I

ALTERNATE

P

t

J

J

F]

)W, LINEAR

g

S L Y , LINEAR

PMT X I

4

SLOW, LINE

LT PMT*2

FAST

4

OTHER

STOP

STOP

? CHANNELS 0

0

START

DECAYS

COINCIDENCE

MULTICHANNEL ANALYZER GATE

CIRCUIT

SINGLE CHANNEL ANALYZER

FIG.12. General block diagram of the detection layout for the measurement of excited state decay times using the single photon statistical method. The electronics of Fig. 10 would also be used. l’rovisions are made for alternate decays, pulse height selection in a slow, linear channel, spectral selection by filters, F, and polarization selection by polarizers, P.

94

SHERMAN K. POULTNEY

curves out to 30 psec with a resolution of 6 nsec and were not affected by impulse response ringing and afterpulsing. Koechlin was probably the first to realize that this single photon technique could be used to measure much faster decay times (e.g. 2 nsec) with a resolution limited only by the transit timefluctuations of the photodevice as outlined by Koechlin and Raviart (71). This single photon technique has recently been justified on the basis of the photon counting statistics discussed in Section IV,B,2 by Miehe, Ambard, Zampach, and Coche (75a).The shape of the light flash is represented by J ( t ) = ni(t),

(23)

where n is the mean number of photons per flash and i(t) is the probability density function of finding a photon at the photosurface at time t . The probability of observing the rth electron at time t , P(r, t ) , is a product of the probability of detecting (r - 1) electrons in the interval 0 to t as given by (35) and the probability of detecting one photoelectron at time t given by (33). ]~-’ - I)! P(r, t ) = m i ( t ) [ m ~ ~ ( t ) exp[-mU(t)]/(r (24) Here the mean number of photoelectrons m is the product of the mean number of photons n and the counting efficiency q,, and U ( t ) is given by (36). Of particular interest is the time distribution of the first photoelectron, P(1, t), P(1,t ) = mi(t)exp[-mU(t)], (25) which for a weakly illuminated photosurface (e.g. m < 0.1) reduces to

P( 1, t ) = mi(t).

(26)

Equation (26) justifies the single photon statistical method where very few of the light flash photons are allowed to strike the photosurface of a photodevice. Again, the observed time distribution curve after many excitations, P(1, i), traces out the shape of a constant shape, bright light flash, limited in time resolution only by the transit time fluctuations and not by the much longer impulse response, ringing, or afterpulses of the photodevice. D’Alessio, Zampach, and Kesque (756) have recently begun to explore the possibility of making fluorescence decay time measurements by eliminating the synchronous start signal and using two photodevices at the single photoelectron level as in Fig. 10. In this paper, they also consider viewing a Cerenkov light flash and so verify the method of Present and Scar1 (57). a. Measurements of’ the lifetimes of exciied states of free atoms. Corney (76) has recently reviewed the many methods for studying the lifetimes of free atoms, molecules, and ions, including the single photon statistical technique which he considers the most accurate and widely applicable method. Figure 13 is a simplified energy level diagram of a hypothetical atom which

SINGLE PHOTON DETECTION AND TIMING

95

LEVEL 2

/

f

LEVEL I

n LEVELS

LEVEL 0 GROUND

FIG.13. Hypothctical energy level diagram of an excited state. Possible excitation . Possible decay modes --. modes - - - - - i

could be part of the sample in Fig. 12. For selective excitation from the ground level to the first level, one studies the decay rate ‘sl to the various lower levels, n, using the single photon technique with either the circuit in Fig. 9 or the one in Fig. 10. In this case, the probability density function, i ( f ) , is given by i(t>

- 4,

N,(O) exp( - t / d ,

(27)

where and Nl(0) is the number of atoms excited to the level 1 at t = 0. Al, is the transition rate for spontaneous decay from I to n. It has been assumed that the excitation is removed in a time short compared to zI and that the source is optically thin. Collisions can shorten the decay lifetime and photon trapping effects can lengthen it so both of these phenomena can themselves be studied by this technique. Typical lifetimes now measured by this technique range from 10 to 100 nsec and are limited by the speed of sample excitation. One excitation method is electron excitation using a pulsed electron gun with high current density, high repetition rate, and as small a spread of excitation energies as is possible. The electrical pulse that drives the electron gun is usually used as the start signal in a circuit of the Fig. 9 type and limits the time resolution to about 1 nsec. The stop signal is produced by the photodevice viewing the sample through a spectrorneter of some type or an optical filter. The spectrometer is generally more useful than filters for studying wide wavelength ranges. It should have good dispersion and especially high speed since the light signal is usually not strong enough to require attenuation to single photon levels. The

96

SHERMAN K. POULTNEY

weak signals mean long observation periods during which equipment stability may need to be monitored. The magnitude and fluctuation of the device noise can also become troublesome. Electron excitation can be modulated so that the digital synchronous detection method described in Section II,G,l can be used to minimize noise. An alternate method of excitation is optical excitation by the absorption of resonance radiation. The excitation is pulsed by focusing resonance radiation from a lamp through a Kerr cell shutter. Start pulses may come from either the electrical shutter pulse or from a photodevice close-coupled to the light pulse. A lifetime of the 3*P level of sodium has been reported as 16.6 f 0.4 nsec using this optical excitation. The method of excitation is very selective in that only the level in resonance is excited. However, it has the following disdvantages; only intense transitions from the ground state can be studied, but those in the visible and short resonant light pulses are difficult to produce. The experiments performed using electron excitation frequently are complicated by radiative cascades from higher levels that get excited at the same time as the one of interest. For example, the excitation cross section for level 1 may be much lower than that for level 2 in Fig. 13. If the mean energy of the electrons is beyond the threshold of level 1 by design or by necessity, level 2 can be excited and repopulate level 1 after the electron beam is turned off. Measurements on level 1 will therefore yield a decay curve consisting of a sum or difference of two exponentials with lifetimes characteristic of levels 1 and 2. A technique to overcome this complication is to view the radiation excited by the electron gun with two photodevices as shown in Fig. 12. The start signal can be a photon detected from the 21 transition by means of a suitable filter and the stop signal can be a photon detected from the In transition by means of another filter. The measurement thus starts when level 1 is known to be populated, but at the cost of a detection rate significantly smaller than the two previous methods. The amount and stability of the dark count becomes very important over the typical run of twenty-one hours for a measurement of the 73S1 to 63P, to 6'S0 cascade in mercury. A 63P, lifetime of 114 f 14 nsec was obtained. Cascades can also be selected on the basis of polarization with suitable analyzers in front of each photodevice. This last technique is limited by the spectral sensitivity of available photodevices since either the first transition is in the infrared or the second is in the ultraviolet. The increased range of spectral sensitivity mentioned in Section II,E is of interest here. The effect of finite instrumental resolving time on the decay time measurements can be unraveled by means similar to those used in molecular and nuclear lifetime studies. In the atomic (and molecular) case, it is usually the turn-off time of the excitation that sets the limit. If one can study the decay time of an excited level with a lifetime much shorter than the instrumental

SINGLE PHOTON DETECTION AND TIMING

97

resolving time, the resulting prompt delay distribution obtained with Fig. 9 is determined solely by the characteristics of the apparatus. The observed timing distribution of the level under study is then the convolution of its true decay shape with the prompt delay shape. For electron excitation, a prompt curve has a full width at half-maximum of from 1 to 4nsec. For lamp excitation, the prompt curve (in this case the shape of the excitation pulse) can be obtained by substituting a lamp not resonant with the level under study. The deconvolution of true decay curves from observed ones knowing the prompt delay curves is discussed i n Section lII,D,l,b and by Corney (76). b. Measurenient of fast fjliorescence decay times of molecules. Fast fluorescence studies are of current interest to biophysicists and biochemists because both the :fluorescent process i’n certain molecules can be studied as a function of their environment and certain of the fluorescing molecules can be used as a tag to study macromolecules. Fluorescence is included as a topic separate from Section III,D,l ,a because of the much broader excitation and emission bands involved and the different interests of those who study it. Excitation can be done by electron beams and other techniques, but the currently popular technique is light pulse excitation. Fast decay lifetimes range from about I nsec to IOpec. Schuyler and lsenberg (770) describe a recently constructed monophoton fluoronieter that uses the single photon statistical technique and a pulsed light source, present examples of performance, and outline an analysis scheme that separates a multiple decay time fluoresence curve from the excitation function. Their sample geometry is similar to that shown in Fig. 12 with one photomultiplier viewing the excitation pulse at high levels and the other viewing the sample fluorescence at the single photon level, all through the appropriate filters, monochromators, and polarizers. The electronics is similar to that shown in Fig. 10, but with the start and stop channels reversed for better performance of the time-to-pulse-height converter and a single channel pulse height analyzer selecting the pulse heights of the single photon events to be analyzed. This latter selection with an RCA 8850 allows a higher data rate as discussed in Section III,C,I without distorting the shape of the observed time distribution. The fluorescence is normally quite bright and may still need to be attenuated to an average of one photoelectron per flash. Coates (776)gives a brief review of the measurement corrections for the “pile-up’’ error which can occur when the above selection is not made. I n practice, the excitation flash need not be very short although it must have a stab’leshape which can be measured by the same monophoton technique. A typical light pulse triggered by a thyratron is about 7 nsec wide. The performance of their instrument was tested by measuring a lifetime of 4.00 & 0.5 nsec for a deaerated solution of 8 x lo-’ M anthracene i n benzene. Ware (78a) has also recently discussed the monophoton technique in his

98

SHERMAN K. POULTNEY

review of transient luminescence measurements. Selinger and Ware (786) have applied this technique to a study of single vibronic levels in benzene at low pressures. Halpern and Ware (78c) have applied it to vibrational relaxation studies in hexafluoroacetone. Finally, Tao (79a) describes a monophoton fluorometer used in his studies of the Brownian rotational diffusion of macromolecules in solution. He used a dye molecule as a tag and measuredthedecay of its fluorescence for both states of polarization after exciting it in one state of polarization. The decays are in general a combination of several exponentials and yield information about the size, shape, and other aspects of the macromolecule in solution. The observed statistical decay curve, F(t), is a convolution "t

F(t) = J- i(s)P(t - S) ds 0

of the shape of the fluorescence i ( t ) and an instrument response function, P ( t ) . The instrument response function is itself a convolution of the system time resolution, R(t), and the excitation function, E ( t ) . P(t)=

fR(s)E(t

- s) ds.

0

For flash lamp excitation, it is customary to measure P ( t ) directly by removing the sample from Fig. 12. The stability of E ( t ) often determines the measurement precision of F(t) rather than R(t) in this case. The problem then is to extract the shape of the fluorescence curve from (29) knowing F(t) and P(t). Analysis methods were originally developed for the similar problem in nuclear physics. Corney (76) summarizes the general method of moments which relates all the moments of i(t) to the moments of F(t) and P ( t ) . It helps if the functional form of i(t) is known. Schuyler and Isenberg (77u) have outlined the solution for a sum of N exponentials and have programmed a computer to plot out both the data and desired decay curve. If the expected i ( t ) consists of a single exponential, a number of simplified relations can be obtained for the lifetime, T, as summarized by Corney (76). The most important one for these considerations is the relation dF(t)/df

=

[ P ( f )- F(t)]/T.

(31)

This equation can be immediately applied to the case discussed in Section III,C,2,b where the instrument response function P(t ) was measured and the excitation function E ( t ) was assumed exponential. The system time resolution, R(t), which depends mainly on the transit time fluctuations, can be obtained from (30) using the appropriate form of (31). Koechlin and Raviart (71) used this analysis in their study of photodevice transit time fluctuations with

SINGLE PHOTON DETECTION AND TIMING

99

light pulses of comparable or greater widths. A late peak in R(t) with some photomultipliers is currently causing problems in fast fluorescence experiments and is described by Stevens and Longworth (79b). The single photon statistical technique of measuring decay curves was first applied to bright fluorescence decays by Bollinger and Thomas (74) who were interested in the shape of the decay at long times in organic scintillators. These shapes depend on the mode of excitation (here different nuclear particles) and allow one to discriminate against detection of unwanted decay particles. Yates and Crandall(73) measured the decay curves of fifteen scintillators for incident gamma rays, finding Naton 136 to have a short decay time of 1.9 nsec. Miehe et al. (7.5~)in an extension of (24) show theoretically and experimentally that the data rates in these measurements can be notably improved by not only selecting actual single photoelectrons but by timing the first photoelectron when two, three, or more are detected. Scintillators are also used as the first element in the photodevice channel of experiments to measure nuclear (or particle) lifetimes or particle velocities as discussed in Section III,D, 1 ,d. If their fluorescence decay were initiated instantaneously by the incident particle, the instrument response function, P(t), would be due entirely to the photodevice time resolution (here the resolution at multiphoton levels) in the manner of (30). However, the decay is not initiated instantaneously and the finite transfer times of the excitation energy will also limit the precision of measurement of a nuclear decay time. These growth times in the scintillator have been studied with the monophoton method by Koechlin and Raviart (71) who later found a rise time of 0.8nsec and fast decay time of 1.6 nsec for Naton 136. Fast scintillators are not, therefore, particularly useful for providing fast light pulses to measure the transit time fluctuations of photodevices. c. Measurements of lifetimes of relaxed excited states of color centers. Bosi, Bussolati, and Spinolo (79c) have used the monophoton technique to study lifetimes of F,M , and R centers in alkali halides. Lifetimes in the range of 20 nsec were obtained to accuracies of 1 nsec and concentration and temperature dependences studied. Cova, Bussolati, and Bertolaccini ( 7 9 4 describe the technique. d. Measurements of lifetimes of excited states of nuclei. Measurements of the lifetimes of excited states of nuclei are usually made by examining a radiative cascade in detail. For example, the beta ray from the decay of '"Hg provides the start signal in a circuit similar to Fig. 10 and the gamma ray from an excited state of 'O3TI provides the stop signal by means of the light flashes they produce in organic scintillators coupled to the photodevices. The energies of the decay products are selected by a slow, linear channel from each photomultiplier. Both of the photomultipliers are closely coupled to the scintillators at a level of 30 or more photoelectrons released from their

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SHERMAN K. POULTNEY

photosurfaces per flash in order to improve the time resolution. The single photon transit time fluctuations (13) can be expected to be improved by the square root of the number of photoelectrons released due to better sampling of the KS1 region. Schwarzschild (80) reviews these techniques and quotes 281 +_ 60 psec for the lifetime of the 279 keV decay of 203Tl.The lifetime is, of course, the slope of a curve each point of which has considerably more uncertainty. The decay curve is determined from the observed curve as discussed in Section III,D,l,b by observing a prompt delay distribution using the gamma rays of 6oCo for example. The two-channel, prompt decay time resolution is typically 0.2 nsec for close-coupled photomultipliers and gives an indication of the start channel jitter in the measurement of scintillator growth and decay times. Meiling and Stary (3) also review these nuclear applications. The use of scintillators adds further uncertainties to the decay time measurements above those discussed for the other applications. Not only are there the growth and decay times of the fluorescence pulse involved, but also problems due to the need to collect a large amount of the fluorescence on the photosurface and the resultant need for large photosurfaces. If the growth time, the collection time spread, and the transit time fluctuation were zero, if the walk effect were eliminated, and if the initial fluorescence decay were a simple exponential, it is clear that the scintillation should be as bright as possible and the timing discriminator trigger level as low as possible so that one could detect the passage of the nuclear particle at that very instant. The trigger level is thus set near the single photoelectron level even though the whole flash seen by the photodevice may produce an average of m electrons. The discriminator should also be blanked after this detection until the flash has decayed. The uncertainty in time for the appearance of the first C photoelectrons has been shown to be

m9c (32) in this simple case. For a fast scintillator, T = 2 nsec and m = 20 or larger, so that E , = 0.1 nsec for C = 1. Before this limit is reached, one must take into account all the effects assumed negligible. The recent state of the theory which includes all these effects and tries to explain the prompt delay curves as a function of trigger level is summarized by Donati et al. (12). The beginner may wish to read an earlier paper first (52). It is this terminology and theory that has been followed in this review, at least for the photodevice analysis. Until one knows the growth time and the transit time fluctuations for the particular experiment, application of the theory requires assumptions as to values and shapes, prediction of a prompt decay curve, and a comparison with experiment which hopefully yields unique values for these two unknowns. Present, Schwarzschild, Spirn, and Wotherspoon (81) measured a E, =

rJclm,

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101

prompt delay curve with width of 0.2 nsec using Naton 136 with m = 100, an Amperex XP1020, and pulse height selection channels. This optimum instrumental resolution occurred at a trigger level of 10 photoelectrons and appeared to be fundamentally limited by the growth time of the light pulse in the scintillator rather than transit time fluctuations or (32). Bertolini, Cocci, Mandl, and Rota (82) found a prompt decay curve time resolution of 164 psec using an XP1020. Miehe ct a / . (62) found a prompt decay curve time resolution of 185 psec using an RCA C70045. Both of these measurements were with a 6oCosource and a Naton 136 scintillator producing multiphoton signals. Short light pulsers are also used in this measurement and typically give better time resolutions. Miehe et a / . (62) obtained 76 psec with the C70045. Decay lifetimes of nuclear states less than the width of the prompt delay curve cannot be measured by this technique.

2. The Lunar Laser Ranging Experiment Accomplishment of the scientific objectives of the Lunar Laser Ranging Experiment which are listed in Table VI required that the light travel time between the earth and the moon be determined daily over an extended period of time to an accuracy of I nsec or better whenever the moon was up (83). The experinient became possible when man could bring a “point retroreflector to the moon. The systems design of the experiment which included practical retroreflector arrays, one of the world’s largest telescopes,

”

TABLE V1 SCIENTIFIC OBJECTIVES OF THE LUNAR LASERRANGING EXPERIMENT” Lunar orbit’

Selenophysicsb Geophysics

Gravitation and relativity

Mean distance Eccentricity Angular position of moon Physical libration parameters‘ Coordinates of arrays w/r center of lunar mass Short tcrni fluctuations in rotation period of earth Station distance from earth rotation axis Station distance from equatorial planeb Motion of poleb East-west continental drift rateb Drift of Hawaii toward Japan Equivalence principle for gravitational self energy

” Significant improvement

is expected in all parameters here listed. Three or more observing stations are required. Three or more retroreflectors are required.

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SHERMAN K . POULTNEY

-

STATUS SENSE

-C

RANGE DELAY GENERATOR

CONTROL

SET

ENCODER 0.1 rn sec

INITIAL VERNIER

-

50 nsec

START

STOP

STOP

I \

T I M E INTERVAL METER

2,600,000,050fOSa: START

STOP

FINAL VERNIER

-50nsec START

STOP

LASER RETURN

LASER OUTPUT

At I I I I 1 I I I A I

LASER OUTPUT

50 nsec

LASER RETURN

FIG.14. Representation of the nanosecond-resolution time-interval measurement system at the McDonald Observatory Lunar Ranging Station. Special logic circuits eliminate any i I count uncertainty in the digital interval. The verniers are time-to-pulse-height converters. From Alley et r d . (83). (Copyright 1970 by the American Association for thc Advancement of Science.)

and a narrow beam, nanosecond-pulse laser indicated that less than one photoelectron would be released at the photodetector per laser firing under average conditions. The nominal round-trip travel time of a pulse of light to the moon and back is 2.5 sec. The problem of measuring this interval precisely was solved as indicated in Fig. 14 by counting a 20 MHz standard clock signal from a start light pulse to a stop light pulse. At each end of this interval, a time-to-pulse-height converter was linked so that it measured the time (about 50 nsec) between a clock pulse and the relevant light pulse, but so that no extra clock pulses were counted. Operation under the varying and often difficult background conditions required that a narrow time gate (e.g. 6 p e c ) be opened at the expected arrival time in addition to requiring a 6arcsec spatial filter and a 0.7A spectral filter. The laser firing rate of 20 ppni and the rapid change of travel time due to earth rotation required an on-line central computer which progranirned the gate generator (among other

I03

SINGLE PHOTON DETECTION A N D TIMING

control duties) and which was then used to record the data. The lunar ephemeris that was used in the prediction of the gate opening time itself was accurate to about I p e c . An accurate time-keeping terminal was provided which also served to monitor the 20 MHz rate. A recent description of the McDonald Observatory station is available (84a), as is a more complete discussion of the role of single photon detection and timing in the experiment (84h).

Figures I5 and I6 display a 50 laser-firing run with 12 individual returns which is an above average return. Figure 15 shows the return in 50 mec blocks as a function of range time relative to the range time predicted by the ephemeris. The run was at night. but during bright moon and so shows random noise counts. Figure 16 examines ten returns in the 50 nsec block as a function of epoch of arrival. The returns are due to single photoelectrons released at the photocathode of the photodetector. The uncertainty of each event is shown as k2nsec due to the present laser pulse width of 4nsec. The return photons were detected at about 0.5 0;)total receiver efficiency based on an RCA C31000F photomultiplier and their arrival time determined by an Ortec 270 constant-fraction-of-pulse-height timing discriminator. Given

cn

I-

z

2 0

9-

50 Nanosecond Intervals

B-

u

IL 0

7-

(r

6-

w m

fz

54-

'1 2

t--llmlk

0

-2000

-1000

0

1000

2000

3000

4000

5000

6000

TIME RELATIVE TO PREDICTED TIME (nsec)

FIG.1 5 . Histogram of 12 lunar returns o f a fifty laser shot run o n 1970 day 075 starting at 04:57 U.T. from McDonald Observatory. Abscissa is range time relative to that predicted in 50 nsec intervals. Random counts are due to high background conditions. Currie (85) (Courtesy 1.A.U and Reidel Publishing Co., Dordrecht, Holland.)

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SHERMAN K. POULTNEY

FIG.16. Residual round trip travel times of the ten lunar returns as a function of epoch of arrival. The returns are due to single photoelectrons. The uncertainty of each event is shown as -+2 nsec due to the present laser pulse width of 4 nsec. Residual is observed range minus calculated. Currie (85). (Courtesy I.A.U. and Reidel Publishing Co., Dordrecht, Holland.)

that the moon moves slowly in time over these short periods, a number of returns can decrease the uncertainty below the f2nsec. The statistics of this run support a precision of f 1 nsec which is still larger than that inherent in this particular photomultiplier. Both timing precision and accuracy are checked internally using the methods and the triggerable light pulser as discussed in Section III,C,3. A series of daily measurements will yield the minimum range and its epoch of occurrence over an extended period. Harmonic analysis of this range time series will permit the determinations of the quantities listed in Table V1 with significant improvements over present knowledge. In some cases, three or more observing stations are required. In other cases (e.g. physical librations), three separate retroreflectors are required. Three U.S. retroreflectors are now fixed in position having been carried to the moon by Apollos 11, 14, and 15. Future range measurements using the planned subnanosecond laser transmitter will be limited in precision by the time resolution of single photon detection devices.

SINGLE PHOTON DETECTION AND TIMING

105

1v. SINGLE PHOTON DETECTION WITH MODERATE TIMING REQUIREMENTS A number of experiments including some of the types discussed in Section III,D require only moderate timing while still requiring single photon detection. In the first class of experiments with moderate timing requirements, a pulsed or modulated source provides a sync signal to start the time interval and so aids in nois:e discrimination. The second class of experiments measures either directly or indirectly the distribution of arrival times of photons from light sources and is generally referred to as photon statistics or photon counting statistics experiments. A . Experiments with Modulated Light Sources

The discussion of photometry and spectrophotometry in Section II,G showed that there were advantages in effectively modulating the weak continuous source and in detecting in synchronism with this effective modulation. The synchronous detection scheme allowed separation of signal from noise in a straightforward procedure. The many experiments with modulated sources discussed in Section II,G should strictly have been discussed here. Only one more such experiment will be mentioned, mainly because it is in an entirely different area of physics. Koons and Fiocco (86)measure the electron density and temperature in a low density reflex discharge i n helium by Thomson scattering of cw argon-ion laser radiation at 4880A. An analog synchronous detection scheme was used to distinguish the scattered radiation from all other radiation entering the detector. A tunable, 1.58A wide interference filter was used to measure the Doppler-broadened scattered radiation as well as discriminate against the background from the plasma and laser. The background count rate was lo5 counts/sec whereas the peak Thomson scattered intensity was equivalent to 64 counts/sec. Integration times were not quoted although error bars of about 102)appear in the data displays. The intensity of the scattered light leads to the electron density and the spectral broadening to the 'temperature. Closely related to these modulation time signature methods are experiments using pulsed light sources. The pulsed light source may be used as an optical radar viewing an extended medium where one is interested in the arrival time of a very weak return in the presence of noise. Repeated flashes then build up the certainty and precision of a return from a certain distance. For example, optical probing of the upper atmosphere combines single photon detection in a height resolution element with the identification of that height element by time of flight techniques. The detection schemes discussed in Section II,D need to be supplemented by timing circuits of moderate

I06

SHERMAN K . POULTNEY

capabilities. Returns are normally assigned to resolution elements of about 13 psec in width (i.e. 2 km in altitude). A single time interval meter (1.e. counting of a gated clock pulse) would waste much of the return from one flash and so workers use a digital bin sorting system or a multistop time-topulse-height converter in order to detect single photons from more than one altitude per flash with the same photodevice. The time-to-pulse-height converter would have much longer ranges and lower precisions than the one discussed in Section 111,B. Kent and Wright (87a) review the aims, techniques, and results of such optical probing of the upper (and lower atmosphere). By recording the back-scattered photons from a pulseof laser light propagating toward zenith, one can measure molecular densities to 80 km to a few percent in about an hour at night with a height resolution of 2 km using typical Qswitched lasers operating at several pulses per minute and using large receiving mirrors (i.e. 10 m2). Precision is shot noise limited up to about this altitude for 10 A or narrower spectral filters and milliradian fields of view. Night sky background and/or photodevice dark counts begin to limit the precision above these altitudes. Accuracy is limited by calibration problems, the presence of aerosols, and the presence of laser light noise. Poultney (87b) reviews this last problem and suggests methods to eliminate it. Part of the problem comes from enhanced photodevice noise due to the intense initial light pulse. If opaque shutters cannot be used in these laser excitation experiments, only careful selection of optical components and photodevices can reduce the enhanced dark noise.

B. Photon Statistics Experiments 1. Introduction

Measurement of photon statistics is the determination of the arrival times of photons from a source by the measurement of the distribution of photoelectrons detected. The former distribution can be directly related to the latter. Photon statistics experiments can thus characterize the statistical properties of a light beam or, if these are known, yield information about the internal behavior of various statistical media which scatter that beam. Two active workers in this field, Pike (88) and Arecchi (89),give recent reviews of photon statistics theory and experiment. The origin of these statistical properties and the scope of their application can be obtained from the following picture. Illuminate a photosurface with a light beam of constant intensity from an ideal laser. The probability of detecting a photoelectron in an ideal photodevice in a short time interval is a constant proportional to the constant intensity and does not depend on the time of the measurement. In other words, the photoemission process takes place completely at random in time

SINGLE PHOTON DETECTION AND TIMING

107

with no correlation between adjacent events (i.e. a Poisson distribution). Now let the laser beam scatter from a medium undergoing statistical fluctuations in some property. For example, consider micron-size particles undergoing Brownian motion in a liquid. The beam incident on the photosurface will now include different Dopper-shifted frequencies and will fluctuate in intensity due to the beating together of the various components. The intensity fluctuations in turn cause an increase in the probability of photoelectron detection at some times and a decrease at others. This variation leads to a departure from ramdomness of the time distribution of photoelectrons. The departure can be measured either by recording the distribution of times between events or by examining the fluctuation of counts obtained in various length counting intervals. The time scale of bunching in time or of increase in counting variance gives information about the relative motion of the particles. Its inverse is a measure of the spectral broadening of the scattered laser line. In mosl cases, this broadening is too small to be measured by the spectrophotometric methods described in Section II,G (e.g. 1.6 KHz linewidth corresponds to a rime scale of 0.17 msec). Similar intensity fluctuations and nonrandom photon statistics are present for laser light scattered from a medium whose dielectric constant is fluctuating for some physical reason. The physical reason can be injected from the outside as with a sound wave or it can be spontaneous due to natural thermal excitations. The spontaneous excitations can be either propagating, as in the case of optical and acoustic phonons which yield Raman and Brillouin scattering respectively, or nonpropagating as in the case of thermal density fluctuations at constant pressure which yield Rayleigh scattering. In the propagating case, there is both a lineshift which is that measured by spectrophotometry and it .linewidth related to relaxation processes which is better measured using photon statistics or its equivalent. The width of the Rayleigh line in pure fluids and liquid mixtures is determined by diffusive processes; the thermal diffusivity for simple fluids and the diffusion constant for mixtures. In the normal fluids, the Rayleigh linewidth is characteristically less than 10'Hz. There is a great deal of current interest in the behavior of this linewidth in the vicinity of a critical point where the linewidth quickly falls to 10'Hz or less. It should be pointed out here that a study of the power spectrum of the fluctuating photodevice current can also provide the above information about the medium and in fact is the currently favored method (90).That the power spectrum can provide this linewidth information is due to the Gaussian nature of the light fields scattered by the thermodynamic fluctuations and the resultant circumstance that all correlation functions in time of order higher than the first can be expressed in terms of the first. The power spectrum involves a second-order correlation function. Degiorgio and Lastovka (91) compare these two approaches to intensity-correlation

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SHERMAN K. POULTNEY

spectroscopy for Gaussian fields with the uncertainty in the linewidth as the criterion. The added promise of photon statistics measurements is that they will allow the measurement of the higher order correlation functions which must be known to describe nonGaussian scattered light. The statistics of scattered light near the critical point of a medium might be expected to be nonGaussian (92),due to the presence of higher order density correlations. An ideal laser beam is itself a nonGaussian field. Photon statistics measurements have been used extensively to study the stationary and the transient statistical properties of real lasers both above and below threshold (89).The ideal laser beam can be transformed to a Gaussian beam by the linear scattering from a medium made of uncorrelated, statistically distributed scatters (e.g. the Brownian particles as above). The same chaotic beam can be expected from a thermal light source. A measurement would show non-Poisson statistic on time scales much shorter than the inverse linewidth. However, the narrow linewidths are more characteristic of scattered laser light than thermal light. A filtered mercury lamp with a spectral width of 1.6GHz (i.e. 0.01 A) would have a correlation time equal to 0.16 nsec. Such a timing precision is nearing the limit of photomultipliers while the linewidth can be easily measured by spectroscopic means. The measurement of the photon statistics of a thermal source was made as a check on the theory in this case and is here discussed in Section IV,B,3 rather than in Section III,D. The reason that typical thermal sources yield Poisson detection statistics is that the fluctuations occur on an extremely short time scale and so are not seen by any detector. Most applications of photon statistics measurements will be in the longer time domains (e.g. microseconds). 2. Theory of Photon Statistics Experiments Consider a photodevice illuminated by polarized light of intensity ni(t). The probability of detecting one count in the interval between t and t + dt is given by

P(1,dt, t ) = q,n

i ( t ) dt,

(33)

where qo is the total counting efficiency, n is the mean rate of photons, and i(t) is the normalized time dependence of the light intensity of the source. The probability that a second count is detected in the interval t T and t

+

+ T + dt is given by

P(1, dt, t : 1, dt, t

+ T ) = qo2n2i(t)i(t+ T ) d t dt.

(34)

If i(t) is constant (i.e. an ideal laser), the probability of detecting one count in any interval is a constant (33) and the probability of detecting two counts separated by any interval T is also a constant (34). These are the properties

SINGLE PHOTON DETECTION AND TIMING

109

of a random, Poisson distribution of counts in time. The joint probability (34) is not normally observed although observations could be made with a large number of coherently illuminated photodevices and timing circuits for a time t to f + T. Ifi(t) is a fluctuating, stationary field, then repeated measurements with a single photodevice can be made. An ensemble average of (34) normalized by an ensemble average of (33) gives the probability of detecting two counts separated by an interval T. At T much greater than a correlation time of i(t), this probability is a constant as before and the counting statistics are Poisson. At T much smaller than a correlation time, this probability is found to be doubled and the counting statistics deviate from Poisson. The ensemble average of (34) is itself not directly measured in general. If a single timing device like a time-to-pulse-height converter is used, not all T may be accessible when the counting rate in the stop channel is high. In addition, dead times in both start and stop channels can be a problem. Davidson and Mandel (93) deal with these issues and the above discussion in detail. A measurement of this second-order correlation gives only a measure of the source linewidth and is equivalent to spectral and power spectrum measurements. The intensity time correlations can alternately be measured using analysis of the linear photodevice signals (89). It is also possible to view different portions of the source and so study spatial correlation effects. Another way of examining the detection statistics of photoelectrons is to study the fluctuations in counts for fixed counting intervals, T. The time dependent probability P ( r , T, t ) of obtaining r counts in the interval t to t + T can also be built up from (33) (W), and equals

P(r, T, t ) = [mU(t)]'exp[-rnU(t)]/r!,

(35)

where f -t T

U ( t )=

j

icp) lip.

(36)

I

Here m is the mean count rate or total counting efficiency qo timesthe incident light intensity in photons, n. If i ( t ) is a constant as for an ideal laser, (35) reduces to P ( r , T ) = (rnT)'e-mT/r!, (37) which was used in slightly different form as (20) and which is also true for a broadband thermal source. Again, P(r,T, t ) is not directly observable with a small number of viewing channels at one time t . If i ( t ) is a fluctuating, random function then P ( r , T ) can be found by taking a time or ensemble average. This operation does not, in general, preserve the Poisson form of (35) and again the fluctuations of i ( t ) lead to a departure from Poisson counting statistics. Since no explicit closed expression for the probability distribution of U is available, the connection between an observed counting distribution, P(r, T ) ,and the field distribution, P(U ) , is made through the normalized

110

SHERMAN K . POULTNEY

factorial moments of the distributions. At times short compared to a correlation time, P ( U ) becomes P(i) which is the photon distribution. Many of the moments of P ( i ) can be measured in this manner although not their time behaviors. The first moment is just the mean mT. The second is related to the variance of the counting statistics and involves an intensity correlation similar to (34). For a weak, Gaussian source, the normalized factorial moment equals one for T much longer than the correlation time of the fields and two for T much shorter. Thus a single counting channel could also be used to measure the linewidth of the source by varying the counting interval T. The variance itself would go from mT at long T to mT( mT) at short T.

+

3. Photon Statistics Experiments Considered below are four separate photon statistics experiments a study of spheres in Brownian motion using the counting interval method, a study of macromolecules in Brownian motion using a counting correlation method, a determination of the arrival time correlation curve of a thermal source using the methods of Fig. 10, and measurements of photodevice noise using several correlation methods. One of the first types of photon statistics experiments was the investigation of various sources and scattered light using the counting interval method. A relevant example here is the study of the statistics of laser light scattered by a dilute solution of monodisperse, micron-size spheres performed by Arecchi et al. (95). After verifying that the angular distribution of the time average of the scattered intensity was that of a single sphere and that the scattered-light spectrum was Lorentzian with the expected width (e.g. a few Hz) as obtained by the power spectrum method, this group investigated the counting statistics in an interval, T, much shorter than a coherence time. A 56 AVP photomultiplier was used with a single channel analyzer and rate meter which had a T variable from 1 to 100 psec. The nonlinear detection circuit introduced a deadtime of 20 nsec and could distort the variance for short T and high count rates. Here the count intervals are much larger than the deadtimes (e.g. lo4).The photocathode was reduced electrostatically to 1 mm2 and contributed a negligible 100counts/sec. The counting statistics for this short T were as expected (i.e. Bose Einstein) with a value of 2 for the normalized second factorial moment. Jakeman and coworkers (96) also investigated the statistics of laser light scattered by micronsize spheres in water at room temperature over a range of T from 1 msec to 200msec. The optical halfwidth of the scattered light was expected to be about 7 H z so that the coherence times would be about 0.1 sec. They used the relatively slow FW130 which was cooled with a dark count of 0.5counts/sec. A typical count rate of single electrons was 30 counts/sec. The periods be-

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SINGLE PHOTON DETECTION AND TIMING

tween samples T were generally equal to T. The number of samples ranged from lo4 to lo6. Factorial moments up to the sixth order were obtained for T = I msec and agreed with factorization theory within experimental precision (3 y < for the fourth moment) (88).The halfwidth of the optical spectrum of known shape was then obtained by determining the dependence of the normalized second1 factorial moment of the counting statistics on the size of the counting period T. The result of fitting the measured curve with the predicted one was 9.9 & 2.2 Hz based on lo4 samples. While the counting interval method is quite convenient for determining the moments of P ( i )for T much less than the coherence time of the source, it can lead to difficult interpretation problems at the longer T needed to obtain the time evolution of the field and the optical linewidth. One solution is to correlate two short counting intervals separated by a variable delay (89). The joint counting distributionscan bestored in a multichannel analyzer which reads the rate mete:rs of each of the photodevices. The results provide at least as much information as the counting interval method and are much easier to interpret. Here one must balance ones goals against the cost of correlating equipment. Pike (88) describes the full time correlation of a photodevice output performed by clipping the output and autocorrelating it with itself or crosscorrelating it with its unclipped value. This clipped correlation method was applied to the measurement of the optical linewidth of laser light scattered from protein molecules undergoing Brownian motion in aqueous solution. This motion (hence linewidth) is controlled by the translational diffusion coefficients of the bovine serum albumin under study. An accuracy of 2:( was obtained in the linewidth with a count rate of 200 counts/sec over a one-hour period. The effect of varying the protein concentration over a wide range could be determined in an experimental time equivalent to just one linewidth measurement by the power spectrum technique. The linewidth was shown to be a function of the pH of the buffer solution for a given concentration of serum. Fig. 17, and the molecule can be seen to uncurl " as the pH is reduced. These experiments involve a second-order intensity correlation function, g"'(T), hhere T is the delay introduced in the correlation. The third type (of experiment is the timing of the arrival of photons from the source. The exa.mple will be the measurements on a thermal source which was mentioned in Section III,C,Z,c and which made use of the method of Fig. 10 (68). This method is very important for short coherence times (less than 10 nsec) where it also becomes necessary to use separate photodevices. The light beam from the source is split and both devices view the same spatial coherence area. The light source was a mercury lamp filtered so that only the 4358 A line i n one polarization was observed. The linewidth was measured spectroscopically to be about I .6GHz or 0.0lOA. The photons were detected by two RCA 8575 photomultipliers and the delay in Fig. 10 adjusted to place "

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SHERMAN K. POULTNEY

0.8

-

0.6

I c

0.2

n -0

400

800 5

1200 (ps)

1600

2000

FIG.17. The effect of changing pH on the diffusion constant (hence size) of the protein bovine serum albumin. The width of the second-order correlation function , 9 ' 2 ' ( ~ is ) proportional to the diffusion constant. Pike (88). (Courtesy of Scottish Universities Summer School.)

zero delay in the center of the display range. The single, noise, and coincident rates averaged about 15 kcounts/sec, 300counts/sec, and 4counts/sec respectively. The time resolution of the system has an important effect on the interpretation of the experiment and was measured using a Cerenkov source as discussed in Section III,C,2,a. Figure 18 shows the result of an accumulation period of 170 hr. The theoretical shape of the time correlation curve is also shown. The time resolution and stability of the electronics was better than 0.2 nsec. The complications discussed by Davidson and Mandel (93) did not enter since the average time interval between events was much longer than the time difference of interest. This time difference was limited to 30 nsec by auxiliary circuits. It is the inverse of this measurement that was proposed in Section III,C,2,c as a means of determining the transit time fluctuations of fast photodevices. Finally, these same techniques can be used to study the question of timecorrelated noise in photodevices. Oliver and Pike (23) used the counting interval method to investigate the photoelectron statistics when an FW- I30 was illuminated with laser light and found them to be very close to Poisson for T from 70 nsec (the system dead time) to 100 msec. Photodevice noise

113

SINGLE PHOTON DETECTION AND TIMING 12200

I I800

w

2

11400

z a

;11000 I

W

a

I% 0

0

0

0

o o ~ o o ~ oeoooo B

000

0

0

10200

L -8 -k

9400-10

I

-: 4 A

h

1

'

6

I

'

8

NANOSECONDS

FIG.18. Counting rate as a function of time delay between single photon detections from the 4358 8, mercury line. Light completely polarized. Accumulation time was 170 hr. From Scar1 (68).(Courtesy of American lnstitute of Physics.)

counting distributions were then taken at room temperature and at -25°C. Correlations at room temperature were less than I in lo4 and cooled less than their measurement limit of 1 in 10'. For times less than 70 nsec, the impulse response showed no evidence of bunching in real time. Other photomultipliers show a different behavior (22). Alternately, one could determine the arrival time distributions of signal and noise using the circuit of Fig. 9 with the change that the photodevice feed both start and stop channels. For laser or wideband illumination, the distribution should be flat as in the wings of Fig. 18. The light probably would have to be attenuated so that high efficiency detection is not essential. It is at the low signal rates that the use of a time-topulse-height converter has advantages over the other techniques. The corrections discussed by Davidson and Mandel (93) may also have to be applied. The question of correlations in times shorter than device dead times would have to be answered by viewing the pulse in real time.

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APPENDIX : SUMMARY OF PHOTOMULTIPLIER NOTATION total gain h average electron transit time P = 2.36 h FWHM of anode current pulse (assumed Gaussian) dynode multiplication factor relative amplitude variance of anode pulse A = 2.36 EA FWHM of SER amplitude distribution Ell2 relative amplitude variance of the gain of a dynode first dynode multiplication 91 factor rl photosurface quantum efficiency total quantum counting efficiency device dark noise rate N d GI

R = 2.36 &pH single photoelectron time resolution (assumed Gaussian) E,, electron transit time fluctuations, K M between cathode and multiplier, SS between dynodes, MS in multiplier, and MA between multiplier and anode W, energy of electron emission from electrode p interelectrode (or total) potential s interelectrode spacing E , ~ time derivation variance T, risetime of anode current pulse

ACKNOWLEDGMENTS I wish to thank my many colleagues for their help in the preparation of this review; especially D. Scarl, D. Currie, and D. Persyk. This work has been partially supported by NASA Grants NGR 21-002-21 1 and N G R 21-002-285. 1 also wish to express my appreciation to the University of Maryland and to C. 0. Alley in particular for having made the opportunity for this study available.

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58a. R. Lakes and S. Poultney, Rev. Sci. Instrum. 41, 1889 (1970). 586. B. Leskovar and C. C. Lo, IEEE Trans. Nucl. Sci. NS-19, No. 3 , 50 (1972). 59. G. Morton, R. Matheson, and M. Greenblatt, IRE Trans. Nucl. Sci. NS-5, No. 3,98 (1958). 60. R. Miller and N. Wittwer, ZEEEJ. Quant. Electron. 1, 49 (1965). 61. D. Gedcke and W. McDonald, Nucl. Instrum. Methods%, 253 (1968). 62. J. Miehe, E. Ostertag, and A. Coche, IEEE Trans. Nucl. Sci. NS-13, No. 3, 127 (1966). 63. W. McDonald and D. Gedcke, Nucl. Instrum. Methods 55, 1 (1967). 64. R. Chase, Rev. Sci.Instrum. 39, 1318 (1968). 65. R. Tusting, Q. Kerns, and H. Knudsen, IEEE Trans. Nucl. Sci. NS-9,No. 3, 118 (1 962). 66. A. DeMaria, D. Stetser, and W. Glenn, Science 156, 1557 (1967). 67. R. Carrnan, J . Reintjes, and H. Fururnoto, IEEEJ. Quanr. Electron. 6, 751 (1970). 68. D. Scarl, Phys. Rev. 175, 1661 (1968). 69. H. Lami, J . D’Alessio, J. Zampach, R. Radicella, and J. Kesque, Nucl. Insrrum. Methods 92, 333 (1971). 70. Y . Koechlin, C. R. Acad. Sci. 252, 391 (1961). 71. Y. Koechlin and A. Raviart, Nucl. Instrum. Methods29, 45 (1964). 72. H. Taylor, Nucl. Instrum. Methods 68, 1960 (1969). 73. E. Yates and D. Crandall, IEEE Trans. Nucl. Sci. NS-13, No. 3, 153 (1966). 74. L. Bollinger and G. Thomas, Rev. Sci. Instr. 32, 1044 (1961). 75a. J. Miehe, G. Ambard, J. Zampach, and A. Coche, IEEE Trans. Nucl. Sci. NS-17, No. 3, 115 (1970). 756. J . D’Alessio, J . Zarnpach, and J . Kesque, Nucl. Instrum. Methods 97, 235 (1971). 76. A. Corney, Advan. Electron. EIecrron Phys. 29, 1 I5 ( I 970). 77a. R. Schuyler and I . Isenberg, Rev. Sci. Instrum. 42, 813 (1971). 77b. P. Coates, J . Phys. E. 5, 148 (1972). 78a. W. Ware, in “Creation and Detection of the Excited State” (A. Lamola, ed.), Vol. I, Part A, p. 213. Dekker, New York, 1971. 786. B. Selinger and W. Ware, J . Chem. Phys. 53, 3 160 (I 970). 78c. A. Halpern and W. Ware, J. Chem. Phys. 53, 1969 (1970). 79a. T. Tao, Biopolymers 8, 609 (1 969). 796. S. Stevens and J. Longworth, IEEE Trans. Nucl. Sci. NS-19, No.1, 356 (1972). 79c. L. Bosi, C. Bussolati, and G . Spinolo, Phys. Rev. Bl, 890 (1970). 79d. S. Cova, C. Bussolati, and M. Bertolaccini, IEEE Trans. Nucl. Sci. NS-19, No. 3, 18 (I 972). 80. A. Schwarzschild, Nucl. Instrum. Methods 21, 1 (1963). 81. G. Present, A. Schwarzschild, I. Spirn, and N. Wotherspoon, Nucl. Instrum. Methods 31, 71 (1964). 82. G. Bertolini, M . Cocchi, V. Mandl, and A. Rota, IEEE Trans. Nucl. Sci.NS-13, No. 3, 119 (1966). 83. C. 0. Alley, R. Chang, D. Currie, S. Poultney, P. Bender, R. Dicke, D. Wilkinson, J. Faller, W. Kaula, G . MacDonald, J. Mulholland, H. Plotkin, W. Carrion, and E. Wampler, Science 167, 458 (1970). 84a. E. Silverberg and D. Currie, in “ Space Research ” (A. Stickland, ed.), Vol. 12. SpringerVerlag, Berlin and New York, 1972. 846. S. Poultney, IEEE Trans. NucI. Sci. NS-19, No. 3, I2 (1972). 85. D. Currie, in “Rotation of the Earth,” Proc. IAU Syrnp. No. 48. Reidel Publ., Dordrecht, Holland, 1972. 86. H . Koons and G . Fiocco, J . Appl. Phys. 39, 3389 (1968). 87a. G. Kent and R. Wright, J . Atmos. Terr. Phys. 32, 917 (1970).

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876. S. Poultney, in “‘Space Research” (A. Stickland, ed.), Vol. 12, p. 199. SpringerVerlag, Berlin, 1972. 88. E. Pike, in “Quantum Optics” (S. Kay and A. Maitland, eds.), p. 127. Academic Press, New York, 1970. 89. F. Arecchi, in “Quantum Optics” (R. Glauber, ed.), p. 57. Academic Press, New York, 1969. YO. H . Cummins, in “Quantum Optics” ( R. Glauber, ed.), p. 247. Academic Press, New York, 1969. 91. V. Degiorgio and J. Lastovka, Phys. Rev. A 4, 2033 (1971). 92. V. Korenman, Phys. Rev. A 2, 449 (1 970). 93. F. Davidson and 1,. Mandel, J . Appl. PhyA. 39, 62 (1968). 94. L. Mandel, Prog. Opt. 2, 183 (1963). 95. F. Arecchi, M. Giglio, and U. Tartari, Phys. Reu. 163, 186 (1967). 96. E. Jakeman, C. Oliver, and E. Pike, J . Pliys. A 1, 406 (1968).

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Advances in Satellite Communications* P. L. BARGELLINI A N D E. S. RITTNER COMSAT Laboratories, Clarksburg, Maryland

VIl. Electron Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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I. INTRODUCTION Communications satellites, a by-product of rocketry and microwave engineering combined, have been made possible by advances in numerous fields of the physical sciences. Launch vehicles, propulsion devices, spacecraft structures, converters from solar to electrical energy, low noise receivers, and high power transmitters are important items entering a complex system affected by the phenomena of propagation, and by the constraints of the physical environment at the satellite position during its useful unattended life in orbit. An attempt will be made here to present certain aspects of communications satellite technology specifically related to Electronics and Electron Physics. For the benefit of the nonspecialist, the general characteristics of satellite communication systems will be first presented, with a brief outline of their development ( I ) .

* The views expressed in this chapter are not necessarily those of INTELSAT. 119

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It is well known that electrical communications allow transmission of information within bounds ofrate, range,coverage, speed, and reliability beyond the capability of other forms of communication. Artificial earth satellites carrying active microwave repeaters, the latest and most spectacular form of electrical communications, offer two fundamental advantages: (a) bandwidth in excess of the amount otherwise available for intercontinental communications, and (6) multiple access, the possibility of communications among several pairs of earth stations “ visible” from the satellite. Advances in electrical communications, whether by “cable ’’ or “radio,” have been characterized by the exploitation of progressively higher carrier frequencies. Bandwidth is required to provide adequate channel capacity, i.e. to transmit large amounts of information within a certain time interval, provided, of course, that no obstacles are encountered in the channels. The electromagnetic spectrum used for communication purposes is filling up rapidly. Little activity existed thirty years ago above 4 x lo7 Hz (A = 7.5 m). Today, everything is taken up to about 4 x 10” Hz (A = 7.5 mm), and the use of even higher frequencies up into the optical range is contemplated. While either “radio” or “cable” systems can be used for overland transmission paths, satellites are today the only available solution for transcontinental links over large expanses of water carrying several thousand telephone conversations and/or a dozen or more TV channels. The second important characteristic of satellites is their unique capability of satisfying the requirements of large communication networks involving numerous earth terminals, resulting in a multinodal topology with variable traffic demands at each node. While a cable is, by its nature, an inflexible two-port network, a satellite is accessible to all stations “visible” by it; hence its unique superiority in this sense. Before the advent of man-made satellites, moon reflection techniques were demonstrated in the late forties and early fifties. In July 1954, voice messages were transmitted over the earth-moon-earth path, and in 1956 communications between Annapolis, Maryland, and Hawaii were established using the moon as a passive reflector. The frequency used was around 430 MHz, with a transmitter power around 100 kW and 26 m diameter antennas. In 1945, a British engineer, Arthur C. Clarke, wrote a prophetic paper predicting active satellites in geosynchronous orbit as soon as adequate rocketry would become available (2). He also stated that the electrical power for the satellite would be obtained by conversion of the sun’s radiation by means of solar cells. Clarke’s paper went almost totally unnoticed until man-made satellites became a reality with Sputnik I (October 4, 1957). Pro’s and con’s of active versus passive satellites were examined in detail

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between 1954 and 1962 (3). Communication experiments were carried out in 1960 in the Echo project, jointly sponsored by NASA, JPL, and the Bell Telephone Laboratories. Passive satellites are gravely handicapped by the inefficient use of transmitter power. I n the case of the Echo balloon, only one part in lo'* of the transmitter power reached the receiving antenna. On the other hand, the advantage of passive satellites is the absence of sophisticated electronics on board, and a potentially infinite capability to multiple access. Although a radio beacon transmitter may be required for easier tracking, elaborate electronics are unnecessary as well as attitude stabilization, at least with spherical satellites. The requirements of very low noise receivers at the earth station, with operating temperature in the neighborhood of 10"K, were met with masers in the R F front end. Clearly, the inverse distance square law for active satellites, compared to the inverse distance fourth power law for passive satellites, gave the former an overwhelming advantage as soon as on-board power, attitude control and stabilization, and reliable electronics were made available. After the early experiments with reflecting balloons, all subsequent systems have used active satellites. Orbital height and inclination are important parameters in satellite systems. From Kepler's laws, the orbital period is

where: a is the semimajor axis of the ellipse and p is the gravitation constant x earth mass = 3.99 x l O I 4 ni3/sec2. With early rockets, only modest payloads could be placed i n low orbits, e.g. around 150 kni altitude with a period of around 1.5 hr. Satellites in low orbits encounter high drag and consequently have a short life. Such satellites pass rapidly overhead and must be tracked; furthermore, if continuous communications between two points on the earth's surface are required, as soon as a satellite disappears beyond the horizon (actually, below an elevation angle of a few degrees when atmospheric attenuation and noise are taken into account), another satellite should rise and provision be made to hand over the traffic to it. I n spite of the tracking and traffic handover problems with individual satellite availability around 20 min, low orbit communications satellite systems were proposed with as many as fifty spacecraft in low orbits to carry traffic over the Atlantic Ocean. Early experiments, such as TELSTAR (1962-1963) and RELAY (1962-1964) proved the feasibility of active satellites i n low and medium (a few thousand km) altitude orbits. Not only were many communication records achieved, but data on the radiation environment were collected which permitted improvement of the design of later spacecraft.

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By increasing the orbital altitude, the period and the area coverage increase. At an altitude of 34,863 km, i.e. about six times the earth's radius, the period corresponds to a sidereal day (23 hr, 56 min). If the orbit is equatorial, the satellite becomes geosynchronous, i.e. it hovers at a fixed point over the earth. The angle subtended by the earth from the satellite is near 19" and the coverage is about four-tenths of the entire earth's surface. Additional advantages are: (a) no Doppler effect, (b) reduced number of thermal stress cycles due to eclipses, (c) easement of the on-board requirements to provide service during eclipses, (d) reduced perturbations induced by the earth's magnetic field, and (e) mild radiation environment, The earth's magnetic field is the cause of the trapping of high energy protons in the Van Allen belts. At low altitudes, i.e. in the inner Van Allen belt (altitude from 1200 to 9000 km), the radiation produces a rapid degradation of solar cells, and it affects other solid state components. Shielding can, of course, be used but with obvious weight penalties. Although the outer Van Allen belt extends from about 9000 to 60,000 km, its peak occurs around 16,000 km; hence, synchronous satellites find themselves in a comparatively mild region of radiation. Despite the obvious advantages of the geosynchronous orbit, the difficulties of achieving it are considerable. The Thor-Delta vehicle which had been used for launching the TELSTAR and RELAY satellites was insufficient to inject directly the corresponding payload, around 80 kg, into geosynchronous orbit from Cape Kennedy (28" latitude). A brilliant but difficult solution was adopted, consisting of launching first the payload in a highly elliptical orbit with apogee at synchronous altitude (4). An added rocket motor, weighing about one-half of the payload, fired at apogee, circularized the orbit, and by the use of thrusters, the orbital plane was changed to achieve zero inclination. After a failure in the first trial, the second and third launches of SYNCOM I1 (July 1963) and SYNCOM 111 (August 1964) were successful, and Arthur C. Clarke's idea, by then almost twenty years old, became a reality. A satellite placed in geosynchronous orbit must be kept in position by counteracting numerous perturbing forces. Solar and lunar attractions, the oblateness of the earth and a slight ellipticity of the earth's equator are major causes of gravitational perturbations. Solar radiation pressure, on the other hand, is the major nongravitational perturbation. To counteract these forces, station keeping or orbit control is necessary. Orbital corrections are obtained by activating on-board thrusters (catalytically dissociated hydrogen peroxide or hydrazine) upon command from the earth. Electrical propulsion is under consideration for the same purpose. Under ideal conditions, longitudinal drift and inclination can be controlled independently, but in practice some interaction between the two is encoun-

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tered. Usually, satellites are allowed todrift under natural forces andcorrective maneuvers are effected only when the drift tends to become excessive. Even after the thruster fuel on board is exhausted and no correction can be made, it is possible to use the satellite for communication between “visible” stations since the natural longitudinal drift rate is quite small (at most, a few tenths of one degree per day). I n addition to orbital control, and in order to allow the pointing of highly directional antennas toward the earth (global beam) or even parts of it (spot beams), satellites must have some form of attitude control. The most common method of attitude control for communications satellites until now has been obtained by spinning a single or dual configuration platform, permitting a pointing accuracy of the antennas on the order of a few tenths of a degree. Attitude control can also be achieved by other means, such as gravity gradient, magnetic field torque, reaction jets, and reaction wheels.

11. THEINTELSAT SYSTEM The great potential of communications satellites was recognized before a decision could be made in regard to actual systems. As early as 1961, a policy statement was released by the U.S. setting forth broad objectives for the future. I n 1962, the U.S. Congress passed the Communications Satellite Act, and in 1963 the Communications Satellite Corporation was established. In 1964, eleven nations signed an Agreement which resulted in the formation of the International Satellite Communications Consortium (INTELSAT), whose purpose is the design, development, construction. and operation of commercial communications satellite systems. With singular foresight of future development, it was decided after some debate to go ahead with exclusively geosynchronous satellites. On April 6, 1965, the first commercial operational satellite was successfully launched from Cape Kennedy, and shortly afterwards, positioned in synchronous, equatorial orbit over the At la tit i c. Figure 1 illustrates the first three generations of satellites, INTELSAT I , 11, and 111. The space segment has grown from one satellite in orbit i n 1965, with a capacity of 240 voice circuits, to eleven satellites in orbit with about 5000 circuits in use at the end of 1971. The number of ground stations has grown from five i n 1965 to fifty-one by the end of 1971. with 62 antennas in 38 countries (5). The increase in communication capacity expressed i n terms of numbers of telephone channels handled by each satellite in conjunction with standard earth stations with 30 m antennas and liquid helium parametric amplifiers is a clear measure of the progress of the past few years.

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YEAR IN-ORBIT MASS ( k g ) LAUNCH VEHICLE PRIMARY POWER (Watts)

0 TRANSPONDERS BANDWIDTHTRANSPONDER (MHz) ANTENNA TYPE CIRCUITS 0 DESIGN LIFETIME

INTELSAT I (EARLY BIRD)

INTELSAT II

INTELSAT Ill

1965 37 DELTA

1967 81 IMPROVED DELTA

1968 127 LONG-TANK DELTA

40 2

75

I20

I

2

25 OMNISQUINTED 240

130 OMNl 240

225 MECH. DESPUN 1200

1.5 y r

3 Yr

5 Yr

FIG.1 . Major characteristics of INTELSAT I, 11, and 111.

Major factors contributing to this progress were: (a) increased size, weight, and power (prime and RF), (b) increased bandwidth of the transponders, (c) improvements in the transponder design, and (d) increased effective radiated power, not only in terms of item (a), but also in terms of antenna directivity. Figure 2 shows the outside appearance of the INTELSAT 1V spacecraft now operational over the Atlantic and Fig. 3 gives some of its characteristics (6). Although stabilization is obtained gyroscopically as in the case of INTELSAT I, 11, and 111, the INTELSAT IV satellites cannot be regarded as a sheer exercise in scaling up of size and power. Two major characteristics make INTELSAT 1V quite different from its predecessors: first, a despun antenna complex for global and spot beam coverage; secofid, the 500 M H z total bandwidth of the transponders is more efficiently used. INTELSAT I , although capable of handling 240 voice circuits, was suitable only for single carrier operation ; its limiting repeaters, designed for maximum conversion efficiency, resulted in a power limited channel capacity. INTELSAT I I and 111, designed for multicarrier operation, with quasi-linear repeaters, are also essentially more power- than bandwidth-limited. This is no longer the case with INTELSAT IV. The spacecraft is 530cm high, 240cm in diameter, and has a mass of 700 kg. Three-axis stability is achieved by the gyrostabilizer principle, which provides nutational stability and continuous pointing of the antennas toward the earth. The gyrostabilizer is in effect a dual-spin vehicle in which gyroscopic stiffness is provided by the outer drum carrying the solar cells, spinning at 51 rpm, while the inner despun platform carries the electronics and is mechanically tied to the antennas.

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FIG.2. INTELSAT IV satellite.

The potential instability arising from the unfavorable ratio of the moments of inertia about the desired axis and the axis normal to it is removed by nutation dampers located on the despun section. The solar cells generate 400 W of electric power. The six antennas and twelve transponders are supported by rotary bearings. The transponders receive signals from the earth at a frequency of 6 GHz and retransmit them at 4 GHz. Depending on the division of R F power between the spot and the earth coverage antennas, and also on the type of modulation and the number of carriers per repeater, each satellite will provide

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INTELSAT IV 0 YEAR

1971 700 ATLAS CENTAUR 400

IN-ORBIT MASS (kg) LAUNCH VEHICLE PRIMARY POWER (Watts) 0 TRANSPONDERS BANDWIDTH/TRANSPONDER (MHz) ANTENNA TYPE CIRCUITS

12 36 MULTIPLE, MECH. DESPUN 6000

0 DESIGN LIFETIME

7 Yr

FIG.3. Major characteristics of INTELSAT IV.

froni 3000 to 9000 voice circuits. The number of TV channels to be carried at one time could be twelve. Satellite systems in operation today make use of either full-time dedicated carriers between two points or multidestination carriers. In both cases the channels are preassigned between any two points i n the system, providing efficient system operation with large traffic-carrying links. The utilization of satellite channels becomes increasingly inefficient when the number of circuits per link is small. A solution to the problem of lightly loaded links is to share satellite channels among earth stations concerned. The channels are then assigned on demand, forming a temporary link between any two earth stations within the entire region covered by the satellite. At the end of the comn~unication,the channels are released and are again available for use. The INTELSAT IV satellite permits the use of demand assignment multiple access techniques (7). Multiple access implies the ability of numerous earth stations to conduct two-way communication amongst each other through the same satellite. The concept is applicable and especially useful in systems with a large number of links, each characterized by low traffic requirements.

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When a second lNTELSAT IV satellite becomes available over the Atlantic the network will be configured so that all stations will continue using one satellite, while a few stations with heavy traffic demands will also use the second satellite. These few locations will therefore need a second antenna for Atlantic service. Additional INTELSAT spacecraft will provide service to the Pacific and Indian Ocean areas. 111. THEORBITA SYSTEM

Mention should also be made of the “Orbita” system of Russian communications satellites, which uses spacecraft of the Molniya type. This system is unique because it is the first, and until now the only, satellite system in the world for domestic communications (8). It is also quite singular because the satellites are placed in highly elliptical orbits rather than i n geosynchronous equatorial orbit. As mentioned in Section I , the inadequacy of early rockets did not permit the achievement of synchronous orbits, and early experiments took place with low and medium orbits. The Soviet Union “Orbita” system was designed to provide coverage of the far northern latitudes of the European and Asian land masses of the U.S.S.R. while minimizing the handicaps of the launch from the cosmodronie of Tyuratam-Baikonur at its relatively high latitude. A 12-hr period highly elliptical orbit with apogee of around 40,000 km over the northern hemisphere is satisfactory to cover the far northern regions. With orbit inclination set at 65”, the oblateness of the earth results i n no rotation of the line of the apsides, thus minimizing the need for orbit maneuvers and corrections. Tracking of the satellites and traffic hand-over from one satellite to another are clearly necessary, but as the satellites move slowly around apogee these tracking problems are eased. Continuity of traffic is obtained by placing two satellites in phase opposition on each of two orbits whose planes are at 90‘ from each other. while the satellite pairs in the two orbits are i n turn i n quadrature. The relatively low perigee of about 500 km and various other constraints tend to limit the in-orbit lifetime of each satellite. Hence, frequent periodic replenishment of the orbit is necessary. Since the launch of the first satellite of this series i n 1965, at least fourteen satellites of the Molniya type have been orbited. The Molniya 1 satellite uses frequencies in the UHF range between 800 and 900 MHz. An extensive network 01’ earth stations permits telephone, data, facsimile, and television transmission over the entire territory of‘ the U.S.S.R. Exchanges of color TV programs between France and U.S.S.R. via Molniya 1 satellites were carried out in 1965-66. More recently, new satellites designated as Molniya 2 have been announced by the U.S.S.R. To the writers’

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P. L. BARGELLINI AND E. S. RITTNER

best knowledge, the first of these satellites was launched from Tyuratam on November 24, 1971. The scant available information indicates orbits similar to those of the Molniya 1 series, with frequencies no longer in the UHF range but rather at SHF with 4 and 6 GHz to be used for the down and up links, respectively. Finally, in 1969 the Russians filed with the International Frequency Bureau of the ITU (International Telecommunications Union) in Geneva provisional plans for the establishment of a geostationary satellite, designated as Stationarnii 1, and 12 related earth stations. This satellite is supposed to be placed at about 80" E longitude, i.e. over the Indian Ocean.

IV. SYSTEMS CONSIDERATIONS Since the channel noise in space communications is essentially Gaussian and white, and additive to the signal, a systems approach can be formulated in terms of Information Theory principles (9, 10). It is well known that the information rate R, i.e. the amount of information that can be transmitted per unit time over a Gaussian channel of bandwidth B (Hertz), is

R

C = B log, (1

+ S/N),

(2)

where C is the channel capacity (bits/sec), S is the signal power (after suitable encoding of the messages), and N is the Gaussian noise power No B, with No representing the noise power density. Channel capacity, which implies perfect transmission, can only be approached. In real systems, even with signal-to-noise ratio higher than the theoretical minimum, a possibly quite small but finite error probability is encountered in the recovery of the original messages. The goal of communication engineering is to design systems characterized by some acceptable compromise among signal-to-noise ratio (SIN),channel bandwidth to informtion rate ratio (B/R),and message error probability. The bit and message error probabilities which are, in general, functions of the coding-decoding and modulation-demodulation techniques used vary considerably from one system to another, but are monotonically decreasing functions of the signal-to-noise ratio, and are also related to the ratio of the transmission rate and the channel capacity. A significant parameter which expi-esses the efficiency of a communication system is the ratio of the energy per bit ( E ) to the noise power density (No). It is easy to show that for a given rate of information transmission not exceeding channel capacity, when the bandwidth B is allowed to approach infinity, the signal-to-noise power ratio S / N goes to zero while the energy contrast ratio E/No tends to a minimum value, which is 0.693(= log, 2). Bandwidth is not freely available, of course, and consequently practical

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systems always fall short of the above mentioned limit situation. Higher values of S / N and E/No are required in all practical cases to an extent which is inversely proportional to the B / R ratio. Thus, actual communication systems are limited by signal power or by bandwidth availability, or by a combination of these two constraints. Although high power transmitters, large antennas, and low noise receivers can be implemented on the ground, limitations of weight, size, and power are encountered on the spacecraft. Modulation techniques capable of trading signal-to-noise ratio for bandwidth expansion of the original signals have been mandatory. Frequency modulation has been almost exclusively used until recently, not only on account of its intrinsic adaptability to satellite systems, but also for reasons of simplicity throughout the system, including the interfacing with ground-based networks. Other systems, such as pulse code and delta modulation, are being experimented with or are under consideration for possible future use. Frequency modulation techniques with feedback around the discriminator or with phase lock loop detection allow a reduction of the operating threshold, i.e. a reduction of the input signal-to-noise ratio for which a processing gain can still be achieved. The processing gain is actually the ratio of detector output to detector input signal-to-noise ratios. Typical values of the energy contrast ratio E / N , range between 10 and 30. In a space communications link using a transmitter power output P , and a transmitting antenna of gain C , , the effective radiated power with reference to the isotropic case (e.i.r.p.) is the product of P , and G, . When a receiving antenna of aperture A , is used, it is easy to show that the product Rr2 of the information rate (R)and the square of the distance ( r 2 ) is related to the system’s parameters as follows: r 2 R = P,G,A,14rr(E/No)KLi,

(3)

where, in addition to the symbols already defined, K = 1.38 x J/”K, Boltzmann’s constant, and Li is the factor expressing incidental losses. The frequency does not appear explicitly in the foregoing equation as a consequence of the use of gain and aperture to characterize the antennas at the link terminals. The choice of the operating frequency depends i n principle upon the system noise temperature ( T )which is i n turn dictated by the external and internal noise sources (11). The main sources of external noise are describable as “cosmic,” i.e. originating outside of the solar system, and “solar,” i.e. originating within it. Cosmic noise sources are designated in turn as galactic or extragalactic. Contributors to galactic noise are: emissions from nebulae near the central part of the galaxy, synchrotron radiation from electrons spiraling in the

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P. L. BARGELLINI AND E. S. RITTNER

magnetic field of the galaxy, and emission from clouds of ionized hydrogen and exploded supernovae. Radio astronomers have identified numerous sources of electromagnetic radiation-among which Taurus A (Crab Nebula), Cassiopeia, and Cygnus are major contributors. In addition to having been investigated in detail, these sources are also used for the purpose of calibrating the large antennas found at the satellite systems’ earth stations. The sun is the most conspicuous radio source. At optical frequencies, it behaves as a blackbody at a temperature of about 6000°K. At radio frequencies below 30 GHz, deviations from Planck’s law are observed in a direction which implies higher equivalent blackbody temperatures. Depending on the sun’s activity, the excess is from one to six orders of magnitude. The phenomenon is frequency dependent since successive regions of the sun (photosphere, chromosphere, and corona) contribute to the apparent temperatures. The sun’s electromagnetic activity varies in accordance with the sun spots’ eleven-year cycle, with additional violent irregular fluctuations during the well-known noise storms which contribute to long distance HF communications blackout over the earth’s surface. Among the planets, Jupiter is by far the largest contributor with noise temperatures up to 50,000”K at 440 MHz. This is a much higher value than the one calculated from surface temperature and is usually explained in terms of additional synchrotron radiation. Venus, with a temperature around 600”K, and the moon, around 200-300°K, are minor contributors. Terrestrial sources are found in the ionosphere, troposphere, and especially i n the atmosphere where lightning discharges contribute to huge amounts of radiation, especially at the low radio frequencies. Ionospheric effects are negligible in terms of radio noise at frequencies above 500 MHz, but tropospheric absorption and atmospheric absorption, especially those produced by rain and clouds, play prominent roles. The overall noise power spectrum observable from the earth has a broad minimum i n the region between 1.5 and 4 GHz; at lower frequencies, the noise temperature increases rapidly on account of terrestrial and extraterrestrial contributions, while at higher frequencies, absorption phenomena in the earth’s atmosphere become predominant.

V. SPECTRUM AND ORBIT UTILIZATION If frequencies were freely available in the electromagnetic spectrum, the optimum region for communications between a spacecraft and earth stations, i n the sense of the lowest overall noise temperature, would be found between 1.5 and 2 GHz. However, because many terrestrial services already occupy this spectrum, commercial communications satellite systems were assigned

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by international agreement in 1963-500 MHz of the spectrum around 4 GHz for the down-links and another 500 MHz around 6 GHz for the up-links. These spectrum assignments are not exclusive; they must be shared with earth-based microwave radio relay systems, thus creating situations of possible mutual interference (12). Neither service should adversely affect the other, since the signal for one represents only noise for the other. With reference to the characteristics of the two classes of systems, the power flux density produced by the satellite transmissions on the earth's surface must be limited to protect the earth-based microwave systems. Conversely, the transmitter power of the earth-based systems must be kept within limits to reduce the interference to satellites and satellite systems. Actual system degradation is a function of numerous variables, including the form of modulation and demodulation used, the type of traffic (telephone, TV. data, etc.), and the kind of multiplexing employed (frequency division, time division, etc.). Progress in electrical communication engineering has been synonymous with the utilization of progressively higher frequencies. The reasons behind this fact are that bandwidth can only be provided in this way, and that bandwidth and channel capacity are directly related. The opening of portions of the spectrum above 10 GHz offers the most direct way of increasing communications capacity. New frequency assignments were agreed upon at the ITU-sponsored World Administrative Radio Conference (WARC) which was held in Geneva, Switzerland, between June 8 and July 16, 1971. The new frequency bands of most interest to commercial communications satellites are those shown i n Fig. 4, since they are allocated worldwide rather than on a regional basis. The frequency bands at 12 and 14 GHz represent a total of 500 MHz bandwidth, both i n the up-link and the down-link, just as the presently used 4 and 6 GHz bands. There is one complication, however, in that the down-link is split into separate 250 MHz bands: 10.95-1 1.2 and 11.45-1 1.7 GHz. This fact will likely complicate future spacecraft and represent an additional economic burden since a single frequency translation at the satellite is no longer sufficient. The other pair of frequency bands of interest to commercial communications satellites are 17.7 to 21.2 GHz i n the space-to-earth direction, with the corresponding up-link at 27.5 to 31.0 GHz. The technology for 12 to 14 GHz is presently under development, and since propagation conditions are significantly better than at the higher frequency bands, it is considered that the 12 and 14 GHz bands are of the most immediate interest. Studies of the next generation of satellites will undoubtedly consider these specific bands which now are available for communications satellites. The geostationary orbit which offers well-known advantages has been studied in terms of the maximum allowable information rate per unit of

132

P. L. BARGELLINI AND E. S. RITTNER la1 BELOW 15 GHz

(b) BETWEEN 15 AND 40 GHz

17 7 0 GHz

19.70 G Hz

21 2 0 GH7

27 5 0 GHz

29 50 GHz

1

31 0 0 GHz

FIG.4. Communications satellite frequency assignments (WARC, Geneva, 197 I).

bandwidth and per unit of orbital angular spacing. The communications capacity of a segment of geostationary orbit has been calculated under the following assumptions (13):

(a) ideal modulation-demodulation processes; (b) neglect of thermal noise, i.e. assumption of no power limitations;

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133

(c) existence of a finite available communication bandwidth; (d) sharing of this bandwidth by a large number of transmitters of equal power on satellites uniformly spaced on equatorial synchronous orbit made possible by exploiting the directivity of the ground station antennas; (e) ground stations’ antennas as uniformly illuminated apertures with a given Djd ratio, where D is the aperture diameter and 1. is the wavelength. With the above-mentioned assumptions, the noise in each channel is produced by the radiation spill-over of the signals from all other channels. Even for an infinite number of satellites, the noise power, as defined above, is constrained by an upper bound which is a function of a single geometrical variable, i.e. the satellite spacing. Neglecting differences in slant range and choosing an optimum spacing A8 = djD, the communication capacity per unit angle and per unit frequency interval is C’ = 2DjA bits/sec/Hz/rad.

(4)

Consequently, the information rate (bitsisec) which can be handled by a segment of synchronous orbit spanning 0 rad with an available (common) bandwidth B is

R

= (2D/A)BO bits/sec.

A bandwidth of 500 MHz and a 30 m antenna at 6 GHz yields, then, a global capacity in the neighborhood of 3.14 x 10” bits/sec, or roughly lo8 telephone channels. In a practical engineering sense, these theoretical results must be corrected to take into account: (a) mechanical problems of tight orbital spacing, (b) real modulation-demodulation processes, (c) effects of thermal noise, and (d) actual antenna configuration (illumination, side lobes, etc.). While items (a)-(c) would lead to lower communication capacities, item (d) leads to an increase of communication capacity. Other possibilities of augmenting the communications capacity are: (a) intersatellite relaying, (b) increase in the allowable interference ratio, (c) channel interleaving of adjacent satellites, (d) reversed use of frequencies (up- and down-links), (e) pseudo-stationary satellites and two-dimensional orbit space (14). Studies in depth of all these possibilities are underway. With the trend of increasing power availability on board, the limitations in terms of bandwidth become stronger, and it is conceivable that satellites of the future may use modulation systems leading to better utilization of the spectrum. Actually, the two problems of spectrum and bandwidth utilization are inseparable. Future efforts will thus be directed toward reaching compromises in this area.

I34

P. L. BARGELLINI A N D E. S. RITTNER

VI. MODULATION, MULTIPLEXING, A N D MULTIPLE ACCESS Modulation is by definition the process whereby intelligence, such as voice, video, and data signals, is transferred to a suitable RF carrier wave. Multiplexing is in t u r n the process whereby a multiplicity of signals is combined on a carrier. Both modulation and multiplexing are well-known processes encountered in many forms of electrical communications. Multiple access, on the contrary, is typical of satellite communications as it defines the capability of, and the mode in which, a number of earth stations at different geographical locations communicate with each other via a single satellite. Numerous combinations of different forms of modulation, multiplexing and multiple access are possible. The choice of a specific scheme depends on many system parameters, and it may be neither unique nor optimum in an absolute sense. The present commercial satellite system uses Frequency Modulation and Frequency Division Multiplex combined with Frequency Division Multiple Access. These techniques, although effective for heavy trunk type traffic, become less efficient when numerous stations carrying light traffic must be given access to a satellite. The major cause for the decreased efficiency lies in the characteristics of the traveling wave electron tubes used in the satellite transponder power amplifier. These tubes exhibit nonlinearity in their input-output characteristics, and also convert input amplitude changes into output phase variations. Both phenomena contribute to the generation of intermodulation noise when several carriers are present at the input. In spite of advances in solid state technology, the traveling wave tube remains superior to any other active device for high power amplification with large gain-bandwidth product. Hence, traveling wave tubes are used on satellites as well as at the earth stations. I n order to keep the intermodulation noise within acceptable limits under multiple access usage, precise power control of the carriers is required, as well as “backing off” of the tube, i.e. reduced amplitude of the input signal by several dBs with consequent reduction of the conversion efficiency from dc to RF. A solution to t h e problem of lightly loaded links is to share satellite channels among earth stations. Channels are no longer preassigned to stations but are assigned on demand, forming a temporary link on a per-circuit basis as required. Channels released at the end of the communication are available to the next request. As in other areas of electrical communications, digital techniques offer distinct advantages over analog techniques i n satellite conimunications. Digital techniques are superior to FM/FDMA analog techniques in the following ways: (a) efficiency i n terms of bandwidth utilization

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and power conversion (dc/RF), (b) flexibility, (c) ruggedness, (d) signal processing, (e) error control or channel encoding, and (f) message compression or source encoding. A flexible digital system known by the acronym SPADE (single channel per carrier, pulse code modulation, multiple access demand assignment equipnient) has been developed by COMSAT for the INTELSAT System. SPADE uses pulse code modulation combined with phase shift keying and frequency division multiple access on demand techniques. The SPADE system, which is characterized by voice operated frequency, has demonstrated the capability of digital techniques to partly avoid the necessity of “backing off” the TWT, with resulting higher overall power conversion efficiency. Time division multiple access (TDMA) techniques offer another solution to the intermodulation problem of nonlinear repeaters. By having each station transmit bursts of information, and by properly synchronizing all stations having access to a satellite, the repeater amplifier can be used at full efficiency with one input only at any given time, thus avoiding, in principle, the intermodulation problems. After some early studies, TDMA tests were carried out via the INTELSAT I (Early Bird) satellite in August 1966 among three stations, with a capacity of 72 preassigned voice channels and a total rate of 6 Mbits/sec. In 1968, a TDMA system developed by the Nippon Electric Company was tested via the ATS-D NASA satellite. The system was characterized by a rate of 13,664 Mbits/sec and had a capacity of 244 variable destination channels. The later generation of TDMA systems comprise the COMSAT/INTELSATdeveloped TDMA-I system and the Kokusai Denshin Denwa (KDD) Company of Japan-developed TDMA Time Assignment-TASI (TTT) system. Both systems operate at a rate of 50 Mbits/sec and are compatible as shown by a large scale demonstration over the Pacific via an INTELSAT 111 satellite. TDMA-I provided over 700 8-bit voice channels for a ten-station configuration with adaptive multidestination capabilities. Channel reallocation was automatically achieved by burst repositioning without interrupting the voice transmission in individual channels (15). The potential possibilities of the digital versus analog approach can be further expanded by combining Time Division Multiple Access with satellite switched Space Division Multiple Access (SDMA) techniques. Effective radiated power can be increased by the use of directional antennas on board. From the quasi-omnidirectional antennas of the early satellites, the progress has been first towards beams providing earth coverage from synchronous orbit (19” beam). More recently, the INTELSAT IV satellite carries as many as six antennas, four of which have global coverage, and two spot beams of about 4.5”beamwidth to cover specific regions of theearth.

136 P. L. BARGELLINI AND E. S. RITTNER

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ADVANCES IN SATELLITE COMMUNICATIONS

The simplified block diagram of the lNTELSAT IV satellite communication subsystem shown in Fig. 5 illustrates the feasibility of several possible interconnections of the twelve transponders and the six antennas. Operational flexibility is thus insured to serve earth stations with both light and heavy traffic with four transponders permanently connected to global transmitter antennas and eight transponders switchable upon command from earth to global or spot beam antennas. Figure 6 illustrates the communications capacity of the INTELSAT 1V transponder for three different forms of modulation-multiplex and multiple access techniques as indicated.

VII. ELECTRON DEVICES The unique electron devices employed in satellite power supplies and communications transponders will be discussed in this section, with particular emphasis upon physical aspects. The radiation environment in space, which impacts upon the performance of some of the solid state electron devices, will be treated first. 1000

900

800

t

700

U

u

a

600

W

n ~

2

P v)

500

2 d

a I-

400

300 0

4

8

12

16

20

STATIONS PER T R A N S P O N D E R

FIG.6. INTELSAT IV transponder communications capacities.

24

138

P. L. BARGELLINI A N D E. S. RITTNER

A . Radiation Environment The potentially hazardous radiation environment encountered by a satellite in geostationary orbit includes trapped protons and electrons, solar flare protons, ultraviolet radiation, alpha particles, and galactic cosmic radiation. In addition, micrometeoroids represent a possible hazard and the spacecraft is exposed to high intensity radiation belts during injection into synchronous equatorial orbit from the initial transfer ellipse. Quantitative evaluation of the various components of this hostile environment has recently been carried out (26)based upon NASA data. The principal radiation damage is produced by charged particles, protons, and electrons encountered over the long operational period spent in synchronous orbit, e.g. seven years for the present generation of INTELSAT spacecraft. The trapped electron and proton integral fluxes are plotted in Fig. 7 as a function of energy. Although the proton flux for energies above a few kiloelectron volts

I o8

I 0'

-

I OE

V

w

, "lo6

5 21 \

lo4

0

c

LL

?

10'

X

3

J

lo2

LL

W _I

0 lLL

2

10'

toc I 0-

Id2

PARTICLE ENERGY (MeV)

FIG.7. Integral flux of trapped electrons and protons at synchronous altitude vs. particle energy. (Reproduced from ref. 16 with permission.)

ADVANCES IN SATELLITE COMMUNICATIONS

139

is substantially lower than the electron flux, the protons are relatively much more damaging because of their higher mass. However, because of the rapid fall-off in proton flux with increasing energy, shielding is readily implemented. It is to be noted that the particle distributions are spatially isotropic. Solar flare activity is not known with any great certainty, but a good indication of the magnitude of the radiation problem may be seen from an examination of the last complete solar cycle, cycle 19, beginning in April 1954 and ending in October 1964. The time-integrated proton flux as a function of energy for this period is shown in Fig. 8, based on the worst case assumption that the geomagnetic field does not provide protective shielding. The contribution to the total cycle during the year 1959, the year of maximum intensity, is also shown in the figure and amounts to about 90% of the total. The integrated flux for cycle 20 up to 1970 is also plotted in Fig. 8. Thus far, sun activity has been much quieter than in the preceding cycle.

l0li

-

5

N

a

I

10"

W

0

z

w

3

U J

Z

0

&

1Ol1

LI

a

I0 '

PROTON ENERGY ( M e V )

FIG.8. Unattenuated integral solar flare proton fluence vs. proton energy. (Reproduced from ref. 16 with permission.)

140

P. L. BARGELLINI AND E. S. RITTNER

0.

..

E

, i

0

E \

'0

t Ln z

W

a LL W

_ _ _ _ JOHNSON CURVE - THEKAEKARA CURVE

a 0.

WAVELENGTH ( p m )

FIG.9. Solar spectral irradiance for air mass zero (AMO). (Reproduced from refs. 17 and 18 with permission.)

The intensity of ultraviolet radiation and its distribution with wavelength above the earth's atmosphere are well known (17). Recently, as a result of extensive new measurements, revisions of the data have been proposed (18). Both sets of data are shown in Fig. 9. The ultraviolet radiation is not penetrating, but is capable of producing darkening in surface-mounted optical components and surface coatings. A small but significant alpha particle content is found in the solar flare emissions as well as in the geomagnetically trapped charged particles. However, the range of the alphas is too limited to represent a hazard, save to surface materials and unshielded components. The integrated intensity of galactic cosmic rays reaching the earth's vicinity is reasonably constant at about lo8 particles/cm2 year (19). The particle intensity and interaction cross sections are sufficiently low so as not to constitute a radiation hazard to satellite components. The hazard from micrometeoroids is also not considered too serious, the principal damage expected being a very slight loss of transparency of surface-

ADVANCES IN SATELLITE COMMUNICATIONS

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mounted windows as a result of an effect akin to sandblasting. The possibility exists of a random catastrophic failure of the satellite caused by puncture of a vital component; however, the probability of such an occurrence is extremely small. Despite the exposure of a satellite placed in synchronous orbit via an elliptical transfer orbit to high intensity radiation belts, the exposure time is generally so small a fraction of the operational lifetime that the corresponding damage is either negligible or represents a minor fraction of the total incurred. In summary, the most damaging constituents of the space radiation environment are the geomagnetically trapped electrons at synchronous altitude and the solar flare protons encountered by the satellite during a period of intense sun activity.

B. Power Generation Large arrays of silicon solar cells have served thus far quite satisfactorily as the prime source of power in communication satellites. The maximum power requirement up till now has been only several hundred watts. Future escalating power needs will probably be met by larger area, deployable, sun-oriented arrays rather than by nuclear thermal sources and direct conversion schemes. Solar arrays with outputs as high as 100 kW are under serious consideration by NASA for future space missions. The areas in which further improvements in solar cells are being sought are higher efficiency, higher electrical output per unit weight, and increased radiation resistance. To this end, cells made from silicon as well as from other materials are under extensive investigation.

I . Silicon Solar Cells In its original form (20), the silicon solar cell consisted of a thin, highly doped p-type layer formed on an n-type base with the solar radiation incident upon the player, and with an ohmic contact on each region. Hole-electron pairs are created in the silicon by absorption of photons with energy exceeding the bandgap. Minority carriers residing within a diffusion length of the junction are collected at the junction, thus producing a photocurrent and useful electrical power in an external load resistance. Early major improvements included the addition of an antireflection coating and of a gridded contact to the front surface to reduce series resistance. Use of the cell in space applications revealed rapid deterioration in performance as a result of radiation damage, particularly by low energy protons. This problem has been solved by the addition of a thin transparent cover

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P. L. BARGELLINI AND E. S. RITTNER

slide, usually of fused quartz,* attached by means of an adhesive to the cell. While the transmission properties of the quartz do not diminish significantly as a result of exposure to the space environment, the commonly employed adhesives darken readily on exposure to ultraviolet. This necessitates the addition of an ultraviolet filter, usually of the interference type, in front of the adhesive. The optical matching is also disturbed by the cover slide addition, and it is necessary to employ an antireflection coating of somewhat higher refractive index (e.g. TiO,) than was previously employed on bare cells (e.g. SiO). Note that it is necessary to take into account the anomalous dispersion in the silicon in optimizing this optical coating. It has also been observed in space applications that the original p / n structure is not as radiation resistant as an n/p structure. This appears to be a consequence of the facts that the contribution to the photocurrent comes mainly from the thicker substrate region, that the diffusion constant for electrons in p-substrates is higher by a factor of 2.8 than that for holes in n-substrates, and that the lifetime of minority carriers is degraded to comparable values by extensive radiation exposure in either substrate type. The rate of degradation with fluence increases with the doping level in the substrate, as expected in material in which the dominant recombination process is of the Shockley-Read (21) variety. Hence, the resistivity of the base material is kept in the range of 2-10 R-cm; higher doping levels would produce higher initial power output but lower output at the end of mission. The doping of the surface n-region corresponds to saturation solubility. The thickness is minimized to reduce recombination losses, since the minority carrier lifetime is quite low (in the nanosecond range) in the highly disturbed surface layer, a typical layer thickness being 0.4 pm. The contacts must be ohmic, highly adherent, of negligible electrical resistance, and humidity resistant. Present practice is to employ a thin evaporated coating of titanium covered by a thicker layer of silver. The back contact covers the entire area; whereas the front contact consists, in a 2 x 2 cm cell, of six grid lines joining a busbar, blocking at least five percent of the incident light. It is essential that the contacts be truly ohmic rather than Schottky barrier contacts to prevent negative contributions to the photovoltage. Since the power output per unit weight is of more concern in space applications than the efficiency, recent practice tends towards decreasing the cell thickness. Some weight savings can be achieved in this way with only a modest sacrifice in power output, corresponding to a loss of photons of energy near the cell threshold for which silicon has a low absorption coeffi-

* A fused quartz cover slide also has a desirably large total thermal emissivity (ca. 0.8), resulting from the strong absorption band at 9 pm, which facilitates radiation cooling of the cell.

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ADVANCES IN SATELLITE COMMUNICATIONS

cient. When such thickness reductions are carried to the point where the base thickness is no longer large compared to the diffusion length, the ohmic contact at the back of the cell becomes a sink for photocarriers and causes an additional degradation in performance. I n principle, this difficulty may be alleviated by adding a thin highly doped p + layer between the semiconductor substrate and the back metal contact, thus introducing a retarding electric field for the electrons in order to direct them back towards the junction. The current-voltage characteristic of a typical flight quality nip 10 R-cm silicon solar cell under a spectrum simulating the sun’s radiation above the earth’s atmosphere (referred to as air mass zero) is shown in Fig. 10. The

I1 5

I1 0

3

I05 IOC

o_

5

95 40 ‘2 a5 k 00

7c

Fic;. 10. I-V characteristic of typical flight quality rt/p silicon solar cell under I sun (AMO) illumination. Base resistivity = 10 12-cm. area 4.0 cm2, thickness = 0.28 mm, temperature = 25 ’ C. 5

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P. L. BARGELLINI AND E. S. RITTNER

short circuit current density is 35 mA/cm2; the open circuit voltage is 0.550 volts; the “fill factor” is 0.73; and theefficiency is 10.0%. The observed short circuit current density is only 66% of the theoretical value for silicon, based upon collection of all holeeelectron pairs generated by solar photons having energies exceeding the bandgap. Thus, the 66% figure results from a grid obstruction loss, a reflection loss (since a single antireflection coating eliminates reflection only at one wavelength), a transparency loss of photons near energy threshold because of the cell’s finite thickness, and recombination losses attending minority carrier transport. The recombination processes are the most important of these. In order to render these negligible in the highly doped surface region, it is necessary to fulfill the following conditions (22): s G Dlw,

w2/2 D z G 1,

(64

(6b)

where s is the surface recombination velocity for minority carriers at the front surface of the cell, D is the diffusion constant, aiid T the lifetime of minority carriers, in this case the carriers i n the highly doped surface region of thickness w. For an nip cell with w = 0.4 ,um and D = 2 cm2/sec, this would require s S 500 cmlsec,

and

In the base region, negligible recombination losses require

where o! is the optical absorption coefficient. This inequality is readily fulfilled at most wavelengths penetrating into the base region, except those in the neighborhood of the cell threshold. Another significant loss occurs in the fill factor, as the theoretically expected (23) value of this quantity for an ideal junction in silicon with an open circuit voltage of 0.550 V is 0.81. This loss is attributable to minority carrier recombination in the space charge region of the junction. If all of the above-mentioned losses could be eliminated, the efficiency of the nip 10 0-cm cell would reach 17%. Sufficiently energetic electrons and protons permanently damage the silicon cell by the formation of displaced lattice atoms, lattice vacancies, aiid associated complex defects. I n particular, defects consisting of a vacancydopant complex or of a vacancy-oxygen complex introduce additional allowed energy states in the forbidden band which serve as electron and hole traps and/or recombination centers. This leads to charge carrier removal and enhanced recombination rates for added charge carriers. For a mission of

ADVANCES IN SATELLITE COMMUNICATIONS

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seven years duration at synchronous altitude, the number of carriers removed constitutes but a minor fraction of the total present initially, whereas carrier lifetime degradation proceeds to a highly significant extent. For penetrating radiation, the lifetime degradation is described by the empirical relation.

where T~ designates the carrier lifetime in undamaged material, 4 is the radiation fluence to which the sample is exposed, and K is the damage constant which is a function of particle energy. This relation also follows immediately from Shockley-Read theory if one assumes that the density of radiation induced recombination centers is proportional to the fluence. The value of T~ is some orders of magnitude higher in the base region than in the highly doped and disordered surface region, whereas the value of K is larger in the surface region. The net result is a more profound lifetime degradation in the base region for the mission duration in question, resulting in a diminution in both the short circuit current and the open circuit voltage of the cell. Typical efficiency degradation data (24) for three 10 0-cm silicon cells exposed to 1 MeV electrons are shown i n Fig. 11. Electrons of this energy are highly penetrating and a fluence of 3 x l0l4electrons/cm2 does essentially

12

-z>

0

10

8

z

w 0 G w

6

4

0

p/n O 3 8 m m

A

n/p O 2 8 r n m

0

n/p 0 15 mm

2

0 I MeV

ELECTRON

FLUENCE ie/cm2)

FIG. 1 1 . Efficiency degradation in 10 R-crn silicon solar cells produced by 1 MeV electron irradiation.

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the same amount of damage as a space exposure at synchronous altitude of seven years. The 0.28 mm thick nip cell, which is the same one for which I-V characteristics are shown in Fig. 10, suffers a decrease in efficiency of about 14% under a fluence of this magnitude. The thinner nip cell exhibits a lower initial efficiency but declines to about the same value at 3 x 1014 electrons/cm*, corresponding to a decrease of about 7%. The explanation is that the thicker cell absorbs relatively penetrating photons of energy in the neighborhood of the cell threshold to which the thinner cell is transparent. However, with sufficient radiation damage, the additional photocarriers generated in the thicker cell die out before reaching the junction, thus wiping out the advantage of the higher initial efficiency. The somewhat thicker p / n cell exhibits the highest initial efficiency of the three and a more rapid fall-off with electron fluence corresponding to about a 35% decrease after exposure to 3 x l O I 4 electrons/cm2. In addition to the thickness effect, the 2.8-fold lower diffusion constant for holes in n-material over that for electrons in p material is the cause of the poorer radiation performance in this instance. It is also clear from Eq. (8) that any improvement in initial efficiency resulting solely from increasing the minority carrier lifetime in the base region will be lost under sufficient radiation exposure. Use of float-zone silicon, which contains a smaller oxygen content than conventionally pulled crystals, leads to a small but significant improvement in performance under electron irradiation (24). A reduction in base resistivity produces a higher voltage output and hence a higher initial efficiency. However, because of the accompanying higher damage constant, the fall-off in efficiency with fluence is more rapid. Thus, the optimum choice of base resistivity lies in the general range of 1-10 R-cm, the precise value depending upon transfer orbit and mission life. Since the minority carrier lifetime saturates with doping density for a Shockley-Read type of recombination center, whereas the open circuit voltage should increase monotonically with doping density up to the solubility limit, the possibility exists of a rise to a second (hopefully higher) maximum in the end of life efficiency at a very much lower base resistivity. For nonpenetrating radiation, e.g. protons of energy sufficient to penetrate the cover slide but insufficient to pass completely through the cell, the situation is more complex than that described above. Near the end of its range, a proton loses nearly all of its remaining kinetic energy in elastic collisions that produce displaced lattice atoms. Thus, for mono-energetic protons stopping in the cell, an appropriate theoretical model describing the nonuniform damage has been advanced (25),consisting of two damaged regions and one undamaged region. Equation (8) is assumed to apply in each of the damaged regions but with a higher damage constant near the end of range. The resulting efficiency-fluence curve falls off somewhat more rapidly than for the uniform damage case. Also, charge carrier removal may

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become more important near the end of the proton range as a displacement density comparable to the doping density is possible. This could lead to the creation of an undesirable junction which would degrade cell performance still more. A special case of great importance arises from the simultaneous presence of nonpenetrating radiation and a small region on the cell surface which is unprotected by the coverglass. The junction underneath the unprotected area is damaged, leading to a highly significant internal conduction path shunting the external load and to a performance degradation out of all proportion to the fraction of exposed area (26). A promising approach (27) towards improving radiation resistance to proton damage is fabrication of a pin cell where the predominant dopant in the n-material is lithium. Lithium is a highly mobile solute, and especially so at the elevated temperatures expected in sun-oriented arrays. Annealing of the radiation damage, or at least a major portion thereof, proceeds spontaneously at the cell operating temperature. The recovery mechanism is not yet fully understood; however, it is hypothesized that the protons produce large clusters of damaged regions which are negatively charged, thus constituting giant recombination centers for holes. The lithium ions are presumably attracted to, and electrostatically shield, these centers. 2. Heterojunction Solar Cells Shortly after the discovery (20) of the silicon solar cell, it was concluded (28) from a general theory of the p/n homojunction cell that the optimum bandgap for solar energy conversion is in the neighborhood of 1.5-1.6 eV, an energy substantially larger than the bandgap of silicon (1.1 eV). This has stimulated fabrication (29) of a p / n solar cell of gallium arsenide, early cells exhibiting an efficiency of four percent as compared with the five percent efficiency o f t he earliest silicon cells. Extensive subsequent development work has led to higher values of efficiency, the highest reported value to date being thirteen percent with typical values of about eleven percent (30). This is disappointing i n view of the theoretical upper limit of about twenty-five percent. The relatively poor performance has been attributed (31) to a high surface recombination velocity, together with a high optical absorption coefficient over most of the spectral sensitivity range of the GaAs cell. A promising approach to overcome this difficulty is to prepare a p/n heterojunction between GaAs (or any other material with a bandgap appropriate for solar energy conversion) and another material of much larger bandgap upon which the light is incident. Carriers generated at a high rate near the interface of the two materials are readily collected by the junction. An efficiency of eleven percent has been claimed (32) for a heterojunction between GaAs and an amorphous nonstoichiometric form of silica (SiO,)

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of low resistivity and large bandgap. Another example is a heterojunction between n-CdS and p-Si for which a conversion efficiency of 5.5% has been reported (33). Still another heterojunction type of solar cell is the thin filmp-Cu,S/n-CdS cell (34) which was not recognized to be of this type until relatively recently (35). Although exhibiting an efficiency of only several percent (reaching 6% as a result of recent improvements), it is notable for a relatively high output per unit weight and for high flexibility. Both attributes are highly advantageous in deployed arrays, particularly of the roll-out variety. Both are consequences of the use of a thin flexible plastic substrate and of a thin vacuum evaporated CdS layer, only a minute portion of which is converted to Cu,S. A further advantage of the thinness of the cell is improved radiation resistance. The cell differs from the heterojunction cells discussed above in that the light is incident upon the lower bandgap material (the Cu,S), in which substantially all ofthe effective optical excitation occurs. Since Cu,S is a polar material, the thermal bandgap (36) (0.9 eV) is smaller than the optical bandgap (1.2 eV), in accordance with the Franck-Condon principle, and further removed from the optimum value than that of silicon. An unusual feature of the Cu,S-CdS cell is that much of the photoeffect appears to arise from the direct photoemission of carriers from the Cu,S over the barrier into the CdS (35,36). Instabilities in the cell performance, however, have heretofore frustrated actual usage in satellite power supplies. There are two distinctly different sources of the instabilities, one ionic and the other electronic. The first of these arises from electrochemical reduction of the Cu,S with the formation of shorting copper nodules whenever the photovoltage exceeds 380 mV, corresponding to the free energy at 25°C of the reaction (37):

cu,s

-

cus + c u .

(9)

Fortunately, the voltage across the cell corresponding to the power maximum is below this critical electrochemical potential ; however, even in this case, electronic instabilities occur (36). These are associated with electron trapping at interface states between the two semiconductors and at states in the CdS near the heterojunction. The trapping occurs as a result of photoexcitation of electrons by long wavelength radiation and produces a time-dependent fatigue effect. This is compensated by hole injection into the CdS produced by short wavelength excitation and subsequent untrapping, producing a time-dependent sensitivity increase. Thus, the electronic instability is highly sensitive to the spectral distribution of the exciting radiation. For a wellsimulated solar spectrum, the competing trapping-untrapping processes are in relatively good dynamic balance and the instability manifests itself as a minor, long term net fatigue effect. A highly similar thin film heterojunction type of solar cell employing a

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heterojunction between p-Cu,Te and n-CdTe is also under development (38). The performance and advantages are fairly similar to those of the p-Cu,S/ n-CdS cell. A major difference physically from the latter cell is that the effective optical excitation takes place in the CdTe layer, the Cu,Te serving as a higher bandgap window and p-type contacting material.

C. Energy Storage Spacecraft power during launch and during eclipse periods associated with vernal and autumnal equinoxes is generally supplied by rechargeable nickel-cadmium batteries. Since the weight of the batteries is comparable to that of the solar array, whereas power is drawn from them for only about one percent of the total mission time, improvements in energy storage are badly needed. The most promising approach to this problem appears to be use of a fuel cell i n a rechargeable mode. Development work on hydrogenoxygen cells for this purpose is being vigorously pursued.

D. Transponder Electronic Derices With reference to Fig. 5, it may be noted that the amplifying devices typically employed in satellite transponders are tunnel diodes and traveling wave tubes. Conventional crystal oscillators, frequency multiplier circuits, and mixer diodes are also employed to effect the frequency translation from the up-frequency (6 GHz) to the down-frequency (4 GHz).

I . Turinel Diodes The choice of tunnel diodes for the front end of the satellite receiver has been dictated by the need for linear amplification at high carrier frequency (6 GHz), large bandwidth (500 MHz), and relatively low noise. A larger area, higher current version is also suitable as a linear amplifier at the downconverted frequency (4 GHz) but is limited in power output; hence, further gain i n a low level TWT is required prior to subdivision of the full bandwidth into smaller channels in the transmitter. The tunnel diode consists of aplnjunction. both sides of which are doped so highly that the Fernii level resides within the conduction band in the n-side and within the valence band in thep-side. Under these conditions the junction width is so small that electrons readily penetrate the barrier via tunneling. Thus, biasing the n-region negatively with respect to the p-region causes a net electron current flow from n to p . As the forward bias is progressively increased. at first the electron reservoir " sees" an increasing density of empty states i n the p-material, and later a decreasing density as the reservoir rises

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above the top of the valence band. At still higher biases, both electrons and holes have sufficient energy to surmount the barrier. The result is a currentvoltage characteristic of the type shown by curve A in Fig. 12, the negative resistance portion of which is employed i n the amplifier. 24 2.2

2 0 1.8

-

16

E

14

1

a

i 00

4

06

1i

04

02 0

1 100

200

300

400

500

600

VOLTAGE ( m v )

FIG.12. I-V characteristics for typical Ge tunnel diode at 300 K . Curve A, Initial; curve B, after degrading; curve C, after extensive degrading.

While tunnel diodes have been fabricated with a large variety of seniiconductor materials (e.g., Ge, Si, GaSb, GaAs, InAs, InSb, PbTe, Sic), germanium (the material with which the original discovery was made) (39) is most commonly employed in commercial units. Since germanium is an indirect bandgap semiconductor, one would expect on theoretical grounds (40)phonon assisted tunneling and a tunneling probability some three orders of magnitude lower than for the direct bandgap case. In the case where the n-type side of the Ge is doped with antimony, fine structure is observed (41) i n the 1- Vcharacteristic at very low temperatures at biases corresponding to the energy of acoustic phonons. Moreover, the observed tunneling current is only in the microampere range. When the n-type dopant is changed to arsenic (the choice in commercial diodes) or phosphorus, the fine structure disappears and the tunneling current increases to the millianipere range. While the higher solubility (42) in Ge of As and P relative to Sb is certainly an important factor, it does not raise the Fermi level sufficiently to populate

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the higher lying (0, 0, 0) valley with electrons so as to permit direct tunneling between bands. To avoid this difficulty (and a similar one in silicon where the energy separation between corresponding bands is even greater), it is postulated ( 4 3 ) that As and P i n Ge (and most donor impurities in Si) produce strongly localized central cell potentials which introduce components into the electron wave function from many points in momentum space, including all of the valleys. This presumably would allow tunneling into any region of momentum space consistent with energy conservation, a phenomenon labeled “ impurity assisted tunneling.” A quantitative theory and supporting experimental proof of this postulate are still lacking. I t has recently been discovered (44) and verified (45) that there is a negative capacitance component, C,, associated with the band to band tunneling regime. The region of existence of the negative capacitance coincides with the region of negative resistance and both quantities peak together. On theoretical grounds it has been shown (44) that

c, = gr, where g is the differential negative conductance and Y is a characteristic time. Interpretation of measured values ( 4 4 , 4 5 ) of C, and g leads to values of the time constant of the order of 100 psec and 10 psec, respectively, much longer than expected tunneling transit times. Moreover, the value of Y varies with bias, both facts suggesting that the measured Ys are probably circuitdiode time constants. At higher forward biases, i n the neighborhood of the valley of the I-V curve, the observed current is higher than the expected sum of the band to band tunneling and the minority carrier injection currents. This “excess” current is of considerable concern, as the growth of this quantity during diode service is the major cause of diode degradation. The origin of the excess current is tunneling at constant energy between conduction electrons and localized energy states associated with defects within the junction, followed by a recombination-like transition to the valence band (or a transition of a conduction electron to a deep lying localized defect state followed by tunneling into the valence band). Since the barrier height is reduced as the forward bias is increased with an attendant large increase in tunneling probability, a relatively modest defect state density can contribute an excess current component comparable to the band tunneling component. This may increase the magnitude of the negative resistance at the diode operating point, thus causing loss in gain (see curve B of Fig. 12). In the limit of extensive defect introduction into the junction, the negative resistance may even disappear (curve C, Fig. 12). Diode behavior with respect to valley current increase is widely varied. I n extreme cases one diode may exhibit an unacceptable increase even under

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P. L. BARGELLINI AND E. S. RITTNER

shelf storage while another withstands the highest temperature allowed by the diode construction (230°C) without significant change. A recent extensive experimental study (46) of this question has produced considerable physical insight and has provided preselection guidelines for weeding out potential failures. The method of fabrication of the diode and the resulting physical structure have been of considerable importance in developing this insight. The diode is fabricated by ball alloying of an arsenic tin alloy into a gallium doped p-type Ge substrate at relatively low temperature to minimize diffusion and to produce a sharp junction. The small junction area required for high frequency performance (- lo-’ cm’) is then obtained by etching the germanium under the alloy ball, producing the mushroom-like structure shown in the scanning electron micrograph of Fig. 13. The “cap” diameter in this instance is about 50 pm, the neck diameter at the junction is about 5 pm, and the length of the “stem” is about 25 pm. Contact to the ball is made by means of a metal mesh supported by plastic rods (not shown in the micrograph). Thus, the junction is subjected to rather substantial stress which can vary considerably among diodes. When the stress exceeds the elastic limit, and after an incubation period, plastic deformation occurs. The initial phase of this deformation, called

FIG.13. Scanning electron micrograph of typical 6 GHz tunnel diode. Magnification 1520 x , (Courtesy of T. D. Kirkendall.)

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creep, results in generation and motion of dislocations and point defects. Arrival of these defects in the junction region produces the allowed energy states leading to the excess current. The incubation time, t i , before which the introduced strain is very small and after which the strain increases linearly with time, is given by the following equation: ti = cd exp[(Q - aa)/kT],

(1 1)

where c and a are constants, d is the junction diameter, Q is an activation energy, and c is the stress. At a critical stress in the neighborhood of lo9 dyn-cm-2, the exponent changes sign and correspondingly the incubation time flips from extremely large to extremely small values. This explains the wide variation in excess current growth from diode to diode. Moreover, if diodes are heated to an elevated temperature (in the range of 100-140°C) for appropriate times (of the order of 1-100 hr), and the room temperature valley current monitored, it should be possible to select out the diodes with higher built-in stress that constitute potential failures. The noise of the 6 GHz tunnel diode amplifier is about four times higher than that corresponding to the ultimate noise limitation imposed by fluctuations in the radiation field incident upon the satellite antenna. Improvement in this regard is possible with the use of an uncooled parametric amplifier with some penalty in weight and power. Pump reliability is also of concern here. Another possibility is the use of the Schottky barrier gate gallium arsenide field effect transistor (47) which is undergoing rapid development and which exhibits advantages of simplicity (three terminal devices), small size, and low power consumption. At higher frequencies, the increased fragility of the tunnel diode may dictate other choices for the receiver front end. Again, an uncooled parametric amplifier or an integrated circuit version of a down-converter are prominent candidates.

2. Traveling Wave Tubes The choice of a traveling wave tube for the output stage of the transmitter section of the repeater has been dictated by the needs for broad bandwidth, high gain, light weight, long life, high reliability, and high efficiency. This latter requirement is of the utmost importance in the output stage which consumes more power than any other constituent of the satellite. A low level traveling wave tube employed in the receiving section of the repeater, although still relatively efficient, is designed for moderately low noise. Figure 14 displays photographs of the completely encapsulated output stage TWT employed in INTELSAT I11 transponders, and of a cross-sectioned tube identical to those employed in the output stage of JNTELSAT IV

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FIG.14. INTELSAT Ill encapsulated output TWT and cross-sectioned INTELSAT IV output TWT.

transponders. With reference to the photograph of the cross-sectioned tube, the electron gun is visible on the left, the helix surrounded by the periodic permanent magnetic (Pt-Co) beam focusing structure is visible in the center, straddled by the input and output connectors, and the collector portion is seen on the right. The performance characteristics of major interest are listed in Table I. The relatively high efficiency is a consequence of low beam interception by the helix, a high beam-helix interaction efficiency, and the use of a single stage of collector depression. The latter refers to the use of a retarding field between helix and collector to reduce the kinetic energy of the landing electrons and the corresponding thermal dissipation in the collector. The slightly lower efficiency in the INTELSAT IV tube is a deliberate trade-off for a lower phase retardation produced by application of less overvoltage. (Overvoltage is the TABLE I PERFORMANCE CHARACTERISTICS OF TRANSMITTER TWT’s Characteristic Overall efficiency (%) Phase retardation (deg) Overvoltage (%) Small signal gain (dB) Saturation output power (W) Bandwidth used (MHz) Weight (kg) Design life (yrs)

INTELSAT 111 (Tube #H235)

INTELSAT IV (Tube #H261)

34-36 40 4-5 56 12-23 250 0.45

30-32 25 0-1 65 5-6 40 0.68 10

I

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voltage applied to the helix in excess of that which corresponds to exact synchronism between the electron beam and the RF wave.) The lower phase shift reduces nonlinearity in the phase shift versus input power characteristic which, in turn, reduces the conversion from amplitude to phase modulation and the accompanying intermodulation interference. The higher gain in the INTELSAT 1V tube results from an increase in the length of the slow wave structure. The lower power output and much smaller bandwidth used in this tube are consequences of the system design, which calls for twelve output transmitters in INTELSAT IV relative to the two employed in INTELSAT 111. This yields advantages of flexibility, less attrition percentagewise in the event of tube failure (also mitigated by the use of 100% redundancy), and amelioration of the problem of cross-talk. The design life is mainly associated with the life ofthe cathode. The cathode employed is an oxide type with a double carbonate coating upon a highly purified nickel base containing a few percent of tungsten and about 0.1% of zirconium activator. The intricate chemistry resulting from the simultaneous presence of the tungsten and the activator, and the reasons why this results in a very well activated and a long-lived cathode, have been discussed long ago (48). Operation of the cathode at a temperature just sufficient to supply the emission needs is also essential to long life, but cannot be achieved unless painstaking efforts are made to avoid a poisoning ambient inside the tube. These efforts include the use of all metal and ceramic parts to permit vigorous outgassing and exhausting of the tube during processing, a getter, an ion barrier between the accelerating anode and the helix provided by appropriate potentials on these electrodes, and extremely careful focusing of the electron beam as it traverses the helix to minimize interception and resulting outgassing. The depressed collector also serves as a sink for ions. The most troublesome aspect of the TWTs, the nonlinearity in the amplitude input-output relationship and in the phase-input power relationship, arises from inherent nonlinearities in the beam-wave interaction. The former arises near the end of the helix from the space charge field associated with the tightly bunched electrons, whereas the latter occurs over the entire length of the helix. Hence, the effects with respect to intermodulation generation tend to be cumulative (49).

VIII. MATERIALS TECHNOLOGY A very wide variety of materials is employed i n satellites, ranging from metals to plastics. All of them have to be space qualified (as do indeed all of the electron devices in the spacecraft),which means passing tests for volatility in high vacuum, vibration, mechanical shock, thermal cycling simulating eclipse, and radiation damage. A few interesting examples of materials employed in INTELSAT IV will be presented here.

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The surface structural members of the satellite body are constructed from aluminum honeycomb with a very high rigidity to weight ratio. Solar cells are attached to the cylindrical solar panel surfaces with a flexible epoxy adhesive. Use is also made of the honeycomb construction for the platform for the antenna farm which is faced with an 0.25 mm thick aluminum sheet attached via an epoxy polyamid film. The platform is covered with a conical sun shield constructed from a 3 mm thick aluminum core honeycomb faced with an 0.008 mm thick aluminum sheet to which metallized quartz mirrors are bonded. The metallization is vapor-deposited silver protected by a nickel alloy coating. The rotor shaft for the despun platform is made of titanium. The global antennas are fabricated from aluminum honeycomb with an 0.05 mm thick aluminum bonded inner face sheet and a fiberglass outer face sheet. The spot beam antenna parabolic reflectors are also made of aluminum honeycomb sandwiched between epoxy fiberglass surfaces with a gold coated polyester mesh embedded in the concave face sheet. The reflector feed horn is attached to an elliptical waveguide of boron fiber-reinforced epoxy which also serves as a structural support for the horn. The propulsion system makes use of a number of exotic alloys. The fuel tanks are made of a titanium alloy containing 6 wt.% aluminum and 4 wt.% vanadium because of its chemical inertness in the presence of hydrazine and its relatively light weight and high mechanical strength. The connection between the tanks and various stainless steel components in the propulsion system is made with special co-extruded tubing of graded composition with length, starting with the Ti alloy and ending with the steel. Valve seats and poppets are constructed from tungsten carbide in a cobalt matrix. The thrusters are constructed of Inconel alloy 600 (72% Ni, 14-17% Cr, 6 - 8 x Fe, 1.75-2.75”/, Nb, 0.1% C max) because of the need for hot strength. Lubrication in the presence of the ultrahigh vacuum space environment constitutes an especially difficult problem. The bearings for the despun antenna platform are lubricated with Vac Kote, an apiezon C oil with a proprietary additive. The nutation damper is lubricated with MoS, . I n the electronic units, the circuit boards are constructed from copperclad glass epoxy laminates with electro-plated solder protection. The multiplexer waveguide filters in the transmitter portion of the repeaters are constructed of silver plated Invar because of its low thermal expansion coefficient which facilitates meeting the stringent requirements on frequency bandpass stability. Since the filters are major contributors to the weight of the communications package, extensive efforts are underway to develop new materials or new approaches to reduce filter weight. Prominent possibilities are fiberreinforced composites of low thermal expansion or surface wave acoustic filters, respectively.

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IX. FUTURE TRENDS Communications via satellite will expand greatly in the future. Forecasts based on prediction of traffic growth and extrapolations of present technology are useful to define a lower bound of this expansion. The definition of a higher bound is more difficult, but can be attempted in terms of possible advances of new technologies resulting from a vigorous research and development program. As new services such as domestic and international videophone, high speed data transmission, audio and visual conference calls, mobile aeronautical and maritime services, telemail, library and educational services, etc. will be made possible, even the most optimistic prediction of the growth of present services and traffic patterns will be exceeded. Future communications satellites will provide communications capacity much greater than those available today. Progress will be made possible by advancements over a broad technological front. The spacecraft stabilization will no longer be obtained by spinning the spacecraft. Inertia wheels will provide stability along the three axes of the spacecraft and the stability will be augmented by microthrusters controlled by orientation sensors. Thus, extremely stable space platforms will be available capable of pointing the high gain antenna beams in the desired directions, with tolerances of at least 0.1" or better. Another advantage of this approach is the theoretical n-fold increase i n electrical power over that obtainable from solar cell panels of equal area on a spinning spacecraft. With multiple independent beams, the same frequency band can be reused many times with a resultant increase of communications capacity. Furthermore, a twofold increase of communications capacity can be obtained by using orthogonal polarization in each beam. A large fraction of the increase in communications capacity will be made possible by adding to the presently available functions of reception, amplification, and transmission on the spacecraft, the switching of signals from and to different earth stations on board, and by using all-digital techniques with time division multiplexing combined with time and/or space division multiple access techniques. Substantial contributions to all these advances in terms of more efficient, more reliable, and novel electron devices are expected.

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ACKNOWLEDGMENTS Thanks are due to the Members of the Technical Staff at COMSAT Laboratories, on whose work this contribution is largely based. One of the authors (E. S . Rittner) is particularly grateful to A. Meulenberg, R. Strauss, and P. Varadi for supplying information, and to them and to R. Arndt, P. Fleming, J. Lindmayer, A. Revesz, R . Rostron, and A. Verbin for critical review of parts of the manuscript.

REFERENCES 1. J. R. Pierce, “The Beginning of Satellite Communications.” San Francisco Press, San Francisco, 1968. 2 . A. C. Clarke, Wireless World, 51, 303 (1945). 3 . J. B. Wiesner, in “ Lectures on Communication System Theory” (E. J. Baghdadi, ed.), Chapter 22. McGraw-Hill, New York, 1961. 4 . H . Rosen, in “Space Communications” (A. V. Balakrishnan, ed.), Chapter 17. McGrawHill, New York, 1963. 5 . S . Metzger, Astronaur. Aeronaut. 6 , 42 (1968). 6. W. L. Pritchard, IEEE Int. Conv. Digest, New York, March 22-25, 1971, pp. 24-25, (Paper I A.2.) 7 . J. G . Puente, W. G . Schmidt, and A. M. Werth, Proc. IEEE 59, 21 8 ( I 971). 8 . K. L. Plummer, Spaceflight 12, 322 (1 970). 9. G. E. Mueller, Proc. IRE 48, 557 (1960). 10. R. W. Sanders, Proc. IRE 48, 575 (1960). 11. A. G . Smith, Proc. l R E 4 8 , 593 (1960). 12. Radio Spectrum Utilization in Space, Joint Technical Advisory Council of the IEEE ai7d rhe Electronic Industries Association, IEEE, New York, 33 (1970). 13. W. E. Bradley, Astronaut. Aeronaut. 6, 34 (1968). 14. P. L. Bargellini, IEEE Inr. Conf. Commun., Boulder, Colorado 5, 37-25 (Paper 37-4). (1969). 15. W. G. Schmidt, et al., IEEE Int. Conf. Commun., Boulder, Colorado 5, 15-13 (Paper 15-3).(1969). 16. R . W. Rostron, AIAA 3rd Commun. at ell ire Systenis Conf., Los Anyeles, California. Paper 7 0 4 8 I ( 1970). 17. F. S . Johnson, J . Meteorol. 11,431 (1954). 18. M. P. Thekaekara and A. J. Drummond, Nature(London)Phys. Sci. 229, 6 (1971). 19. D. P. LeGalley and A. Rosen, “Space Physics,” p. 673. Wiley, New York, 1964. 20. D. M. Chapin, C. S. Fuller, and G. L. Pearson, J . Appl. Phys. 25, 676 (1954). 21. W. Shockley and W. T. Read, Jr., Phys. Rev. 87, 835 (1952). 22. E. S . Rittner, in “Photoconductivity Conference” (R. S . Breckenridge, B. R. Russell, and E. E. Hahn, eds.), pp. 250-256. Wiley, New York, 1956. 23. J. Lindmayer, COMSATTech. Rev., 2, 105 (1972). 24. A. Meulenberg and D. Curtin, private communication. 25. R . Arndt and L. Westerlund, COMSATTerh. Rev. 1, 117 (1971). 26. R. G. Downing, 5th Photovolraic Specialists, 2, D-7, Conf., Greenbelt, Md., October 1965; R. L. Statler and D. J. Curtin, IEEE Trans. Electron Devices 18, 412 (1971); R. W. Rostron, Energy ConverJion, in press. 27. J. Wysocki, Conf. Record 6th Phorovolraic Specialists Conf. 3, 96 (1967).

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E. S. Rittner, Phys. Reo. 96, 1708 (1954). R. Gremmelmaier, Z . Naturforsch. A 10, 501 (1955). A. R . Gobat, M. F. Lamorte, and G. W. McIver, IRE Trans. Mil. Electron. 6,20(1962). B. Ellis and T. S . Moss, Solid Sfate Electron. 13, 1 (1970). T. L. Tansley, Opto-Electron. 1, 143 (1969). H. Okimura and R. Kondo, Jap. J . Appl. Phys. 9, 274 (1970). D. C . Reynolds, G. Leies, L. L. Antes, and R. E. Marburger, Phys. Rev. 96, 533 (1954). A. E. Potter, Jr. and R. L. Schalla, 6th Photovoltaic Specialists Conf. Record, 1,2434, March 1967. 36. J . Lindmayer and A. Revesz, Solid Sfate Electron. 14, 647 (1971). 37. L. Clark, R. Gale, K. Moore, R. J. Mytton, and R. S. Pinder, Proc. Colloq, Int. Cellules Solaires, Toulouse, July 1970, pp. 605-621, Gordon and Breach, London (197 1). 38. J. Lebrun, Colloq. Int. Cellules Solaires, Toulouse, July 1970, Conf.Record 8th Photovoltaic Specialists Conf., Seattle, August 1970, pp. 33-39. 39. L. Esaki, Phys. Reo. 109, 603 (1958). 40. E. 0. Kane, J. Appl. Phys. 32, 83 (1961). 41. J. J. Tiemann and H. Fritzche, Phys. Rev. 132, 2506 (1963). 42. F. H . Trurnbore, BellSystern Tech. J. 39, 205 (1960). 43. H . Fritzsche, “Tunneling Phenomena in Solids” (E. Burstein and S. Lundquist, eds.), pp. 167-180. Plenum, New York, 1969. 44. B. Pellegrini, Aha Freq. 39,429 (1 57E) ( I 970). 45. P. L. Fleming and L. E. Foltzer, Int. Microwave Syrnp. (G-MTT), Washington, D.C., May 16-20, 1971, Paper XI-7 (unpublished). 46. A. G . Revesz, J. Reynolds, and J. Lindmayer, Solid State Electron. 14, 1137 (1971). 47. W. W. Hooper, R. D . Fairrnan, and N . G . Bechtel, Int. Electron Devices Meeting, Washington, D.C., October 11, 1971, Abstract 3.5, p. 32 (1971). 48. E. S . Rittner, Philips Res. Rep. 8, 184 (1953). 49. A. L. Berman and C . E. Mahle, IEEE Trans. Comm. Technol. 18 (I), 37 (1970).

28. 29. 30. 31. 32. 33. 34. 35.

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Acoustoelectric Interactions in 111-V Compound Semiconductors W. J. FLEMING*

AND

J. E. ROWE

Electron Physics Laboratory, Department of Electrical and Computer Engineering, The University of Michigan, Ann Arbor, Michigan

I. Introduction. ..................................... A. Historical Background and Device Applications. ........................ B. Acoustic Noise Generation Manifested by Microwav 11. General Theory of Off-Axis Acoustoelectric Interactions A. Introduction.. . . . . . . . . . . . . . . . . . ......................... ......................... B. Derivation of the General Dispersi C. Reduction to an Equivalent One-Dimensional Dispersion Equation. . . . . . . . . D. Derivation of the rf Conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Exact Solution of the Acoustoelectric Interaction for Collinear Static Fields. . . . . A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Derivation of the Acousto-Helicon Dispersion Equation . . . . . . . . . . . C. Solution of the Acousto-Helicon Dispersion Equation. IV. Solution of the Acoustoelectric Interaction for Arbitrarily ........... Fields and On-Axis Acoustic-Wave Propagation. . .

.......................... B. Solution for the rf Conductivity.. . . . . . . . . . .

162 166 166 170 174 176 177 185

. . . . . . . . . . 186

C. Solution for the Growth Rate of the Acousto D. Incorporation of Empirical Field Factors into the Theory of Acoustoelectric Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Solution of the Acoustoelectric Interaction for Arbitrarily Oriented Static Fields and Off-Axis Acoustic-Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Introduction.. . . . . . . . . . ......................... B. Solution for the Effective oupling Parameters. . . . C. Solution for the Growth Rate of the Off-Axis Acoustoelectric Interaction. . . . VI. Solution of the Acoustoelectric Interaction for Electron-Hole Carrier Transport and Off-Axis Acoustic-Wave Propagation. . . . . . . . . . . . . . . . . . . . . . . . A. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Solution of the Static Carrier Transport System. . . . . C. Solution for the Growth Rate of the Acoustoelectric VII. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

199 206 206 207 215 234

244

* Present address: Research Laboratories, General Motors Corporation, General Motors Technical Center, Warren, Michigan 48090. 161

162

W. J. FLEMING AND J. E. ROWE

I.

INTRODUCTION

A . Historical Background and Device Applications The collections of charge carriers responsible for the transport of electricity in a semiconductor interact with the crystal lattice and exchange energy. In many cases the collections of conduction charge carriers can be almost regarded as an isolated subsystem of the semiconductor which interacts weakly with the lattice and the properties of the subsystem can be studied separately. In this case, the interactions of the drifting conduction carriers with the lattice are treated as collisions where the carriers gain or lose units of quantized lattice-vibrational energy called phonons. However, if the subsystem of conduction carriers is strongly coupled to the lattice by means of acoustoelectric effects, interactions between the drifting carriers and the acoustic lattice-vibrational modes may give rise to an acoustoelectric gain mechanism. In acoustoelectrically active semiconductors, piezoelectric and deformation potential effects generate internal electric fields which accompany the acoustic modes of lattice vibration. Whenever the conduction carriers are drifting faster than the velocity of sound, the space-charge electric fields of the drifting carriers couple to the acoustic waves of the lattice and acousticwave amplification may occur. Analogous to the electron-field interaction in a traveling-wave tube, the acoustic waves grow in amplitude, therein making possible the realization of a solid-state traveling-wave amplifier. Acoustic-wave amplifiers have recently emerged as an important component in signal processing systems which require long signal delay. The essential elements of the acoustic-wave amplifier consist of a bar-shaped specimen of an acoustoelectrically active semiconductor with ohmic contacts at each end across which the drift field is applied. Acoustic transducers are fabricated directly on top of these contacts, and provide the input and output ports of the amplifier. Since the signals propagate at the sound velocity which is some lo5 times lower than the velocity of electromagnetic waves, a 2-cm long specimen will introduce delay times on the order of 10 psec. Moreover, the existence of the acoustic amplification mechanism compensates for transducer and delay media loss, thereby permitting the development of practical devices. Acoustic-wave amplification was first observed in 1961 by Hutson et al. (Z), using CdS as the acoustoelectrically active semiconductor. For several years thereafter experiments were largely confined to this material because of its superior acoustic and semiconducting properties. The results of these early investigations are discussed in detail by McFee (2). In the course of

ACOUSTOELECTRIC INTERACTIONS

163

these investigations it was found that after sufficient amplification of the acoustic waves, acoustoelectric forces bunch the drifting conduction carrier stream into narrow high-electric field domains which manifest themselves as rf current oscillations. These oscillations have in turn been the subject of investigation, since their presence limits the utility of the acoustic-wave amplifier . Acoustoelectric current oscillations i n 111-V compound semiconductors were first investigated by Bray et al. (3). They found that the presence of a transverse magnetic field dramatically enhances the acoustoelectric instability in high-mobility semiconductors such as n-type lnSb and GaAs. As a result of this observation, Bray et a / . (3) suggesfed that the transverse magnetic field gives greater synchronism between the conduction carrier drift velocity and the acoustic-wave propagation velocity. Following this suggestion, both Steele (4) and Turner et a ] . (5) reported identical theories which show that this is indeed the case. The transverse magnetic field reduces the effective rf mobility of the conduction carriers, thereby decreasing the diffusion relaxation time constant and increasing the dielectric relaxation time constant. Under these conditions maximum acoustoelectric gain can occur at significantly lower drift velocities with correspondingly low dc power dissipation levels. This discovery has stimulated interest i n the acoustoelectric properties of high-mobility 111-V compound semiconductors. Particular attention has been given to n-type InSb which, when cooled to a temperature of 77"K, exhibits electronic mobility values on the order of 1 x lo6 cm2/V-sec. High-gain acoustic-wave amplification has been realized by several investigators (6-8). Typically, in the presence of a transverse magnetic field greater than 3 kG, there exists 60 to 70 dB/cm of electronic acoustic gain at frequencies of I to 2 GHz. However, the electronic gain is offset by an acoustic attenuation loss of 10 dB/cm inherent to the semiconductor, and by transducer loss of approximately 40 dB. Nevertheless, net terminal gain in excess of 10 dB and signal delay times up to 10 psec are obtainable. The aforementioned device depends on the bulk amplification of acoustic waves. a process which is inherently inflexible. Since the acoustic signal is inaccessible during its transit time i n the semiconductor bulk, these devices are confined largely to fixed delay components, whereupon additional circuits are required to further process the signal. On the other hand, the recent development of acoustic surface-wave technology permits multiple direct access to the acoustic waves for signal-processing functions. A variety of microwave system components such as amplifiers, isolators, and phase shifters can be constructed on a single substrate package, therein forming circuits capable of autocorrelation, Fourier transformation, and correlation functions (9).

164

W. J. FLEMING AND J. E. ROWE

B. Acoustic Noise Generation Manifested by Microwave Radiation A degrading phenomenon, common to both bulk-type and surface-type acoustic-wave devices is the generation of spurious off-axis acoustic waves. These off-axis waves manifest themselves as acoustic noise, therein masking the properties of the active on-axis acoustic wave. Active on-axis acoustic waves traverse well-defined paths along principal crystal axes. The characteristics of these waves are the subject of the majority of investigations on the acoustoelectric interaction. In the present work, however, the characteristics of off-axis acoustic waves are studied, and considerable physical insight is made possible by investigating one specific example in detail. Particular attention is given to the acoustoelectric interactions which occur in n-type InSb. This 111-V compound semiconductor is especially interesting due to the myriad of phenomena which manifest the existence of the acoustoelectric interactions. Electrical instabilities such as current oscillation (10,11), microwave noise radiation (12,13) and acoustic-wave noise (14) all are manifestations of the acoustoelectric interactions in InSb. A strong on-axis acoustoelectric interaction dominates the off-axis interactions in specimens of n-type InSb which are longer than approximately 1 cm. In shorter length specimens, off-axis acoustoelectric interactions are nucleated and are manifested by the generation of microwave noise radiation (1.?,24). No acoustic transducers are required to generate this radiation. Electrical contacts are made on the ends of a bar-shaped InSb specimen and a static electric field is applied. If the specimen is cooled to 77°K and a static magnetic field is present, microwave noise radiation is spontaneously generated when the applied fields exceed certain threshold values. The radiation has been conclusively related to acoustoelectric effects by several investigators (10,12-14); it occurs whenever the electric field exceeds a. few volts per centimeter and a magnetic field greater than a kilogauss is oriented transverse to the direction of current flow. A physical model of the radiation process can be developed on the basis of the following observations. Due to the high electron mobility in n-type InSb, the presence of a large transverse magnetic field component gives rise to localized high-electric-field regions at diagonally opposite corners of the crystal (15). As a result, localized impact ionization (16) or hole injection (17) may exist at the localized highfield regions and plasma-type instabilities (18) may occur, but rapid recombination of the nonequilibrium holes would abruptly quench the interaction. Furthermore, it has been found that the maximum intensity of the radiation does not occur directly at the contacts, but rather is observed near the center of the specimen (13). In an investigation of the acoustoelectric current oscillations in long InSb specimens, Seifert (19) found that, under conditions for which the radiation will exist, there is a statistical buildup of acoustic

165

ACOUSTOELECTRIC INTERACTIONS

domains in the bulk of the InSb specimens. These observations indicate that the microwave radiation is dependent on the existence of acoustic noise disturbances. Thus, the presence of both a localized plasma interaction region and a bulk acoustoelectric interaction has been observed experimentally in conjunction with the radiation. The radiation process is depicted in the following way. As shown in Fig. 1, the application of a transverse magnetic field B, creates a region of localized plasma at the edge of the contact. I t is assumed that either plasmatype interactions or simply shot noise acts as a nucleation source which RAUATION EMANATES FROM TME REGION OF BULK ACOUSTOELECTRIC CATMOOE

/

/

FIG.1. Physical model of the generation of radiation by off-axis acoustoelectric amplification.

excites, via piezoelectric forces, acoustic disturbances. These disturbances, represented by the wavevector q, are continuously nucleated and emanate from the localized plasma region into the bulk of the specimen. After sufficient amplification of the acoustic disturbances, acoustoelectric forces on the drifting electrons create transient oscillating space-charge dipoles which act as point radiators and generate the microwave emission. Hence, the acoustoelectric instability by itself is not sufficiently strong to excite the microwave radiation, and large-amplitude acoustic disturbances must first be generated by localized plasma-type instabilities. In the localized plasma regions, the streaming carriers flow in all possible off-axis directions due to Hall-field shortingeffects at the contacts (15); the on-axis direction corresponds to travel along the long dimension of the specimen. Representation of the acoustic disturbances by the set of all possible off-axis acoustic waves takes the contact shorting effects into account. As seen in Fig. 1, the off-axis acoustic wave q propagates in the direction (defined by the inclination angle [) for which the acoustoelectric gain is maximum (20).

166

W. J. FLEMING AND J. E. ROWE

The physical mechanism of the radiation is the electromechanical conversion of acoustic noise energy into microwave energy by means of the acoustoelectric interaction. Thus, it is assumed that the intensity variations of the radiation are proportional to the corresponding variations of the acoustoelectric gain.* In the present work, attention is given to the process of off-axis acoustoelectric interaction. 11. GENERAL THEORY OF OFF-AXIS ACOUSTOELECTRIC INTERACTIONS

A . Introduction

In this section the general equations which describe the acoustoelectric interaction between the streaming carriers and the propagating acoustic wave in a cubic 111-V compound semiconductor will be derived (mks units are used throughout). A small-signal theory which is valid in the bulk of the semiconductor is adequate because of the weak piezoelectric coupling in 111-V compound semiconductors which limits the growth rate of acoustoelectric instabilities. Acoustoelectric coupling can also occur via the deformation potential. However, at the frequencies of interest, f 5 10 GHz, the piezoelectric coupling is more than an order of magnitude stronger than the deformation potential coupling; therefore, these effects are neglected in the present study. Details of the piezoelectric and elastic tensor notation used here are discussed by Mason (21). B. Derivation of the General Dispersion Equation

It is assumed that acoustic disturbances exist in the bulk of the semiconductor and can be depicted as plane waves. As shown in Fig. 2, the acoustic wave propagates in the direction 4 with the displacement

6 = 6'exp(jor - j q * x), where 6' is the initial nucleation value of the acoustic-wave displacement, q = q ( M , -trn& + n.2,) is the wavevector, q = w/u, is the wavenumber, v, is the sound velocity and 1, m, and n are the respective direction cosines of the propagation direction 4 = q/q which is measured relative to the crystal coordinate system x = (xl, x 2 , x3).

* Indeed, recent work by T. Ishii [Radiation of electromagnetic waves in piezoelectric semiconductors with amplified sounds. J . Phys. SOC.Jup. 32, 574 (1972)l verifies that the conversion of acoustic energy to microwave radiation is sufficiently intense to account for the observed radiation levels. The radiation is generated by space-charge dipoles, occurring in the current flow, which are created by acoustoelectric forces which stimulate the afore-mentioned interaction.

167

ACOUSTOELECTRIC INTERACTIONS

FIG.2. Acoustic-wave orientation in the crystal coordinate system (xl, x 2 , xj).

The semiconductor provides an elastic medium wherein the acoustic displacement 5 is related to the stress T by Newton’s law of motion,

a2ri

p

-=In

dt2

C~T;~ ax, ’

where i and k index from 1 to 3 and pm is the lattice mass density. An electric field perturbation E, supported by the drifting carriers, and the acoustic disturbance 5, supported by the lattice, are coupled together by the piezoelectric equations of state. It is convenient to write the equations of state in the contracted subscript notation (21) as follows:

T, = c,, S, - e,, Ei

(3)

s, + E i k Ei ,

(4)

and Dk = e k ,

where r and s index from 1 to 6, i and k index from 1 to 3, c,, is the elastic tensor, T, and S,yare, respectively, the stress and strain written in contracted notation, e,, and & i k are, respectively, the piezoelectric tensor and the lattice dielectric tensor, and Dk and E, are the electric flux and field vectors. I n the contracted notation, T, and S, are related, respectively, to Tikand Sik in the following manner (21):

Tr=Tii,

S,=Sii

forrs3,

i=r

T, = T i k ,

s, = 2 s j k

for r 2 4,

i#k

(5)

168

W. J. FLEMING AND J. E. ROWE

and

For cubic I TI-V compound semiconductors (zinc-blende structure, crystal class 4 3m), the physical parameters c r S , eir and & i k exhibit a high degree of symmetry, namely (21) c11 c12 c12

0 0

c12

0 0

O

C

0

4

4

0

0 0 0 0

O e 1 4

=

ri

0 ;&

0

O C 4 ,

0 0 0 el4 and &ik

(7)

c44

0 0 0

0 0

0

0 0

0" El I

1.

(9)

Equations (1)-(9) are combined t o give the following set of six equations:

and

[%,1

0 =-jqel4[;

n m

7 a][:]

r,

where the components of the effective elastic tensor a are given by

+ (m2 + n2)cd4, a Z 2= m2c1 + ( I z + n ' ) ~ ~ ~ , a33= nZcl + (12 + r n ' ) ~ ~ ~ , a, 1

=

Pc, 1

a12 = W c 1 2 a13

and

=

+ C44L -k

c44>3

(1 1)

ACOUSTOELECTRIC INTERACTIONS

169

For convenience, Eqs. (10) and (1 1) are rewritten as c‘g = a .

-

6 - j - e14 ( e E) 4

(13)

where c’ = p , ( o / q ) 2 = pmvs2is the effective elastic constant, = e l l is the lattice dielectric constant, and the matrices a and e are as given below:

[;;; ‘12

a=

[. j. 0

‘13

%;

eA

n m 0 1 m 1 0

(15)

Hence the propagation of the acoustic waves defined by Eq. ( I ) is governed by the piezoelectric wave equations, Eqs. (1 3) and (14). A general acoustoelectric dispersion equation is obtained by determining the effective permittivity E‘ of the semiconductor, where E’ is defined by the relation D = E / E’E. The effective permittivity is established solely by the electric field fluctuations supported on the conduction carrier subsystem. If it is assumed that all field fluctuations can be represented by plane waves as in Eq. (l), the wave equation for electric field fluctuations is obtained from Maxwell’s equations, and can be written as

where q is the wavenumber, c1 = ( p l E , ) - ’ ” is the velocity of light in the semiconductor, p l is the lattice permeability, and E , is the lattice dielectric constant. Solution of the transport equations yields the rf conductivity u which is defined by J = u -E. (The details of this solution are discussed i n Section I1.D.) Substituting this result into Eq. (16) gives the effective permittivity E’ which is defined by

where I is the identity matrix and 44. E is a dyadic product. Note that the rf conductivity u must be derived in the crystal coordinate system x = (xl, x 2 , x3). It is most convenient to derive u in a different coordinate system; for example, the system r = (x, y , z ) where the wave propagation direction 4 is parallel to the 2-direction, the transverse magnetic field component B, is parallel to the ?-direction and the carrier drift velocity is in the x-y Lorentz force plane. Then a rotation matrix M which rotates the (x, y , z ) system into the (x,, x2, x3) system must be determined such that r = Max.

170

W. J. FLEMING AND . I . E. ROWE

If u is the rf conductivity in the (x, y, z ) system, it followsthat u’ = M-’ * u *M is the rf conductivity in the (xl, x 2 , x3) system. When Pq. (17) is used, the piezoelectric wave equations, Eqs. (13) and (14), become (a

- c’l) - 6 - j e14 - (e - E) = 0 4

(18)

and ( E ~ E-‘ c l I). E +,jqe,,(e.

5) = 0.

(19)

The general acoustoelectric dispersion equation follows directly from the simultaneous solution of Eqs. ( 1 8) and (19) and can be written as

-

det[(a/c’ - I). C 1 (E’ - I) - ~ ’ e ] = 0,

(20)

where K’ = e:4 /c’E~is the electromechanical coupling constant and e - l is given by

(21) If no piezoelectric coupling exists, x2 = 0 and the piezoelectric equations are no longer coupled, yielding the dispersion equations det(a -dI) = 0 and det(d - I) = 0. Inspection of Eq. (21) shows that, if the acoustic wavevector 4 lies in any plane formed by the unit crystal axes, any combination of I , rn, and n will contain at least one zero and e - ’ is undefined. I n practice, therefore, whenever e - ‘ is undefined it is more convenient to write Eq. (20) as

-

det[(E’ - I) - t i 2 e * ( a i d - I)-’ e ] = 0.

(22)

C. Reduction to an Equirialent One- Dimensional Dispersion Equation The complete solution of the general acoustoelectric dispersion equation is extremely complex and simplifications must be made in order to obtain mathematically tractable results. When the direction of wave propagation coincides with a principal crystal axis such as a (100) or ( I 10) direction, the acoustoelectric dispersion equation can be easily solved. However, if the direction of wave propagation is in an arbitrary off-axis direction, it i s expedient to use an equivalent one-dimensional acoustoelectric dispersion equation. The derivation of the desired result follows. When the relation J = E is used, the wave equation, Eq. (16), and the second piezoelectric equation of state, Eq. (l4), can be combined, thereby yielding the following result: us

171

ACOUSTOELECTRIC INTERACTIONS

It is convenient to define a relaxed permittivity tensor cR and a piezoelectric polarization field vector 8, as A

c R = &[(I

+ J ~ ~ / w E ~and)

With these definitions and the relation 4

G ,6 jye,,(e = W / Z I ~Eq. ,

*

&)/el.

(24)

(23) becomes

The longitudinal electric field EllA E . 4 and the transverse electric field E, 4 E x 4 can be obtained directly from Eq. (25). Taking the scalar product of Eq. (25) with 4 makes the left-hand side zero and yields the longitudinal electric field Ell

+ E,(ER

*

t',). 4 .

Taking the cross product of Eq. (25) with the transverse electric field

4

and noting that

(26)

4

x

4

=0

gives

Although Eq. (27) is not an exact solution for E,, since the electric field also appears on the right-hand side, it is taken as a reasonable estimate for the magnitude of E,. It is clear that El is reduced by a factor of ( L ) , / C ~ ) *z l o p 9 ; this occurs because of the electromagnetic nature of the transverse electric field components. On the other hand, the longitudinal electric field Ell given in Eq. (26) is comparable to the magnitude of the piezoelectric polarization field and will be dominant in the acoustoelectric interaction. I n fact, if the electric field is purely longitudinally polarized, the wave equation reduces to Gauss' law; this is called the quasistatic approximation. If the quasistatic approximation is used. the equivalent one-dimensional acoustoelectric dispersion equation for off-axis waves can be derived from the piezoelectric wave equations, Eqs. (13) and (14). Since only the longitudinal field components are significant, the electric field flux density DII is related to the electric field E l l by the simple expression Dll = - ( ~ l l / j ( o ) E ~ l ~

(28)

where o , ~is the longitudinal component of the rf conductivity tensor u written in the carrier transport coordinate system (x, y , z ) with 4112. Hence, the longitudinal electric field components i n the crystal ( x l ,x 2 , x 3 )coordinate system are Ell= El14= EII(12,

+ n?t2 + d 3 ) .

(29)

172

W. J. FLEMING AND J. E ROWE

It can be shown (22) that the piezoelectric force term on the right-hand side of Eq. (13) has only a perturbation effect on the normal acoustic modes of vibration. Thus, the normal modes of acoustic vibration can be assumed to be only slightly affected by the presence of Elland the zeroth-order normal modes are determined by the uncoupled eigenvalue solutions for (a - c’l).

6 = 0.

(30)

Here, a is defined by Eq. (15) and cn = pmu$ = c’ is any one of the three possible eigenvalue solutions (effective elastic lattice constants in the absence of piezoelectric coupling) which have the corresponding eigenvectors g A which in turn represent any one of three possible acoustic waves. The set of three possible acoustic waves consists of one which is called the longi(3 z 1 and two other waves which tudinal (compressional) wave because are called the fast- and slow-transverse (shear) waves because g,. 4 NN 0. Note that the approximate eigenvalue solutions obtained from Eq. (30) are correct to the order of ef4/(EIaik) z When the piezoelectric force term is included as a perturbation and the quasistatic approximations of Eqs. (28)-(30) are used, the piezoelectric wave equations, Eqs. (13) and (14), become

perturbation term

and

Here, kA = (11,t 2 ,13)Ais any one of the three acoustic-wave eigenvectors and cAis the corresponding eigenvalue. Squaring both sides of Eq. (31) yields

.

first-order perturbation term

negligible term

If the first-order perturbation term is retained and the negligible term is dropped, a perturbation expansion of the square root of Eq. (33) can be made which yields

ACOUSTOELECTRIC INTERACTIONS

where the acoustic displacement scalar 51

A (51 *

5A)”2

173

has been defined as = 151

1.

The right-hand side of Eq. (32) represents the piezoelectric contribution to the electric field but, since the quasistatic approximation is valid, only the longitudinal component of polarization field enters into the acoustoelectric interaction. Thus, taking the scalar product of Eq. (32) with 4 yields the longitudinal field equation

If Eqs. (34) and (35) are combined by elimination of the scalar variables and E,,, the one-dimensional acoustoelectric dispersion equation is obtained, namely, P m o2- I)(]% + 1) - 2 = 0,

(2

where by

K~

is the effective electromechanical coupling constant which is given K’

= ep2/&,ci.

(37)

I n Eq. (37), c1 is the effective lattice elastic constant determined from Eq. (30) and e p is the effective piezoelectric coefficient given by

Since the piezoelectric matrix e is symmetric [see Eq. (15)], the dyadic identity, (e . 4). = (e * &A). 4, holds and is used to obtain Eq. (38). When the values of e, 4 and t1 are substituted into Eq. (38). i t can be written explicitly as 2(mn5, e p = e14

+ / t i t 2 + lmt,), 15iI

(39)

r3

Here, the subscript A denotes that c1, i2, and are the components of the acoustic-wave eigenvector corresponding to the eigenvalue ci [as determined from Eq. (30)] and /, m, and n are the direction cosines which define the acoustic-wave propagation direction 4. The dispersion equation determines the propagation characteristics of‘ the acoustic wave. Equation (36) is the dispersion equation for the onedimensional acoustoelectric interaction and is solved by means of a perturbation procedure. A convective-type instability with phase velocity i n the neighborhood of the sound velocity is considered. Deviations from the sound velocity are small and the wavenumber can be expanded as q

% f3/2Js

+j a ,

I x I < w/u,,

(40)

174

W. J. FLEMING AND J. E. ROWE

where u = aRe+ jut,,, is complex. The acoustic-wave displacement, given by Eq. (I), will vary as exp[ccR,(q* x)]. If uRe> 0, the acoustic wave exhibits spatial growth. Substituting Eq. (40) into Eq. (36) and solving for Re(a) = aRe yield the acoustic-wave growth rate, (41) Examination of Eq. (41) shows that the growth rate of the acoustoelectric interaction depends primarily on the longitudinal rf conductivity (T,, . I n the next section, the transport and field equations which determine (T,, will be given. D. Derivation of the rf Conductivity

The degree of generality of the conduction carrier transport equations which yield the rf conductivity determines the complexity of the theoretical analysis. There is a hierarchy of special conditions which must be considered either for applicability or simply for utility. I n the present work, the transport equations are developed under special conditions of restricted validity and not only is the mathematical analysis simplified, but the simplifications give valuable insight into the physical basis of the acoustoelectric interaction. The following assumptions are utilized in the present analysis (these assumptions are applicable for the conditions of practicable acoustoelectric device operation) : 1. Quantum effects are negligible and a classical description of the carrier transport, which ignores nonisothermal rf effects, is adequate. 2. Nonlocal effects, such as cyclotron resonance, Landau damping, and intercarrier Coulomb interactions, are negligible and a hydrodynamical model of the conduction carrier transport is utilized. 3. The transport equations are linearized by considering only small-signal perturbations X from the static solution X , of all dynamic variables X u . Perturbations are taken i n the form

Xu(r,0

=

Xdr)

+ .Ur, 0

(42)

and are substituted into the field and transport equations. 4. First-order perturbations are equated and solutions for the rf conductivity are found by assuming that the perturbation can be represented by a plane wave (finite boundary effects are ignored) of the form X(r, r)

= X’(r)exp(jwt -

,jq*r),

(43)

where q is the wavevector of the perturbation which is measured in the carrier transport coordinate system r = (x, y , z).

ACOUSTOELECTRIC INTERACTIONS

175

If the above assumptions are used, a hydrodynamical description of the rf conductivity is obtained. The drifting carrier stream and attendant spacecharge waves are described by the equation of momentum conservation, Faraday's law, and the equations of continuity of current which are, respectively [taking small-signal perturbations as indicated in Eqs. (42) and (43113 CV=T

Q, (E + U O x B + v

m

x B,)

qxE=wB

+ j -V T 2 Nq, NO

(44) (45)

and

where E, , J, and V are defined by

E o = p ~ l . ~ g . J o = Q e N o ~ o , V = V + ~ ( W - U , . ~ ) . (47) Here u, (the carrier drift), No (the carrier concentration), E, (the electric field), B, (the magnetic field), and J, (the current density) are the static equilibrium transport and field variables; v, N, E, B, and J are the corresponding first-order perturbed values; the assumed-constant phenomenological constants v, (33, m*,z ' ~ ,and f ; are, respectively, the momentumrelaxation collision frequency, the electron charge, the effective carrier mass, the average thermal velocity of the carrier, and the trapping factor (which is the fraction of space charge Q, N which arises from the drifting conduction carriers); and po is the static drift mobility tensor which must be calculated from a knowledge of the applied field conditions. Since all other parameters are known, Eqs. (44)-(46) are combined to yield one equation which is only a function of v and E, namely,

Here the following definitions have been made :

and

a, = w - j ;u()' q.

176

W. J. FLEMING AND J. E. ROWE

Equation (48) can be rearranged into the form v = p - E and the rf mobility p is obtained. Combining Eqs. (46) yields the result

Equation (49) is only a function of v (all other parameters are specified) and it can be written as J = p * v, where p is the rf charge density. Combining Eqs. (48) and (49), which are written respectively as v = pa E and J = p - v , yields J = p - ( p * E) = E, where u = p - p, the rf conductivity, is the desired result. The analysis can be extended to include the streaming of different carrier species i by assuming that each species separately satisfies its own continuity equation, q . Ji - w Q i N i= 0. In this case, an aggregate rf conductivity can be defined simply as u = utot= u i ,where Ji = u i E and J,,, = Ji . The rf conductivity ui for each charge species i is still obtained from Eqs. (48) and (49); however care must be taken to assure that the proper field and transport variables are assigned to each species. (Note that the static drift velocities of the carriers in a many carrier system must be obtained from a self-consistent analysis of the dc transport equations.) Some general comments are in order here. First, the trapping factorf; represents the fraction of space charge which is mobile and takes into account the effect of the acoustic wave on the electrons residing in bound states (either donors or acceptors) which exist in the energy gap. The trapped space charge is equal to (1 - f ; ) Q , N and it is assumed that charge bunching in the bound states is in phase with the charge bunching in the conduction band. In this case,f, is a real number between 0 and 1. For in-phase charge bunching to occur, the bound states must reach equilibrium with the conduction band in time intervals which are short compared to the period of the acoustic wave. Finally, the extension of the analysis to include different charge species should be qualified. Different charge species i will separately obey their own continuity equations only when their recombination times are long compared to the period of the acoustic wave. For typical acoustoelectric device operation, the first comment regarding trapping effects is restrictive, especially at microwave frequencies; however, the latter comment is always well satisfied. u

s

xi

xi

INTERACTION FOR 111. EXACTSOLUTION OF THE ACOUSTOELECTRIC COLLINEAR STATICFIELDS A . Introduction Although a simplified one-dimensional dispersion equation was derived in Section II,C, it is instructive to solve the general dispersion equation of Section II,B. The special case of acoustic-wave propagation coincident with

I77

ACOUSTOELECTRIC INTERACTIONS

the ( I lo) crystal direction will be solved exactly. This analysis has been motivated by reports of a distinct mode of acoustoelectric interaction in n-type InSb which depends on the presence of a magnetic field oriented parallel to the direction of current flow (13,23). It is first shown that acoustic waves propagating along a (1 lo) crystal axis may possess both longitudinal- and transverse-field components of piezoelectric coupling. The parallel magnetic field does not affect the longitudinal wave interaction. However, a bulk-type acoustoelectric interaction may arise from the coupling of the transverse electric field components of the interaction between a helicon wave supported by the streaming electrons and an acoustic wave supported by the lattice. This interaction will be called the acousto-helicon interaction. There has been some preliminary analysis of this type of interaction ( 2 4 ) ; however only the simplest case is considered, namely, the interaction between the helicon wave and an acoustic wave propagating along a (100) crystal direction. For the (100) direction of wave propagation, two of the acoustic waves are degenerate and cannot be distinguished. Moreover, no longitudinal piezoelectric coupling exists and the acousto-helicon dispersion equation is greatly simplified (24). On the other hand, for the situation of experimental interest when wave propagation coincides with a ( 1 10) crystal direction, the acousto-helicon interaction has not yet been investigated. When the general theory of the acoustoelectric interaction described in Section 1I.B is used, the derivation of the acousto-helicon dispersion equation in (1 10)oriented lnSb can be described. B. Derivation of the Acousto- Helicon Dispersion Equation

Assume that the long dimension 2 of the lnSb specimen coincides with the [ I 101 direction, then 2 = ( I , 1, O)/J2. By symmetry, identical results will be obtained for any arbitrary (110) axis. Hence, for on-axis wave propagat ion, 4 = 2 = (1, 1, oyJ2, (50) whereupon the components of the effective elastic tensor a of Eq. (15) become a,, = a 2 2

= (c11

and 0 1 2 = (c12

+ c44)/2.

+ c44)/2,

a13

a33 =

c44

= a23 = 0.

(51)

In order to determine the effective eigenvalues cA, the eigenvalue equation (a - ~ ‘ 1 )6- = 0 must be solved, where a is defined by Eq. (15). Equations (51) are substituted into the eigenvalue equation, thereby yielding a11

- c’

a12

0

0

a33- c‘

(52)

178

W. J. FLEMING AND J. E. ROWE

The characteristic equation of Eq. (52) is (a33- c’)[(a11

- c’)2 - a f 2 ]= 0,

(53)

which has the eigenvalue solutions c,1 = a33 = c44,

and The corresponding eigenvectors kn are found by back substitution of each eigenvalue cA= c’ into Eq. (52) and these are represented as

kL1 =(O,

0, 11,

ka2 = (1,

1, O h

and

kA3 = (1,

- 1,O).

(55)

Since 4 . kd1 = 4 - kL3 = 0, waves 1 and 3 are transverse acoustic waves; since cd1 > c d 3 ,wave 1 is the fast-transverse wave and wave 3 is the slowtransverse wave; and since 4 * {, = I , wave 2 is the longitudinal wave. A normalized piezoelectric polarization field 8, is defined as

where e is given by Eq. (15). Thus, the polarization fields associated with each of the acoustic waves are, respectively,

d,,

= (1,

1,O)/J2,

b,,

=

(O,O, I),

and

b,,= (O,O,

0).

(57)

Wave 1, the fast-transverse wave, possesses a purely longitudinal polarization field (since b,, * 4 = 1); wave 2, the longitudinal wave, possesses a purely transverse polarization field (since b,,. 4 = 0); and wave 3, the slowtransverse wave, does not possess a polarization field. Hence, there is a possible acousto-helicon interaction with the longitudinal acoustic wave. The rf conductivity is derived in the conduction carrier coordinate system (x, y , z ) which is shown in Fig. 3. For simplicity all field and transport variables are assumed to coincide with the A-direction. It is assumed that electrons drift with velocity uo = uoA, parallel to the magnetic field B, = Bll = Bll2. Substitution of these quantities into Eq. (48) yields

where G D= o,f/v = w2/q2f,Dis the Doppler-shifted diffusion frequency; yf = G f / o = 1 - f t u o / u , and y = W/w = 1 - uo/u, are, respectively, the

ACOUSTOELECTRIC INTERACTIONS

179

A

x3

A XI

J

FIG. 3. Field configuration for the acousto-helicon interaction.

conduction and the total space-charge drift ratios: ti,, =jioB,,, and jio = p o v / i j = p = Q,/m*ij. [Note that the approximation q FZ w/u, IS used in Eq. ( 5 8 ) . ] Equation (58) is rearranged into the form v = p - E and the rf mobility tensor p is found. Similarly, Eq. (49) can be written out, combined with Eq. (58), and arranged into the form, J = E; whereupon the rf conductivity tensor u is given by us

0

0 (59)

where

C0 = a0v/ij = Q, No ,Go,

v = v + j G = v +joy, lib/ - jdO,), byy= bzz= y/(l + hi),

bxx

=

and

When the wave equation [Eq. (17)] is used, the rf conductivity must be expressed in terms of the crystal coordinates x = ( x l ,x 2 , x3). Inspection of Fig. 3 shows that the r = (x, y , z ) system is simply rotated 45" about the

180

W. J. FLEMING AND J. E. ROWE

1S3-axis [since L = (1, 1, O ) / J 2 is the long dimension of interest here] and the rotation matrix M, defined by r = M * x, is given by

(60) Thus the rf conductivity in the ( x l ,x 2 , x 3 ) system becomes u' = M-' us M, where u is defined in Eq. (59). After performing the transformation, it is found that u' can be written in the form 0'

where

5

[

a'12

4

2

-a;3

4 1 = (oxx + a,,)/2, a;

=

0;3]

4,

- 4 3

6 3

4

4

2

(61)

9

3

= (gxx.-

0,,)/2,

- a,,/J2

and a;3 = O Y Y .

In the acousto-helicon interaction it is assumed that 9112, that is, = (1, 1,O)/J2; thus when u' is taken from Eq. (61), the wave equation [Eq. (17)] becomes

(3

where

and Since the direction cosine n of ij equals zero, the general acousto-helicon dispersion equation is obtained from Eq. (22). The solution of Eq. (22) requires knowledge of the elastic tensor a and the effective piezoelectric tensor e. For wave propagation 4 = (1, 1, O)/J2, these tensors reduce to the following:

ACOUSTOELECTRIC INTERACTIONS

181

,,

where a , a 1 2 ,and a33 are defined by Eq. (51). If Eqs. (63) are used, the expression which appears on the right-hand side of Eq. (22) is evaluated and it becomes, after algebraic simplification,

However, as seen in Eqs. (54), the eigenvalues cA1and cA2are equal to, respectively, a33and (a, + a12).Thus, the terms a; and a;, can be written as

,

,

a; 1 = 1/(2C,,/C’ - 2) and Ui3

= l/(c,*/c’

- 1).

(65)

where cA1and cA2are the eigenvalues which correspond to, respectively, the fast-transverse and the longitudinal acoustic waves. When Eqs. (62), (64), and (65) are used, the general dispersion equation [Eq. (22)] becomes

where - 1 - t i 2 / ( 2 C A l / C ’ - 2),

=

El;

&y3

EY2 = C i 2

- K2/(2CIl/C’- 2),

ag3 =

- 1 - K2/(CA2/C’ - I),

ti2

=&i3,

= e:L/c’&,,

and c‘ = p m d / q 2 .

If Eq. (66) is written out, the general dispersion equation is obtained and, after simplification, it can be written as (&;I

+

E ; ~ ) [ E ; ~ ( E; I E;Z)

+ 2&;:]

= 0.

(67)

182

W. J. FLEMING AND J. E. ROWE

There exist two uncoupled solutions to Eq. (67). The first solution can be written [using Eqs. (61) and (62)] as EY1

+ &Y2

=

[ ( j Z- 1) -

lc2

(CdllC’ -

1)

]=o,

and the second solution can be written as

where A1 = j a y y / m + l q 2 c I 2 / o 2- 1

and A2 = Oyz/WEl.

It can easily be shown that Eq. (68) is the dispersion equation for the quasistatic interaction between the space-charge wave and the fast-transverse acoustic wave, and Eq. (69) is the desired acousto-helicon dispersion equation. Substitution of the expressions for crxx defined by Eq. (59) and c‘ = pmw2/q2 into Eq. (68) yields the usual quasistatic acoustoelectric dispersion equation [e.g., Eq. (8-21) of Steele and Vural (24)],

where v, = (cd1/pm)1/2= ( ~ ~ ~ /is the p ~sound ) ~ velocity / ~ of the fast-transverse = 0-frquo, wave, u p= (Q,2No/e,m*)1/2is the plasma frequency, 0 = 0 - q u o , f, is the trapping factor and ti2 = e:4/~44el I S the electromechanical coupling constant. It is convenient to rearrange the acousto-helicon dispersion equation [Eq. (69)] into the form

”/

(A1

- Az)(A1

+ AJ

(71)

Substitution of the expressions for o y yand o y z defined by Eq. (50) and c’ = p m d / q 2into Eq. (71) yields the acousto-helicon dispersion equation, namely,

183

ACOUSTOELECTRIC INTERACTIONS

+

+

where us = ( ~ ~ ~ / p , , = , ) ~[(c,, ” cI2 2~~~)/2p,,,]”’ is the sound velocity of the longitudinal wave, cI is the velocity of light in the semiconductor medium, w, = vbll = (Q,/m*)BII is the cyclotron frequency, W = w - quo ] electromechanical and ti2 = e:,/ca2 E~ = e:s/[&l(cl + c I 2 + 2 ~ ~ ~ ) is/ 2the coupling constant. Equation (72) is the exact acousto-helicon dispersion equation for ( 1 10)-oriented wave propagation. It should be noted that Steele and Vural (24) have analyzed the acoustohelicon interaction for wave propagation along a (100) crystal direction. For this direction of wave propagation, the analysis is greatly simplified and the acousto-helicon dispersion equation [Eq. (8-7 I ) of Ref. (24)] becomes

(2, )

(A1 f /I2) 7- 1

= ti2,

(73)

where A , , A 2 , and c‘ are defined in Eq. (69); cA1= c 4 4 , K’ = e:,/c,,&, , and us = (C44/p,,,)1’2is the sound velocity of the shear acoustic wave. C . Solution of the Acousto-Helicon Dispersion Equation

In this section, the acousto-helicon dispersion equation, Eq. (72), is solved by means of a perturbation procedure. Equation (72) is rewritten as

where A4 A, Li A3 - jv v k jw,’

Ax 2 A, - j ’

CI2

A3 = 1 - q 2 w2

and

A4 V v2 + w,2 ’

V = v+jS,

A4 = wP2W/w2.

A convective-type instability with phase velocity in the neighborhood of the sound velocity is considered. Deviations from the sound velocity are assumed small and the wavenumber is expanded as

q

= W/D, + j a ,

l a ( 4 w/u,,

(75)

where z = uRe+ joc,, is complex. If a convective instability exists, ocRe must be positive. Substituting Eq. (75) into Eq. (74) and solving for Re(cc) = aRe yield the following:

184

W. J. FLEMING AND .I. E. ROWE

where all terms in the quotient A X / L A, are evaluated for q = o / u , , i.e., the perturbation terms ct in this quotient are negligible. Thus, the factors A3 and A4 become [for ( c J / v J 2 % 11 A3 =

and

-(C,/U,~)~

(77)

A4 = w p 2 y / o .

Equation (76) is valid as long as the following inequality is satisfied: 11\31

If Eq. (77) and I can be written as

%

lh/Vl*

(78)

w 1 0 1 (the most restrictive case) are used, Eq. (78)

9

(;)2

($

(79)

where uo= ( o ~ o ~ )uT” is~ the , electron thermal velocity, and c J is the velocity of light in the lattice. At microwave frequencies, Eqs. (78) and (79) are well satisfied. When the definitions of Eq. (74) are used, the quotient in Eq. (76) is found and, after some algebra, is written as

where 6,

and

&/A3 V

a,

V2/( Vz

+ oC2)

Since the inequality of Eq. (78) holds, the parameter 6, is much smaller than unity and Eq. (80) can be rearranged by retaining first-order perturbations of 6, and it becomes Ax

A-A+

1 z-(1 A,

+j6,av).

Equations (76), (77), and (81) are combined and the growth rate of the acousto-helicon interaction is given by

where y = 1 - uo/us,

Vie = 1 +bf,

vim = w,(l - b i t )

and b;l = bll/(l

+w,~)”~,

bll = W , / V = Q,Bll/m*,

O,

=w ~ / v .

Although the growth rate is positive, indicating a convective instability, for uo > u s , the growth rate is diminished by the factor ( v , / c , )z~ Thus, at the frequencies of interest given by Eq. (79), only vanishingly small

ACOUSTOELECTRIC INTERACTIONS

185

growth rates are possible for the acousto-helicon interaction. This interaction cannot, therefore, account for the existence o f the acoustoelectric interactions enhanced by the presence of a parallel magnetic field. Nevertheless, the derivation and solution o f the acousto-helicon dispersion equation serve as an illustrative example for the application of the general analysis of Section

11,B.

Iv. SOLUTION

OF THE ACOUSTOELECTRIC INTERACTION FOR ARBITRARILY AND ON-AXIS ACOUSTIC-WAVE PROPAGATION ORIENTED STATIC FIELDS

A . Introduction

A general theory of acoustoelectric interaction was developed in Section 11. An analysis as well as a solution of this theory, specialized for the case of

on-axis wave propagation along the (100) crystal axis, is the subject of this section. Whenever the transverse component of the applied magnetic field and the sample current in InSb exceed certain threshold levels, acoustic domains form in sufficiently long-length specimens o f ( 1 10)-oriented n-type InSb. Although the presence of these acoustic domains limits the utility of the acoustoelectric amplification process (6,7) the domains are interesting in themselves. The acoustic domains are manifested by the appearance of rf current oscillations and microwave noise radiation which are the subject of several related investigations (ZO-ZJ). As discussed in Section 1,B, it has been found experimentally that both phenomena possess nearly identical applied field threshold dependences and exhibit two distinct modes of operation. Mode I occurs for high current values and low magnetic field strengths, whereas Mode 11 occurs in the opposite limits. Recently it has been concluded by several investigators that, although a magnetic field enhancement of the hydrodynamical theory of Steele ( 4 ) and Turner et d.(5) can account for Mode I1 operation, more detailed microscopic theories (6,25,26) are required to adequately account for the existence of both Modes I and 11. The results presented here will show that a hydrodynamical theory of the acoustoelectric interaction does not only account for both Mode I and Mode I1 operation, but also yields valuable insight into the physical basis of the acoustoelectric effect in InSb. In order to obtain a tractable solution, the quasistatic approximation is made wherein the rf electric field components, transverse to the direction of wave propagation, are neglected. As shown in Section II,C, the analysis reduces to a one-dimensional problem and the growth rate of the acousto-

186

W. J. FLEMING AND J. E. ROWE

electric interaction is given by Eq. (41). The growth rate is primarily dependent on the determination of the longitudinal rf conductivity o,,which in turn is found from a solution of the field and transport equations, namely, Eqs. (48) and (49).

B. Solution for the vf Conductivity The configuration of the applied fields and transport variables is defined in the conduction carrier coordinate system (x, y , z ) which is shown in Fig. 4. It is assumed that only electrons are present. The electron drift velocity uo is directed along an arbitrary direction [' in the 2-9 Lorentz force plane. For on-axis acoustic-wave propagation, the acoustic wavevector q is taken parallel to the 2-direction which in turn is parallel to the long dimension 2 of the crystal. Since a hydrodynamic theory is utilized and the quasistatic approximation is made, the parallel component of applied magnetic field does not enter into the longitudinal rf conductivity and is ignored. For convenience, since InSb has an isotropic band structure, the transverse component of applied magnetic field B, is chosen in the %direction. Inspection of Fig. 4 shows that

B,=B,i, and

+

q=qA

uo = uOx2 uo,j = (uo cos [')a - (uo sin

[')9.

(83)

h

Y

Z

FIG.4. Field configuration for the acoustoelectric interaction with arbitrarily oriented static fields [shown in the conduction carrier coordinate system (x, y , z ) ] .

ACOUSTOELECTRIC INTERACTIONS

187

Substitution of Eqs. (83) into Eq. (48) yields

0 )is the Doppler-shifted diffusion frequency; where OD = wD(?/ti) = o*/(qY; yr = W,/w = 1 - f t u o J u , and y = W/o= I - uox/u, are, respectively, the conduction and the total space-charge drift ratios; b = ,Go B, and iio = p o v / ? = Q,/(m*i). Note that the approximation q z w/u, is valid in Eq. (84) since all perturbation terms c( [from Eq. (40)] are reduced by the in the solution of the dispersion equation [Eq. (41)]. factor 12% Equation (84) is rearranged into the form v = p - E and the mobility tensor p is given by

where

and

Substitution of Eqs. (83) into Eq. (49) yields the rf charge density p which is given by

where po = Qe N o , p X z = I/y,, p y x = f, 0 % )and pyV= p Z z = 1. The rf conductivity is determined directly from Eqs. (85) and (86) and is given by

188

W. J. FLEMING AND J. E. ROWE

where

and = y(det,).

Q,,

Although the complete solution for the off-axis acoustoelectric interaction could now be obtained from Eqs. (17), (20), and (87), the quasistatic approximation is utilized here. The value of el, is found directly from Eq. (87) and is given by ell = 0,

eJdet,

=

ao/[yf(l

+ 6’) - jw/OD].

(88)

It is convenient to rewrite Eq. (88) into the form wR &I

ell =

Y~ v‘ - j o b D’

(89)

where oR= C J , / E ~ is the dielectric relaxation frequency, w D = V U , ’ / ( U , ~ ~ , ) is the diffusion frequency at synchronism, v’p ( V / v ) [ l + ( b v / i ~ )is~ a] factor which takes into account rf magnetoresistance and electron inertial terms, and V / v = 1 + j w , . When the magnetic field is zero, b -+ 0 and v’ -+ S / v , rf magnetoresistance is no longer present. When electron inertial terms are neglected, o,-+ 0, the factor v‘ becomes equal to 1 + 6’ in accordance with the theory of Steele ( 4 ) and Turner et al. ( 5 ) .

C . Solution f o r the Gro\d-th Rate of the Acoustoelectric Interaction Defining v’ = vie =jv;,,, and substituting Eq. (89) into Eq. (41) gives the desired expression for the acoustoelectric growth rate :

where vLe = 1

+ bf2, b’2

W,

Y=1

v;, = w,(I- b”),

b’/( I

=W/V,

- uox/us,

+ w,’), b

= po

Yf = 1

B, ,

- ftUOX/DS,

ACOUSTOELECTRIC INTERACTIONS

and

w

wR/o

189

+ w/oD.

Equation (90) can be rearranged into a more meaningful form as

where wR/(l

wk

+ bI2),

W’

w;l/w

+ w/wb

and A

wb = wD( 1

+ b ’ 2 ) /1[ - y

f

w,( 1 - b”)wD/w].

In Eq. (91), wk and wb are identified respectively as the effective dielectric relaxation frequency and the effective diffusion frequency. For simplicity, it is assumed that trapping effects are negligible and that space charge arises solely from the conduction electrons which drift along the direction of acoustic-wave propagation 4 (the solution for off-axis wave propagation is described in Section V). Moreover, for on-axis wave propagation in (1 10)-oriented InSb, Eq. (57) shows that the fast-transverse acoustic wave is piezoelectrically active in the quasistatic interaction. When these conditions are utilized, a number of the defined terms in Eqs. (90) and (91) simplify and become

f,= 1,

uox =

ug

O D = Vlls2/VT2,

,

yf

=

y

=

I - U0/I,, ,

2lF = ( C 4 4 / p m ) l ’ 2 ,

and K~

= e?,/E,

c

~

~

.

(92)

For these specialized conditions, Abe and Mikoshiba (27) have previously published a result similar to Eq. (91); however, their work is in error. I t can be shown (28) that in order to correct this error the term q ( y - 1 ) must be dropped from the definition of 4 in Eq. (9) of Ref. 27, where y~ equals o, of the present analysis and Eq. (8) of Ref. 27 remains as written. The derivation and notation of the present theory follow that of Steele ( 4 ) and Turner et al. ( 5 ) and other related work (29, 30); the theory of Steele ( 4 ) and Turner et al. (5) will hereafter be referred to as the STVW theory. When inertial terms are neglected, OJ, -+ 0, Eq. (91) reduces to the corresponding hydrodynamical result of the STVW theory. When the magnetic field is zero, b 40, Eq. (91) reduces to the corresponding hydrodynamical result of Kino and Route (29); and when both inertial terms and magnetic field effects are neglected, w, + 0 and b 0, Eq. (91) reduces to the corresponding hydrodynamical result of White (30). --f

190

W. J. FLEMING AND J. E. ROWE

TABLE I PHYSICAL PARAMETERS FOR N-TYPE lnSb Parameter Electron effective mass Carrier concentrationa Lattice dielectric constan Thermal velocity” Low-field dc mobility4 Elastic constant Elastic constant Elastic constant Lattice mass density Piezoelectric constant Specimen length’ Specimen width‘

Symbol

AT

77°K

Value

Reference

0.013 mo I x 1014cm-3

(31)

17.8 E O

(32)

3 x 107cm/sec 6 x lo5 cm2/V-sec 6.87 x 10” N/m2 3.75 x 10”N/m2 3.12 x lo1’ N/m2 5.77 x lo3 kg/ni3 0.07 C/m2 10 mm 1 mm

(33) (33) (33) (31) (34)

The values of N o and po are chosen arbitrarily and are suitable for high-purity n-type InSb. The average electron thermal velocity is determined by uT = (k,T,/m*)1’2,where k , is Boltzmann’s constant and T, is the average carrier temperature which is taken here as 77°K. The values of L and w are chosen arbitrarily and are typical for the specimens under investigation.

I. Field Dependence The physical parameters (31-34) in Table I are used and the growth rate of the acoustoelectric interaction, given by Eq. (91), is normalized to K’. The quantity u R e / ~ is ’ labeled “gain,” and is plotted as a function of a nornialized drift ratio I- (u0 - uS)/cT;the results of this calculation are shown in Fig. 5. In Fig. 5a the results for the STVW theory are shown and in Fig. 5b the results for the present theory, using Eqs. (91) and (92), are shown. A fixed maximum value of the acoustoelectric interaction growth rate, equal to r ~ ~ ( t o , ~ ~ ) ” ~is/ given 8 1 ~ , by , the STVW theory and it occurs at - y( I bz> = Wnli,, where W,,lin = 2(0,/W,)’” occurs for frequency ,fo = ( w ~ w ~ ) ~ /The ~ / ~parameters ~ T . of Table I give f o = 1.45 GHz, us = ( ~ ~ ~ / p=~2.33 , ) ’ x/ lo5 ~ cm/sec and the STVW theoretical maximum gain ( c ( ~ ~ / =K 4.89 ~ ) x ~ lo3 ~ ~ Np/cni. I n Fig. 5 and in subsequent figures, the Np/cm units are deleted and the acoustic gain is treated as a dimensionless quantity. It is seen from Fig. 5b that when inertial terms are included, the maximum value of the acoiistic gain becomes strongly dependent on the strength of the applied magnetic field. Comparison of Fig. 5b with the

+

191

ACOUSTOELECTRIC INTERACTIONS

20

0

40 (U,-V,)/~~

(a)

80

I0

NEGLECTING INERTIAL TERMS

.M

0

60

:r

.YO

1.0

(uo-~s)/vT=r (b)

Fici. 5 . Acoustic gain

INCLUOING INERTIAL TERMS CI~JK’

as a function of drift velocity

at 1.45

GHz.

numerical results o f corresponding microscopic theories (6,26) shows that no essential difference exists between the results o f the hydrodynamical theory shown here and the more complete microscopic theories. Indeed, another set o f acoustic gain characteristics has been calculated and is compared in Fig. 6 to the acoustic-wave amplification measurements of Route and Kino (6). I n order to obtain best agreement, parameters appropriate to the Route-Kino experiment have been substituted into the theory; namely. = 1.3 x / l o = 5.1 x lo5 cm’/V-sec and N o = 1.4 x I O l 4 cni-3. Acoustic gain in units of dB/cni is calculated from Eq. (91) using the re la t ion (dB/cm) (93) Acoustic gain = 10 10g,~[exp(2x,,)], which, upon evaluation, becomes Acoustic gain

=

8.68xR,,

(dB/cni).

The correlation of theory to experiment is excellent except for the zero magnetic field curve. Although the microscopic theory (f6)gives better agreement

192

W. J. FLEMING AND J. E. ROWE

0

5

10

15

20

Uo/v,-I=-Y

FIG.6. Comparison between the theoretical on-axis acoustic gain and the Route-Kino experiment (6) (solid curves denote theoretical results).

for the zero magnetic field curve, the hydrodynamical theory shown here gives as good, if not better, agreement for the remaining ( B , # 0) acoustic gain curves. Due to the collision-dominated nature of the acoustoelectric interaction in InSb, resonance effects are not pronounced and do not play a major role in the basic mechanisms of the microwave acoustic gain. Figure 6 shows that the essential features of corresponding microscopic theories (6,26)are retained in the present hydrodynamical theory. The relative simplicity of Eq. (9 1) has permitted a detailed investigation of its behavior (35). For example, level curves can be computer-generated using the numerical methods of interval halving and false position. One set of level curves, corres.ponding to the gain characteristics of Fig. 5b, is shown in Fig. 7. The emergence of Mode I operation (10,11) in the region of low magnetic field strengths and high drift velocities is apparent. The general structure of the level curve contour in Fig. 7 is very similar to the corresponding results from microscopic theory shown in Fig. 2 of Harth and Jaenicke (25). Further discussion of the field dependence of the acoustic gain is given elsewhere (35).The effects of carrier trapping on the field dependence of the acoustic gain have also been investigated and are discussed by Fleming (36).

193

ACOUSTOELECTRIC INTERACTIONS

f,

I

f=f,=I4 5 GHz

0

2.00

1.00

u.w

3.00

5.00

TRRNSVERSE MRGNETlC FIELD. k G

FIG.7. Level curve contour of acoustic gain at 1.45 GHz.

2. Physical Mechanism of Mode I Operation

In order to determine the ultimate limit of Mode I gain, as depicted by the hydrodynamical theory, the acoustoelectric growth rate of Eq. (91) is calculated for values of electron drift velocity which are far in excess of the thermal velocity. Acoustic gain is calculated from Eqs. (91)-(93) using the parameters of Table I. A value of electromechanical coupling K~ equal to 1 x is utilized in this calculation and is obtained using Eq. (92) and the appropriate parameters of Table I. The results of the calculation are shown in Fig. 8. Here the present theory given by Eqs. (91)-(93) is also compared to the corresponding theory of Abe and Mikoshiba (27). As discussed elsewhere (28),the theory of Abe and Mikoshiba is incorrect. It is seen that no significant error is present in their theory for electron drift velocities less than approximately 3 x 106cm/sec; however, at large drift velocities, their theory noticeably diverges from the present theory and does not yield high gain peaks. The locations of the sharply peaked maximum gain values which exist for uo > uT can be determined directly from Eq. (91) subject to the simplifications of Eq. (92). The peaks occur when the factor W’ in Eq. (91) equals zero, and this condition is given, in good approximation, by 2

Y 2 = %u s

[I

+

ey(I

+h,’)],

(94)

194

W. J. FLEMING AND J. E. ROWE

lo5

I

10’

I06

VS

I

Io8

VT ELECTRON DRIFT VELOCITY, cm/sec

FIG.8. Comparison of the present theory to the theory of Abe and Mikoshiba (27) at 1.45 GHz.

where wo = ( O R O D ) ” ~ = 2nf0 and b’, 4 b2v/wR. From Eqs. (91)-(94), maximum gain is given, in good approximation, by

[I (Acoustic gain),,,

WR

= 8 . 6 8 ~ ’-

+ (2)2 (1 -k

2v7’ [ I -k

(z)2+ (1

(95 )

At the frequencyf=f,, substitution of the parameters of Table I into Eqs. (94) and (95) yields (Acoustic gain),,, = 623 dB/cm which occurs at uo = 4.26 x lo7 cm/sec for b = 0. This value for maximum gain is 14.7 times greater than the corresponding maximum gain given by the STVW theory; however, it can only occur for uo > vT and b x 0. In the limit, w B wo and b= 0, Eq. (95) becomes (Acoustic gain),,,

= 8 . 6 8 ~ ’ w , / 2 v ~ , (dB/cm).

(96)

For the parameters of Table I, Eq. (96) gives a maximum achievable acoustic gain of 883 dB/cm. Although this maximum value can only be obtained for a drift velocity approximately equal to the thermal velocity, it is. 4 ( 0 R / v ) ” 2 times greater than the maximum gain of the STVW theory and this ratio ranges from 10 to 20, depending on the value of transport parameters wR and v. It is significant to note that the maximum gain value of Eq. (96) corresponds to the maximum attainable gain of White’s theory (30)in the limit wD-+ a,y = -v&, . This observation provides an important clue in the

195

ACOUSTOELECTRIC INTERACTIONS

investigation of the physical mechanism of Mode I operation. In the hydrodynamical theory of the acoustoelectric interaction, it can be shown (24) that diffusion effects are characterized by a diffusion time z D which is approximately equal to w,/w2. When inertial terms are included, as done in the present theory, and no magnetic field is present, the effective diffusion frequency becomes, from Eq. (91), 0;= wD/(l - rZ).As uo + vT and -+ 1, the effective diffusion frequency 0;approaches infinity. At a given frequency, this gives an infinitely long diffusion time z D which allows for more effective space-charge bunching of the streaming electrons. In fact, some preliminary algebra using the equations for conservation of momentum and continuity of current, Eqs. (44) and (46), shows that the condition r2= 1 [which for clarity can be rewritten equivalently as jOv, =j(vT2q2/O)v,] corresponds to exact cancellation of the diffusion term by the inertial term in the equation of momentum conservation. The essential point here is that the fundamental physical mechanism of Mode I operation, as depicted by the hydrodynamical model, is the quenching of diffusion effects by the driftenhanced inertial effects of the streaming electrons, thereby allowing for more effective bunching of the electrons, which results in the emergence of the Mode I operation. Although the hydrodynamical theory is analyzed here for conditions which exceed its estimated range of validity, the refinements of the more complete microscopic theory do not yield results which are significantly different from those of the hydrodynamical theory (35).It appears therefore that the inclusion of electron inertial terms in a hydrodynamical theory suffices as a first-order approximation of the acoustoelectric interaction, even at microwave frequencies. From Eq. (94) it is seen that for w << wo the drift velocity must be unrealistically large in order to quench diffusion effects. Thus Mode I operation will disappear at lower frequencies as has been observed experimentally (10). The effect of the magnetic field on the Mode I gain mechanism is best understood by consideration of the effective diffusion frequency a;, defined by Eq. (91), which can be written as = o,(i

+ b J 2 ) / [+i r2(bt2 - i)].

(97)

In the limit of small drift velocities which corresponds to Mode I1 operation, I- approach zero, thereby reducing Eq. (97) to w; = w,(l b’), in accordance with the STVW theory. However for Mode 1 operation, w , and l- can no longer be ignored. Examination of Eq. (97) in the limit r = 1 shows that, as the magnetic field is increased from zero to a value such that b’2 B I , the effective diffusion frequency shown in Fig. 9 decreases monotonically from w; = 00 to 0;= 0,.This means that the diffusion quenching effects which are present when b x 0 have been eliminated by the presence w , and

+

W . J. FLEMING A N D J. E. ROWE 7

I

P-

O 2 W

3 0

W

a U

2

e

u)

3

0

l

2

3

4

5

TRANSVERSE MAGNETIC FIELD, kG

FIG.9. Field dependence of the effective diffusion frequency at 1.45 GHz.

of a sufficiently large magnetic field. The disappearance of Mode I operation with increased magnetic field strength is observed experimentally (10,11,29) to occur in the neighborhood of 1 to 2 kG. If the conditions w = a,,and r = 1 are taken and the parameters in Table I are used, the condition b‘2 = 1 occurs at B, z 0.9 kG. As seen in Fig. 7 at B , M 0.9 kG the Mode I gain has been reduced to less than one-half its zero magnetic-field value. Physically, the presence of a magnetic field together with large drift velocities gives rise to a coupling of the transverse v,, component of the space-charge wave to the longitudinal u, component. The strong coupling effects enter via the rf Lorentz force term in the conservation of momentum equation. When r2 > 4 and b’2 9 1, Eq. (97) shows that diffusion quenching effects are eliminated and the Mode I gain mechanism is diminished.

197

ACOUSTOELECTRIC INTERACTIONS

+

However, as shown in Fig. 9, for r2< the effective diffusion frequency given by Eq. (97) is enhanced by the presence of a magnetic field and the STVW Mode I1 gain mechanism emerges.

3. Frequency Dependence Further analysis reveals that unlike the STVW theory the gain expression of the present theory, Eq. (91), is not log-symmetric about the frequencyf,. The frequency dependence of the acoustic gain for the STVW theory is shown in Fig. 10a and the corresponding results for the present theory are shown in Fig. lob. It is seen in Fig. 10b that for low drift velocities with r 5 0.75 the frequency of maximum gain is less thanf, , whereas for larger 2 0.75 the frequeacy of maximum gain occurs at drift velocities with frequencies greater than,f, .

I x 106

1x10'

I x 109

I x 10'0

IXlOll

FREOUENCY, Hz (a) NEGLECTING INERTIAL TERMS

~f=fo:145GHz B,=I

I I

kG

I 015,

I

z

a? L3N

? I

IOl'

FREQUENCY. Hz ( b ) INCLUDING INERTIAL TERMS

FIG.10. Frequency dependence of the acoustic gain for B,

=

I kG.

198

W. J. FLEMING AND J . E. ROWE

Although in Eq. (91) the gain expression of the present theory appears relatively simple, substitution of all the defined quantities shows that, as an explicit function of frequency, it is given by a ratio of a sixth-degree polynomial to an eighth-degree polynomial in terms of frequency. Because of this complexity it has been analyzed numerically, using the method of interval halving, in order to solve for the frequency of maximum gain. When fixed values of magnetic field and drift velocity are taken, Eq. (91) is numerically searched for the frequency at which maximum gain is achieved, and the resulting solutions have been plotted in Fig. I I . As before, the parameters of Table I and the simplifications of Eq. (92) are utilized. Figure 1 Ib shows that the maximum gain of the present theory is generally smaller than the maximum gain of the STVW theory; however, at sufficiently large drift ratios the maximum gain of the present theory greatly exceeds that of the STVW theory. A more detailed discussion of these results is given by Fleming and Rowe (35).

J 0

I a0

60

40

( uO- v S i / v T =

.80

I0

r

( a ) FREQUENCY AT WHICH MAXIMUM GAIN IS A T T A I N E D

0

.V@

( uO- v S ) / v T

.60

r

:

( b ) M A X I M U M ATTAINABLE GAIN

FIG.I I . hlaxitnum acoustic gain

1.m

199

ACOUSTOELECTRIC INTERACTIONS

D. Incorporation of Empirical Field Factors into the Theory of Acoustoelectric Interaction In Section 1V.C it was assumed that carrier heating effects are negligible and the dc carrier mobility remains constant, independent of field strength. The constant mobility assumption was made in order to facilitate the comparison of the present theory to other related theories and, more significantly, in order to obtain physical insight. However, in order to obtain agreement with experimental measurements, the theory must be modified to include empirical field factors (28). Field-dependent effects such as mobility saturation and geometrical magnetoresistance are especially important. Although it is possible to obtain analytical expressions which describe these effects (15,37), there is considerable mathematical complexity. Furthermore, in a real semiconductor, imperfections such as bulk inhomogeneities, nonohmic contacts, and surface trapping effects all affect the resultant transport of conduction current. Since it is impractical to take all these factors into account, only the effects of mobility saturation and geometrical magnetoresistance are considered. Moreover, since the other factors are ignored, the effects of mobility saturation and geometrical magnetoresistance are adequately described by simplified empirical field factors. An empirical relation for the mobility saturation is obtained by a least-squares fit to measured I-V characteristic data for three specimens of high-purity n-type InSb (36). For convenience a parameter Y is defined as

where R, = Vo/Iois the dc resistance of the specimen and Rb is the low-field ( E , 5 20 Vjcm) resistance of the specimen. Since no evidence of bulk impact ionization is observed in the measured I- V characteristics, all variations in R , are attributed to variations of the carrier mobility and the parameters Y can also be written as Y = &/po - I , where p,!, is the low-field electron mobility. Hence, Y is also a measure of the carrier mobility variation. Because mobility saturation is an energy-dependent effect, Y is expanded in even powers of J , and the empirical function Y

+~

= a2JO2

~

5

,

~

(99)

is chosen; ci2 and u4 are constants to be determined. Corresponding to each data point i the parameter Roi/RAi = Y i + I is calculated and i t is plotted vs. the applied current density in Fig. 12. Here, 120 data points measured in the absence of an applied magnetic field for IJ,I ,<400A/cm2 and I E, I 5 I20 V/cm are shown.

200

W. J. FLEMING AND J. E. ROWE

In accordance with the method of least squares, the constants a2 and cm4/A2 and a4 = 3.15 ~ l O - ' ~ c m ~ are / A obtained. ~ Note that the contribution of the quartic term in Eq. (99) is negligible for all but the largest values of applied current. For example, the value of the quartic term barely exceeds one percent of the u4 are determined and the values a2 = 6.87 x

00

160 240 3iO 400 CURRENT DENSITY, A/SO. CM

400

FIG.12. Least-squares fit to static field characteristic data.

value of the quadratic term for J, = 484 A/cm2; this approximately corresponds to uo = uT = 3 x lo7 cm/sec. Equation (99) is rearranged into a more useful form as Po = Phk1

f

Jo2

f a4 504) = PhF(Jo),

( 100)

where F(J,) is the desired mobility saturation factor. The parameter a2 can be compared to the parameter p in the conductivity relation cro = ab(l + pEo2). When second-order terms are retained, it is found that the parameter p is equal to - a 2 ' (uo)zvg,where (uO)avg = 6.84 (R-cm)-' is the average low-field conductivity for the data shown in Fig. 12. A value of = -3.22 x cm2/V2 is obtained which is in agreement with the

ACOUSTOELECTRIC INTERACTIONS

20 1

range of - 3.5 < p < - 1.9 x cm2/V2 determined by George and Bekefi (38). The effect of geometrical magnetoresistance in InSb has been the subject of several theoretical analyses (Lf,Z6,37). These analyses follow the earlier work of Wick (39) and Lippman and Kuhrt (40). The complete solution (15,40) of this problem is obtained via a Schwartz-Christoffel conformalmapping transformation, whereupon it is found that a closed-form solution is derivable; however, its complexity limits its usefulness. It is convenient to define a magnetoresistance function g(I) as follows:

where I 2 tan-' (b)/n is the normalized Hall angle, b is the dimensionless po B , product, L and w are the length and width of the specimen, M,(b) = R,(b)/R,(O) is the magnetoresistance ratio, and R,(b) and R,(O) are the specimen resistances in the presence and absence of a transverse magnetic field. It has been shown (15,39) that in the limit L / w 2 2 , the function g ( l ) approaches a limiting form which is independent of the geometrical factors L and w ; e.g., see Fig. 13 of Ref. 39. Moreover, Lippmann and Kuhrt (40) have shown analytically that g ( l ) satisfies the following conditions: g ( l ) % 14bS,/n3

for

b2 @ 1

g ( l ) x 1 - 41n2/nb

for

b2 % 1 ,

and (1 02)

where S , = 1.2021 is a numerical constant. The exact numerical solution for g ( l ) is given by Wick [Fig. 14 of Ref. (39)]and it closely resembles a simple polynomial. On the basis of this observation it is assumed that g(l) can be approximated by a cubic polynomial of the form (valid for b 2 0)

g ( l ) i2 6,

+ 612 + 6, 1, + 6 3 13,

(1 03)

where the empirical constants 6, through 6, are determined by matching the boundary conditionsg(0) = 0 and g(l) = 1 and matching thelimitswhichare given by Eqs. (102). Upon solution, the following values are found:

6,

6,

6,

= 0,

=3 -

= 7 S , / n 2 = 0.8526,

14s3/n2- 21n2 = -0.0915,

and

6,

= 21n2

+ 7S31n2

-

2 = 0.2389.

( 104)

When the values of Eq. (104) are used, the empirical expression of Eq. (103) deviates no more than 4 % from the numerical result of Wick (39).

202

W. J. FLEMING AND J. E. ROWE

The empirical field factors given by Eqs. (100) and (103) can be incorporated into the theory of acoustoelectric interaction in the following manner. If the electron drift velocity u, is specified and the mobility saturation and magnetoresistance effects are independent, the applied current and electric field are determined by J, =

Q, No uo

Eo = (uo/p6). M J b ) F(Jo),

and

(105)

where p; is the low-field electron mobility. It is noted that I-V characteristics calculated from Eq. (105) are a good approximation to the actual measured I-V characteristics (36). Since the field-dependent mobility varies as p, = &/F(J,), the relaxation parameters in Eqs. (91) and (92) become W R -+ w,/F(Jo) = WD

(Q, No Ph/&i)/F(Jo),

F(J,) = ( V6US’/UT’)

+ WD

*

v +v

. F(J,)

=

v,’

*

. F(J,),

F(J,),

and

b

+

b / F ( J o )= P P J W O ) ?

(1 06)

where v h = Q,/m*& is the low-field collision frequency. Comparison to the constant-mobility results of Section IV,C is facilitated by retaining the same parameters of Table I ; however, the relaxation parameters now contain the field dependence given by Eqs. (106), and the applied field conditions J , and E, are determined from Eqs. (105). For convenience, the constant-mobility gain will hereafter be denoted as G(po) and the fielddependent mobility gain will hereafter be denoted as G[p,(J,)]. In Fig. 13a, C [ p , ( J , ) ] is plotted at the frequencyf,, as a function of the normalized drift ratio r. Comparison to the corresponding constant-mobility results of Fig. 5b is made by plotting the gain ratio, defined by the ratio G[po(Jo)]/G(po), and this result is shown in Fig. 13b. Irrespective of the value of magnetic field, the gain is enhanced by the inclusion of the field-dependent mobility. In particular, Fig. 13b shows that the gain ratio increases proportionately to the field factor F(J,). [The factor F ( J , ) given by Eq. (100) increases approximately with the square of r and reaches the value of 2.62 at r = I.] There is no simple expression for the field-dependent enhancement of the gain ratio; however, the underlying mechanism clearly emerges from Eqs. (91) and (92) for the following conditions: I . For b 2 $ my29 1 and (0% v / l y or for b2 6 1, r2 5 1, ( y I 6 W and w k w,: Acoustic gain

N

oD u s 2 v ~ F ( J o ) . N

(1 07)

203

ACOUSTOELECTRIC INTERACTIONS 8

0

20

40

60

( uo- vs ) / v T =

(01

80

10

r

INCLUDING FIELD - DEPENDENT MOBILITY

?

2. 3-

f = f o = l 45 GHz

9 .yI

0

.a0

.m

I 00

(uO-vs)/vT=r ( b ) COMPARISON TO CONSTANTMOBILITY CASE

FIG.13. Effect of field-dependent mobility on the acoustic gain at 1.45 GHz.

IYI

2. For b2 D wV2D 1 and 9 W/b2: Acoustic gain

I yI

-

9 v / o or for b2 D 1, oV2 4 1 and

-

o R / b 2 v&F(J0)/Bl2.

(108)

In the STVW theory, Eq. (107) applies for drift ratios much less than the point of peak gain and Eq. (108) applies for B, # 0 and drift ratios much greater than the point of peak gain. However at the point of peak gain [ I y I = W/(I + b’)], the STVW maximum gain is ~ ~ ( o ~ o ~ and ) ~ ’all~ / 8 z ~ ~ field-dependent effects of Eq. (106) cancel in the product w R o D thereby , negating the possibility of enhanced gain at this point. Thus the gain curve is only enhanced for drift velocities away from the point of peak gain. This collision-induced gain-broadening effect is well known (24). In Fig. 13b, Eq. (107) applies for B, 4 0.2 kG and I-5 0.9 and Eq. (108) applies for

204

W. J. FLEMING A N D J. E. ROWE

B, % 0.2 kG and r % 0.2. As in the STVW theory, the gain curves are broadened by the field-dependent increase of collision frequency. An overall perspective view of the gain at f = f o , including the fielddependent effects of Eq. (106), is illustrated in Fig. 14. Applied current,

f=fo=1.45GHz PO'PO( Jo)

FIG.14. Overall perspective view of acoustic gain at 1.45 GHz (including field-dependent mobility).

I , = J , wz, is calculated using Eq. (105) and the parameters of Table I. The presence and operation regimes of Modes I and I1 of the acoustic gain are evident. In general, the inclusion of a field-dependent mobility has a negligible effect for r 2 0.2 ( I , 5 1.0 A), and Mode I1 effects are relatively unaffected. On the other hand, at larger values of r, the Mode I gain is enhanced by the aforementioned collision-induced gain-broadening effect. For comparison, another perspective view of the gain C [ p , ( J , ) ] has been plotted at the frequency of 10 GHz, and is shown in Fig. 15. The reduction of Mode I1 gain at low values of magnetic field is apparent. The onset of Mode I gain at large values of applied current is so sharp that, for clarity, the gain curves are deleted for gain 2 1.2 x lo3. There are additional effects which arise froni the inclusion of the fielddependent electron mobility in the acoustic gain expression. It has been shown (36) that the existence of a field-dependent mobility results in an

205

ACOUSTOELECTRIC INTERACTIONS

upward shift of the frequency of maximum gain and a correspondingly enhanced value of maximum gain. Depending on the applied field strengths, the maximum gain values of Fig. 1 1 b are enhanced by as much as a factor of two and the frequency values of Fig. 1 la are shifted upward by as much as 50%. Experimental evidence illustrating the importance of the empirical field factors is shown in Fig. 16. The field factors given by Eqs. (100) and (103)

f =I0 GHz

S T -'w 0 X

z

?E 8 0

1.00

3.00

WPLfE? CURRENT. A

Y.00

5.d

FIG.15. Overall perspective view of acoustic gain at 10 GHz (including fie.- depenl ent mobility).

are incorporated in the gain expression of Eq. (93) using the relations of Eqs. (91j, (92), and (106). I n Fig. 16a the theoretical calculations are made using the parameters of Table I, and the experimental acoustic gain values are taken from the work of Hayakawa and Kikuchi (8). The curve labeled G ( p o )shows the results of the theory when no empirical effects are included and the electric field is taken as E, = u,/& using L = 15 mni as per the experiment. Only the effect of magnetoresistance has been included in the curve G(M,), wherein E, = ( u o / p b ) . M,(h). Finally, all empirical factors are included in the curve G [ M , , p O ( J O ) ] ,wherein the effects of mobility saturation are now included in the gain calculation and the electric field is given by Eq. (105). I t is apparent that the empirical field factors must be included in order to obtain good agreement between experiment and theory. In Fig. 16b the complete set of theoretical acoustic gain characteristics, including all the empirical field factors, is compared to the experimental

206

W. J. FLEMING AND J. E. ROWE

2ot

20

I5

10

5

5.~1

I

I

0 (a)

I

I

1

50

100

150

ELECTRIC FIELD, V/cm

200

0 ( b)

50

100

150

200

ELECTRIC FIELD, V/cm

FIG.16. Comparison between the theoretical on-axis acoustic gain and the HayakawaKikuchi experiment (8) (solid curves denote theoretical results).

results and overall good agreement is obtained. Deviations from the experimental results are attributed to discrepancies between the assumed empirical field factors [Eqs. (100) and (103)] and the actual field factors of the experiment.

v. SOLUTION OF THE ACOUSTOELECTRIC INTERACTION FOR ARBITRARILY ORIENTED STATICFIELDS AND OFF-AXIS ACOUSTIC-WAVE PROPAGATION A . Introduction

The physical model of the acoustic noise generation process in highpurity n-type InSb, in the presence of a transverse component of static magnetic field, has been described in Section 1,B. It was concluded that the off-axis acoustoelectric interaction determines the field dependence of the radiation. The growth rate of the acoustoelectric interaction, Eq. (41), is given by the product of the electromechanical coupling constant 'K times a function of the macroscopic electronic and acoustic transport parameters. This equation was analyzed in Section IV for the special case of on-axis acoustic-wave propagation along the ( I lo) crystal direction. Here, the acoustoelectric interaction equations are solved for the general case of arbitrarily oriented off-axis acoustic-wave propagation. The coupling para-

ACOUSTOELECTRIC INTERACTIONS

207

meters, li2 and u s , are first determined in Section V,B; thereinafter the complete solution for the growth rate of the interaction is given in SectionV,C. B. Solution f o r the Efectitle Electroinechanical Coupling Parameters

As discussed in Section I,B, it is found that due to Hall field shorting effects which exist in the vicinity of the contacts acoustic waves are excited, in the Lorentz force plane, in all off-axis directions (measured from the on-axis crystal direction 2).When the Lorentz force plane is defined by an azimuthal angle cp, the direction of acoustic-wave propagation q^ is specified by the quantities <,cp, and 2 as shown in Fig. 17a. However, the off-axis electromechanical coupling constant ic2 and the corresponding phase velocity

A

41 AI ~ A- X PLANE ~

( b ) SIDE VIEW

(c)

TOP VIEW

FIG. 17. Orientation of the off-axis acoustic wave q in a crystal aligned with long dimension along i,in the crystal coordinate system (XI, x 2 , x3).

208

W. J . FLEMING A N D J. E. ROWE

I , m, and n. In order to relate the theory to the physical model of off-axis wave nucleation, the direction cosines of the propagation vector 4 = ( I , m, n) must be expressed in terms of [, cp, and L. In Fig. 17a, the angles cp and [ are defined relative to a crystal with arbitrarily oriented long dimension 2 = (I,, mo , no). Since 4 and f. are unit vectors, Fig. 17a shows directly that v, are given in Eqs. (37) and (39) in terms of the direction cosines

4 . f. = cos [ = I / ,

+ nzm, + nn,

(109)

and

R,

= sin

[.

( 1 10)

From Fig. 17a it is also seen that sin cp

= S/Ro

and

cos cp

= C/Ro,

where S (which is parallel to the a3-L plane) and C (which is parallel to the are determined with the aid of the special views shown in Figs. 17b and 17c. Inspection of Fig. 17b shows that

R1-a2 plane)

S

=

( q 3 - E,)/cos I,!/,

(113)

where sinI,!/=L.a,=n,,

ij3

-- 4 * a 3 = n

and

L,

= cos

[(Z a,) = no cos 4,. *

Combining Eqs. ( 1 lo), ( 1 1 I), and (113), and using the relation lo2 + mo2 no2 = 1 yield

+

sin cp

= (n - no cos

L. L =

4,)/RI2sin [,

(1 14)

+

whcre R , , Li ( l o 2 mo2)1’2is the projection of on the 9,-f2 plane. On the other hand, inspection of Fig. 17c together with Fig. 17b shows that

c = ( 4 ; - L,)/cos x,

( 1 15)

where ij; = (4

9,) + (S sin $) sin S sin $

and

= (R,

x,

tan

= mo/Io,

sin p)n0= no sin

5 sin cp

Z;, = cos [(Z* 9,) = m, cos [.

4 g2 = m, *

ACOUSTOELECTRIC INTERACTIONS

Combining Eqs. (1 lo), ( 1 12), and ( 1 15) yields

m

I/[%].

+ (nosin isin cp) m0 - rn, cos ( R12

209

(116)

Rewriting Eqs. ( 1 14) and ( I 16) provides expressions for n and m, respectively, whereas an expression for / is found by substituting Eqs. ( 1 14) and ( I 16) into Eq. (109). When these steps are carried out, the appropriate transformation equations are obtained, namely, 1 = I , cos

m

= m,

sin (

l- R12

(m, cos cp +no I, sin cp),

sin cos i -. ( I , cos cp - n,m, sin cp), R ,2

+

and

n =no cos [

+ R,, sin i sin cp,

(1 17)

where 4 = (I, m, n), L = (I,, m, , no), and R,, = (1,’ i- mo2)1’2,Although Eqs. (1 17) are not valid for R , , = 0, where L = (0, 0, I ) , the case = ( I , 0, 0) will, by symmetry, give the same results as =(O, 0, I). Note that when the sum of the squares of these equations is completed, the identity 1’ + mz + n2 = I is satisfied. The off-axis acoustic-wave propagation conditions are determined from the solution of the uncoupled eigenvalue equation, Eq. (30). It is useful to first establish the following general properties. As discussed in Section KC, there are three propagating waves-the longitudinal acoustic wave and the fast- and slow-transverse acoustic wave. These waves will hereafter be designated, respectively, as the LG, FT, and ST waves. Corresponding to each of these waves, the off-axis electromechanical coupling parameters ~’(cp, i) and ~,(cp, 5) are computed using Eqs. (37), (39), and ( I 17). For cubic 111-V compound semiconductors (crystal class 43 m), Mason (21) has shown that all possible values of the electromechanical coupling parameters are found in 1/48 of the total range of the direction cosines I , m , and n. This region will be called the basis region and is conveniently defined by the region formed by a right-spherical triangle with vertices at the crystal directions [IOO], [ I lo], and [ I I I]. As shown in Fig. 18, the direction cosines need only be permuted over the limits of the basis region, i.e., when all values of I, m, and n are taken within the limits

and

210

W. J. FLEMING AND J. E. ROWE L

T

XI

FIG.18. Basis region of the direction cosines in the crystal coordinate system ( X I , xz

3

x3).

then all possible values of K’ and u, will be obtained. Moreover, the limits of Eq. (1 18) define a basis range for each of the direction cosines. There are only three directions of wave propagation 4 in the basis region for which a purely longitudinal wave and two purely shear waves can propagate, namely, the [loo]-, [I lo]-, and [ill]-vertex directions. It is these principal crystal directions along which the long dimension L of semiconductor specimens is usually oriented and which will be analyzed here; other possible values of L are not commonly utilized and are not considered. If Eq. (117) is used, the direction cosines are expressed in terms of cp, <, and L , and if i is held constant the basis range of cp and the azimuthal symmetries of ~ ’ ( qcan ) be determined from Eqs. (12), (15), (37), and (39); the results are given in Table 11. Utilization of these symmetries greatly reduces the computational effort. Tabulation of ti2 over the basis range of cp will give all possible values of t i 2 in the full 27c range of azimuthal rotation. Although the eigenvalues cI (and the corresponding sound velocities u, = Jc,/i,,,) possess the same symmetry as K’, only the projection of the eigenvectors k1 on 4, i.e., kl. 4, possesses the same symmetry as ti’. Hartmann and Bers (41) have tabulated all possible values of the electromechanical coupling parameters in InSb. [Although they derive the effective value of K * in a heuristic manner, they nonetheless obtain the same result as was derived in Section II,C, namely, Eqs. (37) and (39).] Within the basis

21 1

ACOUSTOELECTRIC INTERACTIONS

TABLE I1 AZIMUTHAL SYMMETRIES OF Reference orientation of specimen i

THE

OFF-AXIS ELECTROMECHANICAL COUPLING CONSTANT Symmetry

Periodicity

Recursion relations

Basis range of g, (ra4

region shown in Fig. 18, each of the three acoustic waves gives rise to a maximum electromechanical coupling constant at a particular propagation direction g,, . If the parameters of Table J are used, the conditions for which ti,?& occurs can be numerically determined, and these are given in Table 111. Furthermore, the general properties of the off-axis coupling constant along the boundary lines of the basis region are also summarized. The latter information is essential for the proper identification of the different off-axis acoustic waves which may exist concomitantly in 111-V compound semiconductors. Note that the LG and FT waves achieve maximum coupling for on-axis wave propagation, whereas the ST wave achieves maximum coupling for wave propagation which is approximately 29" off the [IOO] crystal direction. Moreover, the values of Q, in Table 111 are particularly useful for understanding the overall angular dependence of the off-axis coupling constant. As a consequence of the 48-fold periodicity of ti2(cp, c), if a propagation = (I, m, is given at which ti:=, occurs, it is known that direction Q, values will occur at all equivalent directions ( l m n ) m a x . other peak Since ( 1 10)-oriented specimens are most commonly utilized in experiments, this crystal reference direction is chosen for an illustrative example of the solution for the coupling parameters. By symmetry (21), identical results are obtained for any equivalent ( 1 lo) orientation. For convenience, L = ( I , 1 , O)/J2 is chosen as the crystal reference direction. Jf a transverse component of magnetic field is directed along a particular ayimuthal angle cp, all off-axis wave propagation is confined to the Lorentz force plane and is a function only of the inclination angle <. Hence, the values of cp and L are fixed and the direction cosines I, m, and n are determined as a function of [ using Eq. (1 17). Since the tensor a given by Eq. (15) is real and symmetric, the Jacobi diagonalization method of solution can be used to

TABLE 111

GENERAL PROPERTIES OF THE OFF-AXIS COWLINGPARAMETERS Coupling constant value on the boundary line' Acoustic wave LG FT

ST

~k~~value" 4.633 x 9.970 x 4.182 x

(imardirection*


-

<110?

<522)

Sound velocityn u, (cm/sec)

Line I

Line 2



- < I l l )

Line 3 < ] l o >- <111>

3.938 x lo5 2.325 x lo5 1.911 x lo5

0 nonzero 0

nonzero 0 nonzero

nonzero nonzero 0

~k~~and us are computed using the parameters for InSb of Table 1. ~k~~is achieved whenever the wave propagation direction coincides with a crystal direction which belongs to the set of equivalent

&..

crystal directions listed. The boundary lines make up the periphery of any one of the 48 equivalent triangular basis regions; one such region is shown in Fig. 18.

213

ACOUSTOELECTRIC INTERACTIONS

solve the uncoupled eigenvalue equation, Eq. (30). For each of the three eigenvalue solutions, the coupling parameters ti2 and u, are calculated using Eqs. (37) and (39). Since the FT wave dominates the acoustoelectric interaction in (1 10)oriented specimens, its coupling characteristics are most important and are shown in Fig. 19. Note that, depending upon the value of the inclination FAST-TRANSVERSE WAVE REF DIR ~(110)

26-

0 X 0

v,

-

-z \-.

'.

\

=>- 2 0 -

---

,---5

'.--

, .-_ -----_----

!=

0

0 -I

w

>

-

I4-r

I A 2 ANGLE = 0 DEG A2 ANGLE = I 5 DEG

2 3

A2 ANGLE=30DEG

15

30

4 A2 ANGLE. ARCTAN (SQRT ( 2 ) ) A2

ANGLE= 7 5 DEG

6 A2

ANGLE.90 DEG

5

45

60

75

90

INCLINATION ANGLE, DEGREES

FIG.19. Characteristics of the fast-transverse acoustic wave in [I 101-oriented InSb.

angle, acoustoelectric interactions involving the FT wave may be initiated with widely varying phase velocities and coupling constants. More specifically, in a given azimuthal plane and with a suitable source of off-axis acoustic waves present, as many as three separate FT waves may, by superposition, be concomitantly amplified. For example, in the cp = 15' plane shown by curve 2, three separate ranges of nonvanishing coupling exist; namely, 0 5 ( < 38", 38 < ( < 59', and 59 < ( $90'. This behavior will be discussed in detail in Section V.C. The overall angular dependencies of the off-axis coupling constants are conveniently illustrated by the computer-generated plots shown in Fig. 20. The recursion relations of Table I1 are used and the coupling constant for each type of acoustic wave is calculated. For on-axis propagation along ( = 0 in a ( I 10)-oriented specimen, Fig. 20 shows that only the FT wave

LONGITUDINRL ACOUSTIC-URVE

COWLING

REFERENCE CRYSTRL DIRECTION = 11101

-

FRST-TRRNSVEAK ACOUSTIC-NAVE COUPLING MFLRENCE CRYSTR OlRCCTlON

Ill01

RZIMUTHRL ANGLE. DEGREES

SLW-TRRNSVERSE ACOUSTIC-URVE COUPLING REFERENCE CRlSTRL DIRECTION = 11101

u

.OO

yS.00

92.00

135.00

180.00

225 00

RZIMUTHRL RNGLE. OEGREES

210.00

315.00

8

ACOUSTOELECTRIC INTERACTIONS

215

supports an acoustoelectric interaction, whereas all waves are active for offaxis propagation. In agreement with Table 11, the twofold mirror symmetry about cp = 180" is apparent in the numerical results shown here. Moreover, values for each wave as discussed in conjunction with Table 111, the peak occur in Fig. 20 at all equivalent directions (/mn),,,ax. The angular dependencies of the off-axiscoupling constants have also been computed for (100)- and ( 1 1 I)-oriented specimens. These results, together with a more detailed analysis of the off-axis wave coupling characteristics, are given elsewhere by Fleming (36). C. Solution f o r the Gro\i,th Rate oj'the Ofl-Axis

Acoustoelectric Jnteraction The physical niodel of the radiation process in n-type InSb was shown in Fig. 1 . For the purpose of analysis, the off-axis acoustoelectric interaction of Fig. 1 is depicted here in the crystal coordinate system (x,, x 2 ,XJ shown in Fig. 21. Here, B, is the component of applied magnetic field which is maintained transverse to the long dimension L of the InSb specimen; uo, the direction of electron drift, is parallel to L (assuming that the acoustic amplification occurs in the bulk of the specimen, as shown in Fig. 1 ) ; 4 is the direction of off-axis acoustic-wave propagation ; and (, the inclination angle, and cp, the azimuthal angle, define the direction of off-axis propagation 4 relative to L. The same azimuthal angle cp also specifies the orientation of B, relative to the crystal axis 23 (because 4 is constrained to follow B, through the Lorentz force which acts on the drifting electrons in the vicinity of the contacts where the acoustic waves are nucleated). Thus, as shown in Fig. 21, the inclination angle ( is defined in the plane of the Lorentz force, namely, the L-4 plane which is tilted at the azimuthal angle cp. The solution for the growth rate of the off-axis acoustoelectric interaction is given by Eq. (41), and requires a determination of the quantities ti', v , , and o,,. As discussed in Section V,B, the off-axis electromechanical coupling constant 'it and sound velocity us are calculated, for each of the three acoustic waves, from Eqs. (37) and (39). On the other hand, the longitudinal rf conductivity o,,is derived using the solution method of Section IV,B, wherein a hydrodynamical model of electron transport is utilized and the quasistatic approximation is made. Since the direction of electron drift uo is parallel to the long dimension 2 of the specimen, the field configuration already analyzed in Section IV,B, and shown in Fig. 4, will correspond to the configuration of Fig. 21 when the angle (' is replaced i n Fig. 4 by the angle (. ~

FIG.20 (opposite). Off-axis coiipling constants

in

I 10'-oriented InSb.

216

W. J. FLEMING AND J. E. ROWE ONE OCTANT O F A UNIT SPHERE CENTERED IN THE CRYSTALLOGRAPHIC COORDINATE SYSTEM

I

A

x2

FIG.21. Relative orientations of the transverse component of magnetic field B,, the acoustic wave 4 and the electron drift velocity uo . (The long dimension of the specimen is in the f. direction and the transverse dimensions are in the and f; directions.)

Hence the analysis of Section IV,B also applies to the present case, (r,, is given by Eq. (89), and the growth rate of the acoustoelectric interaction is given by Eq. (90), wherein the term uoxbecomes equal to uo cos 5. In the present section, electron trapping effects are ignored. However the field-dependent effects of Section IV,D are important and are included. When Eqs. (90) and (93) are combined, and the aforementioned conditions are utilized, the desired expression for off-axis acoustic gain is obtained, namely

ACOUSTOELECTRIC INTERACTIONS

217

and v

= V;

. F(Jo),

W,

=w~/Y,

I,

=

( Q ,N o U ~ ) W J ’ .

In Eq. ( I 19), the off-axis coupling parameters ~ ’ ( c p , i)and v,(cp, [) are determined from Eqs. (37) and (39), which in turn depend upon the solution of Eq. (30). The mobility saturation factor F ( J o ) is calculated from Eq. ( I 00) and the trapping factor has been set equal to unity. All remaining symbols in Eq. (1 19) have been previously defined and retain their meaning. 1. Results for (100)-Oriented Specimens

The conditions whereupon off-axis acoustic gain occurs are determined by the solution of Eq. (119). This equation is solved separately for each acoustic wave in the azimuthal plane of the Lorentz force for all directions of off-axis propagation 0 5 s n / 2 . Table 11 shows that for ( 1 10)-oriented specimens, Eq. (119) need only be solved in the basis range 0 5 cp 5 n/2 and all other values of gain (holding the field strengths constant) are obtained by the recursion relations. The region defined by the basis range of cp and 0 5 i 5 n/2 will hereafter be called the basis domain. In the present case, the basis domain is illustrated in Fig. 22. Stereographic representation of the basis domain is utilized and the unit crystal sphere of Fig. 21 is viewed from abovethe [OOl]axis. Forcp = 0, the wavepropagation direction 9 varies from the [110] direction to the [TI01direction as [ goes from 0 to n/2, whereas, for cp = n/2, 4 varies from the [110] to the [OOl] direction as igoes from 0 to n/2. Inspection of Fig. 22 shows that the basis domain is comprised of six equivalent basis regions such as the one which was shown in [TOO]

[1001

FIG.22. Stereographic view of the basis domain in a [ I 101-oriented crystal

21 8

W. J. FLEMING AND J. E. ROWE

Fig. 18. The connecting boundary lines of each of these basis regions are identified by the labels L, , where i = 1,2, or 3 and the subscript i corresponds to the line identification number given in Table 111. If Eq. (1 17) is used with (I,, m a ,no) = (1, 1, O)/J2, the boundary lines of Fig. 22 are expressed as functions of cp and [ and the results are as follows: (1) For the L , - L; line where 1 = 0, 0 5 cp 5 4 2 ;

( I 20a)

+ cos PO>, o 5 cp _I n/2;

(1 20b)

tan [ = I/cos cp, (2) For the L, line where I tan [ = I/($

= n,

sin cp

(3) For the L; line where - 1

and cpl

=n

tan i = l/(cos cp - JZ sin cp),

(4) For the L , - L; line where m

= c0~-~(2/3)''~,

o 5 cp 5 cp,;

(120c)

= t7,

tan i= 1/(J2 sin v, - cos cp),

cp,

5 cp 2 n / 2 ;

( I 20d)

and the L;' - L'; line and the L i - L; line coincide, respectively, with the cp = 0 and the cp = n/2 directions. Equations (120) are solved and the results are shown in Fig. 23.

0

'PI

'Pp T I 3

r/2

AZIMUTHAL ANGLE, 'P

FIG.23, Solutions for the boundary lines of the equivalent basis regions in a [110]oriented crystal.

ACOUSTOELECTRIC INTERACTIONS

219

It has been found that acoustic waves propagate in the off-axis direction for which the acoustic gain is maximum (20). Furthermore, the coupling constant may go to zero whenever the value of ( coincides with a boundary line L i ,and all possible values of the coupling constant occur within each basis region. Hence, it might be concluded that a distinct wave of each acoustic-wave type may exist in each basis region. There are six equivalent basis regions in the basis domain and in the full 2rr-rotation of cp there are 24 equivalent basis regions; thus there would be as many as 24 different waves possible for each acoustic-wave type, giving a grand total of 72 possible waves. However, as indicated in Table 111,the coupling constant only goes to zero for certain acoustic waves at certain boundary lines. For a given azimuthal plane defined by the cp-orientation of B , , the correct number of possible waves is determined by increasing and taking the nature of boundary lines crossed into account. For example, as ( crosses an L, line, only the FT wave coupling goes to zero, whereupon only the FT wave type supports an additional wave. The complete results of this consideration are listed in Table IV, with the use of Fig. 23 together with Table 111. I t is found that the LG, FT, and ST acoustic-wave types give rise to, respectively, 2, 3,and 4possible waves within the basis domain. Thus there are only nine possible waves instead of 18 within the basis domain. If the nature of the boundary lines at cp = 0 and cp = rr/2 is taken into account, the number of occurrences of each wave in the full 2rr-rotation of cp is obtained. These results are also given in Table IV and it is found that there is only a total of 27 instead of 72 possible waves. The nine distinct waves which exist in the basis domain will hereafter be identified by the acoustic-wave type followed by the wave identification number. For example, the second possible wave of the FT type is identified as the FT-2 wave. The appropriate value of ~ ' ( ' p ,[) and z',(cp, [) are determined using the solution method of Section V.B, and these values are substituted into Eq. ( I 19) in order to obtain the off-axis acoustic gain for each of the three acousticwave types. Although other conditions are considered, a situation of experimental interest [f'= 10 GHz, BL 2 2 kG and I , 5 2 A-see Ref. (Z3)] is studied in detail. Physical parameters suitable for n-type InSb at 77°K are listed in Table I and these are used throughout the remainder of the investigation. For each acoustic-wave type, the acoustic gain is calculated as a function of the off-axis inclination angle <, and typical results are shown in Figs. 24 and 25, wherein only the basis range of azimuthal angles is shown (0 5 cp 5 n/2). The acoustic-wave types are designated and each point of maximum gain corresponds to a distinct wave which can be identified using Table IV. Figure 24 shows that for an applied current of 0.1 A, whereupon uo/u, k 1 ,

<

220

3

u

cl

4

d d d N

W. J. FLEMING AND J. E. ROWE

k

Y 11

a

k

5

a

V V

2 VII

ts

a v

3

8

a

VII V

0

II

0

a

-N-e

22 1

ACOUSTOELECTRIC INTERACTIONS

0

30

60

90

INCLINATION ANGLE, DEGREES

FIG.24. Off-axis acoustic gain in < I lO'\-oriented InSb at I0 GHz for B , A.

5 kG and

:

10 = 0.1

maximum acoustic gain occurs for the on-axis FT-1 wave at [ = 0, independent of cp. Note that whenever the longitudinal component of electric drift velocity, uo cos (, exceeds the sound velocities of the off-axis acoustic waves, other possible waves of Table IV appear at other points of maximum gain in Fig. 24. On the other hand, for values of applied current greatly in excess of 0.2 A, whereupon c, 4 zio < r T , every possible wave listed i n Table 1V appears as shown in Fig. 25. Here the far off-axis FT-2 and LG-2 waves dominate, and exhibit the greatest values of acoustic gain, as seen, respectively, in the = 0'' and cp = 30 ' azimuthal planes. The calculation of greatest significance is the determination of the points of maximum gain. These points give the directions at which the off-axis waves propagate and the gain values which they achieve. Gain characteristics like those shown in Figs. 24 and 25 are numerically scanned to determine maximum gain values for each of the possible waves (36). When this procedure is carried out, the maximum values of acoustic gain have been calculated for Eq. (1 19) and are plotted in Fig. 26. By superposition, at a given

222

W. J. FLEMlNG A N D J. E. ROWE

value of applied current, each maximum gain value corresponds to a distinct wave propagating in the approximate off-axis direction which is given by the angle i in the parentheses attached to the wave designation. The resultant rms gain, with all possible waves taken into account, is also shown in Fig. 26. It is assumed that the intensity of microwave noise radiation is proportional to the total rms value of the acoustic gain. 1

61

g a

2-

'p

= 60"

m

LG

0

30

60

90

INCLINATION ANGLE, DEGREES

FIG.25. Off-axis acoustic gain in ( I IO\-oriented InSb at 10 GHr for B, lo

=

=

5 kG a n d

1.5 A .

If the initial amplitudes of the off-axis waves are not strongly dependent upon the value of the applied current, then the rms gain characteristics in Fig. 26 will be similar to the experimental radiation growth characteristics. However, direct comparison of the theoretical gain characteristics to experiments is difficult because of the variability of the wave nucleation conditions with applied current which is not described by this theory. This uncertainty can be circumvented by maintaining the applied field strengths constant and examining the azimuthal dependence of the acoustic gain ; the theoretical results are seen in Figs. 27 and 28.

223

ACOUSTOELECTRIC INTERACTIONS

The method of solution which yields the computer-generated azimuthal patterns such as i n Fig. 27 is a point of practical interest and will be briefly discussed. The eigenvalue equation. Eq. (30), is solved for a selected set of cp and ( values which are chosen to uniformly span the basis domain of Fig. 23. At each point (cp, i)the coupling parameters x Z and v , ~ for , each wave type, are computed and stored. Then the boundary-line solutions Liof Eqs. (120) are calculated and, if Table 1V is used, the ( ranges of existence for each acoustic-wave type are determined and stored. The maximum values of

0

05

15

10

0

05

10

I 5

4PPLIED C U R R E N T , A

4PPLIED C U R R E N T , A

FIG.26. Off-axis acoustic gain in ( 1 10)-oriented InSb at 10 GHz for BL

1

5 kG.

off-axis gain for Eq. ( I 19) are found using a numerical scanning method of solution. When this procedure is employed, simple recall of the appropriate coupling parameters for each wave type and azimuthal plane under consideration solves Eq. (1 19) for as many values of applied field strength as are desired (36). The maximum gain values are sorted according to their proper wave identification by comparing the point at which the maximum occurs to the iranges determined by the boundary lines L i. Finally, the recursion relations of Table I1 are used to generate the complete azimuthal pattern of the offaxis gain and the results are plotted. The relative shape of the azimuthal pattern of rms acoustic gain correlates well with the experimental azimuthal patterns of microwave noise radiation. This agreement is shown in Fig. 29, where the theoretical G,,, curve has been taken from Fig. 28 and the experimental pattern of radiation labeled G, has been taken from Fig. 5 of Fleming and Rowe (23). Several additional

<

224

W . J. FLEMING AND J. E. ROWE

I

FIG.27. Azimuthal pattern of the off-axis acoustic gain in (llO)-oriented InSb at 10 GHz for Bl = 3.5 kG and lo= 1 A .

FIG.28. Azimuthal pattern of the rms acoustic gain in < I 10)-oriented lnSb at 10 G H z for lo= 1 A.

ACOUSTOELECTRIC INTERACTIONS

225

FIG.29. Comparison between the theoretical pattern of the rms acoustic gain G,,, and the radiation pattern G, of the Fleming-Rowe experiment (13) for / I IO)-oriented InSb.

points of agreement between this theory and the experimental results of microwave noise radiation are dxussed in detail by Fleming (36). Arizumi et al. (10) have performed a series of experiments giving particular attention to the Mode 11 radiation occurring in sufficiently long-length (110)-oriented specimens of InSb. In addition to the low-field Mode I1 radiation, they also observed a higher-field mode of radiation which they call the “ Buchsbaum mode” of radiation. The Buchsbaum mode is the same as the one observed in the Fleming-Rowe experiment (I.?), and will be designated here as Mode 111. This mode is distinguished from Mode I 1 because it is unrelated to the concomitant presence of the transit-time current oscillations; its onset nearly coincides with the application of the voltage pulse and it exists regardless of the specimen length or orientation. In Fig. 30, theoretical acoustic gain patterns are calculated using the aforementioned procedure and these are compared to the experimental results of Aoki et al. (42). The applied electric field values of 12 V/cm and 65 V/cm in Fig. 30a are equivalent to applied current values of 0.35 A and 1.8 A for B, = 4 kG [see Eq. (IOS)]. Aoki et a!. have concluded that the Mode I11 radiation is “different” from the Mode I1 because of the “very different” azimuthal radiation patterns, as shown in Fig. 30b. However, the

226

W. J. FLEMING AND J . E. ROWE

(b)

FIG.30. Comparison between the theoretical rms acoustic gain and the radiation patterns of the Aoki-Hayakawa-Arizumi experiment (42). (a) Theory: rms acoustic gain in (1 10)-oriented InSb. (b) Experiment: radiation from (1 10)-oriented lnSb (arbitrary scale). The ( I 12) and ( 1 1 1 ) labels indicate the porientations of the transverse specimen faces.

present theory shown in Fig. 30a readily accounts for the change in the shape of the radiation patterns and it is apparent that the anisotropy characteristics of both Modes TI and 111 arise from the amplification of off-axis acoustic waves. Decomposition of the theoretical gain pattern of Fig. 30a into individual wave components shows that the strong central peak of the Mode 111 pattern at qo = 0 arises from the off-axis amplification of the FT-2 wave. The central peaks of the Mode TI1 pattern occur in the cp = 0 Lorentz force plane,

227

ACOUSTOELECTRIC INTERACTIONS

whereupon acoustic dispersion effects are minimized for the FT wave (36). As seen in Fig. 19, the phase velocity of the FT wave is independent of the off-axis inclination angle in the cp = 0 plane, and this is the only azimuthal plane for which this condition can occur. Examination of Figs. 28 and 30a shows that the azimuthal pattern of rms acoustic gain C,,,(cp) changes shape depending on the operating conditions. The general characteristics of G,,,(cp) can be cataloged by a systematic analysis (36), and the results are summarized in Table V. The anisotropy characteristics of G,,,(q) are predictable using Table V. For example, if the conditions which apply to the experiment of Fleming and Rowe (23) are considered (j-2 4 GHz, I , 2 0.3 A, and B , 2 2 kG), the waves which are listed in Table V under the intermediate applied current heading and are marked by the footnote ( d ) determine the shape of G,,,,,(cp). The waves so marked are the LG-2 wave and the FT-2 wave which achieve maximum gain, respectively, at q = k35" and at cp = 0 with 180" rotational symmetry. Figures 27 and 28 apply for the aforementioned conditions and clearly exhibit these anisotropy characteristics. TABLE V AZIMUTHAL ANISOTROPIES OF THE DOMINANT WAVESI N THE OFF-AXISACOUSTOELECTRIC THEORY FOR ( 1 IO'>-ORIENTED lnSb

Acousticwave tY Pe

LG FT

ST

Azimuthal angle of dominance" and periodicity (Azimuthal angle in degrees and k = 0, :k I , 4 2, . . . )

Wave identification number

Low applied currenth

Intermediate applied currentc

1

(90 -I k 180)'

2

negligible

negligible [-(1-35) + k 180]"

I 2 3 I

2 3 4

(isotropic)" negligible [ - ( L55)1 A 180Id-' - ( t 4 3 ) - 1 k 180 - ( + 2 2 ) 4 k 180 negligible negligible

negligible ( k 180)d*e [- ( - 5 5 ) t k 1801' negligible negligible - ( I 6 1 ) i k 180

9 0 i k I80

" T h e azimuthal angle of dominance is the angle at which maximum off-axjs gain is achieved; these results require BI 2 2 kG or, equivalently, b % 1 . * lo 5 0.3 A or, equivalently, uo/ur 5 0.06. 0.3 5 lo 5 3 A or, equivalently, 0.06 5 u o / r T 5 0.63. Determines the shape of Grms(q)at high frequencies. fZ, 4 GHz. Determines the shape of G,,,,s(rp) at low frequencies, .fs 4 GHz.

'

228

W. J. FLEMING AND J. E. ROWE

2. Results for (100)- and ( 1 1I)-Oriented Specimens As discussed above, the off-axis acoustic gain equation, Eq. (1 19), need only be solved for those directions of wave propagation which are contained by the area of the basis domain. The basis domain of the [loo]-oriented crystal is shown in Fig. 31. When Eq. (1 17) is used with ( I , , m, , no) =

(P

( a ) BASIS DOMAIN

( b ) BOUNDARY-LINE SOLUTIONS

FIG.31. Boundary lines of the basis domain in a [lOOI-oriented crystal.

(1, 0, 0), the boundary-line solutions of Fig. 31 are as follows: (1) For the L , line where 1 = m, tan i= I/cos cp,

0 5 cp 2 n/4;

(121a)

0 5 cp S n/4;

(121b)

(2) For the L2 line where I = n, tan i = l/sin cp,

and the L , - L,' line and the L,' - L,' line coincide, respectively, with the cp = 0 and the cp = 71/4 directions. Equations (121) are solved and the boundary-line solutions are plotted in Fig. 31b. As before, when the nature of the boundary-line crossings is taken into account, the number of possible waves is determined. The results of this analysis are given in Table VI. The basis domain of the [Ill]-oriented crystal is shown in Fig. 32a. The basis domain is comprised of three full equivalent basis regions plus

229

ACOUSTOELECTRIC INTERACTIONS

TABLE VI POSSIBLE WAVES

Acousticwave type

Wave identification number

LG FT

1

IN A

[ 100]-ORIENTED CRYSTAL

Occurrence in full 2~-rotation of P

Range of existence'

p=O

O
p=rr/4

4 4 4 4 8

none all none none none

all

all none

(52

= cos-'d.5)

~~

ST

1

2 I 2

5 < L 2 5 > L 2 k

L

5 > 5 2 3

5 < 5 2

5>L3

none

a The range of existence gives the inclination angle limits for which the acoustic wave can exist in the basis domain of Fig. 31 b.

two partial basis regions. If Eq. (1 17) is used with (I,, m a , no) = ( I , I , l)/J3, the boundary-line solutions are as follows: (1) For the L , line where 1 = 0, tan [ = J2/(J3

cos cp

(2) For the L , line where - I

+ sin cp),

rc/6 5 cp 5 742;

( 122a)

= m,

(1 22b) [Too]

'p

( b ) BOUNDARY -LINE SOLUTIONS

FIG.32. Boundary lines of the basis domain in a [ I Ill-oriented crystal.

230

W. J. FLEMING A N D J. E. ROWE

(3) For the L,' line where m tan

= 0,

c = J~/(sin cp - J3

cos cp),

n/3 2 cp 5 n/2;

(122c)

(4) For the L , line where - I = n, tan

c = 2J2/(J3

cos cp - sin cp),

n/6 5 cp 5 n/3;

(122d)

and the L,' - L; - L,' line and the L; -''L line coincide, respectively, with the cp = n/6 and the cp = n/2 directions. The boundary-line solutions of Eqs. (122) are plotted in Fig. 32b. When Table I11 is used to take the nature of the boundary-line crossings into account, the number of possible waves in the [ 1 1 11-oriented crystal is determined and they are listed in Table VII. Kokoschinegg and Seeger (43) report experimental results wherein the radiation characteristics of arbitrarily oriented InSb specimens have been measured. This mode of radiation is identified as Mode 111 since it occurs in short-length specimens at intermediate applied field values. In agreement with Table 11, they indeed find that a (loo)-, a (1 lo)-, and a ( 11 1)-oriented specimen exhibit, respectively, a fourfold, a twofold, and a threefold periodicity in the azimuthal radiation patterns. Moreover, threshold characteristics of the Mode TI1 radiation for specimens oriented along the three principal axes show little variation [see Fig. 2 of Ref. (43)] which substantiates the present theory that Mode I11 radiation arises from the off-axis amplification of acoustic waves (36). In particular, a theoretical gain characteristic has been calculated in order to correspond to the experimental measurement of Kokoschinegg and Seeger (43) and these results are shown in Fig. 33. Applied current values for the theoretical results of Fig. 33a have been determined using Eq. (105) to give a constant applied electric field of 50 V/cm. Further analysis shows that the emergence of the fourfold pattern of radiation P, is accounted for by the ensuing dominance of the off-axis FT-2 wave (see Table VI). Seifert and Sablatschan ( 4 4 ) report azimuthal patterns of Mode 11 transittime current oscillation amplitudes in ( 100)-oriented InSb which correlate well with the corresponding theoretical patterns of off-axis acoustic gain ; these results are shown in Fig. 34. The transit-time current oscillations manifest the existence of acoustic domains which arise from the acoustic gain integrated over the thermal phonon frequency spectrum. The frequency of maximum acoustic gain basically controls the formation of the domains and hence of the oscillations. Since the frequency of maximum acoustic gain occurs near f = f o = 1.45 GHz, the theoretical off-axis acoustic gains of Fig. 34a have been calculated at this frequency. A11 16 oscillation lobes in Fig. 34b are accounted for by the off-axis theory of Fig. 34a; however, the relative magnitudes do not directly correspond. Further investigation reveals

TABLE VII POSSIBLE

Acousticwave type

Wave identification number

WAVES IN

A

[ 1 1 1 ]-ORIENTED CRYSTAL

Occurrence in full 2~-rotation OfP

"1

p

+6

:

= cos-'V''p,

rrih <

Range of existence" 5 2 = cos-w,L

5 n:'3

C3

9 0

cos-'(f)]

~ [ <3cp 5 ~ / 2

0

cp= TI2

2

P

rn

LG

FT

ST

~.

2 3

I 3 3

1 2

3 6

1 2

3 6

3 4

3 3

1

5-= il 5 none

iL, none

5 s 5 3

ikc LL

none none none

> :

Ll

5 > 5 3

none

6
LI < 5 < L,' 5 >-. L * '

n cl

5 < 5 2

zn

none

5

2 ' .

i 2

2

i>L2

5iL2 5 .> L1

none none

;1 s >

i
5
5 4 5 2

8

L, < 5 < 5>L3

none

L

L , < 5 < L,' none 5 > Lt'

0 4

2

none none

5 :.'

.- -

52

_ _

" The range of cxistence gives the inclination angle limits for which the acoustic wave can exist in thc basis domain of Fig. 32b.

N c W

232

W. J. FLEMING A N D J. E. ROWE

1.1 GHz, E,=50 V/cm

2

J

u''i20 'I

3% t

0

n/2

3n/2

n

AZIMUTHAL ANGLE.

0

2n

rg

lo)

o

r/2

D

Sn/2

2n

y , RADIANS

(b)

FIG.33. Comparison between the theoretical rms acoustic gain and the radiation patterns of the Kokoschinegg-Seeger experiment (43). (a) Theory: rim acoustic gain in (100)-oriented JnSb. (b) Experiment: Mode 111 radiation from
that the eight strong lobes appearing at q = k15" and all multiples of n/2 in Fig. 34b correspond to the off-axis amplification of the ST-2 wave, whereas the four lobes appearing at the (1 lo) transverse crystal directions correspond to the FT-2 wave and the four lobes at the { 100) directions correspond to the FT-1 wave (see Table VI). Seifert and Sablatschan (44) note that the realization of the regular azimuthal patterns of oscillation in Fig. 34b requires special care in the preparation of the specimen surfaces, i.e., opposite faces must be smoothly polished and strictly parallel for good results. The strongly disparate oscillation peakk at cp = f 15" in Fig. 34b are attributed to an undetermined dependence upon the surface properties of the specimen. As in Section V.C.1, numerical results such as those shown in Figs. 33a through 34a have been analyzed (36) and are summarized in Table Vlll.

233

ACOUSTOELECTRIC INTERACTIONS

3n/2

(100)

8,22 k G , I,, UNSPECIFIED

(b)

FIG.34. Comparison between the theoretical off-axis acoustic gain and the transittime current oscillation pattern of the Seifert-Sablatschan experiment ( 4 4 ) . ( 3 ) Theory: acoustic gain in <<100;-oriented InSb. (b) Experiment: transit-time current oscillation amplitude in < IOO\-oriented InSb (arbitrary scale). The ,'loo) and i110: labels indicate the porientations of the transverse specimen faces.

As before, Table VIII can be used to predict the resultant anisotropy characteristics of G,,,(cp). For example, at low frequencies, with large magnetic fields and intermediate applied currents in ( I 1 ])-oriented InSb, the FT-2 wave determines the shape of G,,,(cp) and there are six distinct peaks in the G,,,(cp) characteristic occurring at cp = 90 f 30' and all successive multiples of 120".

234

W. J. FLEMING AND J. E R O W

TABLE VIII THE DOMINANT WAVESIN THE OFF-AXISACOUSTOELECTRIC THEORY FOR
AZIMUTHAL ANISOTROPIES OF

Specimen orientation and acousticwave type

Wave identification number

Azimuthal angle of dominance" and periodicity (Azimuthal angle in degrees and k = 0, iI , 1 2 , . . . ) Low applied currentb

+

k 90)d (k 90)'.

(45

negligible 45 k 90 negligible

+

ST

(isotropic)d negligible negligible (30 k 120)'. negligible 90 k 120 (90 j ,34) -t k 120 negligible negligible

+ +

FT ST N

Intermediate applied current'

+ (45 + k 90)'. 45

k 90 k 90

negligible -(&21)+ k 9 0 negligible (30 -tk 120)' 90 k 120 negligible [(90 1 30) t k 120]'*' negligible negligible 30 -t k 120 90-1 k 120

+

The azimuthal angle of dominance is the angle at which maximum off-axis gain is achieved; these results require B1 2 2 kG or, equivalently, b % I . lo 5 0.3 A or, equivalently, u,/uT 5 0.06. 0.3 5 fo 5 3 A or, equivalently, 0.06 5 uo/vT 5 0.63. ' Determines the shape of G,,,,s(v)at high frequencies,f? 4 GHz. at low frequencies,fz 4 GHz. Determines the shape of Gr,,,$(~)

VI. SOLUTION OF THE ACOUSTOELECTRIC INTERACTION FOR ELECTRON-HOLE CARRIER TRANSPORT AND OFF-AXIS ACOUSTIC-WAVE PROPAGATION A . Introduction

When sufficiently large static fields are applied to a semiconductor, noneqnilibrium minority carriers can be generated by impact ionization and carrier injection processes. Recent work by Greebe (45) and Fischler (46) has shown that the acoustic gain supported by minority carriers is comparable to that of the majority carriers. Of particular interest here is the fact that the hole-supported acoustoelectric interaction can account for the microwave radiation nucleated by hole injection which was observed in n-type InSb by Fleming and Rowe (13).

ACOUSTOELECTRIC INTERACTIONS

235

The theory of acoustoelectric interactions developed in the previous sections will be extended here to include all possible electron- and holesupported waves. This work is significantly different from that of Greebe (45) and Fischler (46) because it (1) takes into account the effects of an applied static magnetic field on the static carrier transport system; (2) includes the rf effects of carrier diffusion, carrier inertial terms, and magnetoresistivity ; and (3) allows for arbitrarily directed off-axis acoustic-wave propagation. B. Solution of the Static Carrier Transport System

The static carrier transport system is depicted by a bulk hydrodynamic model which ignores finite boundary effects. Moreover, the possible existence of adiffusion gradient andthe processes ofcarrier generation and recombination are not considered here. Such conditions are consistent with the analysis of the acoustoelectric interaction to be developed in Section V1.C. For convenience, it is assumed only that majority carrier electrons and minority carrier holes are present, and that the application of a transverse magnetic field confines all carrier flow to the Lorentz force plane; the field configuration for this system is shown in Fig. 35. Here, the static carrier

FIG.35. Field configuration of the static electron-hole transport system.

coordinate system (x, y , z ) is aligned with the $-direction parallel to the long dimension t of the specimen, and the 2-direction parallel to the transverse component of magnetic field B, . The azimuthal orientation of B, does not enter into the solution of the static carrier transport system because 111-V compound semiconductors possess isotropic band structure ; thus B, can be taken parallel to 2.

236

W. J. FLEMING A N D J. E. ROWE

The flow of each carrier species i is governed by the equation of momentum conservation, namely, ~ 0i = , +PO,

,(Eo + ~ 0i x, B,).

(1 23)

In the above equation, uo, is the static carrier drift velocity, i is an index parameter which takes on the designations “e” and “h” (denotingelectronand hole carriers), p o , is the static carrier drift mobility and E, is the static electric field. The plus sign in Eq. (123) corresponds to hole flow, whereas the minus sign corresponds to electron flow. Since all carrier flows are confined to the x-y Lorentz force plane, taking the cross product of Eq. (123) with the 2-directed magnetic field B, gives a result which can be used to rearrange Eq. (123) into the form ~ 0 i(1,

+ bi2)= * P O ,

iE0

+ p i , i(E0 x

B,>,

(124)

where b i A / p o , B, 1 . In Eq. (124), the carrier drift velocity is given explicitly in terms of the applied fields. If Eq. (124) is written out separately for each carrier species e and h, and the field configuration of Fig. 35 is used, a set of four equations is obtained. Upon the elimination of the static electric field components Eo, and Eo, , the four equations reduce to two equations which give the components of hole drift velocity in terms of electron drift velocity. The resulting equations can be written as follows :

where

and aXy= - a y x = be

+ b,, .

The above expression is particularly useful since the specification of the drift velocity of majority carrier electrons and the value of transverse magnetic field directly determine the drift velocity of minority carrier holes. It is desirable to note certain general properties of the electron-hole transport system. For example, when the sum of the squares of carrier drift components is taken using Eq. (125), it can easily be shown that the magnitude of the hole drift velocity is related to the magnitude of the electron drift velocity by the expression /UO,hl = Iu0,el

‘ (kLO,h/LLO,e)[(l

f

+ bh2)1”z.

( 1 26)

ACOUSTOELECTRIC INTERACTIONS

237

Similarly, Eq. (125) also shows that the angle O', measured between the electron and hole drift velocities (as shown in Fig. 35), is fixed by the value of magnetic field and is given by 0'

= 7c -

(0,+ ah),

(127)

where 0' L cos-'(G O , h . i i O , e )

and

OiLttan-'IbiJ.

In the absence of carrier recombination and generation, the static conduction current density Jois given by JO

=

QeJ'Ou0.h

- QeNouo,e,

( 128)

where Q, is the magnitude of the electronic charge, and Po and N o are the equilibrium hole and electron carrier densities. As before, the field and transport variables are expressed in terms of the drift velocity u ~ of, the ~ majority carrier electrons. If the field configuration of Fig. 35 is used, Eqs. (125) and (128) can be combined to yield the following relation:

where No' A N o + Pou'axx and Po' P o u ' u X y Moreover, . the magnitude of the static electric field can be determined from Eq. (124) and written as follows:

Similarly, the ratio of the Hall electric field component Eoy to the drift electric field component Eo, can also be found from Eq. ( I 24), and is equal to EoyIEox = -tan(@,

- i O , e),

(131)

where 0, A tan-'(po,, B,) is the electron Hall angle and l o , ,A tan-' ,) is the angle of electron flow shown in Fig. 35. x (uoy, A general solution for the static electron-hole transport system of Fig. 35 can be obtained by utilizing the following procedure. Values for the electron and hole densities, N O and P O , are specified (note that the value of N o should be chosen greater than Po because electrons are assumed to be the majority carriers). Appropriate values for the electron and hole mobilities are used, a magnetic field B , is specified, and a value of electron drift velocity luO,,l is chosen. First, the magnitude of the hole velocity and the direction of hole drift relative to electron drift 0' are found, respectively, from Eqs. (126) and (127). Then, the direction of electron drift ( o , c relative to the crystal long dimension L is chosen and the components of conduction current density J, and static electric field E, are found using Eqs. (l29)-( I 3 I ) .

238

W. J. FLEMING AND J. E. ROWE

It is significant to note that once the magnetic field B, is specified and the electron-hole drift parameters are chosen, the angular relationship of the vectors u,, ,, u,, ,, and E, in Fig. 35 is fixed. Thus, as the angle of electron drift l o ,,is increased, these vectors maintain their relationship to one another and simply rotate as a unit about the a-9 origin. The angle ('o,e is usually chosen to correspond to certain boundary conditions. For example, if the net transverse current J o y is set equal to zero, Eq. (129) indicates that the ratio of transverse to longitudinal electron drift velocity must be chosen as follows : Lloy, e l u o x , e

(1 32)

= Po'lNo'.

By definition, it is true that l o , 4k tan-'(u,,, Juox, ,); hence, for J , , = 0, the angle to, is specified by Eq. (I 32). When this value of (',, is substituted into Eq. (131), the ratio of Hall electric field to drift electric field, Eoy/Eox, can be determined and it agrees with the corresponding result given by Eq. (5) of King (37). Other boundary conditions of interest are (,, = 0 and = 0, which correspond, respectively, to the Suhl effect hole injection mechanism described by Shockley (47) and to the short-circuiting of the Hall field ( E o y= 0) at the contact-semiconductor interface. When high values of electric field are applied to a semiconductor, nearly equal densities of electrons and holes are generated by bulk impact ionization. Under these conditions, a diffusion gradient is established across the lateral dimension of the specimen by the presence of a transverse magnetic field. For this case, Swartz and Robinson (18) have shown that electrons and holes flow collinearly in a thin layer located adjacent to the lateral specimen surface toward which the Lorentz force is directed. Hence, the present analysis only applies for moderately large values of electric field, whereupon bulk impact ionization does not prevail. Nonetheless, the present analysis adequately depicts the static electron-hole flow when the minority carrier holes are generated by localized generation and injection mechanisms. Note that the effects of spatially dependent recombination processes are ignored here ; this implies that the above analysis is necessarily limited to local regions of the semiconductor wherein carrier recombination is slow and the density of minority carrier holes is relatively uniform.

co,

C. Solution .#or the Growth Rate of the Acoustoelertric Intevuction As before, the off-axis acoustoelectric interaction is described by the equivalent one-dimensional dispersion equation (derived i n Section I1.C) and the rf conductivity is determined from the small-signal field and transport equations (derived in Section lI.D). The growth rate of the interaction is

239

ACOUSTOELECTRIC INTERACTIONS

given by Eq. (41), wherein the values of the electromechanical coupling constants l i 2 and u, are found using the solution method of Section V.B, and the longitudinal rf conductivity o,,must yet be determined. If the static carrier transport system is analyzed using the solution method of Section VI.B,the electron and hole drift velocities u ~ and , u ~ ~ can . be ~ determined. Specification of the azimuthal orientation 4" of the transverse magnetic field and the assignment of a long dimension direction L locate the directions of the drift velocities u~,, and uo, ,, in the crystal coordinate system, as shown in Fig. 36. It is assumed that an acoustic wave propagates

LORENTZ FORCE , PLANE

A +

x2

L

FIG.36. Relative orientations of the transverse magnetic field B,, the acoustic wave 4 and the electron and hole drift velocities uo. and uo,,, [shown in the crystal coordinate system (x,, s2, xd].

<

along the direction 4 at the off-axis angie which is measured in the Lorentz force plane. The rf conductivity must first be determined. Tn the interaction depicted by Fig. 36, it is comprised of contributions from both electrons and holes. As discussed in Section II,D. an aggregate conductivity is taken as clot= c i .where i is summed for e and h, corresponding to the electron contri-

1 i

bution and the hole contribution. I t follows that the aggregate longitudinal l oil. i . An appropriate expression for q , i, rf conductivity ( o , l ) l oequals

1 I

corresponding to each carrier i , i s derived using the solution method of Section IV,B,wherein a hydrodynamical model of carrier transport is utilized

240

W. J. FLEMING AND J. E. ROWE

and the quasistatic approximation is made. For simplicity, the carrier trapping effects and empirical field factors of Section IV will be ignored here. Thus oil, is given by Eq. (89) which, after settingf, equal to unity, can be written out for each carrier species i as follows: 011, i

= W R . iEI/(Yi

(133)

vi' - j ~ / w Di ),,

where wR, i I);

= 0 0 ,i/&t 7

= ij/Vi[l

OD, i =

+ (b;vi/v;)z],

vi u s 2 ( ~i>iu$, , i

7

b, = lp o,iB,I,

and Note that the rf effects of carrier diffusion, carrier inertial terms, and magnetoresistivity are included in the above expression, respectively, by the terms w D ,i , w " , i , and b ; . If these effects are neglected ( w D , -+ co, w " , -+ 0, and bi-+O), Eq. (133) reduces to the special cases investigated by Greebe (45) and Fischler (46). Examination of Figs. 4 and 36 shows that the appropriate values of ii' in Eq. (133) are

i,'= i- iO,e and Ch' = Co,e + 0' - i, ( 134) depends on the chosen boundary condition (see Section V1.B) where io,e and 0' is given by Eq. (127). If B , = 0 and the direction of electron drift is taken parallel to 2,< o , e = 0 and 0' = n, Eqs. (134) reduce to <,' = i and ih'= n - i,in accordance with the special case of collinear electron-hole drift along the direction @. It is convenient to resolve the term vi' into real and imaginary parts, and to rewrite Eq. (133) into the form

Ai = y i Vke, i

=

1tke, i ,

I

+ b:2,

B; = y i vim, ; - W / O D , ;, vim, i

= W " , ;(l

-

biz)

and

+

bj2 = bi2/(1 a:,i). The aggregate conductivity (a,,)totis found using Eq. (135) and the relation (011),,, = all, i . In the growth rate expression of Eq. (41) for the electronI

~. hole interaction under analysis here, ol, is set equal to ( o , , ) ~It ~is ~convenient

24 1

ACOUSTOELECTRIC INTERACTIONS

to resolve the tern1 all/wsl, which appears in Eq. (41), into real and imaginary parts as follows: Call.,

all/wci = ( a l l ) t o J = ~ ~I, = RRe -in,,,

(136)

WE1

where %e

=

c

(OR, ~

~

i

/

~

~

j

~

,

1

R,,

=

1w R , B; J W D , ~ i

and

D i 2 = A i 2 + Biz.

When Eqs. (41) and (136) are combined, the desired expression for the growth rate of the off-axis electron-hole acoustoelectric interaction is obtained and can be written as

where the appropriate values of K~ and P ,are found using the solution method of Section V,B, and the parameters R,, and R,, are determined using Eqs. (133)-(136). Note that if the minority carrier holes are absent, w R , = 0, Eq. (137) reduces to the proper expression for the electron-supported inter: action, namely, Eq. (90) for the case of on-axis wave propagation, or Eq. (1 19) for off-axis wave propagation. In summary, the following procedure can be utilized to solve the problem of off-axis electron-hole acoustoelectric interaction which is depicted in Fig. 36. First, the values of the transverse magnetic field B, and the electron drift velocity u ~ are , chosen, ~ whereupon the solution method of Section VI,B determines the values of the hole drift velocity u ~ and , the ~ angles ( o , e and 0 ’ .When the azimuthal angle cp and the off-axis angle ( are chosen, the electromechanical coupling parameters rc2(cp. i)and u,(cp, l ) ,for each acoustic wave, are determined using the solution method of Section V,B. Finally, the growth rate of the acoustoelectric interaction is calculated, for each acoustic wave, using Eq. (137). As i n Section V,C, a systematic solution method can be developed; however, care must be taken to include all possible off-axis interactions. For example, inspection of Fig. 36 shows that due to the arbitrary orientations of the electron and hole drift velocities uo, and uo, , the wave propagation direction 4 must be taken through the full 2n-rotation of [ in order to obtain all possible solutions to Eq. (137). Preliminary analysis of Eq. (137) indicates that the growth rate of the electron-supported interaction is generally smaller when holes are present.

,

242

W. J. FLEMING AND J. E. ROWE

However, when the wave propagation direction 4 is rotated toward the direction of hole drift u ~ , new ~ , interactions supported by hole drift can appear. If the total rms acoustic gains of all possible waves are calculated, as was done in Section V,C, the rms gain level for the electron-hole interaction is found to be more than double the level of the corresponding electron-supported interaction investigated in Section V,C. Hence, notwithstanding the simplified nature of the theory of electron-hole interaction developed herein, it nonetheless can account for the microwave radiation nucleated by minority hole injection which was observed in n-type InSb by Fleming and Rowe (13). Further investigation of this interaction is surely warranted.

VII. SUMMARY In the above discussion particular attention was given to the development of a physical model to depict the process of acoustic noise generation in 111-V compound semiconductors. On the basis of experimental results, the acoustic noise process was described in terms of the excitation of spurious off-axis acoustic waves, nucleated by localized sources such as impact ionization or minority carrier injection. It was assumed that the intensity of the acoustic noise was proportional to an aggregate rms total of the acoustic gains of all possible acoustic waves. Hence, a general formulation of the offaxis acoustoelectric interaction, specialized for 111-V compound semiconductors, was fully developed in Section TI. Considerable physical insight was made possible by the application of this theory to one specific example, namely, the acoustoelectric interactions which occurred in n-type InSb at 77°K. These interactions are especially interesting since their existence is manifested by electrical instabilities such as rf current oscillations and microwave noise radiation. Moreover, the acoustic noise itself, which degrades the performance of acoustic-wave devices, is also described by this theory. The special case of on-axis acoustic-wave propagation along the ( 1 10) crystal axis of InSb, in the presence of a parallel magnetic field, was analyzed exactly in Section 111 in order to illustrate the solution of the general acoustoelectric theory. When arbitrarily oriented static fields were allowed, the general theory was approximated by an equivalent one-dimensional solution and a concise expression for the growth rate of the acoustoelectric interaction was obtained in Section IV. It was found that when a transverse magnetic field was present, and a hydrodynamical model of conduction carrier transport was utilized, the solution for the acoustic gain of on-axis acoustic-wave propagation given in Section IV,C was in essential agreement with the results of more detailed

ACOUSTOELECTRIC INTERACTIONS

243

microscopic theories. It was concluded that the major correction required to extend the hydrodynamical model of acoustic gain to microwave frequencies was the inclusion of electron inertial terms in the equation of momentum conservation. Further analysis revealed that the physical mechanism for the emergence of a separate high-field mode of acoustic-wave amplification (Mode I) was the drift-enhanced quenching of electron diffusion effects. Moreover, it was found that the frequency of maximum acoustic gain, as given by this theory, did not occur at the fixed frequency fo = ( Q ~ W ~ ) ' / ~ but rather it was dependent upon the exact values of electron drift velocity and magnetic field strength. Excellent correlation of this theory with recently reported measurements (6,8) of microwave acoustic gain was obtained. When large applied fields were present, empirical field factors (which account for carrier heating and geometrical magnetoresistance) were incorporated into the theory to give best agreement with experiment. In Section V the solution for the acoustic gain of a wave propagating in an off-axis direction, and in the presence of arbitrarily oriented static fields, was investigated in considerable detail. The effective values of the off-axis electromechanical coupling parameters were first determined in order to define the conditions for which off-axis acoustic gain could be achieved. Then a solution method was developed which gave the gains of all possible acoustic waves, and their appropriate identification according to a systematic categorization procedure. Extensive computer investigation of the theory yielded substantial agreement with experimental results. An especially significant point of agreement, among several additional points, was the correlation of the theoretical azimuthal patterns of acoustic gain with experimentally of microwave radiation. observed patterns (IO,I3,43) The theory of acoustoelectric interaction was solved in Section VI for the case of electron-hole carrier transport. A straightforward solution for the proper static drift velocities of the carriers was given by a self-consistent analysis of the static carrier transport system. When the static solution was used, the gain of the electron-hole supported acoustoelectric interaction was derived in Section VI,C. It was found that the summation over all possible electron- and hole-supported wave interactions yielded substantially higher rms gain levels, therein accounting for the observation ( I S ) of microwave radiation nucleated by minority-carrier hole injection in n-type InSb.

ACKNOWLEDGMENTS The authors wish to acknowledge the support of this work by the Rome Air Development Center under Contract No. F30602-71-C-0099. In addition the authors very much appreciate the significant contributions made by Mrs. June Corkin and Mrs. Wanita Rasey in editing and typing the manuscript.

/ ~ ~ T ,

244

W. J. FLEMING A N D J. E. ROWE

REFERENCES 1. A. R. Hutson, J. H. McFee, and D. L. White, Ultrasonic amplification in CdS. Phys. Rev. Lett. 7, No. 7, 237-239 (1961). 2. J. H. McFer, Transmission and amplification of acoustic waves. 111 ‘‘ Physical Acoustics” (W. P. Mason, ed.), Vol. IV, A, pp. 1-44. Academic Press, New York, 1966. 3. R. Bray, C. S. Kuniar, J. B. Ross, and P. 0. Sliva, Acoustoelectric domain effects in 111-V semiconductors. J. Phys. Suc. Jap. 21 (Suppl.), 483488 (1966). 4. M. C. Steele, Magnetic field effect on acoustoelectric gain in semiconductors. RCA Rev. 28, No. I , 58-63 (1967). 5. C . W. Turner, T. Van Duzer, and K. P. Weller, Acoustic-wave amplification in highmobility semiconductors at microwave frequencies. Electronics L e f t . 3, No. 4, 162-1 63 (1967). 6 . R. K. Route and G. S. Kino, Acoustoelectric amplification in InSb. I E M J . Res. Develop. 13, No. 5 , 507-509 (1969). 7. J. Livingstone and W. Duncan, Acoustoelectric amplification at microwave frequencies in InSb in crossed electric and magnetic fields. Bril. J . Appl. Phys. 2. No. 10, 141 1-1421 ( 1969). 8. H. Hayakawa and M. Kikuchi, Ultrasonic amplification in high electric field under transverse magnetic field in InSb. Appl. Phys. Lett. 17, No. 2, 73-75 ( I 970). 9. E. Stern, Microsound components, circuits, and applications. IEEE Tram. Microivaae Theory Tech. 17, No. 11, 835-844 (1969). 10. T. Arizumi, T. Aoki, and K. Hayakawa, Two different modes of acoustoelectric oscillation and microwave emission from n-InSb. J . Phys. Soc. Jap. 25, No. 5 , 1361-1369 ( 1968). 11. C . W. Turner and J. Crow, Acoustoelectric oscillations with field-dependent period in indium antimonide. Appl. Phys. Lett. 11, No. 6 , 187-1 89 ( 1 967). 12. C. W. Turner, Microwave emission from indium antimonide stimulated by acoustic wave amplification. J . Appl. Phys. 39, No. 9, 4246-4252 (1968). 13. W. J. Fleming and J. E. Rowe, Emission of microwave noise radiation from InSb. J . Appl. Phys. 42, NO. I , 435-444 (1971). 14. W. Duncan and J. Livingstone, Microwave acoustic noise emission from InSb. Phys. Lett. A 32, No. 2, 121-122 (1970). 15. C. W. Turner and K . P. Weller, Dc flow considerations for crossed-field acoustic amplifiers and other solid-state traveling-wave devices. 1EEE Trans. Electron Devices 16, NO. 9, 787-797 (1969). 16. A. H. Thompson and G. S. Kino, Noise emission from InSb. J . Appl. Phys. 41, No. 7 , 3064-3075 (1970). 17. B. Ancker-Johnson and C. L. Dick, Jr., Low-field injection in n-InSb. Appl. Phys. L e f t . 15, No. 5 , 141-143 (1969). 18. G . A. Swartz and B. B. Robinson, Coherent microwave instabilities in a thin-layer solid-state plasma. J . Appl. Phys. 40, No. I I,4598461 1 (1969). 19. F. Seifert, Helicon diagnostic of acoustoelectric domains in InSb. Electron. Lett. 4, NO. 17, 356-357 (1968). 20. A. R. Moore, R. W. Smith, and P. Worcester, Off-axis acoustoelectric domains in CdS. IBM J . Res. Develop. 13, No. 5 , 503-506 (1969). 21. W. P. Mason, “Physical Acoustics and the Properties of Solids.” Van Nostrand, Princeton, New Jersey, 1958. 22. A. R. Hutson and D. L. White, Elastic wave propagation in piezoelectric semiconductors. J . Appl. Phys. 33, No. I , 4 0 4 7 (1962). 23. J. Gorelik, M. Zinman, B. Fisher, and A. Many, Effect of longitudinal magnetic field on acoustoelectric amplification in n-InSb. J. Appl. Phys. 41, No. 2, 4 4 5 4 5 0 (1970).

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245

24. M. C. Steele and B. Vural, “Wave Interactions in Solid State Plasmas.” McGrawHill, New York, 1969. 25. W. Harth and R. Jaenicke, A theoretical explanation of the low-field microwave emission from InSb. Appl. Phys. Lett. 14, No. I , 27-29 ( I 969). 26. K. P. Weller and T. Van Duzer, Crossed-field acoustic amplification in extrinsic high-mobility, nondegenerate semiconductors. J . Appl. Phys. 40, No. 1 1 , 42784289 ( I 969). 27. Y. Abe and N. Mikoshiba, Magnetic field dependence of acoustoelectric current oscillation in n-InSb. Appl. Phys. Lett. 13, No. 7, 241-243 (1968). 28. W. J. Fleming and J. E. Rowe, Parameter dependence of acoustoelectric amplification inInSb. Appl.Phys.Lert. 18,No.3,96-99(1971). 29. G. S. Kin0 and R. K. Route, Sound wave interactions in InSb. Appl. Phys. Lett. 11, No. 10, 312-314 (1967). 30. D. L. White, Amplification of ultrasonic waves in piezoelectric semiconductors. J . A&. Phys. 33, NO. 8, 2547-2554 (1962). 31. 0. Madelung, “Physics of 111-V Compounds.“ Wiley, New York, 1964. 32. G. H. Glover and K. S. Champlin, Microwave permittivity of the InSb lattice at 77°K. J. Appl. Phys.40, No. 5, 2315-2316 (1969). 33. L. J. Slutsky and C . W. Garland, Elastic constants of indium antimonide from 4.2”K to 300°K. Phys. Reu. 113, No. I , 167-169 (1959). 34. G. Arlt and P. Quadflieg, Piezoelectricity in Ill-V compounds with a phenomenological analysis of the piezoelectric effect. Phys. Status Solidi 25, No. I , 323-330 ( I 968). 35. W. J. Fleming and J. E. Rowe, Acoustoelectric effects in indium antimonide. J . Appl. Phys. 42, No. 5, 2041-2047 (1971). 36. W. J. Flerning, Generation of microwave radiation in InSb by acoustoelectric amplification. Tech. Doc. Rep. No. RADC-TR-71-151. Air Force Systems Command, Rome Air Development Center, Grifiss Air Force Base. New York (1971). 37. J. E. King, Monisothernial conduction in indium antimonide with orthogonal electric and magnetic fields. J . .4ppl. Phys. 40.No. 13. 5350-5360 (1969). 38. E. V. George and G. Bekefi, Effects of contacts on the emission from indium antimonide. Appl. Phys. Lett. 15, No. I , 33-35 (1969). 39. R . F. Wick, Solution of the field problem of the germanium gyrator. J . Appl. Phys. 25, No. 6, 74 1-756 ( I 954). 40. V. H. J . Lippniann and F. Kuhrt, Der Geonietrieeinlluss auf den transversalen niagnetischeri Widerstandseffekt bei rechteckformigen Halbleiterplatten. Z . Notftrjbrsch. A 13, No. 6 , 462-474 (1958). 41. C. S. Hartmanil and A. Bers, Acoustic-wave propagation and amplification in InSb. Quart. Progr. Rep. No. 93, Massachusetts Institute of Technology, Cambridge, pp. 139- I45 (April 15, 1969). 42. T. Aoki, K. Hayakawa. and T. Arizumi. Acoustoelectric oscillation in ri-InSb. J . Jap. Soc. Appl. Phys. 39 (Suppl.), 7-1 I (1970). 43. P. Kokoschinegg and K. Seeger, Anisotropy o f microwace eniission from ri-type InSb. Proc. lEEE56, NO. 12, 2191-2192 (1968). 44. F. Seifert and E. Sablatschan, Acoustoelectric excitation in [I001 oriented 1nSb rods. Solid Stofa Commtn. 7, No. 24, 1833-1 835 (1969). 45. C. A. A . J. Greebe. Use of minority carriers for ultrasonic aniplification in piezoelectric semiconductors. P/i.vs. Lett. A 28. No. 6. 4 5 5 4 5 6 (1968). 46. C. Fischler, Acoustoelectric amplification in a many-carrier system. J . Appl. Phys. 41, No. 4, 1439-1443 (1970). 47. W. Shockley. *‘ Electrons and Holes in Semiconductors,” pp. 3 18-328. Van Nostrand, Princeton, New Jersey, 1950.

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Current Saturation Mechanisms in Junction Field-Effect Transistors* EDWARD S. YANG Departnierit of Electrical Engineering and Conipurer Science, Columbia Llniaersity, New York, New York

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................... Review of the Literature.. . Governing Equations. . . . . . ......................................... Gradual Channel Approximation (GCA). . . . . . . . . . . . . . . . Saturation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Depleted Channel Model., . . . . . . . . . . . . B. Finite Channel Model.. . . . . . . . . . . . . . . . .............. VI. Numerical Calculation . . . . . . . . . . . . . . . . . . . VII. Current Saturation in MOSFETs.. . . . . . . . . . VIII. Conclusion ..................................................... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I. 11. 111. IV. V.

247 250 253 255

264

1. INTRODUCTION A junction field-effect transistor (JFET) is an active semiconductor triode in which the current is primarily carried by the majority carriers. An n-channel JFET consists of a lightly-doped n-type channel sandwiched between two heavily dopedp-type gate layers. Figure I shows the original model of a JFET as presented by W. Shockley ( I ) . The two gates are externally connected and additional electrical contacts are attached to the two ends of the channel via the n + regions. The drain current flows parallel to the metallurgical gate junctions which are reversely biased. The reverse bias across the gate p-n junctions depletes free carriers from the channel and produces space-charge regions extending into the channel. As a result, the electric field and the carrier density within the channel are modulated by the application of the external gate voltage. The theory of operation of the JFET was presented by Shockley for devices having a channel length (L) of two or more times the channel width (2a). Shockley’s analysis is based on the gradual channel approximation (GCA) which assumes that the change of channel width along the channel is small in comparison with the width of the channel. This assumption implies

* This work is supported by the National Science Foundation under Grant GK-18772. 247

248

EDWARD S. YANG

that the electric field along the channel is much smaller than the electric field normal to the channel. In addition, total depletion of free carriers in the spacecharge region and charge neutrality in the channel region are assumed. The transition between these two regions is taken to be abrupt. An important concept in Shockley's model is the pinch-off of the conductive channel. A pinch-off voltage is defined as the potential drop across a space-charge region of width a of a reverse biased p-n junction. In other words, when the drain voltage with respect to the gate reaches pinch-off voltage, all free carriers are

0

DR41N

-k

L,

FIG.1. Shockley's original model of a junction field-effect transistor.

depleted from the channel at the drain. According to the GCA, the drain conductance becomes zero when the drain voltage equals the pinch-off voltage. The drain current is then saturated and it remains constant even at a further increase of the drain voltage. However, the complete pinch-off of the conducting channel can not be reconciled with the large drain current in all experimental devices. The inadequacy of the gradual channel approximation to describe the JFET after saturation results from the strong two-dimensional field distribution near the drain. Under the current saturation condition, the electric field along the channel near the drain is comparable to the field normal to the channel. This two-dimensional field distribution violates the GCA which assumes negligible electric field along the direction of the channel. Unfortunately, the analysis of the two-dimensional problem in JFET saturation involves nonlinear partial differential equations which have no anajytic solutions. As a result, it is necessary to introduce approximations both for the simplification of mathematical manipulation and for the understanding of the physical mechanisms involved.

CURRENT SATURATION MECHANISMS IN JFETS

249

11. REVIEWOF THE LITERATURE

Shockley recognized that the gradual approximation would fail completely in a region near the drain at pinch-off. He pointed out that the extrapolation of GCA beyond its range of validity led to zero channel width and infinite electric field along the channel for a drain voltage greater than the pinch-off voltage. The point at which this situation occurred was designated extrapolated pinch-off point or expop. Using expop as the boundary, he divided the channel into the gradual and depleted regions. In the depleted region, it was assumed that the electric field and potential distribution were determined by the fixed charges of the impurities. A graphical procedure was employed to join the two solutions near the expop. The joining of the solutions was simply guessed at. Later, an analytical matching method was used by Prim and Shockley who obtained a matching factor analytically (2). More recently, Wu and Sah presented a more refined matching procedure (3). They showed that the nonzero differential drain conductance could be accounted for by the channel-length modulation after saturation. The drain conductance of JFETs was calculated and compared favorably with experimental results for the first time. Another proposed explanation of the saturation mechanism has been the saturation of the carrier drift velocity at a high electric field ( 4 ) . The effect of nonlinear mobility on JFET was first considered by Dacey and Ross who modified the gradual channel approximation by assuming that the electric field was in the tepid range (5). By using an approximate expression for the mobility as a function of the electric field, Trofinienkoff and Tarney (6,7) obtained an analytic solution extending the theory of Dacey and Ross. Grosvalet et al. (8) calculated the potential distribution along the center line of the channel and they postulated that the saturation of the drift velocity was responsible for the saturation of the drain current for their device. Zuleeg measured the saturation current for short devices at various temperatures and found the same temperature dependence as the limiting drift velocity (9). The significance of the field dependent mobility on the JFET was further demonstrated by Hauser who investigated devices with small channel lengthLo-width ratios (/@. A model was developed to calculate the shape of the junction depletion region including circular gate geometries near the ends of the channel. The model was essentially an extension of Shockley’s original model to nonparallel gate junctions. A significant feature of the model which differed from previous models was the absence of complete channel pinch-off in the current saturation region. The minimum channel width of the order of the Debye length was postulated. Earlier, Sevin had considered a saturation model with finite channel width for the JFET (11). Combining the gradual channel approximation and the saturation velocity

250

EDWARD S . YANG

in the pinched-off region, Grebene and Ghandi (12) proposed a two-region model at saturation. In this model, the GCA is considered valid for the region near the source in which the electric field is below the carrier-saturation field. The second region is defined for the drain end in which the critical field is exceeded. In this region, a conductive channel with finite channel width is formed. From theoretical considerations, Kennedy and O’Brien showed that current saturation could exist in structures exhibiting either a constant or a field-dependent carrier mobility throughout the entire source-drain channel (13). An independent study of the dependence of the saturation characteristics on the nonlinear mobility was made by Mo and Yanai (14). They presented a two-region model similar to Grebene and Ghandhi’s work except for the assumption that the electric field in the region near the drain is not necessarily greater than the critical field. Drain resistances were obtained and compared with experimental values to within a factor of two. There is one common feature in all the foregoing mentioned articles; the authors have started from some assumptions about the shape of the channel and the free carrier concentration inside the channel. This means that the saturation mechanism has been predetermined. In order to find out the actual channel shape and carrier distribution, such a priori assumptions can not be made. The only possible way to find out a solution for the nonlinear partial differential equations is the utilization of a digital computer. Recently, numerical calculations on JFET have been reported by Kennedy and O’Brien (15,16), and by Kim and Yang independently (17). These calculations clarified the internal current conduction picture at saturation. They also showed that Shockley’s complete pinch-off model is a good approximation for devices with large L/a ratios (long devices). I n short devices (small L/a ratios), however, the nonlinear mobility effect plays a strong role in current saturation. An experimental technique was developed by Tango and Nishizawa (18) using electrodes to measure the potential distribution inside the channel. The result was consistent with the computer calculations. However, precise measurement of the channel using electrodes is not possible because of the size of the channel of practical devices. With the exception of the works of Tango and Nishizawa, the measurement of the saturation drain resistance has been employed to evaluate the validity of models for JFET. 111. GOVERNING EQUATIONS

In the analyses of JFETs, it is usually assumed that the current is carried by the majority carriers alone and the recombination is negligible. With these two assumptions, the equations governing the operation of an n-channel JFET may be written in the following forms:

CURRENT SATURATION MECHANISMS IN JFETS

V2Y = -(9/EEJ(ND

- n),

J, = 9D,, Vt7 - 9pnn VY, V . J, = 0,

251 (1)

(2) (3)

where Y is the electrostatic potential, 9 is the electronic charge, E is the dielectric constant, is the permittivity, N , is the donor density, n is the free electron density, J, is the current density, D, is the electron diffusion constant, and p , is the electron mobility. A more complete set of equations including the effect of minority carriers is given by Kennedy and O’Brien (15). The foregoing equations may be solved under various assumptions. We shall first present Shockley’s gradual channel approximation since it is the foundation of all subsequent works on the theory of field-effect transistors. The depleted channel model and the finite channel model will then be discussed. In addition, numerical calculations and experimental results will be covered.

IV. GRADUAL CHANNEL APPROXIMATION (GCA) (19) It is assumed that the JFET may be divided into the space-charge region having fixed charges and the neutral conducting channel with an abrupt transition (Fig. I). In the space-charge region, the electric field is considered to be mainly along the J’ direction which implies that h 2 Y / 6 x 29 62Y/6y2. The Poisson’s equation is simplified to

(4) where b is half of the neutral conductive channel width. By taking y = + a as the reference potential and by assuming that the electric field is along the x direction inside the channel, two boundary conditions are obtained: Y=O

at y = a ,

dY/sj) = 0 at

y

= 6.

The solution of Eq. (4) with these boundary conditions gives the potential inside the space-charge region : Y = (qND/EEo)[(y2 - a’) - ( y - a ) ] ,

b I J y (5 a.

The potential inside the conductive channel isobtained by letting y gives Y , = (qNo/EEo)[a2 - h 2 I 2 , h 2 J y J.

(5) = b which

(6)

The channel potential Y c as a function of x is shown through b(x) which is yet to be determined.

252

EDWARD S. YANG

Since the current in the channel is assumed to be purely drift current, the first term in Eq. (2) is negligible. Integration of the current density in the neutral channel produces the drain current per unit length in the z direction in the following form:

By solving Eqs. (6) and (7), and by integration, the relation between x and b may be expressed as

where V,, = q N D a 2 / 2and bs is half of the conductive channel width at the source. By using Eqs. ( 5 ) , (6), and (8), the electrostatic potential is plotted in Fig. 2 in two dimensions. In the figure, the potential is normalized by the pinch-off voltage Vp. The current-voltage characteristics may be obtained by setting x = L in Eq. (8) and using Eq. (6):

( dyj) -

I D -- _ 2a 3L [yCD U 3-2

S; ‘

(3 - 2 Jyj)] - ,

(9)

where

0 .l 0.9

Fz

2

-

3

9

0.8

I

FIG.2. Electrostatic potential and channel shape based on the gradual channel approxinlation.

253

CURRENT SATURATION MECHANISMS IN JFETS

Yc = M implies that h = 0, i.e. the conducting channel is completely pinched i5 clear that the above analysis applies only for Y c 5 M . Figure 3 shows the drain characteristics described by Eq. (9). The drain current for YcD2 M has been assumed to be constant. Modification of the GCA to include the effect of nonlinear mobility has been reported by Dacey and Ross (9,and by Trokimenkoff and co-workers (6,7,20). These works are not discussed here because they introduce further complexity which may be distracting to the central theme of saturation mechanisms.

off. Since b 2 0, it

0.0

0.5

1.0

1.6

w,, a

FIG.3. Drain characteristics of a JFET based on GCA (19).

V. SATURATION MODELS A . Depleted Channel Model When the applied drain voltage is greater than V,, Shockley's theory predicts that there will be a completely depleted drain region. The boundary between the space-charge region and the neutral region moves towards the source side as indicated by the dashed line in Fig. 2. The point xp is the separation line of the gradual channel region and the completely depleted region. It is assumed that there is no free carrier in the region for x > x,. In this

254

EDWARD S. YANG

depleted drain region, the potential is obtained by solving the two-dimensional Laplace’s equation for a rectangular geometry which gives, after simplification,

+ 4(x, y ) = Y + A , + AleRX’2a cos(ny/2a),

U X , Y> =

(10)

where !I’ is given by Eq. (5). The constants A , and A , are evaluated by Wu and Sah by allowing the continuity of electric field and electrostatic potential at x = x, - +a and x = x,, respectively. By using the fact that x, is a function of the drain voltage, they derived an approximate drain conductance based on this channel-length modulation effect. The theoretical results of the drain resistance rD together with experimental data for a device with L/a = 19.2 are shown in Fig. 4 (3). A simplified expression of the saturation drain resistance for long devices is given by r D = qpnN D

nz(V,

+

VG

- V,)(X, - + ~ ) / 3 1 D .

(1 1)

Since most commercial units have large L/a ratios, the foregoing equation is very useful for design purposes. In any event, the results of Wu and Sah show that the gradual channel approximation is very good for long devices. The nonzero drain conductance after saturation can be accounted for by the channel-lengt h modulation.

0

I

2

3

U

FIG.4. Normalized drain resistance versus drain voltage (3). D = 2a in text.

CURRENT SATURATION MECHANISMS IN JFETS

255

In matching the solutions, it has been assumed that the GCA is valid at x p .This is a serious assumption since the two-dimensional field is very strong at x p .I n other words, the a2Y/ax2term in Eq. ( I ) may contribute significantly to invalidate the GCA (21). Another possible difficulty in this procedure is that the effect of the nonlinear mobility has been ignored. Trokimenkoff and Nordquist presented a theory that included the nonlinear mobility effect and they used Shockley’s matching procedure. It should give better results if the matching method of Wu and Sah is used together with the Trokimenkoff approximation for the nonlinear effect. B. Finite Channd Model Extrapolation of the GCA beyond the pinch-off point implies a channel completely depleted of mobile carriers. Such a conclusion is physically unreal since the drain current has a nonzero value after saturation. By reducing the length-to-width ratio of a JFET, Grosvalet and co-workers found that the experimental results did not agree with the theory of the depleted channel model. Consequently, they postulated that the limiting value of current is attained when the carriers reach their limiting velocity in the drain region of the channel. Their postulation was based on the following evidences. Firstly, they found that the variation of the saturation current with temperature agreed with the temperature dependence of the limiting velocity. Zuleeg has confirmed this result with more measurements. Secondly, the experimental pinch-off voltage, saturation current, and transconductance of the short device were significantly different from the predicted values of Shockley’s theory. These data, however, correlated well with the calculation of the limitedvelocity theory obtained from an analog computer. Therefore, they concluded that the channel is not depleted of mobile carriers when the drain current reaches saturation. The internal picture of the channel under velocity saturation condition has been depicted by Sevin, Hauser, and by Grebene and Ghandhi. Figures 5 and 6 show the finite channel models proposed. I n Fig. 5, Sevin assumed that the saturated channel width is a function of the gate voltage which controls the magnitude of the drain current. Furthermore, when the drain voltage is increased beyond the pinch-off, the space-charge region is extended toward the drain contact. In Hauser’s model the width of the channel has a minimum value equal to or greater than two times the extrinsic Debye length (L,,). When this minimum channel width is attained an increase of drain voltage would result in a decreased carrier concentration in the channel rather than a decreased channel width. The depletion of carriers produces a higher electric

256

EDWARD S. YANC

s

0

FIG.5. The model according to Sevin ( I ] ) and Hauser (10).

field in the channel which could lead to velocity saturation. When the maximum carrier velocity is achieved, the drain current is expressed as

I,

= 2qna,

6Z,

(1 2)

where u, is the saturation velocity of carriers, n is the carrier density in the saturated channel, and 6 z L,. Hauser pointed out that, for very short devices, it is possible for n to exceed the thermal equilibrium carrier density. Furthermore, the velocity saturation may take place before 6 is reduced to L,. When this occurs, no depleted region is formed near the drain of the channel. The model of Grebene and Ghandhi is similar to that of Hauser with the following exceptions. After a saturated channel is formed, increase of the drain voltage produces a longer channel which extends towards the source.

r

GATE

i SOURCE

ORAIN

FIG.6 . The model according to Grebene and Ghandi (12).

CURRENT SATURATION MECHANISMS IN JFETS

257

This is following closely the reasoning of Wu and Sah who called this effect channel-length modulation. The potential distribution is obtained by solving the two-dimensional Poisson’s equation within the saturated channel. In Fig. 6 , region 1 represents the section where the GCA is valid and region I1 represents the saturated channel with finite width 6 . The value of 6 is given by Eq. (12) with n = N , . The drain resistance after saturation is given by rd

= (LEo/Id)[ I

+

(vd

n/2f?o a)2]”2

(1 3)

where Eo is the critical field. The experimental results agree well with the above equation. However, it must be pointed out that there are two important assumptions involved in the formulation of this model. They are Lja > 5 and S G a. With these assumptions, the model is applicable only to long devices with negligible conductive channel width at saturation. Mathematically, the assumption S < a means that the sotution of Poisson’s equation i n the work of Grebene and Ghandhi deviates only slightly from that of Wu and Sah who solved the Laplace equation. Because of the assumptions involved, the conclusion of Grebene and Ghandi concerning the channel shape and carrier accumulation are somewhat doubtful. The finite channel model provides a path for current flow after saturation which avoids the difficulty i n the depleted channel model. However, there is no unique choice of a saturated channel width although two times the extrinsic Debye length seems to be the dimension one may logically conceive. In short FETs, the channel width cannot be easily defined and the finite channel model is difficult to employ. From the very complexity of the problem, it seems that the numerical approach using a large-scale computer is necessary in finding out the saturation mechanisms.

V1. NUMERICAL CALCULATION I t is obvious that both the depleted-channel and finite-channel models are not adequate to describe the JFET i n saturation. Therefore, numerical calculation becomes the only possible way to find out the detail behavior of these devices. Such calculations have been presented by Kennedy and O’Brien and by Kim and Yang. The calculation made by Kennedy and O’Brien involves the solution of the Poisson’s equation and the continuity equations for majority and minority carriers using the electrostatic potential and carrier densities as dependent variables. The model considered by Kim and Yang ignores the effect of minority carriers and assumes constant quasiFermi level across a reverse biased p-jz junction. The electrostatic potential and quasi-Fermi level are chosen as dependent variables. In general, the two analyses lead to essentially the same conclusion on the channel shape, electrostatic potential and carrier density before the carriers attain the saturation

258

EDWARD S. YANG

velocity. One unique result in the work of Kennedy and O’Brien is that a double layer of charges is induced in the channel when the velocity saturation field is reached. Figures 7-9 shows the two-dimensionally distribution of electron density for a short JFET with L/a = 2 (17). The voltages and the electron density are normalized by V, and N , respectively. It is seen that the electron density in the channel in Figs. 7 and 8 is greater than 0.6ND.Furthermore, the channel width is not constant and it cannot be defined clearly. For Vgs= 0, the finitechannel model seems to be a reasonable approximation (Fig. 8). On the other hand, setting the gate voltage Vgs= V, leads to an almost completely depleted channel. The result in Fig. 9 indicates that the function of the gate voltage is to reduce the effective channel width. Under large gate voltages, the short device becomes an effective long device. Calculation for a long device (L/a = 8) gives an almost completely depleted channel near the drain similar

I

vq9=0.0 v,

= 1.0

0.1

FIG.7. Carrier distribution of a JFET with L/a = 2.

Yo. = 0.0 V,, = 3.0

FIG.8. Carrier distribution of a JFET with L/a = 2.

CURRENT SATURATION MECHANISMS IN JFETS

V ,,

=

1.0 V,,

259

3.0

:

FIG.9. Carrier distribution of a JFET with L/a = 2.

to that of Fig. 9. One interesting result in this calculation is the channellength modulation effect which can be seen by comparing Figs. 7 and 8 at the tips of N = 0.8. The drain resistance is calculated from the computer data and is shown in Fig. I0 (22). In this figure, experimental results for two commercially available JFETs are also presented. The theory and experiments seem to be in reasonable agreement. Using a model i n which the gate width is smaller than the distance between source and drain contacts, Kennedy and O’Brien calculated the potential and carrier distribution after saturation (16). Their results for long devices were essentially the same as those discussed in the foregoing paragraphs. For a short device, however, they have obtained a very distinct double-layer charge distribution as shown in Fig. 1 I . The explanation according to Kennedy and O’Brien is the following: At small values of applied voltage the carrier velocity in this channel is directly proportional to the electric field; a decrease in channel cross section produces an increase in electric field and hence, an increase in current density. If, instead, the applied voltage is sufficient to attain velocity saturation within this narrow conductive channel, the increased electric field cannot produce a proportionate increase in current density. A consequence of this situation is mobile carrier accumulation until current continuity is established. In addition, a region of carrier depletion is formed to overcome the electrostatic charge attributable to the region of carrier accumulation ; thereby longitudinal electric fields of equal magnitude exist at the source and drain contacts of this structure. The depleted part of the double-layer extends between the gate junction space-charge layers, and thus it appears that the channel pinch-off has taken place at a lower biasing voltage than theoretically predicted for this semiconductor device. Furthermore, an increase in source-drain voltage increases the channel width rather

260

EDWARD S. YANG

0

1

“ds -

2

“P

FIG.10. Differential drain resistance versus drain-to-source voltage (22).

than decreasing it as would be consistent with conventional JFET theory. This increased channel width, due to induced carrier accumulation, results in an increase in source-drain current. The volt-ampere characteristics of three JFET structures (L/a = 5.0, 1.0, and 0.143) are shown in Fig. 12. The fundamental nature of the double-layer was further illustrated by Kennedy and O’Brien using a mechanical analog of a JFET which showed carrier depletion and accumulation. Their results seems to be consistent with an earlier investigation by M. Chester who showed the existence of a configuration emf due to the change of geometry in a conducting metal (23). The calculated V-I characteristics by Kennedy and O’Brien generally showed strong current saturation effect, even for a planar-type JFET (15). Such consistency in results introduces some doubts in this reviewer’s mind since existing experimental data on planar-type short JFET do not have current saturation. In 1964, Teszner and Gicqual (24) reported their findings on planar-type JFETs which showed both pentode-like and triode-like

CURRENT SATURATION MECHANISMS IN J E T S

26 1

B D

P-TYPE

AICIE

11111 .1

,1111

FICIA

Arb‘

Fic. 11. Electrostatic charge distribution in the channel of a short JFET with L/u = I ; V,,: 0 V ; Vd,= (a) 3.0 V, (b) 5 V, (c) 7.0 V (16). Chargelq cm’: A = 1.0 x lo”, E = 3.0 x 1016, c= 1.0 x 1016, D = 3.0 x 1 0 1 5 , G 1.0 x 1015. _ _ carrier depletion;

_ _ _ _ - - _carrier _ accumulation.

characteristics. Furthermore, Zuleeg (25) has investigated multichannel fieldeffect structures and obtained nonsaturated V-I characteristics. It appears that the triode characteristics is the consequence of the space-charge-limited current which may not be accounted for in the structures of Kennedy and O’Brien. By using the model of Fig. 1 with a graded impurity profile, Kim and Yang (26) obtained the ’result of carrier accumulation without doublelayer charge distribution (Fig. 13). Therefore, space-charge-limited current becomes possible for V,, = 0. Since the space-charge-limited current does not

EDWARD S. YANG

262

1

1

1

1

I

2

3

1

1

I

4

5

6

7

Source- drain voltage in volts

FIG.12. The calculated drain characteristics obtained by Kennedy and O'Brien (16). W, = a and W, = L in text.

I

1

FIG.13. Distribution of electron concentration for a graded channel JFET, showing carrier density exceeds the thermal equilibrium value a t the center of the channel.

CURRENT SATUKATION MECHANISMS I N JFETS

263

lead to the saturation of drain current, the triode characteristic is produced. The application of a gate voltage, however, may reduce the carrier density to below the thermal equilibrium value (Fig. 14). Thus, we see the two conflicting forces at work: the drain voltage produces the space-charge-limited current by inducing carrier accumulation and the gate voltage prevents such a current flow by depleting carriers from the channel. The presence of both triode- and pentode-type characteristics may be accounted for by these two competing mechanisms.

0.1

0.1

FIG. 14. Distribution of electron concentration showing carrier density is below the thermal equilibrium value at the center of the channel.

VII. CURRENT SATURATION IN MOSFETs Although this article reviews only the saturation mechanisms for JFETs, it should be pointed out that the same mechanisms describe the operation of surface type field-effect transistors (MOSFET). The special features in MOSFETs are the depth of the inversion layer and the surface mobility. Majority of works on current saturation of surface FETs assume complete depletion in the drain region (27-32). The finite saturation drain resistance is attributed to the channel-length modulation (27-29). Computer calculations are made although these calculations are less rigorous than those in JFETs (30,31). The space-charge-limited current (SCLC) has been considered by quite a few authors (32-34). However, the punch-through MOS devices (29) do not have counterparts i n JFETs. These devices are made by using a lightly doped substrate and a short channel length. The importance of velocity saturation in certain MOSFETs has been demonstrated (35,36).

264

EDWARD S. YANG

VIII. CONCLUSION In this review article, we attempt to present the highlights of the theory of current saturation mechanisms in junction field-effect transistors. For long devices (having large length-to-width ratios), there is no doubt that Shockley’s GCA together with the depleted channel (Wu and Sah) near the drain after pinch-off is an excellent approximation. For short devices, exact nature of carrier distribution has been obtained by numerical calculations. Mathematically, the calculation of Kennedy and O’Brien is more exact and should give more reliable results. The double-layer that created a depleted drain channel is physically reasonable in explaining the current saturation after the normal pinch-off condition is reached. Unfortunately, they have not presented experimental results to justify their work. The model considered by Kim and Yang is mathematically less rigorpus, but the results are supported by experimental evidences. Space-charge-limited current is physically realizable in very short JFET structures which produce triode-like characteristics. The models proposed by Sevin, Hausen, and Grebene give physical insight on short devices but they must be used with caution.

REFERENCES 1. W. Shockley, Proc. IRE 40, 1365 (1952). 2. R. C. Prim and W. Shockley, IRE Trans. Electron Devices ED-4, (1953). 3. S. Y. Wu and C. T. Sah, Solid-State Electron. 10, 593 (1967). 4. E. J. Ryder, Phys. Rev. 90, 766 (1953). 5. G . C. Dacey and I. M . Ross, Bell System Tech. J . 34, 1149 (1955). 6. F. N. Trofimenkoff, Proc. IEEE 53, 1765 (1965). 7. K . Tarney and F. N. Trofimenkoff. Proc. IEEE54, 1077 (1966). 8. J. Grosvalet, C. Motsch, and R. Tribes, Solid-State Electron. 6, 65 (1963). 9. R . Zuleeg, Proc. IEEE 53, 21 I I (1965). 10. J. R. Hauser, Solid-state Electron. 10, 577 (1967). 11. L. S. Sevin, Jr., “ Field-Effect Transistors.” McGraw-Hill, New York, 1965. 12. A. B. Grebene and S. K. Ghandhi, Solid-State Electron. 12, 573 (1969). 13. D. P. Kennedy and R . R. O’Brien, Solid-State Electron. 12, 829 (1969). 14. D. L. Mo and H. Yanai, IEEE Tram. Electron Devices ED-17, 577 (1970). 15. D. P. Kennedy and R. R. O’Brien, IBM J. Res. Develop. 13, 662 (1969). 16. D. P. Kennedy and R. R. O’Brien, IBMJ. Res. Develop. 14, 95 (1970). 17. C.-K. Kim and E. S. Yang, IEEE Trans. Electron Devices ED-17, 120 (1970). 18. H. Tango and J. Nishizawa, Solid-State Electron. 13, 139 (1970). 19. C.-K. Kim, Ph.D. dissertation, Columbia Univ., New York, 1970. 20. F. N. Trofinienkoff and A. Nordquist, Proc. IEE 115, 496 (1968). 21. C.-K. Kim and E. S. Yang, Proc. IEEE58, 841 (1970). 22. C.-K. Kim, I E E E Trans. Electron Devices ED-17, 1088 (1970). 23. M. Chester, Phys. Rev. L e n . 5, 91 (1960); Plrys. Rev. 133, A907 (1964). 24. S. Teszner and R. Gicquel, Proc. IEEE52, 1502 (1964). 25. R. Zuleeg, Solid-State Electron. 10, 449 (1967).

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265

26. C.-I(. Kim and E. S. Yang, Solid-Stare Electron. 13, 1577 (1970). 27. S. R. Hofstein and G . Warfield, IEEE Trans. Electron Devices ED-12, 129 (1965). 28. V. G . K. Reddi and C . T. Sah, IEEE Trans. Electron Devices, ED-12, 139 (1965). 29. D. Frohnian-Bentchkowsky and A. S . Grove, IEEE Trans. Electron Devices ED-16, (1 969).

30. 31. 32. 33. 34. 35. 36.

H. E. Loeb, R. Andrew, and W. Love, Electron. Lett. 4, 352 (1968). J. E. Schroeder and R. S . Muller, IEEE Trnns. Electron DevicesED-15, 954 (1968). J. A. Geurst, Solid-State Electron,9, 129 (1966). W. P. Dumke, IEM Res. Rep. RC-1573 (1966). G . T. Neumark and E. S. Rittner, Solid-State Electron. 10, 299 (1967). R. Zuleeg and K. Lehovec, IEEE Trans. Electron Deoices ED-15, 987 (1968). G . Baum and H. Beneking, IEEE Trans. Electron Devices ED-17, 481 (1970).

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Electronic Engineering in River and Ocean Technology RICHARD 0. ROWLANDS* Ordnance Research Laboratory, The Pennsylt1atiia Stare University, University Park, Pennsylvania

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

. . . . . . . . . . . . . . . . . . 214

................................... ................................... B. Sound Ray Tracing.. . . ................................... C. Surveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Fishing.. . . . . . . . .

283 285

B. Television. . . . IX. Helium Speech Pro ................................. X. Data Transmission ................................... 295 . . . . . . . . . . . . . . . . . . 295 A . Types of Links.. . . . . . . . . . . . . . . . . . . . B. Cable Connections

I. INTRODUCTION The previous review in this series that covered a related field was edited by Schooley ( I ) and appeared in 1964. It will be assumed that the reader is familiar with that review so as to avoid too much repetition, as many of the

* The author was with the Office of Naval 261

Research when this work was started.

268

RICHARD 0. ROWLANDS

instruments that he described are widely used. In the intervening years, the greatest progress has come about as a result of the breakthrough in the production of cheap integrated circuits. This has made it economical to use expendable components and systems where these would be difficult to recover. It has enabled circuits to be miniaturized for location in places that were previously inaccessible. It has also made compact special purpose computers readily available so that data can be processed on Iocation instead of having to be recorded and brought back to station for processing. The value of this facility has been tremendous, as results are quickly available and any changes in procedure necessary to effect improvements can be put into operation immediately.

11. WATERQUALITY MEASUREMENT Concern for the deterioration of the. environment during the last few years has given an impetus to the development of instruments that are capable of measuring various physical parameters, particularly those that contribute to the pollution of water. Henning (2) describes an instrument that has been used for such a purpose in Lakes Erie and Ontario to measure temperature, pressure, suspended solids, pH, conductivity, and dissolved oxygen. Methods of measuring the various parameters will now be discussed. A . Temperature

1 . Sensing Devices

The most common way of measuring temperature is to measure the change in electrical resistance of a material which is subjected to that temperature, a high sensitivity being obtained by balancing the resistance of the material against highly stable resistors in a Wheatstone bridge arrangement. Semiconducting materials having a high temperature coefficient have been developed for this purpose. These are known as thermistors and are manufactured in a variety of shapes and sizes. In underwater measurements, it is necessary to have the physical size of the sensor as small as possible so that it does not disturb the thermostructure of the environment. The most common form for this application is a hermetically sealed glass-coated bead. Thermistors have a resistance of the order of 10 MQ and a temperature coefficient of from - 2 to - 6 % per "C. Measurement accuracies of 0.I"C have been reported (2). For higher accuracies, a platinum wire is used. An instrument employing this method is described by Brown (3) for which an accuracy approaching +O.OI"C has been obtained.

ELECTRONIC ENGINEERING IN RIVER AND OCEAN TECHNOLOGY

269

The resonant frequency of a quartz crystal is temperature dependent, the temperature coefficient being determined by the direction in which the crystal is cut. Hewlett-Packard has developed a probe based upon this principle that has a resolution of 10-50C.Two crystals are used, one having a high and the other a low temperature coefficient. These are built into two solid state oscillator circuits whose outputs are fed into a mixer to obtain the difference frequency which is zero at - 5°C. This difference frequency increases approximately lo00 Hz per degree centigrade so that it is necessary to measure the number of cycles over a two-minute period in order to attain the maximum accuracy possible.

2. Temperature- Depth Profile An expendable instrument that is very widely used for measuring and recording temperature-depth profiles in the ocean has been described by Francis and Campbell (4). These measurements are known as bathythermographs or BTs. The complete system consists of a strip chart recorder, a launcher, and a canister containing a probe. The launcher is portable as shown in Fig. 1 and can be easily installed on board ship. A cutout view of

FIG.1. Expendable BT launcher.

270

RICHARD 0. ROWLANDS

the canister is shown in Fig. 2 . When this is placed in the loading breach and the breach is closed, electrical connection is established between the probe and recorder. The probe is launched by manually retracting a release pin and it slides under its own weight down a discharge tube which guides it into the water. On reaching the sea water, a triggering circuit is completed which starts the chart drive on its measurement cycle. The probe is a small ballistically shaped device containing a precision thermistor connected to a spool o f fine wire. The wire is unreeled as it drops vertically through the water. The other end of the wire is wound on a second

FIG.2. Expendable BT canister.

spool retained within the canister. As the ship moves horizontally, this wire is also unreeled. The dual spooling technique allows the probe to free-fall from the exact point of sea-surface entry without being affected by the moving ship or wave motion. The nose of the probe is weighted and the entire unit is spin stabilized to assure a known rate of descent corresponding to the depth calibration of the chart. The probe takes 90 sec to drop 500 m, by which time all the wire will have been payed out and the temperature-depth profile will have been recorded. B. Salinity

The easiest way of getting an indication of the salinity of sea water is to measure its conductivity. Conductivity, however, is also dependent upon temperature and pressure. The relationship is such that, in order to obtain a figure for salinity to an accuracy of k0.02 ppt, the following accuracies would be required in measuring the three parameters: Conductivity f1 in 5000, Temperature + 1 in 3000, Pressure

+ 1 in 250.

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271

One solution would be to measure the three parameters separately and transmit the measurements by FM telemetry to a computer on board ship that would then calculate the salinity. An alternative method is used in a salinometer described by Brown ( 3 ) in which temperature and pressure compensation are incorporated in the instrument itself. This simplifies the telemetry since only one channel of considerably lower accuracy is required. In this instrument, conductivity is measured by using two coils wound on toroidal cores and clamped side by side so that there is a common path linking them. A signal applied to one coil will induce a current in the sea water acting as a secondary and this will in turn induce an output current in the second coil, its magnitude being a function of the sea water conductivity. This system of measurement has t k advantage that it does not use electrodes that corrode when in contact with the sea water. First and second order compensation for temperature and pressure are achieved by the use of bridge circuits containing the sensing elements. These are interconnected with the conductivity circuit using rather complicated feedback arrangements to achieve the desired compensation. This instrument appears to be the best of its kind available, as it constitutes over 909: of those used in the field. However, a panel meeting at the Naval Research Laboratory, Washington, D.C., in April 1971 to discuss oceanographic instrumentation deficiency was divided in its findings. The laboratory instrument personnel had a much higher opinion of the instrument based on its testing and calibration in the laboratory than did operators who tended to be somewhat skeptical based on its use in the field, since, if anything goes wrong, it needs a highly skilled technician familiar with the circuitry to service the instrument. C . Turbidti) Minute solid particles suspended in water both scatter and absorb incident light. An estimation of their density may therefore be obtained by making use of this phenomenon. Let Z, and I , be the incident and transmitted intensities of light through a sample of thickness d. The transmission equation is I , = t o e - T d ,where T is the attenuation per unit length or turbidity due to the two factors. We may therefore write

Where the turbidity is high, it may be calculated from a measurement of these parameters. I n the ocean, however, it is generally low so that I t is nearly equal to 1, and a small error in the measurement of either can produce a large error in T. Since the incident light is either transmitted, absorbed, or

272

RICHARD 0.ROWLANDS

scattered, it is possible to write I,, = 1, + Z, + I , , where I, and I, are the intensities absorbed and scattered, respectively. Then,

The value of I, will have a constant relationship to I, for a particular type of suspended matter and so the equation may be written:

T = u/4logerl

+WS/It)l.

An instrument that measures the ratio of I, to I , may therefore be used to measure turbidity provided that it is calibrated for use in each particular location. This type of instrument is not dependent upon keeping the intensity of the source constant. A problem results from fouling of the optical surfaces, and a technique for overcoming this has been patented (5). It consists essentially of four probes arranged as shown in Fig. 3. L1 and L2 are light sources,

d

FIG.3. Probe arrangement for measuring turbidity.

while P1 and P2 are photoconductive devices. When L1 is on, P2 receives the direct light and PI the scattered light, and vice versa when L2 is on. Differences in the transparencies of the optical surfaces of P1 and P2 and in the optical to electrical transfer functions of the detectors may therefore be minimized by taking the arithmetic or geometric mean of the readings using the two sources. The ratio of scattered to transmitted light is obtained directly as an output voltage from a high gain amplifier in which the output of the photocell

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273

receiving the transmitted light is connected to its input while the other is connected into the amplifier’s negative feedback circuit. D. Dissolved Oxygen

The presence of a plentiful supply of oxygen in water is necessary for the well-being of aqueous animal life. A convenient method of measuring the concentration of dissolved oxygen in water is by using a galvanic cell that depends upon the availability of oxygen for its operation. Such a cell has been described by Mackareth (6). I t consists of a perforated silver cathode surrounding and insulated from a permeable lead anode. The cell’s electrolyte is a mixture of equal volumes of saturated solutions of potassium carbonate and potassium bicarbonate. The electrochemical reactions that take place at the cathode and anode, respectively, are 0 2

2Pb

+ 2H2O -t- 4e

+ 4(OH)-

- 4e

-

4(OH)-,

2Pb(OH), .

The current that flows in the external circuit through a low resistance load is therefore proportional to the rate at which oxygen is supplied to the cell. This is made available through a gas-permeable polythene membrane that covers the outer face of the cathode and separates it from the surrounding water. The outer face of the cathode is slightly gnarled to allow free movement of the hydroxyl ions. The rate at which oxygen seeps through the membrane is proportional to the oxygen’s partial pressure and to the membrane’s area and coefficient of permeability and is inversely proportional to its thickness. The incorporation of a Mackareth cell in a practical instrument has been described by Briggs et al. (7) and Henning (2). An impelle,r driven by a small electric motor is used to cause the water to flow at a rate in excess of 10 cm/sec over the surface of the membrane to replenish the oxygen that permeates into the cell. The output current from the cell is temperature dependent, the change being about 6%) per degree centigrade. To compensate for this, the cell has a thermistor encapsulated with it. The instrument is complete with battery and will operate without attention for at least a week at depths down to 25 m. E. Pollution Dispersion A characteristic of the present age is the deep public concern regarding pollution. This has made the study of the manner in which sewage effluent and other waste products are dispersed in river estuaries and in the sea, a

274

RICHARD 0. ROWLANDS

task of prior importance. Rather than try to detect the presence and concentration of these products themselves as they are dispersed, it is more convenient to use a foreign substance that can be more easily detected. This substance can be introduced at the normal place of discharge of the effluent into the water. Various substances have been used for this purpose, ranging from dyes through fluorescent tracers, and bacteria that produce colored spores to radioactive isotopes. Briggs et ul. (8) chose bromine-82 as a tracer because its half-life of 36 hr is short enough to eliminate contamination problems, yet long enough to allow sufficient delay between irradiation and use. It also emits three y-photons per disintegration which makes it easily detectable. The submersible y-scintillation detector used to measure the dispersion of the tracer was housed in a streamlined body and towed by a catamaran to prevent the water from being disturbed ahead of the instrument. A phosphor consisting of sodium iodide crystals with thallium as an impurity was used as the detector. The light emitted by the phosphor impinged upon a photomultiplier tube whose output was amplified before being transmitted by wire enclosed in the armor of the towing cable up to the towing vessel. These units, together with a 24V to 1500V static convertor for supplying power to the photomultiplier, were housed in the submerged body. An ultrasonic transducer connected via the cable to an echo sounder was mounted on the upper surface of the housing and used to determine the depth of the instrument below to the surface of the water. Two versions of the submersible body were constructed, one capable of being towed at a speed of 5 mjsec at a depth of 3 m and the other at 3 mjsec at a depth of 10 m. 111. SURFACE WAVES

A . Expenduble Buoy An improved design of an expendable wave-buoy using a novel form of accelerometer has been reported by Clayton and Smith (9). The accelerometer is shown in Fig. 4 in its damping bowl and uses a diaphragm spring as the common electrode in a six-element RC ladder phase shifting network. The six separate electrodes are made in printed circuit form, using a doublesided glass fiber board with plated-through holes for the connections to the electrodes. The six 1 M Q resistors are soldered directly to pads on the back of the electrode board to minimize stray inductance. The advantages of the diaphragm spring are considered to be as follows: (a) I t is simple to make a stiff spring in a reliable small electrode spacing, giving high resonant frequency and appreciable air damping at this resonance (60 Hz for the accelerometer built). (b) The spacing and alignment of the electrodes relative to the diaphragm

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l'g' OFF ADJUS

SHAFT SEAL

I

IOOrnrn

4

FIG.4. Accelerometer for expendable buoy.

is set by clamping ring-shaped shims of appropriate thickness between the diaphragm and printed electrode board. Disturbance of the alignment due to handling is not as likely as in the case of a cantilever spring. The accelerometer is suspended from a flexible rubber mounting in a fluid damping bowl so that it takes up the apparent vertical. The complete accelerometer unit is encapsulated in an expanded polyurethane float, of 0.915 m diameter, together with the low power radio transmitter and batteries. A loaded whip aerial is used for transmission of the amplitude modulated 27 M H z carrier to the ship. B. Hybrid Wave Buoy

The main difficulty encountered in measuring sea surface statistics over a wide frequency band is the large dynamic range required to accommodate the large amplitude swell components down to a few millimeters at high frequencies. Baker (10) overcame this problem by using two measuring systems, each working over a limited frequency band. The buoy was designed so that it rode with the long wavelength components and supported an array of resistive wave probes in the sea surface. The vertical acceleration of the buoy was recorded so that the amplitude of the long wavelength components could be derived. The two-dimensional array of eight probes was used to

276

RICHARD 0. ROWLANDS

detect the instantaneous surface heights relative to the buoy and to give directional information regarding the properties of the sea surface at the high frequencies. Both capacitive and resistive probes were evaluated prior to the final design. The latter were found to be more accurate for use in sea water. The probes consisted of nichrome resistance wire wound in a helix on a central coil form consisting of a length of PVC insulated wire. The signals representing acceleration, pitch, roll, and compass heading as well as those from the wave probes were converted to dc analog voltages which were transmitted via a multiway electrical cable to the ship for recording on a multitrack tape recorder.

IV. TIDES Two instruments for measuring tides have recently been described, one for use on the continental shelf by Collard and Spencer (11) and the other for deep sea studies by Snodgrass (12). Both are constructed on the same principle. The equipment for recording the data and for aiding recovery is housed in a buoyant aluminum sphere which is mechanically coupled to a ballast frame that makes the whole contraption negatively buoyant. The amplitude of the tide is obtained from the variation in water pressure at the sea floor. This is measured by means of a pressure transducer that is located below the sphere but mechanically coupled to it by a framework and electrically by cable. The instrument is dropped or laid on the ocean floor to gather and record data and is left there for a period of several days to several months. When the ship returns to recover the instrument capsule, it sends out an acoustic command which results in the capsule being released from the ballast frame, enabling it to float to the surface. Radio, light, and acoustic beacons have been used to locate the instrument during recovery operations. A pressure transducer is used that converts pressure to frequency. In the shallow water gauge, the transducer consists of a diaphragm whose flexure changes the value of a tuning capacitor in an oscillator. In deep water, the tide variations are less and so a more sensitive transducer with a lower dynamic range is used. A tungsten filament 1 cm in length is held in tension, one end being connected to the diaphragm. A magnetic field is applied across the wire and a direct current is passed through it. Random oscillations of the wire will cause the current to be modulated. These modulations are coupled through an amplifier back to the wire using positive feedback and cause the wire to vibrate at its resonant frequency which is a function of the wire tension and, thus, of the pressure on the diaphragm. Both surface and internal waves can cause the pressure monitored by the instrument to vary. Fortunately, there is a large gap between the lowest

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frequencies of waves and the frequencies of tides. Their effects may be minimized by averaging the measurements over a period of 2 to 15 min depending upon the amount of smoothing required.

V. OCEANCURRENTS A . Horizontal Currents One of the disadvantages of a mechanical current meter is that water has to flow through it, making it vulnerable to fouling by marine life. Sea water, however, is a conductor of electricity and when a conductor moves in a magnetic field, a voltage is produced in a direction that is perpendicular to the plane defined by the direction of motion and the magnetic field. It is therefore much easier to design an instrument that cannot easily be fouled based upon this principle than by using a mechanical sensor. Such an instrument, suitable for anchoring to the sea bed, has been described by Hanff (13). A flat magnetic coil 17 cm in diameter with its axis vertical is encased in a watertight container and, as such, produces a vertical magnetic field around the edges of the container. Two pairs of electrodes, electrically in contact with the surrounding waters, are located at right angles at the edge of the container. The magnetic field is alternated at a frequency of 20 Hz and any movement of the water past the electrodes will induce a voltage at this frequency between them. This voltage is proportional to the water velocity and the magnitude of the field. The strength of the field is reduced to some extent by circulating electrical currents that are induced in the water. Spurious voltages are also picked up by the electrodes as a result of electrolysis. The signal is therefore detected by synchronous means in order to suppress the noise. The electronic circuits are housed in a cylindrical body located above the electrodes as are a pair of flux-gate magnetometers mounted on gimbals that are used to sense the direction of the earth’s magnetic field and from which the direction of flow of the sea water may be calculated. The instrument was tested against a mechanical current meter in the North Sea and, while the mechanical meter failed almost immediately due to it being blocked by a jellyfish, the electromagnetic instrument worked satisfactorily during the two days of the test. The instrument has a low time constant, having been designed to give an independent reading every half-second. The electromagnetic principle has also been used by Drever and Sanford ( 1 4 ) i n an instrument designed to measure the amplitude and direction of current as a function of depth. This instrument is allowed to fall freely from the surface of the ocean to the floor. I t is assumed that, at all depths, its

27 8

RICHARD 0. ROWLANDS

horizontal velocity is equal to that of the ocean. Sea water is again treated as a moving conductor and, in cutting the vertical component of the Earth’s magnetic field, a potential gradient is produced in a horizontal direction that is perpendicular to that of the movement of the water. Layers of water moving at different velocities would exhibit different potential gradients were it not that these differences are averaged out by the conducting properties of the medium. An insulated conductor connected to a voltmeter inside the instrument will have a potential between its ends that is proportional to the velocity at that depth and, by completing the circuit externally through the sea water, the reading on the voltmeter will represent the difference between the velocity at that depth and the average velocity. The latter must be determined by some other means. A number of practical problems arise. The instrument must be stabilized so that it maintains a vertical aspect while falling. The voltage induced in the conductor inside the instrument is proportional to its horizontal length which should therefore be as long as possible. Electrodes have to be used to complete the circuit through the sea water and these will also pick up electrolytic voltages that are dependent upon salinity and temperature. These problems are simultaneously solved by fitting the instrument with four fiber glass fins that cause it to rotate while it falls, thus stabilizing its motion. The rotation causes the voltage induced in the conductor to alternate, thus enabling it to be easily separated from the other spurious voltage. Lastly, the use of fins enables the length of the conductor to be considerably increased, contact with the sea water being made at the ends of opposite fins. Temperature and salinity effects are minimized by using salt water inside a polyvinyl tube as the conductor. Porous glass plugs seal the salt water in the tube while, at the same time, providing low resistance electrical contact with the sea water. This enables the electrodes to be placed in close proximity at the center of the instrument, the electrode chambers being separated by a thin beryllium oxide plate which acts as a good thermal conductor and as an electrical insulator. A cutaway view of the sensor is shown in Fig. 5. ELECTRODE BLOCK I

IN BERYLIUMOXIOE WALL

S

SSURE EQUALIZING PLUG

PLUG

FIG.5. Electric field sensor,

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279

The vertical motion of the instrument causing the conductor to cut the horizontal component of the earth's magnetic field will also produce an unwanted alternating voltage. This is cancelled by connecting a flat coil with its axis horizontal in series with the measuring circuit so as to produce an equal and opposite voltage. Acoustic telemetry is used to relay the nieasurements to the launching ship. This instrument has been successfully used to measure the velocity profile of the Gulf Stream at various locations. B. Vertical Currents A new instrument for measuring vertical current in the ocean has been developed at Woods Hole Oceanographic Institute by Webb et al. (15). The principle of operation of the instrument is that, when suitably ballasted, it will come into equilibrium at a predictable depth of water of known temperature and density. I t is a solid of revolution about its vertical axis except for eight vanes projecting outward at an inclined angle of 45". Any vertical movement of the water acts on the vanes and rotates the whole instrument. The main housing is an aluminum tube slightly over 1 m in length. Its internal diameter is 145 mni and it has a wall thickness of 12 mm. A recovery aid and a flasher are connected to the top end cap, while all the sensors and the complete electronic package including a strip chart recorder are fastened to the lower end cap and are removable in a single unit. The vanes are flat polypropylene square plates of 130 mm on a side and 10 mm thick. They cause the instrument to make one revolution for every 110 cm of relative vertical flow. The number of revolutions are counted by using a magnetic compass capacitively coupled to four stator electrodes driven by square wave signals in phase quadrature. The phase of the signal picked up by the compass is proportional to the instrument's relative bearing and this phase information is then converted to amplitude information for recording. I n certain experiments, the rotation may be too fast for this circuit to be able to follow, in which case a supplementary circuit is also used. In this circuit, the compass output is connected to a Schmitt trigger which generates a pulse every time the compass passes north in either direction. These are fed into a 7-bit counter, the last four stages of which are converted into an analog output for recording. The direction of revolution may always be found from the primary counts since the instrument invariably slows down long enough for this to operate before changing direction. Temperature is measured as a 10-bit binary number, but this is converted into two 5-bit analog voltages for recording. The other parameter of interest is pressure which is recorded as a direct analog signal.

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It is necessary for the accompanying oceanographic vessel to keep track of the instrument both in bearing and depth. For this purpose, an acoustic transmitter is located at the base of the instrument. Its operating frequency is 5120 Hz at an input electrical power of 40 W. It radiates omnidirectionally and may be detected under good conditions at ranges of up to 24 km. The depth of the instrument is obtained from the telemetered pressure readings. The telemetry system operates as follows. A marker pulse of duration 8 msec is transmitted regularly every 4 sec. Each pulse triggers a staircase generator whose voltage increases through 128 steps during the 4 sec interval. This is compared with the voltage corresponding to the pressure reading and, when the two are equal, a second acoustic pulse is transmitted. The time delay between this and the marker pulse is therefore a measure of the pressure. The instrument consumes 130 mW of power, more than half of which is used by the acoustic transmitter. It is capable of operating for up to 60 days. Recovery is by presetting a timer to cast a ballast weight after a fixed period, thus causing the instrument to surface.

VI. NAVIGATION

A number of navigational systems are in use, varying in range from inshore applications to worldwide coverage. The Decca system was a wartime invention which was used with great success during the Normandy landings. It operates on the principle of comparing the phase of signals received from land-based transmitters. Assume that two transmitters at different locations are locked in phase. A receiver lying anywhere along the line that perpendicularly bisects the base line joining the two transmitters will receive the two signals in phase. There will be other points on the baseline spaced at intervals of half a wavelength where the signals are in phase. If one were to start at all these other points in turn and move away from the baseline but still keeping the signals in phase, a family of hyperbolae would be traced out with the two transmitters as the focal points. This is known as a “ pattern and the areas between the hyperbolae are lanes.” Decca receivers carried by ships measure fractions of a lane and so identify the ship’s position line within a lane. Two position lines are needed to fix the position of a vessel, and this requires a second pattern. The most economical use of transmitters is produced by having one “ Master” station operating with three symmetrically disposed “ slave” stations. This arrangement produces three patterns, called “ Red ”, “ Green”, and “Purple”, which provide pattern cover over an area and is known as a “chain.” The receiver would not be able to distinguish between signals from individual transmitters if they were on the same frequency, and so each transmitter ”

“

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operates on a different frequency from the others, but all frequencies are harmonically related so that the two signals used for a pattern can be frequency multiplied in the receiver to a common frequency before comparing their phases. In practice, each Decca Chain has its own basic frequency “f” which is approximately 14 kHz. The transmitted frequencies are 6f for the Master station and 5S, 8S, and 9ffor the Purple, Red, and Green stations, respectively. To produce the comparison frequency for the Red pattern, the Master signal is multiplied by four and the Red signal by three, making a common frequency of 24f at which phase comparison can be made. Similarly, the comparison frequencies for the Green and Purple patterns are 18f and 30L respectively. To correct for lane ambiguity, identical transmissions from all stations are radiated in time sequence at the same frequency “f.” A report by Pierce and Woodward (16) traces the development of long range radio navigation systems in the United States and reviews the present status of Loran A, Loran C, and Omega. There are now 81 Loran A stations in the world, forty-seven of them being operated by American personnel. The advantages of Loran A are that it is familiar and enjoys international status in the marine and air communities, the equipment is technically and economically within reach of the widest number of marine users, and it currently provides complete United States coastal coverage. The 30 Loran C stations provide accurate coverage over 6,000,000 square nautical miles or four percent of the surface of the earth. Four Omega stations have been in operation since October, 1967. The Navy intends to install the remaining four stations by late 1972 or early 1973 to provide worldwide coverage. The system does have cyclic ambiguity but, when it is in full operation, the receiver will always have from 5 to 6 signals at its disposal so this should not cause any problem. The newest navigation facility is the Navy Navigation Satellite System (NNSS), which was designed originally for military use but was made available free of charge to commercial users in 1967. The system consists of four transit satellites in circular polar orbit at an altitude of approximately 600 miles above the earth. Each one circles the earth every 108 min. The orbits of the satellites are accurately known as a ground-based station monitors each satellite and predicts its next orbit on each pass. Details of this orbit and time data is beamed to the satellite which then stores it and retransmits it back to earth every two minutes on two frequencies, namely, 150 M H z and 400 MHz. Since the satellite is moving relative to the earth’s surface, there is a Doppler shift in these carrier frequencies as measured by an observer on the earth depending upon his position relative to the satellite at the time of observation. A Doppler shift of a particular magnitude will

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define the observer's position as lying somewhere along a hyperbola on the earth's surface and the change in Doppler shift between two successive transmissions will define his position unambiguously. In contrast to the other systems, continuous information is not available as the observer can only compute his position when a satellite is within radio range. However, each of the four satellites is within range of every point on the earth at least twice a day. A comparison of the various systems is given in Table I which is due to Chernof (17). TABLE 1 LONGRANGENAVIGATION SYSTEMS Estimated maximum range (nautical miles)

Estimated accuracy (nautical miles)

Frequency range

Estimated user equipment cost (production equipnients)

200-300

0.25-1 .O

90.0-130 kHz

Loran-Ah Loran-C' Omega*

700-900 1200-1 500 5000

0.5-3.0 0.2-0.5 1 .o-2.0

$30,00O/month lease including ground stations s I0,OOO

Transit satellite system-high accuracy user equipment' Transit satellite system-standard accuracy user Equipnien tJ'

Wor Idw ide

System

Decca"

Worldwide

1.75-2.0 kHz 90-1 10 kHz 10.2 kHz 13.6 kHz 0. I 150 MHz (approximately) 400 MHz

0.5 (approximately)

400 MHz

$10-20,000

$10-20,000 $50,000 with computer

$20-25,000 with data processor/computer ~

Operational with localized coverage, limited to about 240 mile range at night because of sky wave interference. Operational with localized coverage, limited by sky wave interference. Relatively inexpensive. Operational with localized coverage, limited by sky wave interference. Relatively accurate except with sky wave. * Planned to give worldwide coverage, using eight ground stations and four operating frequencies. Presently in developmental stage with four ground stations and two operating frequencies yielding lane ambiguity every 24 nautical miles. Dual channel receiver provides refraction corrections for highest accuracy. High accuracy computation program. Single channel receiver eliminates refraction correction. Computer replaced by special purpose data processor/computer and readout. a

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Exploration ships, giant tankers, and passenger liners need pinpoint navigation and, for these, a backup system is necessary. Reinhartsen (18) has described a system in which an acoustic Doppler unit and a gyrocompass are used to dead reckon from one satellite fix to the next in shallow water, while VLF/Omega is used in deep water. If a ship already has a computer on board, the same computer may be used for the dual purpose of navigation and any other functions for which it may be required. A number of authors have described such applications (19-21). One of them describes the study of the accuracy of a satellite navigation receiver in a fixed position and it was found that all fixes were contained within a 0.07 nautical mile circle provided that the satellite passes were between 10" and 80" elevation, If the ship is moving, its velocity must be fed into the computer, otherwise an error is produced.

VII. SONAR APPLICATION Sonar was developed during the war for the detection of enemy submarines and those systems used for military applications carry a security classification. More recently, sonar has been used increasingly in civilian applications such as in depth sounding, hydrographical surveying, fish counting, and scuba diving. Some representative systems for these applications will now be described. A . Fish Coirntiny

Sonar has been used for counting medium-sized individual fish such as cod and salmon and for estimating the size of shoals of small fish such as sprats and herring. A method of doing the latter has been described by Forbes (22). The system is based on the assumption that, after correcting for beam spreading and attenuation due to sound absorption, the intensity of the echo is proportional to the density of the fish population regardless of depth. A time varied gain amplifier is used to make this correction and the echo is quantized into 20 logarithmic amplitude levels. It is more important to know the position of the shoal relative to the bottom than to the surface since some varieties of fish are only to be found near the sea bed. Two complete echo sounders are therefore used, one as the main signal channel operating at 400 kHz and the other to provide a bottom lock facility, operating at 300 kHz. A beam width of 1.5" and a pulse length of 100 psec are used, giving a resolution cell of about 1.2 m3 at the maximum range of 160 m. The system is capable of operating in two modes. For counting fish in mid-water, the output is integrated and sampled at twenty 10 msec intervals, thus locating each echo within a depth of 7.5 m. For

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counting fiish near the sea bed, the intervals are shortened to 1 msec, making the depth increments 75 cm, starting at 15 m above the sea bed. In both modes it is possible to count fish down to 15 cm above the sea bed without interference from the bottom echo. No estimate of the accuracy of the method can be made since there is no independent way of checking the system. Although the target strength of a fish varies with aspect, and the ship may not always pass over the center of a shoal, if many measurements are made, then on a statistical basis a rough estimation of size distribution may be made. In sea bed trawling, the trawl skipper must estimate when he thinks there are enough fish in the trawl for him to haul it in and empty it. It would be to his advantage if he had an instrument that would count the fish as they entered the trawl. Such an instrument in its prototype stage has been described by Cooke (23). The design objectives were to obtain echoes with a signal-to-noise ratio of at least 10 dB from 34 cm cod at a maximum depth of 500 m and to count only those echoes returned from within 1.2 m of the sea bed, this representing the height of the opening at the mouth of the trawl. The transmitting frequency used was 30 kHz at a level of 130 dB and a time varying gain amplifier was used to compensate for inverse square law spreading. As echoes were received, the counts were fed into an open-ended shift register having an overall delay time of 2 msec, corresponding to a depth range of 1.3 m. The arrival of the echo from the sea bed was used to switch the open end of the shift register to a digital calculator so that only the counts in the register at that time would be computed. Errors arise because the distance varies between the transmitter which is located near the surface and the trawl which is located at the sea bed. The area covered by the beam varies as the square of the depth. This means that some fish that do not enter the trawl are counted, whereas others are counted more than once. To compensate for this, the number of counts is divided by a factor that is proportional to the square of the depth. Another factor that causes the system to be inaccurate is that, as target strength is not taken into account, two fish that enter at the same time will be counted as one. Because of the inaccuracy of the instrument, a ratio factor is used to divide the depth-corrected echo count in order to produce the final fish count that is displayed on the instrument panel. This factor is continually updated from tow to tow and is obtained in the following way. When the skipper hauls in his first trawl, he estimates the size of his catch. This will be different from the reading on the instrument. The ratio of reading to catch is then the correction factor that the instrument uses to obtain the fish count from the echo count on the next trawl. When this is brought in, the skipper again estimates his catch and a new ratio is calculated. The instrument from now on updates the old ratio using a recursive formula that makes use of the new information obtained on each trawl. The instrument

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was used on sea trials and the accuracy was reported to be +50% for approximately 60 % of all tows. I n the study of fish migration, it is desirable to have an instrument that is suitable for counting fish in rivers. One way of doing this is to observe the change in the conductivity across a section of water when a fish is present, but in order to get a reliable measurement, it is necessary to confine the fish channel to a narrow tube. There is a danger that this might interfere with the migration of the fish and an alternative technique using sonar in the normal river channel has been described by Braithwaite (24).The direction of motion of the fish is determined by using two beams a short distance apart and observing the order in which the fish pass through the beams. Two sets of transducers are used, one set being placed at the bottom of one of the river banks, while the other is mounted in a floating housing on the opposite side. In this way, the V-shaped beams cover the full width of the rivers and are designed to be effective for a change of 2 to I in the river level. The frequencies used in the two directions are 1 and 0.8 MHz and tuned receivers are used to prevent mutual inteference. The equipment is unsuitable for use immediately downstream of any waterfall or turbulent rapids due to the volume reverberation arising from air bubbles in the water. The performance is also affected by suspended solid matter when the river is in flood. B. Sound Ray Tracing

One of the purposes of taking bathythermographs is in order to be able to predict how sound rays will propagate through the ocean. For hydrographical surveying using sonar, the ideal condition is iso-velocity water. In this case, sperhical spreading of the sound occurs, the ray paths being straight lines radiating from the center of a sphere. Sound velocity, however, is a function of salinity, temperature, and pressure, but whereas salinity is usually constant over an extensive region and pressure varies in a predictable manner with depth, the temperature varies both daily and seasonally. A knowledge of how the sound will propagate based on bathythermograph measurements is therefore essential if the times at which the echoes return from the ocean floor are to be correctly interpreted in terms of range. The method of calculating the ray paths is usually to approximate the temperature depth profile piecewise with a series of straight lines. The ray paths within these regions of uniform temperature gradient are arcs of circles. The method of calculating and displaying these paths has progressed from paper and pencil through the development of special slide rules ( 2 5 )to the use of computers. A commercial instrument working on the analog principle is now available that calculates the sound ray paths and displays them on a cathode ray tube (26).Five temperature gradient layers that are adjustable in depth and

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600 -

L

FIG.7. Ray diagrams.

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RANGE - METERS

FIG.8. Intensity-loss contours (dB).

gradient as potentiometer settings are available, while a sixth layer takes account of constant pressure gradient only. The sound rays are displayed with 0.5" spacing within a beam of width that is adjustable from 5" to 40". The location of the sea bed is adjustable to a depth of 6500 m, and rays reflected from this and from the surface are displayed. The design of a more sophisticated digital calculator has been described by Tate (27). This operates directly on the output of a bathythermograph unit and calculates sound intensity levels as well as displaying ray paths. A typical BT profile is shown in Fig. 6, the crosses being the sampling points used to compute the ray diagram in Fig. 7 and the intensity-loss contours shown in Fig. 8. C . Surveying

The systems described so far have been one-dimensional in that they have only been able to resolve in range from the elapsed time between the transmission of the pulse and receipt of the echo. For hydrographical surveying, two-dimensional information is required, which is obtained by scanning.

I . Sector Scan A sector scanning sonar which has been found useful for a variety of applications was developed by Mitson and Cook (28). I t fills a gap between the resolution obtainable with most geological sonar equipment and sea floor photography. As it makes use of a number of interesting techniques, a description of it will now be given. The transducer housing is 0.9 m long and

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0.24 m wide. It contains one transmitting element that transmits a wide angle 300 kHz cw pulse of 9.1 msec duration, thereby giving a range resolution of 0.15 m. The receiving array has a beam width of 3" in the plane of its long axis and 5 to 19" in the plane of its short axis. It contains 75 elements connected in groups for the purpose of scanning. Modulation scanning is employed to sweep the narrow beam continuously over a 30" sector. This technique may be explained as follows: Let us suppose we have two transducers A and B a distance h apart as shown in Fig. 9, and let us suppose that

\I

\I

\,

\I

FIG.9. Scanning diagram.

the signals picked up by the transducers are modulated by the frequencies f and f - f d , respectively, and then summed. Let us further suppose that these frequencies are in phase at t = 0. A signal approaching the transducers from the broadside direction will be in phase at the transducers and, although this signal will appear as two distinct frequencies at the outputs of the modulators, they will still be in phase at or near the time t = 0 and will add coherently. At a later time t = T , the phase of the signal that modulates A will have advanced wd T radians relative to B and the broadside signals will no longer be in phase. However, consider a signal approaching from an angle 6, where cos 8 = f d d/A,and 1 is the wavelength of the signal in the water. The phase of the signal at B will be wd z rad ahead of that at A . Hence, after modulation, the two signals will be in phase and will add coherently. It will be seen that this technique results in a beam that scans automatically in a

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clockwise direction. The technique may be extended to an array of transducers by progressively decreasing the modulation frequency from one end of the array to the other. The array used in the equipment may be positioned with its long axis horizontally or vertically. Horizontal scanning displays the scene ahead in plan view, while vertical scanning displays it in cross section or, in other words, gives a side view of what is ahead. The echo return is displayed on a B-scan scope. That is, scanning is performed horizontally, increasing range is displayed vertically, and the return signal is used to intensity modulate the beam. This may be better understood by reference to Fig. 10 which shows the wreck of H.M.T. Fontenay. The photograph on the left obtained by horizontal scanning shows the aspect and size of the wreck, while that on the VERTICAL SCAN

HORIZONTAL SCAN

t

SURFACE FIG.10. Horizontal and vertical scanning displays

t

BOTTOM

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RICHARD 0. ROWLANDS

right employing vertical scanning indicates its height. The bright band on the right-hand side of the latter picture is the bottom of the ocean. The width of this band represents the amplitude of the sand waves. The surface is on the left of the picture. The sharp discontinuity in the bright band is the acoustic highlight from the front of the wreck and the distance by which this extends to the left is an indication of its height. Reflections from the middle and rear portions extend the bright patch vertically. Sand waves are visible in the horizontal scan photograph and it is of interest that the equipment was used to study the mobile sand forms resulting from the strong tidal currents in the English Channel. The widespread occurrence of sand waves with wavelengths of between 2 and 40 m were observed. Assuming that the steeper face of a sand wave is in the direction of sand transport, it may be possible to use such observations to predict the future history of large sandbanks. This is important because the oil tankers operating in this area only clear the sea bed by about one meter. The range displayed can be from 0 to 100 or from 100 to 200 m. The recording of the display is performed by means of a closed circuit television system and a video tape recorder. Stabilization for f 15" of pitch and & 10" or roll are accomplished by means of gimbals controlled by a vertical gyroscope, and yaw is controlled by ship's gyrocompass. Azimuth steering and transducer mode and tilt are all controlled manually. The equipment is proofed for immersion in sea water to a depth of 5 m and at temperatures of - 10°C to + 30°C. The transducer is protected by a free flooding hemispherical dome in the form of a steel ribbed cage covered by terylene or canvas. It is fitted and removed at a convenient port near the operating area. The present design is not acoustically satisfactory as interference is serious in the horizontal mode at tilt angles greater than 10". The equipment has also been used to view fishing trawlers in operation down to depths of 160 m, although detail is best seen at depths of between 30 and 90 m using small tilt angles. A view of a bottom trawl with the transducer in the horizontal mode revealed details of otter boards, dan lenos, bridles and backstraps, net shape, headline and groundrope, tickler chain, and turbulence trails. Noise is generated as the trawl is towed along the sea bed, as many of its parts are made of metal. These are rubbed or knocked together when the trawl is moving over uneven ground producing a variety of sounds ranging from a musical tinkle to an unpleasant screech. Being continuous sounds, these produce vertical smears down the display. Noise was also observed to come from ridges and discontinuities of the sea bed. Observations were made to correlate the existence and intensity of this noise with the rate and direction of tidal flow. A preliminary reconnaissance of the nature of fish shoals has been made

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on herring, sprats, and cod. The shapes of shoals are much more diverse than would appear from an echo sounder record. It is possible to count the fish in some shoals, and it was established that packing density increases with the size of the shoal. The behavior of single fish has been studied. A 10 m shark was tracked to determine the relation between fish length, swimming speed, and tail beat frequency. A transponding acoustic fish tag has been developed for use with the scanner. The acoustic properties of the tag had to be such that the sensitivity of the receiving section was adequate to detect the transmitted sonar pulse up to a range of 370 m, and the acoustic pulse transmitted by the tag had to provide an adequate signal-to-noise ratio at the sonar receiver. A pulse length of 3 msec was chosen to make the signal appear as a rectangle on 31 lines of the display raster and thus be easily distinguishable from other echo returns. A maximum interrogation rate of four times per second placed a high demand on battery power. Three mercury cells were used, each having a nominal voltage of 1.4 V and 85 mA-h capacity with an operating life of 32 h. The transducer which was used for transmitting and receiving consisted of a small lead zirconate-titanate cylinder which was fitted to the fish so that its axis was vertical under normal swimming conditions. The dead zones were therefore immediately above and below the fish. Miniature electronic components were used and the uncased package measured 4.7 cm long by 0.8 cm diam. After encapsulation, its weight in water was 3 g. In sea trials in which a large plaice was tracked for 15 h, a Petersen tag was attached to the fish and the acoustic tag was tied to this with a short length of monofilament nylon. Contact was sometimes lost through the fish burying but was always reestablished by steering over the fish's predicted position. 2. Side Scan

The difference between a short range and a long range sonar, basically, is that the latter is larger, more powerful, and operates at lower frequencies; other problems have to be overcome, however, and so a description will be given of how these problems were overcome in a long range side scan sonar developed by the British National Institute of Oceanography. In side scan sonar, the surveying vessel proceeds on a straight course and periodically transmits a short pulse of sound at right angles to her track. The beam angle is narrow in the horizontal direction but much wider in the vertical direction, being inclined down from the horizontal by about 10 to 20". The variation in the echo strength with time produces a one-dimensional indication of the target strength of the sea floor in terms of distance at right angles to the direction of travel. A plan view of the sea floor is produced line by line from each pulse as the vessel proceeds on its course.

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It was calculated that the optimum signal for operating at depths of up to 8000 m and a range of 12 nautical miles would be a 30 msec pulse at a frequency of 6.5 kHz and power level of 50-60 kW. In order to get a 2" horizontal beam, an array length of 5 m would be required. A vertical beam of 10 to 20" angle including usable minor lobes was obtained with an array width of 1.25 m. A number of factors made it preferable to mount the array in a separate body that could be towed at some distance and depth behind the ship rather than on the ship itself. It is well known that amplitude distortion occurs when a signal is transmitted at a high power density into water, especially at shallow depths. Tests were therefore conducted at variable depths to see if the radiated power of the system, which comes out to 3 W ern-', would cause any problem. It was found that, at a depth of 120 m, a power density as large as 5 W cm-2 produced no more than 10% distortion. Another problem was yaw stability. Sound takes approximately 30 sec to make the round trip to the maximum range and, during that period, the array would have to be held steady in yaw to better than the horizontal beamwidth. This would not be possible with the array attached to the ship. Tests carried out with a $-scale model of the proposed design fitted with both yaw and roll/pitch gyros showed that if the model was running at 120 m depth or more, it yawed by 3" for every 2" of ship yaw. Later, it was fitted with a gyro-controlled rudder which improved on this figure by a factor of 3. Heave measurements made with an accelerometer showed that there was a surprising degree of coupling between the towing point and the vehicle. By mounting the array in a body which is towed some distance behind the ship, a higher signal-to-noise ratio is achieved since the main source of interfering noise is the ship's engine. Another advantage of towing the array at depth is that it is below the sharp thermoclines that often exist near the surface and which distort the ray paths. In its final design, the vehicle carries the sonar array in a filament-wound glass-epoxy center section on. bearings fitted at each end in aluminum bulkheads. The aluminum array frame carries 144 transducer elements arranged 24 by 6, whose performance can be measured by in situ accelerometers. The frame can be remotely rotated through 240" to look either to port or starboard and to adjust the sound launching angle for the particular propagation conditions that apply. The vehicle contains its own compressed air supply for deballasting as well as sensors for monitoring depth, water temperature, roll, pitch, yaw, and heave. The inside of the vehicle is free flooding and the wall provides about dB attenuation to the transmitted sound. The towing head assembly consists of a ball and socket joint, the ball being also part of the cable termination. The strain cable that is used for towing contains about 80 signal and power conductors in addition to the sonar coaxial cables. The power amplifier for driving the array is contained in the vehicle.

+

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Each transducer consists of a stack of 11 lead zirconate titanate disks held in compression by a center bolt. It has a flared aluminum radiating head with an active diaphragm diameter of about 21/3, and approximates a rigid piston in displacement. It is protected from stress corrosion in sea water by a layer of epoxy resin fused on electronically. It fits into a pressure-tight housing and is held in position by a clamping ring around the compliant edge of the radiating head. Its electroacoustic efficiency is over 90%, and it has a power handling capacity of 600 W at a duty cycle of 1/6. The transmitting amplifier is connected to a transformer with a number of secondary windings, each winding driving one or more rows of the transducers. The secondary turn ratios are adjusted to give the desired radiation pattern in the vertical plane. Timed switches are used to connect the amplifier to the transformer primary during the transmit period and to short out the secondaries during the receive period. Each transducer is in series with a pair of parallel diodes across which the outputs are taken. The array is divided lengthwise into six sections, the outputs of all the transducers within a section being summed in phase. For yaw correction, the signal derived from the gyrocompass is used for rudder control by means of a servo system, but this is backed up by an electronic beam steering system. This locks the receiving beam on to the direction in which the last pulse was transmitted, compensating for any residual yaw during the listening period. The way in which this is done is to change the phase of the six sections by a progressively greater amount from one end to the other. The mechanism used for doing this consists of synchro resolvers coupled to a mechanical gear box linked to the servo loop. This system has been used successfully in the Mediterranean and the Atlantic, although the deep shadow zone due to the effect of pressure on the velocity of sound sometimes prevents the system from getting returns from its full maximum theoretical range. The nulls between the minor lobes serve as useful range markers on the final display.

VIII. FISHING A . Electric Field

An electric field induced in the ocean will cause a current to flow through any fish that happens to be in the vicinity of the field. The reaction in the fish can vary from fright through electrotaxis to tetanus, depending upon the strength of the field and the species of the fish. The electrical system needs to be capable of generating high power because of the low conductivity of sea water, but it has been found that it is only necessary to apply this power intermittently in the form of pulsed direct current in order to obtain the desired reaction.

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Shrimp normally burrow in the mud during the daytime and are not then available to bottom trawl. An electrical array located ahead of the trawl has been used to induce the fright reaction in the shrimp causing them to exit out of the mud to be scooped up by the following trawl (29,30).This enables shrimp fishing to be conducted around the clock. One of the problems of fishing with a seine net is the slow process of hauling in the net to remove the fish. An electrical fish pump is inefficient unless there is a concentration of fish around the nozzle. The electrotaxis reaction has been used to achieve this concentration. This reaction comes about because fish, like other animals, have two separate nerve conduction paths, one taking messages in the form of dc pulses to the brain and the other from the brain. In the presence of an electric field, one or the other of these paths will be inhibited depending upon the orientation of the fish relative to the field. The fish can only swim if the path that carries impulses from the brain to the spine muscles is kept open. In other words, an electric field inhibits the fish from swimming in any direction except towards the positive electrode. This electrode is therefore located in the vicinity of the nozzle, while the negative electrode is located around the periphery of the net. The tetanus reaction has been used to prevent fish from taking evasive action when they see a trawl approaching (31).Electrodes placed in front of the trawl stun the fish which are then drawn into the trawl. A possible development in the future as envisioned by Klima (32) could be an automated fishing platform. This might consist of submerged tentlike structures and pulsed fight sources that would be used to attract fish. These would subsequently be harvested by using an electric field to concentrate them around the nozzle of a suction pump. B. Television

The use of television and photographic cameras to survey scallop beds has been described by Seidel (33). The equipment was mounted on a towed sled which could be maneuvered into any desired altitude above the sea bed by an operator on board the towing vessel, who controlled to vanes located near the rear end of the sled. It was found that this was the best position for locating the moveable vanes provided that there were two static vanes at the forward end. The towing vessel was equipped with an echo sounder so that if an obstacle was detected, the operator would be able to guide the sled over it. An underwater television camera, a 16 mm motion picture camera, and the three 500 W quartz iodide lights were mounted on the sled. Two men were required to operate the system, one to guide the sled and the other to monitor and record data. The latter would watch the television monitor and as soon as scallops appeared, he would turn on the motion picture camera,

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obtain a Loran fix, and record the height of the vehicle above the ocean floor which was generally in the region of 2 m for best viewing. This technique may be a valuable tool for substantially reducing unproductive search time of commercial vessels engaged in this type of fishing.

IX. HELIUM SPEECH PROCESSING The physiological effects associated with diving are generally solved by supplying the divers with a helium-oxygen breathing mixture. This, however, affects the divers’ speech, making it dificult for them to communicate with each other and with the surface support units. The main cause of the problem is that the velocity of sound in the mixture is higher than that in air. For mixtures suitable for operation at a depth of SO0 m, the velocity can be as high as 2.7 times that in air. This causes all the speech frequencies to be increased by that ratio, while the envelope of the speech pattern remains unaltered. The solution to this part of the problem is to decrease all frequencies without distorting the envelope and to perform this in real time. Numerous processors have been constructed to do this (34-36) and most of them perform well enough to be suitable for incorporation in practical equipment. None of the systems, however, provides perfect intelligibility due to the fact that they do not compensate for changes brought about by increased pressure (37) and some of the more subtle effects that are not yet completely understood. One of the techniques employed divides the speech signal into a large number of frequency bands which, between them, cover the input speech range. The amplitude of the signal in each channel is measured and used to control that of a corresponding output signal at a suitable lower frequency. Another solution is to sample short sections of the speech, the samples being placed in a temporary store and replayed at a suitably lower rate. During voiced sounds, the sections are taken from the most significant part of each larynx period and the remainder of the speech is rejected. During unvoiced sounds, the sections are taken less regularly and are more closely spaced. A more sophisticated technique involving the generation of the nth root of the signal by the use of a digital computer has also been employed. It is difficult to say which of these techniques is the best since the evaluation has to be performed subjectively.

X. DATATRANSMISSION A . Types of Links The simplest way of transmitting data from a submerged instrument to a platform is by direct acoustic transmission through the water. The most

296

RICHARD 0. ROWLANDS

favorable condition for this is when both terminals are stationary so that they do not create any flow noise which could mask the signal. Upper bounds on the data rate have been calculated (38) under ideal conditions where the only losses are inverse square law spreading, attenuation due to absorption, and forward scattering. Under practical conditions, the data rate will be well below these bounds as there will usually be some interference due to multipath propagation. Where acoustic transmission is not practicable, especially if the instrument is located at the sea surface, a radio link may be employed. It is sometimes advantageous to use this type of link even when the instrument is located below the surface, in which case it is connected by wire with a radio telemetry buoy that is floating on the surface. Where the instrument is towed behind a ship, the most convenient way of transmitting the data is by an electrical cable. This may be single or multiconductor and may be separate from the towing cable or built into it.

B. Cable Connections In many applications where electrical measuring instruments are towed behind a ship, it is advantageous to have the electrical conductors built into the towing cable for protection against mechanical hazards. There remains the problem of what is the best method of separating the conductor from the cable at the outboard end. It has been the custom to use a special socket for this purpose, the instruments being plugged directly into this. It constituted a weak link in the system, however, as it was difficult to protect it from mechanical damage, especially during the process of laying the instrument in the water and hauling it on board. Another approach to the problem has been described by MacLennan (39) in which the connector was eliminated altogether. The sea end of the cable was permanently shorted to the outside of the warp during manufacture. Data signals from the instrument were injected into the cable by means of a transformer whose primary winding was permanently connected by an electrical cable to the instrument package and whose low impedance secondary winding was connected to two clamps. These were used to secure the transformer to the warp, enabling it to be put on or taken off at the most convenient moment. They also made electrical contact with the warp, one clamp being connected as near as possible to the cable. A diagram of this arrangement is shown in Fig. 11 together with the equivalent circuit. The signal voltage out of the secondary is applied across the impedance of the warp R, and that of the seawater between the clamps R, . These are effectively in parallel with the characteristic impedance of the cable Z. The result is that an attenuated signal is injected into and trans-

ELECTRONIC ENGINEERING IN RIVER AND OCEAN TECHNOLOGY INPUT

I

COPPER CONDUCTOF?

I

1

I

. .

1

STEEL CABLE

297

1

I,

,I

a,

I,

4

8

i

!

\ f CLAMPS

1

-1

SHORT

FIG.11. Cable connection and equivalent circuit.

mitted down the cable to the receiver on board ship. The system is electrically very inefficient, but in many towing applications this is outweighed by the high mechanical reliability of the clamping device. C . Pulse Repeater Systems

Data from underwater instruments are often transmitted by cable to an oceanographic vessel for recording or processing. Ordinarily, the data rate is low and the distance over which it is required to be transmitted is relatively short. Under these circumstances, the electrical performance required of the cable does not call for any special techniques to be used except for armoring to take whatever strain may be exerted upon it. A requirement occasionally arises for a high data rate system capable of operating over distance long enough for the signal to need amplification enroute and cheap enough to implement so that the cable may be abandoned when the experiment is over. An experimental system was described by King et al. (40). Their objective was the design of a system capable of transmitting over a distance of up to 200 miles at a data rate of 1.35 x lo6 bits/sec. The objectives were accomplished by the use of a special miniature coaxial cable with built-in repeaters having a gain of about 20 dB and powered by direct current transmitted down the cable. A number of different designs of

298

111

RICHARD 0. ROWLANDS

cable were tried out, the final configuration consisting of a center conductor, 1 mm in diameter, of electroformed wire composed of high tensile strength steel with an electroplated overlay of 0.1 mm of copper. The insulation was solid low density extruded polyethylene. The return conductor was a copper tape 0.07 mm thick, thickly coated with solder, and having the overlapped seam soldered shut. With a diameter over the dielectric of 3.25 mm, the breaking strength was 100 kg and the weight per nautical mile in sea water was 25 kg. The impedance was 51 R and the attenuation 10 dB/km, both at 1 MHz. Alternative systems using a much cheaper balanced pair wire were developed by Rowlands and Rohm (41,42). In one version of their system, the repeater consisted of only four components, the circuit being as shown in Fig. 12. The circuit operates as follows. Direct current is transmitted down

t I f 0

INPUT

-

c 0

OUTPUT

I

0

FIG.12. Repeater schematic.

0

both wires in the longitudinal mode using the sea water as the return path, whereas the signal is transmitted as a transverse voltage across the two wires. The direct current and the signal are separated at the repeater input by means of the center-tapped transformer. The former, flowing through the Zener diode, produces a voltage drop which is used as the collector-emitter voltage to power the transistor. The transistor is normally cut off as the emitter and the base are at the same voltage. When a small positive pulse appears at the input, the transistor conducts and a current flows through the output transformer winding, causing an amplified pulse to be transmitted down the next length of line. The pulee is distorted as it travels down the wire link, but the authors have shown that this can be compensated for by making the inductance of the transformer windings (that are connected across the ends of the wire) low compared with the impedance of the wire.

ELECTRONIC ENGINEERINGI N RIVER AND OCEAN TECHNOLOGY

299

Another version employing a more complicated integrated electronic circuit is capable of two-way operation. The direction of amplification is determined by the direction of flow of the direct current. This is a useful facility where the station operator might wish to command the data-gathering equipment to change its mode of operation as a result of his analysis of the data or for any other reason. The overall dimensions of the pressure resistant repeater case are 60 mm long by 6 mm diam. ACKNOWLEDGMENTS The bulk of this work is based upon a conference on “Electronic Engineering in Ocean Technology” that the writer attended. He wishes to thank Mr. F. W. Sharp of The Institution of Electronic and Radio Engineers, 8-9 Bedford Square, London WCIB3GR, England, for permission to quote extensively from and reproduce some of the diagrams that appeared in the conference proceedings. In addition, the author is grateful to the following: Dr. J. Chernof, Director, Space Navigation and Tracking, I.T.T. Aerospace Laboratories, San Fernando, California, for permission to use the material in Table 1 ; Dr. J. C. Cook, Admiralty Research Laboratory, Teddington, Middlesex, who supplied the photographs for Fig. 10 (these photographs were first published in the North Sea Spectrum Proceedings); and The Sippican Corporation, Marion, Massachusetts, for the photographs that appear as Figs. 1 and 2.

REFERENCES 1. A. H. Schooley, Adoan. Electron. Electron Phys., 19, 1-54 (1964). 2. M. L. Henning, IERE Conf. Proc. No. 19,29 (1970). 3. N. L. Brown, in “Marine Sciences Instrumentation” (F. Alt, ed.), Vol. 4, p. 563. Plenum, New York, 1968. 4. S. A. Francis and G . C. Campbell in ‘‘ Marine Sciences Instrumentation (F. Alt, ed.), Vol. 3. Plenum, New York, 1965. 5. R. Briggs, British Patent No. 1,128,446 (1968). 6. F. J. H. Mackareth, J. Sci. Instruni. 41, 38 (1964). 7. R. Briggs, K . V. Melbourne, and G . Williams, IERE Conf. Proc. No. 19, , (1970). 8. R. Briggs, A. R. Agg, and K. G. Robertson, IERE Conf. Proc. No. 19, 15 1970). 9. C. H. Clayton and N. D. Smith, IERE Cot$ Proc. No. 19, 289 (1970). 10. W. F. Baker, IERE Conf Proc. No. 19, 307 (1970). 11. P. G. Collard and R. Spencer, IERE Conf. Proc. No. 19, 341 (1970). 12. F. E. Snodgrass, Science 162, 78 (1968). 13. M. Hanff, IEREConf. Proc. No. 19, 371 (1970). 14. R. G. Drever and T. Sandford, IERE Conf. Proc. No. 19, 353 (1970). 15. D. C. Webb, D. L. Dorson, and A. D. Voorhis, IEREConf Proc. No. 19,323 (1970). 16. J. A. Pierce and R. H. Woodward, Ofice Nuval Res. Tech. Rep. 620 (1971). 17. J. Chernof, I.T.T. Aerospace Laboratories, ‘‘ Economic Benefits of Ownership of Shipboard Satellite Navigation Equipment,” Cleveland Assembly of Radio Technical Commission for Marine Services (1969). 18. D. R. Reinhartsen, I.T.T. Aerospace/Optical Division, “The Geo Nav System,” Marine Geodesy Symposium, New Orleans (1969). 19. M. J. R. Fashani, IERE Conf. Proc. No. 19, 259 (1970).

300

RICHARD 0.ROWLANDS

E. E. Clark and B. Matthews, IERE Conf. Proc. No. 19, 211 (1970). R. W. Sudweeks, IERE Conf. Proc. No. 19, 239 (1970). S. T. Forbes, IERE Conf. Proc. No. 19, 95 (1970). C. H. Cooke, IERE Conf.Proc. No. 19, 81 (1970). H. Braithwaite, Brit. Acousf. SOC.Proc. 1 (2), Paper 71SC15 (1971). R. L. Montresor, “The ORL Range Calculator,” Serial No. NOW 65-0123-d-8. Ordnance Res. Lab., Pennsylvania State Univ., University Park, Pennsylvania (1966). 26. H. S. Antman, Under Sea Tech. 12 (7), 21 (1971). 27. D. C. Tate, “The Design of a Digital System for the Real Time Prediction of Underwater Sound Propagation,” M.S. Thesis in Elect. Eng. The Pennsylvania State Univ., University Park, Pennsylvania (1970). 28. R. B. Mitson and J. C. Cook, IERE Conf. Proc. No. 19, 187 (1970). 29. E. F. Klima, US.Fish Wildl. Serv., Fish. Ind. Res. 4 (3, 165 (1968). 30. W. R. Seidel, US.Fish Wildl. Serv., Fish. Ind. Res. 4 (6), 163 (1969). 31. C. 0. Kreutzer, in ‘‘ Modern Fishing Gear of the World,” Vol. 2, p. 581. Fishing News (Books) Ltd., London, 1964. 32. E. F. Klirna, Marine Tech. SOC.J . 4 (5), 80 (1970). 33. W. R. Seidel, Bureau of Commercial Fisheries, “Video Scallop Assessment System,” F A 0 Technical Conference on Fish Finding, Purse Seining and Aimed Trawling, Reykjavik, Iceland (1970). 34. D. A. A. Roworth, IERE Conf. Proc. No. 19, 529 (1970). 35. J. S. Gill, R. J. Morris, and M. E. Edwards, IERE Conf.Proc. No. 19, 523 (1970). 36. W. R. Stover, J. Acoust. SOC.Amer. 41, 70 (1967). 37. R. F. Quick, “ Helium Speech Translation Using Homornorphic Techniques,” Phys. Sci. Res. Papers No. 425. Airforce Cambridge Res. Lab., Bedford, Massachusetts (1 970). 38. R. 0 . Rowlands and D. E. Marsh, IEEE Nat. Telem. Conf. Rec. 308 (1968). 39. C. N. MacLennan, ZERE Conf. Proc. No. 19,489 (1970). 40. B. E. King, E. Raisbeck, L. 0. Schott, and L. R. Wrathall, IRE Trans. Commun. Sysf. 9, 159 (1961). 41. R. 0 . Rowlands and E. L. Rohm, U.S. Patent No. 3,457,508 (1969). 42. R. 0. Rowlands and E. L. Rohrn, U.S. Patent No. 3,499,985 (1970). 20. 21. 22. 23. 24. 25.

Author Index Numbers in parentheses are reference numbers and indicate that an author's work is referred to, although his name is not cited in the text. Numbers in italics show the page on which the complete reference is listed.

A

Abe, Y., 189, 193, 194,245 Adams, N., 67, 115 Adelnian, M., 61(29), 92, 115 Agg, A. R., 274(8), 299 Alley, C. 0.. 101(83), 102, 116 Ambard, G., 94, 99(75a), 116 Ancker-Johnson, B., 164(17), 244 Andrew, R., 263(30), 265 Anlauf, K. G . , I1(26), 12(26, 28). 36 Antes, L. L., 148(34), 159 Antman, H. S., 285(26), 300 Aoki, T., 164(10), 185(10), 192(10), 195(10), 196(10), 225, 226, 243(10), 244, 245 Arams, F., 47(8), 114 Arecchi, F., 65, 6 / , 106, 108(89), 109(89), 110, 1 I1(89), 115, 117 Arizunli, T., 164(10), 185(lO), 192(10), 195(10), 196(10), 225, 226, 243(10), 244, 245 Arlt, G . , 190(34), 245 Arndt, R., 146(25), 158 Arnold, S. J., 2( 1 I ), 19(40), 22(40), 24, 32, 37

Benedek, G., 67, 115 Beneking, H., 263(36), 265 Bennett, W. R., 2(3), 36 Berman, A. L., 155(49), 159 Bers, A,, 245 Bertolaccini, M., 99, 116 Bertolini, G., 101, 116 Bhatia, A. B., 19(41), 37 Birenbaum, L., 63, 115 Birk, M., 71, 75, 90, 92, 115 Blais, N. C., 10(22), 36 Boileau, A,, 61, 115 Bollinger, L., 93, 99, 116 Bosi, L., 99, 116 Boutot, J., 52, 74, 75(55b), 78, 92, 115 Bradley, W. E., 132(13), 158 Braithwaite, H., 285, 300 Brandmiiller, J., 54(24), 115 Brau, C. H., 23, 37 Bray, R., 163, 244 Briggs, R., 272(5), 273, 274, 299 Bronfin, B. R., 26(51), 37 Brown, N. L., 268, 271,299 Bunker, D. L., 10(22), 36 Bussolati, C., 99, 116 C

B Baker, W. F., 275, 299 Bargellini, P. L., 133(14), 158 Barrett, J., 67, I15 Basco, N., 34, 37 Bauer, W., 47(10), 114 Baum, G., 263(36), 265 Beaulieu, A. J., 2(4), 36 Bechtel, N. G . , 153(47), I59 Bekefi, G., 201, 245 Bell, R., 58, 115 Bender, P., 101(83), 102(83), 116

Callear, A. B., 19(37), 34, 37 Campbell, G . C., 269,299 Carman, R., 88, 116 Carrion, W., 101(83), 102(83), 116 Cashion, K., 18, 19(34), 37 Champlin, K. S . , 190(32), 245 Chang, R., 101(83), 102(83), 116 Chapin, D. M., 141(20), 147(20), 158 Charters, P. E., 12(27), 14(27), 34(27), 36 Chase, R., 81, 116 Chernof, J., 282, 299 301

AUTHOR INDEX

Chester, M., 260(23), 264 Chevalier, Ph., 74, 75, 78, I15 Chu, B., 67, I15 Clark, E. E., 283(20), 300 Clark, L., 148(37), 159 Clarke, A. C., 120, 158 Clayton, C. H., 274, 299 Coates, P., 51, 53, 54, 55, 64, 97, 115, 116 Cocchi, M., 101, 116 Coche, A., 79, 94, 99(75a), 101(62), 116 Cohen, N., 26(50), 37 Collard, P. G., 276, 299 Cook, J. C., 287,300 Cooke, C. H., 284, 300 Cool, T. A., 2(10, 12), 29, 30(52), 34, 36,37 Corney, A,, 94, 97, 98, 116 Cottrell, T. L., 22, 37 Cova, S., 99, 116 Crandall, D., 92, 99, 116 Crow, J., 164(11), l85(lI), 192(11), 196(11), 244 Crowe, K., 62, 115 Cumniins, H., 107(90), I17 Currie, D., 101(83), 102(83), 103, 104, 116 Curtin, D. J., 145(24), 146(24), 147(26), I58

D Dacey, G. C., 249, 253, 264 D'Alessio, J., 88, 94, 116 Davidson, F., 109, 112, 113, 117 Dawson, P. H., 21(43), 22(43), 23(43), 24(43), 26(43), 3 1 (57), 32(57), 37 Degiorgio, V., 107, 117 De Maria, A,, 87, 116 Dennison, E., 69, 115 Deutsch, T. F., 2(8), 4(15), 36 Dick, C. L., Jr., 164(17), 244 Dicke, R., 101(83), 102(83), I16 Djeu, N., 31(56), 37 Donati, S., 49, 71, 100, 114 Dorson, D. L., 279(15), 299 Downing, R. G., 147(26), 158 Drever, R. G., 277, 299 Drummond, A. J., 140(18), 158 Dumke, W. P., 263(33), 265 Duncan, W., 163(7), 164(14), 185(7), 244 Dzhidzhoev, M . S., 17(32),37

E Edwards, M. E., 295(35), 300 Ellis, B., 147(31), 159 Emanuel, G., 26(50), 37 Esaki, L., 150(39), 159

F Fairman, R . D., 153(47), 159 Falk, T. J., 2(10), 36 Faller, J., 101(83), 102(83), 116 Fasham, M. J. R . , 283(19), 299 Ferguson, M. G., 22(45), 37 Fiocco, G., 105, 116 Fischler, C . , 234, 235, 240, 245 Fisher, B., 177(23),244 Fisher, M., 47(8), 114 Fleming, P. L., 151(45), 159 Fleming, W. J., 164(13), 177(13), 185(13), 189(28), 192, 193(28), 195(35), 198, 199(28, 36), 202(36), 204(36), 215, 219(13), 221(36), 223, 225, 227, 230(36), 232(36), 234,242, 243( I3), 244,245 Foltzer, L. E., 151(45), 159 Foord, R., 54, 55, 113(22), 115 Forbes, S. T., 283, 300 Foster, K. D., 30(55), 34, 37 Francis, S. A,. 269, 299 Fritzche, H., 150(41), 151(43), 159 Frohman-Bentchkowsky, D., 263(29), 265 Fuller, C. S., 141(20), 147(20),158 Furumoto, H., 88, 116

G Gale, R., 148(37), 159 Garland, C. W., 190(33),245 Gatti, E., 49, 65, 67(38), 70, 71, lOO(12, 52), 114, 115 Cedcke, D., 79, 80(61, 63), 81, 116 George, E. V., 201, 245 Gerrv, E. A,, 9(17), 36 Geurst, J. A,, 263(32), 265 Ghandhi, S. K., 250, 256, 264 Gicquel, R., 260, 264 Giglio, M., I10(95), 117 Gill, J. S., 295(35), 300 Glenn, W., 87,116

303

AUTHOR INDEX

Glover, G. H., 190(32), 245 Gobat, A. R . , 147(30), 159 Gorelik, J., 177(23), 244 Grant, G., 62, 115 Grebene, A. B., 250, 256, 264 Greebe, C. A. A . J., 234, 235, 240, 245 Green, W. H., 33(61), 37 Greenblatt, M., 77, 116 Gregg, D. W., 9(18), 36 Grernmelmaier, R., 147(29), 15Y Greytak, T., 67, 115 Gross, R. F., 2(9), 36 Grosvalet, J., 249, 264 Grove, A . S., 263(29), 265 Gumnick, J., 62, 115 Gunter, W., 62, I f 5

H

J Jacobs, T. A,, 2(9), 26(50), 36, 37 Jacobson, T. V., 33(60, 62), 37 Jaenicke, R . , 185(25), 192, 245 Jakernan, E., 110, 117 Javan, A., 2, 36 Jeffers, N. Q., 32, 34, 37 Johnson, F. S., 140(17), 158 Jonathan, N., 12. 36 Jones, R., 54, 55(22), 64, 113(22), 115

K Kane, E. O., 150(40), 159 Karplus, M., 10(23), 36 Kasper, J. V. V., 2, 36 Kaula, W., 101(83), 102(83), 116 Kennedy, D. P., 250, 251, 259, 260, 262, 264

Hachenberg, O., 47(10), 114 Hacker, H., 54(24), I15 Halpern, A , , 98, 116 Hancock, G., 19(39), 22(39), 23, 24, 25, 37

HantT, M . , 277, 2YY Harris, L., 52, 115 Harth, W., 185(25), 192, 245 Hartniann, C. S., 245 Hauser, J . R.. 249, 256, 264 Hayakawa, H., 163(8), 205, 206, 243(8),

Kent, G., 106, 116 Kerker, M . , 66(40), 115 Kerns, Q., 71, 75(53), 85, 90, 92(53), 115, I16

Kesque, J., 88, 94, 116 Khokhlov, R . V., 17(32), 37 Kikuchi, M., 163(8), 205, 206, 243(8), 244 Kim, C.-K., 250, 251(19), 253(19), 255(21), 258(17), 260(22), 261, 264, 265 Kirnbell, G . H., 2(1 I), 19(40), 22(40), 24, 30(55), 31(57), 32, 33(60, 62), 34, 36, 37

244

Hayakawa, K., 164(10), 185(10), 192(10), 1 9 3 I O), I96( I O), 225( 10, 42). 226, 243( lo), 244, 245 Helvey, F., 48( 1 1 ), 114 Henning, M. L., 268, 273, 2YY Heroux, L., 50, 114 Herriot, D. R., 2(3), 36 Herzberg, G., 316). 36 Herrfield, K. F., 19, 21, 37 Heydtmann, H., 12(29), 16(29), 36 Hiltner. W., 68, 115 Hofstein, S. R., 263(27), 265 Hooper, W. W., 153(47), 159 Hutson, A. R., 162, 172(22), 244

I Isenberg, I., 97, 98, 116 Ishii, T., 166

King, B. E., 297, 300 King, J. E., 199(37), 201(37), 238, 245 Kino, G. S., I63(6), I64(16), l85(6), 189, 191, 192, 196(29), 201(16), 243(6), 244, 245

Klima, E. F., 294, 300 Knudsen, H., 85, 116 Koechlin, Y., 90, 94, 98, 99, 116 Kokoschinegg, P.,230, 232, 243(43), 245 Kondo, R., 148(33), 159 Koons, H , 105, 116 Korennian, V.. 108(92), 117 Kowalski, E., 42(1), 43, 45, 79, 82, 89, 90, I I4 Krall, H., 48(1 I), 50, 72, 77, 114, 115 Kreutzer, C. O., 294(31), 300 Kuhrt, F., 201, 245 Kuniar, C. S., 163(3), 244 Kunrz, P. J., 9(19), ll(19, 26). 12(26), 36

304

AUTHOR INDEX

L Lakes, R., 62(30), 63, 75, 89, 115, 116 Lambert, J. D., 19(36), 37 Lami, H., 88, 116 Lamorte, M. F., 147(30), 159 Larouche, R., 34(64), 37 Lastovka, J., 107, 117 Lebrun, J., 149(38), 159 Lee, K. P., 34(64), 37 LeGalley, D. P., 140(19), 158 Lehovec, K., 263(35), 265 Leies, G., 148(34), 159 Leskovar, B., 76, 81, 116 Lewis, I., 44, 114 Light, J. C., 1 l(24, 25), 36 Lin, M. C., 33(61), 37 Lindmayer, J., 144(23), 148(36), 152(46), 158, 159 Lippmann, V. H. J., 201, 245 Litovitz, T. A., 19(35), 21, 37 Livingstone, J., 163(7), 164(14), 185(7), 244 Lo, C. C., 76, 81, 116 Loeb, H. E., 263(30), 265 Lombard, F., 49, 114 Longworth, J., 99, 116 Love, W., 263(30), 265

M MacDonald, G., 101(83), 102(83), 116 Macdonald, R. G., 12(27), 14(27), 34(27), 36 McDonald, W., 79, 80(61, 63), 81, 116 McFee, J. H., 162, 244 McIntyre, D., 66(41), 115 McIver, G . W., 147(30), 159 Mackareth, F. J. H., 273, 299 MacLennan, C. N., 296, 300 Madelung, O., 190(31), 245 Mahan, B. H., 22, 37 Mahle, C. E., 155(49), 159 Mandel, L., 109, 112, 113,117 Mandl, V., 101, I16 Many, A,, 177(23), 244 Marburger, R. E., 148(34), 159 Marsh, D. E., 296(38), 300 Martin, F., 49, 114 Mason, W. P., 166, 167(21), 168(21), 244

Matheson, A. J., 22, 37 Matheson, R., 74(56), 77, 115, 116 Matthews, B., 283(20), 300 Maylotte, P. D., 11(26), 12(26), 36 Meiling, W., 45, 55, 77, 79, 82, 89, 90, 91, 100, 114 Melbourne, K. V., 273(7), 299 Melchior, H., 47(8), 114 Melliar-Smith, C. M., 12, 36 Metzger, S., 123(5), 158 Meulenberg, A., 145(24), 146(24), 158 Miehe, J., 79, 94, 99, 101, 116 Mikoshiba, N., 189, 193, 194, 245 Miller, F., 61, I15 Miller, R., 77, 92, 116 Millikan, R. C., 17(38), 19(38), 37 Mirels, H., 2(9), 36 Mitchell, A. C. G., 3(14), 36 Mitson, R. B., 287, 300 Mo, D . L., 250, 264 Mok, M. H., 9(21), 11, 36 Montresor, R. L., 285(25), 300 Mooradian, A., 68, 115 Moore, A. R., 165(20), 219(20), 244 Moore, K., 148(37), 159 Moore, R., 65(37), 115 Morris, R. J., 295(35), 300 Morton, G., 47(7), 48, 49, 50, 56, 57, 58, 77, 114, 116 Moss, T. S., 147(31), 159 Motsch, C., 249(8), 264 Mueller, G . E., 128(9), 158 Mulholland, J., 101(83), 102(83), 116 Muller, R . S., 263(31), 265 Mytton, R. J., 148(37), 159N

Nemeth, E. M., 9(19), 11(19), 36 Neumark, G . T., 263(34), 265 Nishizawa, J., 250, 264 Nordquist, A,, 253(20), 264 Norrish, R. G . W., 34, 37 Nussli, J., 45, 72, 75, 114 0

O'Brien, R. R., 250, 251, 259, 260, 262, 264 Ogryzlo, E. A,, 29(54), 37

305

AUTHOR INDEX

Okimura, H., 148(33), 159 Oliver, C., 54, 55(22), 64,65, 110(96), 112, 113(22), 115, 117 Ostertag, E., 79, 101(62), 116

P Pacey, P. D., 11(26), 12(26), 13(31), 14, 17(31), 36 Patel, C. K. W., 1(1), 8, 18(33), 36, 37 Pearson, G. L., 141(20), 147(20), 158 Pellegrini, B., 151(44), 159 Persyk, D., 48(11), 72, 77. 114, 115 Pierce, J. A., 281, 299 Pierce, J. R., 1 l9( I), 158 Pietri, G., 45, 52, 63, 71, 72, 74, 75, 78, 92, 114, 115 Pike, E., 54, 55(22), 64,65, 106, 110(96), 111, 112, 113(22), 115, 117 Pilloff, H. S., 31(56), 37 Pirnentel, G. C., 2, 3(13), 36 Pinder, R . S., 148(37), 159 Platonenko, V. T., 17(32), 37 Plotkin, H., 101(83), 102(83), 116 Plumrner, K. L., 127(8), 158 Polanyi, J. C., 2(5), 9, 11, 12, 13(31), 14, 16(29), 17(31), 34, 36 Potter, A. E., Jr., 148(35), 159 Poultney, S., 62(30), 63, 75, 89, 101(83), 102(83), 103(84b), 106, 115, 116, 117 Present, G., 84, 85, 94, 100, 115, 116 Prim, R. C., 249,264 Pritchard, W. L., 124(6), 158 Puente, J. G., 126(7), 158

Q Quadflieg, P., 190(34), 245 Quick, R. F., 295(37), 300

R Radicella, R., 88, 116 Raff, L. M., 10(23), 36 Raisbeck, E., 297(40), 300 Rankin, C. C., 11(24), 36 Raviart, A , , 90, 94, 98, 99, 116 Read, H. W., 22(45), 37 Read, W. T., Jr., 142, 158 Reddi, V. G. K., 263(28), 265

Reinhartsen, D. R., 283, 299 Reintjes, J., 88, 116 Revesz, A. G., 148(36), 152(46), 159 Reynolds, D. C., 148(34), 159 Reynolds, G . , 67, 69, 115 Reynolds, J., 152(46), 159 Rittner, E. S., 144(22), 147(28), 155(48), 158, 159, 263(34), 265 Robertson, K. G., 274(8), 299 Robinson, B. B., 164(18), 238, 244 Rohm, E. L., 298, 300 Rosen, A., 140(19), 158 Rosen, H., 122(4), 158 Rosner, S. D., 9(19), 11(19), 36 Ross, I. M., 249, 253, 264 Ross, J. B., 163(3), 244 Rostron, R . W., 138(16), 139(16), 158 Rota, A,, 101, 116 Route, R. K., 163(6), 185(6), 189, 191, 192, 196(29), 243(6), 244, 245 Rowe, J. E., 164(13), 177(13), 185(13), 189(28), 192(35), 193(28), 195(35), 198, 199(28), 219(13), 223, 225,227, 234, 242, 243( I3), 244, 245 Rowlands, R. O., 296(38), 298, 300 Roworth, D. A. A., 295(34), 300 Russell, D., 11(25), 36 Ryder, E. J., 249(4), 264

S

Sablatschan, E., 230, 232, 233, 245 Sah, C. T., 249, 254(3), 263(28), 264, 265 Sanders, R. W., 128(10), 158 Sandford, T., 277,299 Scarl, D., 63, 84, 85, 88, 90, 94, 111(68), 113, 115, 116 Schalla, R. L., 148(35), 159 Schawlow, A. L., 2,36 Scheer, J., 61, 115 Schmidt, W. G., 126(7), 1 3 3 1 3 , 158 Schooley, A. H., 267,299 Schott, L. 0.. 297(40), 300 Schroeder, J. E., 263(31), 265 Schrotter, H., 54(24), 115 Schuyler, R., 97, 98, 116 Schwartz, R. N., 19, 37 Schwarzchild, A., 100, 116

306

AUTHOR INDEX

Searles, S. K., 31(56), 37 Seeger, K., 230, 232, 243(43), 245 Seidel, W. R., 294, 300 Seifert, F., 164, 230, 232, 233, 244, 245 Selinger, B., 98, I16 Sengers, J., 66(41), 115 Sevin, L. S., Jr., 249, 256, 264 Sharma, R. D., 23,37 Sharpe, J., 45(6), 114 Shaw, S., 62,115 Shirley, J. A,, 34, 37 Shockley, W., 142, 158, 238, 245, 247, 249, 264 Silverberg, E., 103(84a), 116 Simon, R., 47(9), 114 Slater, D. H., 12, 36 Slawsky, Z. I., 19, 37 Sliva, P. O., 163(3), 244 Slutsky. L. J., 190(33), 245 Smith, A. G . , 129(1 I), 158 Smith, H., 50, 114 Smith, 1. W. M., 19(39), 22(39), 23, 24, 25,37 Smith, N. D., 274, 299 Smith, R., 67, 115 Smith, R. W., 165(20), 219(20), 244 Snodgrass, F. E., 276,299 Sommer, A,, 58, 59(25), 62(25), 115 Sona, A., 65, 67(38), 115 Spencer, D. J., 2(9), 36 Spencer, R., 276, 299 Spicer, W., 58, 115 Spinolo, G., 99, 116 Spirn, I., 100, 116 Stary, F., 45, 5 5 , 11, 79, 82, 89, 90, 91, 100, 114 Statler, R. L., 147(26), 158 Steele, M. C . , 163, 177(24), 183, 185, 188, 189, 195(24), 203(24), 244, 245 Stephens, R. R., 2(10, 12), 29, 30(52), 34, 36.37 Stern, E., 163(9), 244 Stetser, D., 87, 116 Stevens, S., 99, 116 Stover, W. R., 295(36), 300 Suart, R. D., 2( 1 I ) , 19(40), 22(40), 24, 3 1(57), 32, 37 Sudweeks, R. W., 283(21), 300 Svelto, V., 49, 70, 71, lOO(12, 52), 114, 115 Swartz, G . A,, 164(18), 238, 244

T Tam, W. G., 21(43), 22(43), 23(43), 24(43), 26(43), 34(64), 3 7 Tango, H., 250,264 Tansley, T. L., 147(32), 159 Tao, T., 98, 116 Tarney, K., 249, 253(7), 264 Tartari, U., 110(95), 117 Tate, D. C., 287, 300 Taylor, H., 91, 116 Teszner, S., 260, 264 Thekaekara, M. P., 140(18), 158 Thomas, G., 93, 99, 116 Thomas, S. J., 9(18), 36 Thompson, A. H., 164(16), 191(16), 201(16), 244 Tiemann, J. J., 150(41), 159 Topp, J., 54, 115 Townes, C. H., 2, 36 Tribes, R., 249(7), 264 Trofimenkoff, F. N., 249,253,264 Trumbore, F. H., 150(42), 159 Tull, R., 66(39), 68, 115 Turner, C. W., 163, 164(11, 12, 15), 165(15), 185, 188, 189, 192(11), 196(11), 199(15), 201(15), 244 Tusting, R., 71, 75(53), 85, 90, 92(53), 115, 116 V

Van Den Bergh, H. E., 34,37 Van Duzer, T., 163(5), 185(5, 26), 188(5), 189(5), 191(26), I92(26), 244, 245 van Laar, J., 61, 115 Voorhis, A. D., 279(15), 299 Vural, B., 177(24), 183, 195(24), 203(24), 245 W

Wampler, E., 101(83), 102(83), 116 Ware, W., 97, 98, 116 Warfield, G., 263(27), 265 Webb, D. C . , 219,299 Weller, K. P., 163(5), 164(15), 165(15), 185(5,26), 188(5), 189(5), 191(26), I92(26), I99( 1 3 , 201( I 5), 244, 245

307

AUTHOR INDEX

Wells, F., 44, 114 Werth, A . M., 126(7), 158 Westerlund, L., 146(25), 158 White, D. L.,162, 172(22), 189, 194,

Wright, R., 106, 116 Wu, S. Y., 249, 254(3), 264 Wysocki, J., 147(27), I58

244,245

Wick, R. F., 201, 245 Wiesner, J. B., 121(3), I58 Wilkins, R. L., 26(50), 37 Wilkinson, D., 101(83), 102(83), 116 Williams, B., 47(9), 114 Williams, G., 273(7), 299 Wiswall, C. E., 32, 34, 37 Wittwer, N., 77, 92, 116 Wolber, W., 51, 5 5 , 63, 115 Wong, W. H., 9(20), 12(28), 36 Woodall, K. B., 12(28), 36 Woodward, R. H., 281, 299 Woonton, G . A,, 34(64), 37 Worcester, P., 165(20), 219(20), 244 Wotherspoon, N., 100, 116 Wrathall, L. R., 297(40), 300

Y Yanai, H., 250, 264 Yang, E. S., 250, 255(21), 258(17), 261, 264, 265

Yardley, J. T., 23, 37 Yates, E., 92, 99. 116 Young, C. E., 9(19), 11(19), 36

2 Zampach, J., 88, 94, 99(75a), 116 Zatzick, M., 52, 56, 58, 66, 68, 115 Zemansky, M. W., 3(14), 36 Zinman, M., 177(23), 244 Zuleeg, R., 249, 261, 263(35), 264, 265

Subject Index A Acoustic disturbances, general dispersion equation and, 166-167 Acoustic gain, in (11 ])-oriented crystal, 228-234 Acoustic telemetry, in ocean current measurement, 279 Acoustic transducers, 162 Acoustic-wave amplifiers, 162 Acoustic waves bulk amplification and, 163 off-axis, 164 Acoustoelectric dispersion equations for, 169-171 rf conductivity in, 174-1 75 Acoustoelectric instability, 165 Acoustoelectric interactions in compound semiconductors, 161-243 empirical field factors in, 199-206 electromechanical coupling parameters for, 207-215 for electron-hole carrier transport and off-axis acoustic wave propagation, 234-242 exact solution for collinear static fields in, 176-185 field dependence in, 190-191, 199, 203 fixed maximum value for, 190 frequency dependence in, 197-198 growth rate of, 188-198,215-216, 239-242 magnetoresistance function in, 201, 205 mobility saturation factor in, 199-200 off-axis, 166-176,206-234 on-axis, 185-206 radiation process in, 165 solution of for static fields, 185-206, 208-234 Acousto-helicon dispersion equation derivation of, 177-183 solution of, 183-1 85 Acousto-helicon interaction, field configuration for, 179

Astronomy, photometry and spectrophotometry, in, 68-69

B Background noise, in signal photoelectrons, 55-56 Bandwidth, in communications satellites, 128-1 29 Bathythermographs, 285-287 Bell Telephone Laboratories, 121 Bialkali photosurfaces, 54 Billiard-ball atom, in classical mechanics, 19 Boltzmann distributions, 12-16 Brillouin scattering, 40, 42, 67, 107 British National Institute of Oceanography, 291-293 Brownian motion, 110-1 11 Buoys, expendable and hybrid-wave, 274-276

C Cable connections, in rivers and ocean, 296-297 Cape Kennedy, satellite launchings from, 122 Carbon monoxide de-excitation of, 25 ground vibrational state of, 24 infrared chemiluminescence of, 24 Carbon monoxide laser, 31-32 Carrier transport system, acoustoelectric interactions and, 234-242 Cassiopeia, electromagnetic radiation from, 130 Cerenkov (Cherenkov) light pulse, 88, 92 Cerenkov light source, 90 Cerenkov radiation, 53 light pulses and, 88 in windows, 54 308

309

SUBJECT INDEX

Channel-length modulation, JFET and, 257-259 Chemical lasers, 1-36 characteristics favorable to, 2 6 2 9 continuous-action, 29-32 laser systems and, 29-36 oscillator part of, 20 pumping reaction in, 9-16 reaction mixtures used in, 28 relaxation of excited state in, 16-26 translational part of, 20-26 vibrational excitation of, 26-27 vibrational transition in, 5-7 Chemical laser systems, computer simulations of, 26 Chemical photomultiplier, 78 see also Photomultiplier Collinear reactive systems, quantum mechanical solutions for, 11 Collinear static fields, acoustoelectric interactions and, 176185 Color centers, lifetimes of excited states for, 99 Color TV programs, French-Russian, 127 Communications satellites see also Satellite advances in, 119-157 circuit boards for, 156 cosmic noise in, 129-1 30 energy storage in, 149 frequency and bandwidth in, 132-1 33 future trends in, 157 in geostationary orbit, 120, 122, 138 inertia wheels for, 157 INTELSAT system in, 124-127 materials technology for, 155-156 modulation, multiplexing, and multiple access in, 134-137 power generation for, 141-149 propulsion system for, 156 proton damage in, 146-147 Russian, 127-1 28 spectrum and orbit utilization in, 130-1 33 surface structural members of, 156 systems considerations in, 128-130 transponder electronic devices in, 149-155 traveling wave tubes for, 153-155 tunnel diodes for, 149-153 Communications Satellite Act (1962), 123

Compound semiconductors, acoustoelectric interactions in, 161-243 COMSAT, 135 Conduction charge carriers, collectors of, 162-163 Constant-fraction-of-pulse-height timing discriminator, 103 Continuous electron multipliers, 50-52 gain and gain statistics for, 50-52 Cosmic ray particles, fluorescence and, 53 Crab Nebula, electromagnetic radiation for, 130 Current-saturation mechanisms, in junction field-effect transistors, 247-264 Cygnus, electromagnetic radiation from, 130

D Data transmission, in river and ocean technology, 295-299 Decay curves, single-photon statistical technique for, 98-99 Decay time measurements finite instrumental resolving time and, 96 scintillators and, 100 Decca chain system, in navigation, 280-282 Device noise in channel photomultipliers, 5 5 light signal and, 54-55 Digital detector, synchronous, 65 Discrete dynode multipliers, gain and gain statistics for, 48-50 Dispersion equation, acoustoelectric, 169-1 71 Doppler-broadened scattered radiation, 105 Doppler-shifted frequencies, on photosurface, 107

E Earth, noise power spectrum from, 130 Earth magnetic field, 122 Echo project, 121 Electrical communications, advances in, I20

310

SUBJECT INDEX

Electric field, in ocean, 293 Electromagnetic radiation, galactic and extragalactic, 130 Electromagnetic spectrum, filling up of, 120 Electromechanical coupling parameters, 207-2 I 5 Electron-hole carrier transport, 234, 242 Electronic engineering data transmission in, 295-299 helium speech processing in, 295 in navigation, 280-283 in river and ocean technology, 267-299 sonar applications in 283-293 Electron multipliers continuous, 50-52 photodevice and, 70 in single photon detection and timing, 47 Electric-phonon interactions, energy loss through, 60 Emission eoefficients, in chemical lasers, 18 Excited state block diagram for, 93 lifetimes of, 92-101

G

Galactic noise, in communications satellites, 129-130 Gas lasers mechanism of, 1-2 single-pulse mode in, 92 Gaussian noise, in communications satellites, 128 CGA (gradual channel approximation), 247-248, 250-253 for finite-channel JFET model, 253-257 Geostationary orbit advantages of, 131-132 hazardous environment of, 138 Geosynchronous satellite, 120-122, 131-132, 138

H Hamiltonian equations of motion, I0 Helium speech processing, 295 Heterojunction solar cells, 147-149 H F laser, transversely sparked, 32-33

F Fabry-Perot interferometers, 67 Fast crossover timing, in photomultipliers, 80

Fast decay time, of excited state, 92-93 Fast fluorescence decay times, of molecules, 91 Field-effect transistors, junction, see JFET Fish counting, sonar in, 283-285 Fishing, electronic engineering in, 293-295 Flame laser, 30-31 Flash-induced laser, 34 Flash photolysis, 2 Free atoms, lifetimes of excited states in, 94-95 Frequency bands, for communications satellites, 130-133 Frequency Division Multiple Access, 134-1 35 Frequency modulation, in communications satellites, 129 Frequency Modulation and Frequency Division Multiplexing, 134

I Impurity assisted tunneling, in communications satellite, 151 Infrared chemiluminescence, of carbon monoxide, 24 INTELSAT I, 11, and 111 satellites, 124, 153-155 INTELSAT IV satellite, 124-127, 153-155 communications capacity of, 137 INTELSAT system, 123-127, 135-138 Intensity-correlation spectroscopy, I08 International Frequency Bureau, 128 International Satellite Communications Consortium, see INTELSAT International Telecommunications Union, 128

J Jet Propulsion Laboratory, CalTech, 121

31 I

SUBJECT INDEX

JFET (junction field-effect transistors) channel-length modulation and, 257-259 current saturation mechanisms in, 247-264 drain conductance of, 249 electrostatic charge distribution in, 261 extrapolated pinch-off point (expop) in, 249 field-dependent mobility of, 249 finite-channel model of, 255-257 literature on, 249-250 governing equations for, 250-253 mobile carrier accumulation and, 259 numerical calculations for, 257-263 saturation models in, 253-257 Shockley model of, 248 Shockley theory in, 253 space-charge region and neutral conducting channel in, 251 Johnson noise, 39 detection of, 45 photoelectrons and, 43 Jupiter, noise temperatures of, 130

K Kepler’s laws, 121 Kerr cell shutter, 96 Kokusai Denshin Denwa Co., 135 KSI region, in photomultiplier, 72-73

L Laser(s) carbon monoxide, 31-32 chemical, see Chemical lasers continuously operating, 2 flame, 30-31 flash-induced OH, 34 operating principle of, 3 transverse-flow, 34-35 transversely sparked HF, 32-33 vibrational transition and, 5-7 Laser beam, as non-Gaussian field, 108 Laser flow, relaxation in, 24 Laser systems, 29-36 Lasing action continuous, 29-32 general conditions for, 3-5, 27-29

Lennard-Jones 6-1 2 intermolecular function, 21 Light beam, arrival time distribution of photons in, 42 Light fields, thermodynamic fluctuations and, 107 Light pulse, thyratron-triggered, 97 Light pulsers Cerenkov, 88-89 photomultiplier and, 85-86 Light signal, noise generated by, 55 Light source, filtered thermal, 90 Lithium, in communications satellite, 147 Long-range navigation systems, 282 Loran A, 281-282 Loran C, 281-282 Lunar Laser Ranging Experiment, 91, 101-104

M McDonald Observatory, 102-103 Macromolecules, in Brownian motion, 110 Magnetoresistance function, in acoustoelectric interactions, 201, 205 Maryland, University of, 91 Maxwell-Boltzmann law, 6 Microchannel wafer photomultiplier, 52 Mobile carrier accumulation, JFET and, 259 Modulated light sources, experiments with, 105-106 Modulation, in communications satellite, 134-1 35 Molecules, fast fluorenscence decay times and, 97 Moon, point retroreflector on, 101-102 MOSFETS (metal oxide field effect transistors), current saturation in, 263

N

Nanosecond laser transmitters, 41 National Aeronautics and Space Administration, 121, 135, I38 National Research Laboratories, 31 Naval Research Laboratory, 271

312

SUBJECT INDEX

Navigation systems electronic engineering in, 280-283 long-range, 282 Navy Navigation Satellite System, 281 Nippon Electric Co., 135 Noise see also Background noise; Photomultiplier noise cosmic, 129-1 30 Johnson, 3 9 , 4 3 4 5 in photomultipliers, 53 Noise pulse height distribution, 51 Nonresonant exchanges, long-range interaction theory and, 23 Nuclei, excited states for, 99

0 Ocean currents electronic engineering and, 277-280 horizontal, 277-279 vertical, 279-280 Oceanography, survey scanning in, 287-293 Ocean technology data transmission in, 295-299 electric field in, 293 fishing and, 293-295 sonar applications in, 283-293 Off-axis acoustic gain, for (lOO)-oriented crystals, 217-234 Off-axis acoustic-wave propagation, and arbitrarily oriented static fields, 206-234 electron-hole carrier transport and, 234-242 Off-axis acoustoelectric interactions, 164-165 general theory of, 166-176 growth rate of, 215-216, 241 Off-axis electron-hole interactions, 241 Omega navigation system, 281-282 On-axis acoustic wave propagation, 185-206 (100)-oriented crystals, off-axis acoustic gain in, 217-234 ( 1 1 1 )-oriented crystals, off-axis acoustic gain in, 228-234 Optical masers, 2 see also Laser($

P Photocathode quantum efficiency measurement for, 6 1-62 room temperature noise and, 54 Photodetector, photoelectrons released at, 103 Photodevice(s) see also Photomultiplier(s) background noise and, 52-57 basic elements of, 70 calibration and stability of timing circuits in, 90-91 cooling of, 45 electrical noise and, 81 fluctuating current of, 107 gain and detector circuits of, 4 2 4 5 gain mechanisms and statistics for, 46-52 impulse response and afterpulses in, 91-92, 94 light multiplier and, 86-87 light pulsers for, 86-88 photon detector performance of, 56-57 photosurface of, 57-58 prepulsing in, 92 single-photon method in, 40-41 single-photon timing and detection charge of, 74 statistical behavior of, 71 stop signal from, 95 suitability of, 45 Photodevice timing capabilities and limitations, 69-78 Photodevice transit time fluctuations, 98-99 Photoelectrons detection statistics of, 108-109 quantum counting efficiency of, 63-64 Photoemissive materials, device noise and, 40 Photoemission process, 59-61 Photoemitter, energy band model for, 59 Photometry, in astronomy, 68 Photometry experiments in laboratory, 66-68 light intensity and, 64 Photomultiplier(s) channel, 78 Cherenkov radiation and, 53 constant-fraction-of-pulse-heigh t, 8 I

313

SUBJECT INDEX

Photoniultipliers(s) conventional fast, 72-77 crossed-field, 77-78 device noise and, 53-55 with discrete linear dynodes and electrostatic focusing, 69 fast time response, 50, 75, 80 with focused multiplier, 46, 63 KSI region in, 72-73 new photoemissive materials in, 61 RCA C31000F, 103 small photosurface in, 77 time interval measurement circuit and, 82 time resolution improvement in, 75-76 transit time fluctuation in, 73 twelve-dynode, 74 Photomultiplier anode, Gaussian current pulse from, 44 Photomultiplier noise background noise and, 55-56 as single-electron noise, 54 Photomultiplier pairs, time difference distribution for, 85 Photon, anode pulse width for, 71 Photon counting practices, photomultipliers and, 56 Photon detection, single, see Single photon detection Photon detection experiments, 64-69 Photon detection performance tests, 56-57 Photon statistics experiments and measurements, 106-1 14 theory of, 108-110 Photosurfaces quantum efficiency of, 57-63 types and characteristics of, 58 Physical lasers, 2 see also Chemical lasers; Laser(s) Piezoelectric force term, in acoustoelectric disperson equation, 172-1 73 Piezoelectric polarization field, defined, I78 Pile-up error, in fast decay time measurement, 97 Poisson distribution in photon statistics experiments, 108-109 in single-electron response, 50 Population inversion, partial and total, 7 Potential barrier, tunneling through, 11 Potential energy curve, for diatomic molecule, 6

Potential surface, attractive, 11 Protein molecules, i n Brownian motion, 111 Proton flux, of communications satellite, 138 Pulse repeater systems, underwater, 297 Pumping reaction, chemical laser and, 9-16

Q Quantum efficiency, enhancement of, 62-64

R Rarnan scattering, 40, 42, 67, 107 Raman-shifted frequencies, 67 Rayleigh scattering, 42, 67 RELAY satellite, 121-122 Repulsive interaction energy, in chemical lasers, 19 River and ocean technology data transmission in, 295-299 electronic engineering in, 267-299 navigation and, 280-283 ocean currents in, 277-280 sonar applications in, 283-293 surface waves in, 274-276 tides in, 276-211 water quality measurement in, 268-274 Rockets, early payloads of, 121 Rotational relaxation, in excited state, 17 Russian communications satellites, 127-128 S

Satellite(s) in geosynchronous orbit, 120-122, 131-132, 138 inverse distance square law for, 121 orbital control and drift in, 123 Satellite communications see also Communications satellites advances in, 119-157 electronic devices for, 137-155 power generation in, 141-149 solar Rare activity and, 139-141 spectrum and orbit utilization in, 130-1 33 Satellite navigation systems, 282

314

SUBJECT INDEX

Scanning techniques in river and ocean technology, 287-293 side scan in, 291-293 Schottky barrier, in communications satellite, 142 Scintillators decay time measurements in, 100 energy transfer in, 93 Secondary electron emission, improvement in, 47-48 Semiconductor, photoemission for, 59-60 see also JFET SER (single-electron response), 49-50 amplitude distribution in, 51-52 theoretical derivations of, 49 time measurement of, 71 SER amplitude, 70 SER amplitude distribution, 57, 63, 73 Sharma theory, 22-23 Shockley-Read recombination process, 142- I45 Shrimp fishing, electric field and, 294 Signal photon rate, 64 Silicon solar cells, in satellite power generation, I41 -147 Single-electron noise, photomultiplier noise as, 54 Single photon, fast timing with, 69-104 Single photon detection, 39-1 14 with moderate timing requirements, 105-1 14 photodevice gain and detection units in, 42-45 time derivation circuits and, 79-80 Single photon distribution, 48 Single photon precise timing experiments, 92-1 04 Single photon time resolution, block diagram for, 84 Single photon timing characteristics, of selected photodevices, 74 Single photon timing methods, 83-87 Solar cells heterojunction, 147-1 49 satellite power and, 120, 141-147 silicon, 141-147 Solar flare activity, communications satellite and, 139-141 Solar noise, in communications satellites, 129-141

Sonar applications, 283-293 in fish counting, 283-285 sound ray tracing and, 285-287 in surveying, 287-293 Soviet Union, Orbita satellite system of, 127-1 28 Space-charge-limited current, JFETS and, 263 Space Division Multiple Access (SDMA) techniques, 135 SPADE digital system, in communications satellites, 135 Spectrophotometry in astronomy, 68 in laboratory, 66-68 Spectroscopy, intensity-correlated, 107- I 08 SSH (Schwartz, Slawsky, and Herzfeld) theory, quantum mechanical approach to, 19-22 Stationarii-1 Satellite, 128 Statistical decay curve, 98 Steric factor, in chemical lasers, 19 STVW (Steele-Turner) theory, in acoustoelectrical interactions, 189-198 Sun, as radio source, I30 SPP also Solar (ad'.) Surface waves, in river and ocean technology, 274-276 Surveying in river and ocean technology, 287-293 sector scan in, 287-291 side scan in, 291-293 SYNCOM I1 satellite, 122 SYNCOM 111 satellite, 122

T

TDMA (time division multiple access) technique, in satellite communications, 135 TELSTAR satellite, 121-122 Tides, in river and ocean technology, 276-277 Time assignment-TASI system, 135 Time derivation circuits, 79-82 Time-interval measurement system, in Lunar Laser Ranging Experimcnt, 102 Time-to-pulse-height converter, 102, I 1 3

315

SUBJECT INDEX

Timing circuits, calibration and stability of, 90-91 Timing discriminator, 100 constant-fraction-of-pulse-height, 103 leading-edge, 79 Total population inversion, 7 Transponder electronic devices, in communications satellite, 149-1 55 Transverse discharge laser, 33 Traveling wave tubes, for communications satellite, 153-155 Tunnel diodes, for communications satellite, 149-1 53 electron micrograph of, 152 Tunnel diode amplifier, noise of, 153 Tyuratam-Baikonur launch site, USSR, 127

U Underwater data transmission, 295-299 Underwater pulse repeater system, 297

V

Van Allen belts, 122 Vibrational energy distribution, of CO molecules, 26 Vibrational levels, radiation lifetimes for, 18 Vibrational transition, laser operation and, 5-9 Vibration-vibration energy exchanges, 23 VLF/Omega navigation systems, 283

W Wafer, channel multiplier and, 52 Water pollution, dispersion of, 273-274 Water quality measurement, 268-274 dissolved oxygen in, 273 pollution dispersion in, 273-274 salinity in, 270-271 temperature in, 268-270 turbidity in, 271-273 Woods Hole Oceanographic Institute, 279

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