Particles on Surfaces 8: Detection, Adhension and Removal

Particles on Surfaces 8: Detection, Adhesion and Removal

K.L. Mittal, Editor

VSP

Particles on Surfaces 8: Detection, Adhesion and Removal

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PARTICLES ON SURFACES 8: DETECTION, ADHESION AND REMOVAL

Editor: K.L. Mittal

UTRECHT Ÿ BOSTON 2003

VSP (an imprint of Brill Academic Publishers) P.O. Box 346 3700 AH Zeist The Netherlands

Tel: +31 30 692 5790 Fax: +31 30 693 2081 [email protected] www.vsppub.com www.brill.nl

© VSP 2003 First published in 2003 ISBN 90-6764-392-0

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.

Printed in The Netherlands by Ridderprint bv, Ridderkerk

Contents

Preface

vii

Part 1: Particle Analysis / Characterization and General Cleaning-Related Topics The nature and characterization of small particles R. Kohli

3

Surface and micro-analytical methods for particle identification D.A. Cole, J. Humenansky, M. Kendall, P.J. McKeown, V. Pajcini and J.H. Scherer

29

The haze of a wafer: A new approach to monitor nano-sized particles K. Xu, R. Vos, G. Vereecke, M. Lux, W. Fyen, F. Holsteyns, K. Kenis, P.W. Mertens, M.M. Heyns and C. Vinckier

47

Particle transport and adhesion in an ultra-clean ion-beam sputter deposition process C.C. Walton, D.J. Rader, J.A. Folta and D.W. Sweeney

63

Particle deposition from a carry-over layer during immersion rinsing W. Fyen, K. Xu, R. Vos, G. Vereecke, P. Mertens and M. Heyns

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The use of surfactants to reduce particulate contamination on surfaces M.L. Free

129

The use of rectangular jets for surface decontamination E.S. Geskin and B. Goldenberg

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Ice-air blast cleaning: Case studies D. Shishkin, E. Geskin, B. Goldenberg and O. Petrenko

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Development of a technique for glass cleaning in the course of demanufacturing of electronic products E.S. Geskin, B. Goldenberg and R. Caudill

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Part 2: Particle Adhesion and Removal Mechanics of nanoparticle adhesion — A continuum approach J. Tomas

183

A new thermodynamic theory of adhesion of particles on surfaces M.A. Melehy

231

Particle adhesion on nanoscale rough surfaces B.M. Moudgil, Y.I. Rabinovich, M.S. Esayanur and R.K. Singh

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Advanced wet cleaning of sub-micrometer sized particles R. Vos, K. Xu, G. Vereecke, F. Holsteyns, W. Fyen, L. Wang, J. Lauerhaas, M. Hoffman, T. Hackett, P. Mertens and M. Heyns

255

Modified SC-1 solutions for silicon wafer cleaning C. Beaudry, J. Baker, R. Gouk and S. Verhaverbeke

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Investigation of ozonated DI water in semiconductor wafer cleaning J. DeBello and L. Liu

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Possible post-CMP cleaning processes for STI ceria slurries R. Small and B. Scott

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The ideal ultrasonic parameters for delicate parts cleaning T. Piazza and W.L. Puskas

303

Effects of megasonics coupled with SC-1 process parameters on particle removal on 300-mm silicon wafers S.L. Wicks, M.S. Lucey and J.J. Rosato

315

Influences of various parameters on microparticles removal during laser surface cleaning Y.F. Lu, Y.W. Zheng, L. Zhang, B. Luk’yanchuyk, W.D. Song and W.J. Wang

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Particle removal with pulsed-laser induced plasma over an extended area of a silicon wafer T. Hooper, Jr. and C. Cetinkaya

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Particle removal by collisions with energetic clusters J. Perel, J. Mahoney, P. Kopalidis and R. Becker

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. vii–viii Ed. K.L. Mittal © VSP 2003

Preface This volume documents the proceedings of the 8th International Symposium on Particles on Surfaces: Detection, Adhesion and Removal held under the auspices of MST Conferences in Providence, Rhode Island, June 24–26, 2002. This event represented a continuation of the series of symposia initiated in 1986 under the aegis of the Fine Particle Society. Since 1986 this topic has been covered on a regular biennial basis (except no symposium was held in 1994) and the proceedings of these earlier symposia have been properly documented in six hard-bound books [1–6]. As mentioned in the Preface to the book Particles on Surfaces 7: Detection, Adhesion and Removal [6] the study of particles on surfaces is extremely crucial in a host of diverse technological areas, ranging from microelectronics to optics to biomedical. In a world of shrinking dimensions and with the tremendous interest in various nanotechnologies, the need to understand the physics of nanoparticles becomes quite patent. With the interest in and concern with nanoparticles comes the need for new and more sensitive metrological and analysis techniques to detect, quantitate, analyze and characterize very small particles on a host of substrates. Also even a cursory look at the literature will evince that currently there is a high tempo of activity in devising new ways or ameliorating the existing techniques to remove real small particles. The technical program for this symposium was comprised of 30 papers covering many different aspects of particles on surfaces. It should be mentioned that throughout the symposium there were lively and illuminating discussions and certain areas where an urgent and dire need was felt for intensified R&D efforts were highlighted. Now coming to this volume, it contains a total of 21 papers covering many ramifications of particles on surfaces. Apropos, this volume also contains a paper which was presented in the earlier symposium but was not published at that time. It must be recorded that all manuscripts were rigorously peer-reviewed and all were revised (some twice or even thrice) and properly edited before inclusion in this volume. Concomitantly, this volume represents an archival publication of the highest standard. It should not be considered a proceedings volume in the usual sense, as many proceedings volumes are neither peer-reviewed nor adequately edited. This volume is divided into two parts: Part 1: Particle Analysis/Characterization and General Cleaning-Related Topics; and Part 2: Particle Adhesion and Removal. The topics covered include: nature and characterization of small particles;

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Preface

surface and micro-analytical methods for particle identification; haze as a new method to monitor nano-sized particles; particle transport and adhesion in ionbeam sputter deposition process; particle deposition during immersion rinsing; ice-air blast cleaning; rectangular jets for surface decontamination; factors important in particle adhesion and removal; mechanics of nanoparticle adhesion; particle adhesion on nanoscale rough surfaces; various techniques for cleaning or removal of particles from different substrates including wet cleaning, use of modified SC-1 solutions, use of surfactants, ozonated DI water, ultrasonic, megasonic, laser, energetic clusters; and post-CMP cleaning. Yours truly sincerely hopes that this volume and its predecessors [1–6] would be of immense value to anyone interested in the world of particles on surfaces, and these volumes collectively would serve as a resource for information on contemporary R&D activity in this extremely technologically important area. Acknowledgements This section is always the pleasant part of writing a Preface. First, I am thankful to Dr. Robert H. Lacombe, a dear friend and colleague, for taking care of the organizational aspects of this symposium. Special thanks are due to the reviewers for their time and efforts in providing many valuable comments which are a prerequisite for a high standard publication. The authors must be thanked for their interest, enthusiasm and contribution which were essential ingredients in making this volume a reality. Finally my sincere appreciation goes to the staff of VSP (publisher) for materializing this book. K.L. Mittal P.O. Box 1280 Hopewell Jct., NY 12533 1. K.L. Mittal (Ed.), Particles on Surfaces 1: Detection, Adhesion and Removal. Plenum Press, New York (1988). 2. K.L. Mittal (Ed.), Particles on Surfaces 2: Detection, Adhesion and Removal. Plenum Press, New York (1989). 3. K.L. Mittal (Ed.), Particles on Surfaces 3: Detection, Adhesion and Removal. Plenum Press, New York (1991). 4. K.L. Mittal (Ed.), Particles on Surfaces: Detection, Adhesion and Removal. Marcel Dekker, New York (1995). (Proceedings of the 4th Symposium.) 5. K.L. Mittal (Ed.), Particles on Surfaces 5&6: Detection, Adhesion and Removal. VSP, Utrecht (1999). (Proceedings of the 5th & 6th Symposia.) 6. K.L. Mittal (Ed.), Particles on Surfaces 7: Detection, Adhesion and Removal. VSP, Utrecht (2002).

Part 1 Particle Analysis / Characterization and General Cleaning-Related Topics

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 3–28 Ed. K.L. Mittal © VSP 2003

The nature and characterization of small particles RAJIV KOHLI∗ Maxtor Corporation, 2452 Clover Basin Drive, Longmont, CO 80503, USA

Abstract—Nanosize particles are of fundamental and practical interest for advanced materials and devices. As feature sizes shrink, nanoparticle contamination will also become increasingly important and will present an ongoing challenge to achieve and maintain high product yields. In order to employ appropriate material and product development strategies, or preventive assembly and remediation strategies to control nanoparticle contamination, it is necessary to understand the nature of nanosize particles and to characterize these particles. Particles in the size range 0.1 nm to 100 nm present unique challenges and opportunities for their imaging and characterization. Critical information for this purpose is the number and size of the particles, their morphology, and their physical and chemical structure. A brief review of the nature of small particles is presented. Emerging techniques for characterizing particles, such as scanning near-field optical microscopy (SNOM), hot electron microcalorimetry, multiphoton microscopy and Raman chemical imaging, are briefly described. Keywords: Small particles; characterization; innovative imaging techniques; SNOM; atom probe; HAADF-STEM; Raman microscopy; multiplexed multiphoton microscopy (MMM).

1. INTRODUCTION

Small particles in the submicrometer and subnanometer size range are of fundamental interest in a wide variety of industries. The development of advanced nanomaterials and nanodevices involves the efficient application of nanometer size particles. By contrast, nanometer size particles as contaminants are a leading cause of failure of components and end products in widely diverse industries, such as electronics, semiconductors and optics. For example, in the data storage industry, minimizing contaminant particles on hard disk drive components is critical to drive performance and high product yield. The current nominal flying height at which the head flies over the disk is 17 to 25 nm which will be even lower in future product designs. If a particle of similar dimensions is trapped between the head and the disk, it can cause a catastrophic failure of the drive [1].

∗

Present address: RKAssociates, 2450 Airport Road, #D-238, Longmont, CO 80503, Phone: (1-303) 682-3217, E-mail: [email protected]

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In order to continuously advance material developments, or to develop remediation strategies to minimize or eliminate contaminant particles from the manufacturing process, it is necessary to understand the interactions of nanometer size particles. This, in turn, requires detailed characterization of these particles. As the particle size becomes smaller, high-resolution qualitative and quantitative methods are required to measure and physically and chemically characterize these particles. A number of methods have been developed for imaging and characterizing particles from micrometer size to the atomic scale [2-7]. These methods take advantage of the complete range of properties of the materials. Many of these methods are commercially available, while other methods have been successfully demonstrated. Here we discuss recent developments and applications of selected less-common methods that hold tremendous promise for imaging, physical characterization and chemical analysis of nanometer and subnanometer-size particles. 2. NATURE OF SMALL PARTICLES

2.1. Sizes of small particles In referring to small particles, the size of the particles can be discussed in terms of various physical phenomena. For example, the interactions of particles much larger than 1 µm in diameter are increasingly dominated by gravitational forces, while van der Waals and other forces tend to dominate their interactions below that size. Particles with diameters of 0.3 to 0.7 µm are of the same size as the wavelength of visible light, which is the limit of resolution (Abbe diffraction limit) in conventional optical microscopic observation of particles of that size. However, as we shall see in Section 3.3.4, scanning near-field optical microscopy makes it now possible to bypass the Abbe diffraction limit to resolve particles as small as 30 nm. Particles in the size range 20 to 100 nm are referred to as ultrafine, while nanometer size particles have diameters smaller than 20 nm. Due to the need to understand aerosol behavior, two additional classes of particle sizes have been defined. Very small particles refer to particles smaller than 5 nm, while molecular size defines particles with diameters smaller than 1 nm [8]. 2.2. Particle interactions The physical nature of very small particles (<20 nm) cannot be thought of in terms of classical surface or volume continua. Rather, the molecules statistically associated with the particle will tend to define their physical and chemical interactions. As Table 1 shows, the number of molecules associated with a particle increases with increasing particle size, but the fraction of the molecules at the surface decreases with increasing particle size. For a particle of 20 nm diameter, the number of molecules at the surface is only about 12%, but the number is nearly 90% for a particle of 2 nm diameter. Consequently, the overall behavior of very

The nature and characterization of small particles

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small particles is governed by the surface and binding energies of the molecules in the particle. These particles are neither solid nor liquid, and do not behave like individual molecules. Such particles are regarded as a complex structure whose behavior depends on the positions of the individual molecules and the combined electronic charge distribution [9, 10]. Table 1. Characteristics of molecules associated with very small particles Particle size (nm)

Cross-sectional area (10-18 m2)

Mass (10-25 kg)

Number of molecules

% of molecules at the surface

0.5 1.0 2.0 5.0 10.0 20.0

0.2 0.8 3.2 20 80 320

0.65 5.2 42 650 5.2 × 103 4.2 × 104

1 8 64 1 × 103 8 × 103 6.4 × 104

– 100 90 50 25 12

Only simple interactions of very small particles are presently well understood. Due to the technological importance of very small particles in advanced materials and nanotechnology, advances in kinetic theory, solid state chemistry, quantum mechanics and aerosol dynamics are essential to better understanding of particle interactions. Combined with the very high spatial resolution and chemical composition capabilities of newer characterization techniques, it will be possible to predict the behavior of very small particles in complex systems in the future. In turn, these predictions will provide the basis for understanding the transport, adhesion and detachment of these particles in real systems, as well as making it possible to design materials with specific properties. One example is the recent synthesis of monodisperse Fe-Pt nanoparticles of controlled size (3-10 nm) and composition to yield chemically and mechanically robust ferromagnetic nanocrystal assemblies for very high areal density magnetic recording (terabits per unit area) [11]. 2.3. Elucidating the fundamental interactions of very small particles One major source of particles is chemically-induced transformation of gaseous matter into particles. These particles can subsequently grow by condensation and coagulation into larger particles at a growth rate that depends on factors such as particle size and concentration [12-14]. This gas-to-particle transformation is important for assembly processes in which gaseous precursors such as acid gases are present, or for products that employ volatilizable materials, such as motor bearing grease and lubricants. The understanding of gas phase reactions in the formation of particles has advanced considerably, but important chemical and physical mechanisms are still unresolved, particularly for particles smaller than 10 nm size.

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As noted earlier, such particles have to be considered as complex structures whose properties and interactions are determined by the number and position of the molecules on the surface. In fact, the interactions of these particles will be largely between the molecules at the surface, which are, in turn, determined by atomic, electronic and nuclear motions. These interactions typically occur on timescales of picoseconds (10-12 s) to subzeptoseconds (10-21 to 10-22 s). For example, subpicosecond X-rays or electrons [15, 16] or femtosecond pulsed lasers [17] can probe events such as creating and breaking of chemical bonds, while attosecond pulses [18-20] can be used to study the motions of electrons that bind atoms together. The motions of nuclei within the electrons happen on an even briefer timescale and the recently proposed source of zeptosecond laser pulses should help to illuminate strong nuclear interactions [21]. 3. MEASUREMENT AND CHARACTERIZATION OF PARTICLES

3.1. Sizing and classification Several techniques are available to count, size and classify single ultrafine particles as small as 2 nm in diameter [13, 14]. For example, the ultrafine condensation nucleus counter can detect particles down to 3 nm with a counting efficiency of >70%, while differential mobility size spectrometry can provide size distribution of particles in the <1 to 200 nm range [22-30]. Recently, the first condensation nucleus counter (CNC) capable of detecting individual ions has been developed [31]. However, many of these methods do not provide any information on the size distribution of individual particle types. To overcome these limitations, an on-line, semicontinuous double size spectrometry method has been developed to provide size and effective density of single particles in the range 3 to 50 nm [32]. In this method, particles in a narrow size range are selected by an electrical mobility size classifier and then resized by a hypersonic impactor [33, 34]. The first step selects the particles by their Stokes diameter, which is the geometric diameter of spherical particles. The second step sizes the singly-charged particles by their aerodynamic diameter, which is dependent on the particle mass as well as the Stokes diameter. The impactor flow is supersonic and the particle capture is measured by an electrometer. The collection efficiency of the impactor is better than 80% for particles down to 3 nm diameter. Most differential mobility size spectrometry instruments are designed to operate at ambient pressure for probing aerosol particles in the atmosphere. By contrast, in semiconductor fabrication contamination from nanometer-sized particles formed at low pressures can lead to significant yield loss [35]. In response, differential mobility analyzer instruments have been developed for low-pressure operation [36, 37]. These instruments employ larger diameter and longer connecting tubes between the instrument and the vacuum pumps, together with mass flow controllers especially designed for low pressures. These features ensure a low

The nature and characterization of small particles

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pressure drop and a large evacuation capacity. The instrument has successfully demonstrated accurate mobility classification of particles in the size range 6-12 nm at pressures as low as 200 Pa, approaching the operating pressures in semiconductor fabrication. 3.2. Particle analysis The chemical composition of nanosize particles is important information needed to develop a complete understanding of the behavior of these particles. Traditionally, the particles are collected by one or more of the available sampling methods on a filter, substrate or grid located in an impactor and analyzed using off-line techniques, such as electron microscopy and vibrational and mass spectroscopy [2, 30, 38, 39]. One method that is increasingly used for offline analysis of individual particles is laser microprobe mass spectrometry (LMMS). The particles are irradiated with a high power pulsed laser and the fragments are analyzed by mass spectrometry [40, 41]. LMMS can detect trace metals, inorganic compounds, and organic compounds in individual particles [42-45]. However, because it is an offline technique that requires the particles to be exposed to a vacuum, the particle composition can be affected. In addition, there is a significant time delay in returning data because the samples must be analyzed in a remote laboratory. 3.2.1. Single particle analysis Recently, a number of instruments have been developed for on-line collection and analysis of single aerosol particles in real time [30, 46-48]. In these instruments, the particles are aerodynamically sized followed by chemical analysis by mass spectrometric methods to obtain information about molecules and not just elements. The particles are desorbed and ionized in the source region of the mass spectrometer. Ionization can be achieved by non-laser thermal vaporization [49-52] and analyzed by a magnetic sector mass spectrometer or by a quadrupole mass spectrometer [53], or an ion trap [54, 55]. Alternatively, particles can be ionized chemically [56-58], by electron impact [39, 53], or by laser vaporization [59-65]. Aerosol time-of-flight mass spectrometry (ATOFMS) has been successfully demonstrated in a field-transportable instrument for real time on-line analysis of single aerosol particles down to 0.1 µm [59-62]. These real-time instruments have been successfully demonstrated to also provide information on multicomponent crystallization [66], compound speciation [67], surface coatings [68] and even the oxidation state of particles [69]. 3.2.2. High-resolution X-ray spectroscopy Semiconductor energy-dispersive spectrometers (EDS) and wavelength-dispersive spectrometers (WDS) are commonly employed as analytical tools for off-line chemical identification of particles, but these detectors cannot resolve closelyspaced or overlapping X-ray peaks in complicated spectra. For example, the severe peak overlaps between the Si Kα and the W Mα X-ray lines prevent their identification by semiconductor EDS [70]. High-resolution X-ray detectors are

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required to meet the analysis requirements for small particles, particularly particles with a diameter <0.1 µm. The leading techniques for developing high-resolution detectors are based on the use of semiconductor thermistors, superconducting edge transition detectors, superconducting tunneling junctions, and magnetic calorimeters [71-75]. With these methods it is possible to obtain an energy resolution of 3 to 13 eV full width at half maximum (FWHM) that is an order of magnitude better than the resolution obtainable with semiconductor EDS (~ 130 eV at FWHM) and is comparable to semiconductor WDS (~ 2 to 20 eV at FWHM). Of the techniques mentioned above, the superconducting edge transition detector has been most often applied for particle analysis. In a typical configuration of such a detector system, also referred to as microcalorimeter EDS, there is a metal film to absorb the X-rays, a thermometer to measure the temperature of the electrons in the absorber, and a coupling to a heat sink (Fig. 1). When a particle or a photon interacts with the absorber, the incident energy is converted to heat. The corresponding temperature rise is measured by a superconductor tunnel junction that is cooled to well below the phase transition temperature. The amplitude of the current pulse through the junction is directly proportional to the incident energy. The fundamental energy resolution limit of these detectors is of the order of 1-3 eV, depending on the absorber material. Present detector technology has achieved a resolution of 3-7 eV, which makes these de-

Figure 1. Schematic of a typical microcalorimeter EDS system.

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vices very well suited to high-resolution X-ray detection. For example, with a 0.3 µm W particle on a Si substrate it was possible to resolve the Mα, Mβ, Mγ and the Mζ peaks for W using microcalorimeter EDS (Fig. 2). Similar results were obtained on a TiN sample. The Lα peak, both Lβ peaks and even the Lη peak for Ti was clearly resolved [70]. Microcalorimeter EDS offers one additional advantage. With its high-energy resolution, all peak shapes and integrated peak intensities are accessible, making it possible to measure chemical shifts in the X-ray spectra. This can provide chemical binding state information [70]. 3.2.3. Laser-induced breakdown spectroscopy Laser-induced breakdown spectroscopy (LIBS) is an atomic emission spectroscopic technique in which successive nanosecond laser pulses ablate a small amount of material from the surface [76-79]. The resulting microplasma emits fluorescence radiation from excited atoms and/or ions that is characteristic of the

Figure 2. Microcalorimeter EDS spectrum of a tungsten particle on a silicon substrate (courtesy of National Institute of Standards and Technology, Boulder, CO, USA).

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elements in the sample. If the same point is ablated successively, the LIBS spectra provide in situ cross-sectional analysis of the material. Raman microscopy can achieve very high spatial resolution (~ 1 µm), which gives spectra largely free of contamination from surrounding material. By combining these techniques, elemental analytical data and the chemical composition of the material of interest can be obtained in situ. The advantages of combining Raman microscopy with LIBS to identify and analyze pigment particles in artworks have been demonstrated recently [80]. It was determined that the original white paint on a Byzantine icon was 2PbCO3·Pb(OH)2, but that the subsequent restorative work used ZnO paint. The LIBS technique can also yield information simultaneously on the size, number density, mass and composition of a wide range of particles, including metal hydrides, coal particles, halons, and elements (As, Be, Fe, Mn, Ni and others). Particles as small as 175 nm have been successfully measured, corresponding to an absolute detectable mass of the order of 10-15 g [77]. This shows the very high sensitivity of the LIBS technique for particle characterization. By combining LIBS with scanning near-field optical microscopy (SNOM), it is possible to map and correlate elemental chemical composition of surfaces with the surface topography [81]. In this method, surface topography is first mapped by scanning the surface with the SNOM probe. The probe is then positioned over a feature of interest, such as a surface contaminant particle, which is vaporized by a laser pulse. Optical emissions from the resulting plasma plume are analyzed to obtain LIBS spectra. 3.3. Particle imaging techniques 3.3.1. Scanning transmission electron microscopy High-resolution electron microscopic techniques have been developed in response to the need to understand the fundamental properties of nanosize particles. This includes chemical, structural and morphological information of particles. A very attractive feature of recent scanning transmission electron microscopy (STEM) instruments is the ability to form an electron probe with diameters down to 0.3 Å using aberration correction of the electron lenses [4, 82, 83]. This is achieved with a field-emission gun that provides the signal strength to view and record images, spectra and electron diffraction patterns. In addition, there are a great variety of available detectors that have been developed to simultaneously collect imaging and analytical signals in dedicated STEM instruments (Fig. 3). This makes the STEM an exceptional nanoanalytical tool that can provide detailed information on composition, electronic and crystal structure with atomic resolution and sensitivity [82]. By collecting high-angle annular dark-field (HAADF) images, information about structural variations across the sample can be obtained at the atomic level. Electron energy-loss spectroscopy (EELS) and X-ray energy dispersive spectroscopy (XEDS) provide quantitative data on elemental composition, electronic

The nature and characterization of small particles 11

Figure 3. Imaging and analytical modes in the scanning transmission electron microscope.

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structure or oxidation state of the sample. In fact, work has been recently reported on the distribution and unambiguous identification of individual gadolinium atoms inside a chain of endohedral Gd-metallofullerenes separated by 1 to 2 nm [83]. Surface topography or surface chemistry of nanoparticles can be obtained by secondary electron spectroscopy (SES) or Auger electron spectroscopy (AES). Nanodiffraction patterns can be acquired from individual nanoparticles to provide information on their crystallographic structure, as well as their structural relationship with the surrounding material, and perhaps also the morphology of the particles. The resolution of STEM images is determined primarily by the incident probe size, the stability of the microscope, and the inherent properties of the signal generation process. Modern high-resolution microscopes can provide point resolution of 1.3-1.7 Å, although recently lattice imaging has been demonstrated at 0.750.89 Å [84, 85] with aberration correction. This level of resolution can be exploited to obtain direct structural information on wide band gap materials at a monoatomic level, such as the 600 dislocation in Si-Ge/Si structures [86]. In addition, by using the microscope as a quantitative measuring instrument employing quantitative statistical experimental design, it is possible to measure atom positions with a precision of the order of 0.01 Å [87]. At this level of precision, highly refined solid state theoretical calculations can be made and validated to predict from first principles the exact properties of materials and the interactions between materials. 3.3.2. High-angle annular dark-field (HAADF) STEM imaging For true quantitative 3D analysis, a single projection of 2D images will not be adequate for a complete description of the object being examined in a STEM. It is necessary to turn to tomography to reconstruct the 3D object from a tilt series of 2D projections. The most common mode of electron tomography is conventional coherent bright field (BF) TEM. However, for crystalline particle imaging and analysis, diffraction (and Fresnel) contrast makes reconstruction of the structure from coherent signals problematic. Other (incoherent) signals must be used that are insensitive to diffraction contrast to reduce or eliminate such problems. Highangle annular dark-field (HAADF) imaging in the STEM does provide images of high compositional contrast, shows little or no diffraction effects, and in which the signal is approximately proportional to the square of the atomic number Z. This is the reason it is also known as ‘Z-Contrast’ imaging [82, 88-93]. HAADF images are formed by collecting high-angle (typically a few degrees or more) scattered electrons with an annular dark-field detector in dedicated STEM instruments. The images originate from interaction with atomic nuclei and are therefore sensitive to differences in atomic number. The contrast of HAADF images is ● strongly dependent on the average atomic number of the scatterer encountered by the incident probe; ● not strongly affected by dynamical diffraction effects; ● not strongly affected by defocus; and

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not strongly affected by sample thickness variations. Spatial resolution is limited by the size of the focused incident probe. The spatial resolution and field of view of HAADF STEM imaging complement perfectly the ultra-high-resolution technique of atom probe tomography and the much lower resolution X-ray micro-tomography. In commercial microscopes, the HAADF signal can be detected very simply by lowering the camera length to values of around 100 mm or less. Both BF (transmitted beam) and dark field (diffracted beam) electrons then fall on the central BF-STEM detector, while the HAADF electrons fall on the annular dark-field detector. Typical HAADF acceptance angles are 2.5 to 6 degrees. HAADF images can be obtained at the same resolution as STEM BF and DF images (atomic resolution with a field emission gun). The specimen must be thin (<40 nm) for most high-resolution imaging applications. The HAADF technique does have some limitations: ● HAADF imaging is only quasi-spectroscopic; ● the image resolution is not as high as that of HREM images; ● thick specimens cause beam broadening and degradation of the spatial resolution; and ● HAADF images have a much poorer signal-to-noise ratio compared to HREM images. The HAADF technique shows great promise for very high-resolution analysis. For example, STEM images of a Pt catalyst on a Al2O3-Ce2O3 support are shown in Fig. 4. The dark round features in the BF image can be either ceria or platinum grains. Only the HAADF image clearly shows the platinum crystals. There are two potential sources of artefacts in the HAADF technique: 1. HAADF imaging is more strongly dependent on thickness of the specimen than back-scattered electron imaging. Specimens with strong thickness variations may show high intensity in thicker areas. In such specimens, the HAADF signal is not necessarily indicative of high atomic number. 2. Structures such as dislocations may show up strongly in HAADF images without any local concentration of high-atomic number material. Small changes in crystal tilt will normally lead to strong changes in dislocation contrast, similar to the effect seen in TEM BF and DF images. ●

3.3.3. Field-emission environmental SEM The field-emission environmental scanning electron microscope (FE-ESEM) is an instrument with unique capabilities [94, 95]. In conventional scanning electron microscopy a relatively high vacuum in the specimen chamber is required to prevent atmospheric interference with the primary or secondary electrons. By contrast, nonconductive and uncoated specimens can be examined in an FE-ESEM at high chamber pressure (10 Pa to 1.33 kPa) and temperatures up to 1273 K. Since the residual gas pressure range in the specimen chamber can exceed saturated wa-

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Figure 4. STEM images of an aged platinum catalyst on Al2O3-Ce2O3 support. (a) BF image; (b) DF image; (c) HAADF image (courtesy of FEI Company, Portland, OR, USA).

ter vapor pressure, water-containing specimens can be imaged without drying out. In such “wet mode” imaging, the specimen chamber is isolated from the rest of the vacuum system. When the electron beam (primary electrons) ejects secondary electrons from the surface of the sample, the secondary electrons collide with water molecules, which, in turn, function as a cascade amplifier, delivering the secondary electron signal to the positively biased gaseous secondary electron detector. The water molecules are positively ionized, and thus they are attracted toward the specimen, serving to neutralize the negative charge produced by the primary electron beam. The applied accelerating voltage can be matched to the required edge and penetration effects, while the gas pressure can be varied to remove all specimen charging. The field-emission gun produces a brighter filament image (primary electron beam) than either tungsten or lanthanum hexaboride (LaB6) sources, and the ac-

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celerating voltage may be lowered significantly, permitting nondestructive imaging of fragile specimens. The key benefits of the FE-ESEM imaging technique are listed below: ● True secondary electron imaging at high chamber pressure (to 1330 Pa); ● no charging of non-conductive samples; ● low-Z materials can be observed; ● contaminated samples can be observed; ● porous material can be imaged; ● hydrated samples remain fully stable; and ● no coating interference. There are two important benefits in X-ray analysis with the FE-ESEM of uncoated specimens. 1. No X-ray lines from the coating interfere with the characteristic X-ray spectrum generated in the specimen. The absence of conductive coatings rids the potential absorption and interference artefacts. 2. X-ray analysis can be performed at high accelerating voltages. No charging artefacts are observed which allows the operator to choose any acceleration voltage for optimal X-ray analysis.

Figure 5. Image of a diesel exhaust particle at approximately 650 Pa chamber pressure in an FEESEM (courtesy of FEI Company, Portland, OR, USA).

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This combination of characteristics makes the FE-ESEM ideal for obtaining high magnification secondary electron images of low atomic number materials in their uncoated, natural and stable state (Fig. 5). 3.3.4. Scanning near-field optical microscopy (SNOM) The key requirements for characterizing nanometer-scale objects are high sensitivity and high spatial resolution. Although scanning tunneling microscopy (STM) and atomic force microscopy (AFM) provide exceptional spatial resolution of the order of 1 nm or less, neither technique provides chemical identification of surface species. The reason for this is that in STM and AFM only the outer electrons of the surface atoms are involved in the interactions of the probe tip with the surface. No spectroscopic information is obtained from the inner shell structure of the atom. Recently, an infrared AFM has been developed and successfully demonstrated as described in Section 3.3.9. Scanning near-field optical microscopy (SNOM) can meet both these requirements of high sensitivity and high spatial resolution [96-99]. Its unique advantage is the existence of a spatial dimension that makes it possible to perform chemical identification. From theoretical considerations, the fundamental optical diffraction limit of resolution is given by 0.61λ/nsinθ, where λ is the wavelength of the employed light and n sinθ is the numerical aperture [100]. This limits the resolution to approximately 250-400 nm for visible light. SNOM overcomes the Abbe diffraction limit in the optical regime by scanning a nanometer-sized aperture probe (50100 nm) in close proximity (1-15 nm) to the sample surface. As a result, the light is concentrated as a subwavelength source that also acts in the optical near field. A commercial SNOM system consists of one or more optical microscopes for reflection or transmission mode operation; the SNOM stage with the scanner and the SNOM sensor module with a shear force detector; the SNOM control unit with the laser and associated optics; and a software control system for fine positioning and automated operation. Most commonly, the SNOM probe tip is maintained at a constant distance from the sample surface by optical detection of the damping of an oscillating probe tip by shear force. Non-optical distance controls have also been implemented [96-99]. Tapered aperture probes with effective aperture sizes of 50-100 nm are routinely fabricated by adiabatic pulling of optical fibers during heating with a laser [101]. Alternatively, the probe tip can be fabricated by etching glass fibers at the tip [102], or by tube etching [103]. Tube etching produces very smooth probe tips with no pinholes and with optical transmission coefficients of 10-3 compared with 10-5-10-6 for pulled fiber tips [104]. The probe is coated with a thin metallic film of aluminum to concentrate the light within the probe. The effective aperture size that can be achieved with aperture probes is 8-10 nm, which may be the practical limit of spatial resolution with these probes because of the finite skin depth of real metals, although a spatial resolution of ~ 5 nm has been reported [105]. One of the best optical metals is aluminum for which the penetration depth is ~ 8 nm for green light.

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Other methods for fabricating aperture probes include focused ion-beam milling [106] and microfabrication [107, 108]. These methods would make it possible to fabricate inexpensive and highly reproducible probes. Using a microfabricated silicon cantilever probe with a quartz tip, a FWHM (full width at half maximum) resolution of 32 nm has been demonstrated [107]. A high resolution SNOM image of a sample of a polymer is shown in Fig. 6. The diameter and the depth of the pit are 100 nm and 5 nm, respectively. Judging from the width of the edge of the pit, the lateral resolution of the SNOM image is about 10 nm and the vertical resolution is about 1 nm (T. Kataoka, personal communication). To overcome the limitations of aperture probes, an apertureless SNOM technique has been demonstrated in which a sharp vibrating tip is used to scatter the near field of the sample to achieve spatial resolution of 1 nm [109]. However, in this configuration the resolution is limited by the radius of curvature of the tip itself. By replacing the physical aperture with a nanoscopic active medium that acts as a light source, such as dye molecules, quantum dots, or diamond color centers, single-molecule resolution can be achieved [110]. Specific chemical information has been successfully obtained by combining SNOM with experimental methods such as cathodiluminescence [96], infrared spectroscopy [111-113], surface-enhanced Raman spectroscopy [99, 114, 115] and fluorescence imaging [99, 115, 116]. SNOM has also been combined with laser-induced breakdown spectroscopy in a single instrument to achieve spatially-

Figure 6. The SNOM image of a pit in a polymer sample (courtesy of Osaka University, Osaka, Japan).

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resolved chemical imaging of surface particles [81]. Recently, nanoscale atmospheric pressure laser ablation mass spectrometry has been demonstrated at a spatial resolution of less than 200 nm [117]. Figure 7 shows SNOM images of bacteria bred to produce green fluorescence protein. In transmission mode, the location of the fluorescent protein is clearly distinguished. The origin of the fluorescent light is approximately 20 nm below the surface of the bacterium. Recent information on SNOM and its wide range of applications for particle imaging and analysis can be found in several publications [96-99]. 3.3.5. Three-dimensional atom probe imaging The 3-dimensional atom probe (3DAP) is a quantitative technique that provides atomic scale 3-dimensional elemental maps of atoms within a volume 20 nm × 20 nm × 100 nm of a conductive sample [118, 119]. As with the STM, a single atom and its neighbors can be imaged. However, 3DAP provides two major advantages over the STM: ● Elemental analysis in which each single atom is chemically identified by time-of-flight; and ● position-sensitive detection, which makes the chemical map of the atoms truly three dimensional. In a typical 3DAP system, single atoms are field evaporated from a needleshaped sample mounted on a cryogenically-cooled goniometer (Fig. 8). Atoms are ionized from the surface under a very high electric field and projected toward a position-sensitive detector placed at a distance of 250 to 650 mm from the sample. Ionization occurs from the surface of the specimen regularly, which makes it possible to ionize atoms by atomic layer, as well as by atomic order, thereby achieving atomic layer resolution. Atoms are chemically identified by time-of-flight mass spectrometry. The detector gives an accurate measurement of the ion impact positions and masses. The very high magnification of the instrument yields highly accurate (0.2 nm) impact coordinates, from which the original positions of the atoms at the tip surface are derived. Modern 3DAP instruments are equipped with a reflectron energy compensator, and are able to achieve a mass resolution, m/Dm, larger than 300 [118]. With this performance, most of the alloying elements contained in complicated nanocrystalline alloys can be identified without any ambiguity. An example of element and concentration mapping obtained by a 3DAP is shown in Fig. 9. In the elemental map of the omega phase precipitated in an aged Al alloy, individual Al, Cu, Mg and Ag atoms are shown [120]. By counting the number of atoms in each pixel, the elemental map can be converted to a concentration profile. 3DAP gives very accurate compositional information on the interface of nanosized particles embedded in a matrix phase. This type of analysis is impossible with an analytical transmission electron microscope because the typical thin foil thickness of TEM specimens is larger than 200 nm. If the particles embedded in the matrix are smaller than the thickness of the sample, the EDS spectra obtained from the nanosized particles will always be influenced by the surrounding matrix.

The nature and characterization of small particles Figure 7. Images of green fluorescent protein bacterium. On the left is the AFM shear-force topographic image. The SNOM transmission image is on the right, clearly showing the capability of SNOM to identify functional groups (courtesy of Omicron Vakuumphysik, Germany).

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Figure 8. Schematic diagram of a 3-dimensional atom probe.

Figure 9. 3DAP elemental map of the omega (Ω) phase in an Al-1.9Cu-0.3Mg-0.2Ag alloy aged at 180°C for 10 hours. (a) is the concentration map; (b) and (c) are the concentration profiles obtained from the marked regions (courtesy of the National Research Institute of Metals, Japan).

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3.3.6. Multifocal multiphoton microscopy By producing an array of high aperture foci, multifocal multiphoton microscopy (MMM) provides real-time, light-efficient three-dimensional fluorescence imaging at high resolution, but without the need for a detection pinhole. This technique uses focused light from an ultrafast laser to produce light pulses of high peak intensity [121]. It creates and scans an array of focused spots, thereby reducing the scan time by a factor equal to the number of foci. The reduction of the distance between the foci increases not only the speed or image brightness but also the interference between neighboring focal fields given by the lens point-spread function. To overcome the interference effects, the MMM includes two transparent glass masks mounted onto a microlens array, each with a different pattern of holes. The optical path length through each microlens differs by greater than the laser pulse length making it possible to move the foci as close as 3.5 µm. This method is referred to as time multiplexing (TMX). Eventually, the interfocal distance can be reduced to the point that lateral scanning will not be needed. The superior axial resolution of a TMX-MMM is illustrated by the images of a spiky pollen grain (30 µm) in Fig. 10. Without TMX, the x-y image shows significant haze (Fig. 10a). TMX removes the haze (Fig. 10b). The reconstructed three-dimensional images of the pollen grain also show similar improvement: the multiplexed image (Fig. 10c) exhibits much better definition than the 3-D image without multiplexing (Fig. 10d). MMM (2- or 3-photon) has specific advantages compared to a confocal microscope: ● The excitation wavelength is longer; ● resolution is comparable to a confocal microscope without the need for a confocal pinhole, making optical alignment easier; ● more scattered light is collected which would be blocked by the pinhole in confocal microscopy; ● it scans up to 256 foci allowing much shorter acquisition times and increased image brightness; and ● foci can be aligned in a single line as close as 400 nm apart allowing x, zscans or x, y-scans. Potential applications of MMM relevant to particle imaging are listed below: ● Real-time 3D fluorescence microscopy on biological materials, including live cells; ● imaging kinetic phenomena involving metallic ions under different conditions; ● single particle tracking; ● biological cell manipulation; ● single molecule microscopy; and ● picosecond resolution microscopy and time-resolved imaging spectroscopy of particles.

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3.3.7. Magnetic resonance force microscopy imaging Magnetic resonance force microscopy (MRFM) is a rather new technique, whose ultimate goal is to image single electron spins [122-126]. This will make it possible to produce 3-dimensional, non-destructive, in situ, atomic-resolution images of atoms, molecules, defects in solids, dopants in semiconductors, and binding sites in viruses. The method makes use of the very small forces between the magnetic moments of nuclei or electrons and a magnet. In a typical setup, a thin silicon cantilever is poised above a tiny sample containing the particle to be imaged. A magnetic particle mounted on the cantilever interacts with tiny volumes of magnetic atoms in the sample. By applying a high magnetic field gradient, a thin sheet of the sample is selected in which the magnetic moments are in resonance with an external rffield. The magnetic field and the rf-field are modulated to generate a force at the mechanical resonance frequency of the cantilever. The MRFM device is operated in ultra-high vacuum and at liquid helium temperatures. This microscope uses beam deflection to detect sensor oscillations instead of interferometry in order to suppress tip-fiber interactions. Estimates of the magnetic force exerted by a single electron range from 1 to 10 zN (1 zeptonewton (zN) = 10-21 N). Forces as small as 1.4 aN (1 attonewton (aN) = 10-18 N) have been detected to date [124]. 3.3.8. Near-infrared Raman chemical imaging A near-infrared Raman imaging microscope (NIRIM) has been recently developed to map chemical distribution on solid surfaces [127]. Since Raman spectroscopy is an inelastic light scattering process, it is very well suited to characterizing the chemical species on the surface of composite and biological materials. The major advantage of Raman imaging over other mapping techniques, such as SEM-EDS or SEM-WDS and AES or XPS, is that it can be performed under ambient conditions without the need for a high energy excitation source. The unique feature of the NIRIM is that it collects the entire multi-wavelength Raman spectra from each point in the illuminated area. This is accomplished by employing fiberbundle image compression in which 100 fibers are arranged in a 10 × 10 square array. The resolution of the microscope is determined by the magnification of the objective and can be as small as the wavelength of the laser light (λ ≤ 1 µm). The results from mapping of H3BO3 on B4C and TiAlN on stainless steel showed good correlation with SEM-EDS analysis [128]. 3.3.9. Near-field infrared atomic force microscopy Scanning near-field microscopy has been extended into the infrared region of the spectrum [111-113] to obtain chemical information at 10-100 nm spatial resolution in nanomaterials and integrated circuits. In this method, the probe with a metallized AFM tip is operated in tapping mode, which extracts only the modulated part of the infrared radiation, while suppressing background light detection. Simultaneously, an IR beam (wavelength 10 µm) is focused on the AFM tip from

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Figure 10. Effect of TMX on the 3D MMM image of a spiky pollen grain. Clockwise from top (a) x-y image shows significant haze; (b) TMX removes the haze; (c) reconstructed 3-D image with multiplexing; (d) reconstructed 3-D image without multiplexing (reprinted with permission from the Optical Society of America, cited in Ref. [121]).

Figure 11. Surface topography (left) and IR absorption images of PS (middle) and PMMA (right) (courtesy of Max Planck Institut, Martinsried, Germany).

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a tunable CO2 laser. The light scattered from the metallized AFM tip is collected by a concave mirror and focused onto a detector. The changes in IR absorption at different laser wavelengths are measured while scanning the tip over the sample. The contrast between the sample components changes according to their relative absorption. For example, thin (15 nm) Au islands on a Si substrate appear bright, with a material contrast of 20-30% and a spatial resolution of 30 nm [112]. Similarly, the infrared contrast offered by vibrational resonance in a sample composed of two immiscible polymers (polystyrene (PS) embedded in a polymethyl methacrylate (PMMA) matrix) shows contrast reversal when the wavelength is changed from the absorption line of PS to the absorption line of PMMA (Fig. 11). The contrast is strongly enhanced in the near field of the Au probe tip, which is the first direct evidence of surface-enhanced infrared absorption. 4. SUMMARY

Recent developments in techniques for high-resolution imaging and characterization of nanometer-scale particles have been discussed. Single particle chemical composition analysis can be performed down at the ionic level by precision sizing and ionization followed by mass spectrometry of the ionized species. Highresolution (<1 Å) particle imaging techniques include scanning transmission electron microscopy with high angle annular dark field (HAADF) imaging. Atomic force and scanning tunneling microscopies have been successfully combined with analytical capabilities to provide chemical information at the nanoscale. Similar capability has been successfully demonstrated below 100 nm in scanning nearfield optical microscopy (SNOM) combined with Raman, fluorescence and mass spectroscopies. A hot electron microcalorimeter-based EDS detector has the potential to provide significantly higher resolution X-ray analysis of particles than semiconductor energy-dispersive spectrometers. REFERENCES 1. L.-H. Zhang and R. Koka, Data Storage 6(4), 15 (1999). 2. J.C. Vickerman (Ed.), Surface Analysis: The Principal Techniques, Wiley, New York, NY (1997). 3. G. Somorjai, in: The New Chemistry, N. Hall (Ed.), pp 137-166, Cambridge University Press, Cambridge (2000). 4. B. Fultz and J. Howe, Transmission Electron Microscopy and Diffractometry of Materials, Springer Verlag, Berlin (2001). 5. Z.L. Wang (Ed.), Characterization of Nanophase Materials, Wiley-VCH Verlag, Weinheim (2000). 6. W.M. Bullis, D.G. Seiler and A.C. Diebold (Eds.), Semiconductor Characterization. Present Status and Future Needs, AIP Press, New York, NY (1996). 7. D.G. Seiler, A.C. Diebold, W.M. Bullis, T.J. Shaffner, R. McDonald and E.J. Walters (Eds.), Characterization and Metrology for ULSI Technology, AIP Conference Proceedings No. 449, AIP Press, New York, NY (1998). 8. O. Preining, Pure Appl. Chem. 64, 1679 (1992).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 29–46 Ed. K.L. Mittal © VSP 2003

Surface and micro-analytical methods for particle identification DAVID A. COLE,∗,1 JOHN HUMENANSKY,2 MARIUS KENDALL,3 PATRICK J. MCKEOWN,1 VASIL PAJCINI3 and JUERGEN H. SCHERER2 1

Evans East, 104 Windsor Center, Suite 101, East Windsor, NJ 08520 Evans PHI, 6509 Flying Cloud Drive, Eden Prairie, MN 55344 3 Charles Evans & Associates, 810 Kifer Road, Sunnyvale, CA 94086 2

Abstract—The ultimate instrumental method for particle analysis should provide elemental composition, chemical bonding, and exact compound identification of organic, inorganic and metallic particles of any size and shape. Since this hypothetical method does not exist, scientists are forced to use a variety of techniques that accomplish a subset of these requirements. Surface analysis methods such as Auger Electron Spectroscopy (AES), Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) and X-ray Photoelectron Spectroscopy (XPS, also known as ESCA) fulfill many of the desired criteria while confining analysis to the outer surface of the particles. Micro-beam methods such as Energy Dispersive X-ray Spectroscopy (EDS), Micro-Fourier Transform Infrared Spectroscopy (micro-FT-IR) and Raman spectroscopy fulfill many of the same criteria and can examine larger analytical volumes. The fundamental characteristics of these six methods will be discussed in light of the specific requirements and restrictions needed for particle analysis. Typical case studies from a variety of industries will be used to highlight the technique selection process. Keywords: AES; EDS; ESCA; far-field spectroscopy; FT-IR; near-field spectroscopy; particle; Raman spectroscopy; surface analysis; TOF-SIMS; XPS.

1. INTRODUCTION

Surface and micro-analytical methods are routinely used to determine elemental composition, chemical bonding and exact compound identification of organic, inorganic and metallic particles. However, the various methods differ in utility for examining particles, particularly those <20 µm in diameter. Historically, large particles, those >10 µm in diameter, were often examined by near-surface and bulk analytical methods such as Energy Dispersive X-ray Spectroscopy (EDS) and conventional (far-field) vibrational spectroscopy such as micro-Fourier Transform Infrared (FT-IR) Spectroscopy and micro-Raman spectroscopy. Ad∗

To whom all correspondence should be addressed. Phone: (1-609) 371-4800, Fax: (1-609) 371-5666, E-mail: [email protected]

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vances in Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) and Xray Photoelectron Spectroscopy (XPS) also known as Electron Spectroscopy for Chemical Analysis (ESCA) have made it possible to perform surface analysis on these particles. Particles >0.1 µm in diameter can be examined by micro-Raman, TOF-SIMS and EDS. For particles <0.1 µm in diameter, EDS, Auger Electron Spectroscopy (AES) and near-field IR and Raman spectroscopies are better choices. Note that in this paper conventional far-field traveling-wave IR and Raman are referred to as micro-FT-IR and micro-Raman spectroscopies, whereas non-propagating evanescent-wave IR and Raman are referred to as near-field IR and near-field Raman spectroscopies, respectively. The much smaller sampling volumes for near-field IR and Raman spectroscopies are the primary advantages over the conventional FT-IR and Raman spectroscopies. The judicious selection of the most appropriate method for a given analysis is often based on physical properties of the particle such as size, composition and volatility, as well as the type of information desired. It also depends on the industry sector from which the sample originated since custom systems have been developed, most notably for semiconductor wafer analysis. Table 1 summarizes six properties that often dictate which method is most appropriate for analysis of a given particle. XPS, TOF-SIMS, FT-IR and Raman spectroscopies all offer chemical bonding information, which is extremely valuable for identifying organic particles. These four methods, and in particular XPS and TOF-SIMS, are also used to analyze inorganic particles. XPS and TOF-SIMS also can be used for metallic particles. The most important property that often dictates which of these four methods should be used for chemical bonding information is the minimum particle size. XPS and micro-FT-IR are generally limited to particles around 10 µm in diameter, whereas chemical bonding analysis by TOF-SIMS is limited to particles around 2 µm. Micro-Raman spectroscopy is capable of examining particles as small as 0.5 µm to 1 µm in diameter provided the material is a strong Raman scatterer. Chemical bonding information from particles as small as 50 nm can only be obtained using near-field FT-IR and near-field Raman spectroscopies. The volatility of the sample can also dictate method selection. Volatile samples are easily analyzed by FT-IR and Raman, since ambient conditions can be employed. Conversely, XPS and TOF-SIMS are performed under ultra-high vacuum conditions that would change volatile samples, unless specialized sample handling methods are utilized. Additional techniques, namely AES and EDS, are available when only elemental analysis is required. Along with TOF-SIMS, these techniques can provide elemental analysis of submicrometer particles. However, because TOF-SIMS is difficult to perform quantitatively, EDS and AES are more widely used. EDS and AES systems generally incorporate components allowing electron microscopy, thereby providing elemental composition and particle morphology. EDS analysis is easier to perform on a wide variety of samples and in many instances EDS is selected over AES due to the larger number of installed EDS systems. It is some-

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what limited in that the volume from which characteristic X-rays are produced is on the order of 1 µm3. In comparison, the volume from which Auger electrons are produced is the sampling depth (1-10 nm) times roughly either the electron beam diameter or the area over which the electron beam is rastered. Although both AES and EDS can be used to analyze submicrometer particles, the surrounding substrate will generally be detected in either case. The special class of submicrometer plate-like particles is best examined by AES, since a larger portion of the analysis volume can be confined to the particle. 2. DISCUSSION

2.1. X-ray Photoelectron Spectroscopy (XPS) XPS provides quantitative analysis of all elements except hydrogen and helium, as well as chemical bonding or oxidation state identification [1]. Moreover, measurements can be made on virtually any solid material. However, it has several fundamental features that limit the applicability for particle analysis, namely large analysis areas (>10 µm in diameter) and shallow sampling depth (<10 nm). An XPS spectrum is obtained by irradiating a sample with X-rays and measuring the number and energy of the emitted electrons. The measured kinetic energy, KE, of an emitted photoelectron is related to the binding energy of the electron, BE, by BE = hν-KE-Φ, where hν is the X-ray energy and Φ is the combined work function of the sample and spectrometer. Thus, the binding energies of electrons can be calculated from the measured kinetic energies. This is of great value, since the binding energies of photoelectrons are indicative of the atoms from which they originate and the oxidation states of those atoms. By examining the relative abundance of the electrons, one can calculate the approximate concentration of all detected elements (except hydrogen and helium) within the sampling volume. XPS sampling volumes generally resemble extremely thin rectangular boxes or elliptic cylinders, with the widths and lengths typically ≥10 µm, and the thickness on the order of a few nanometers. Therefore, particles suitable for XPS analysis must be ≥10 µm in diameter. But since the sampling depth is <10 nm, only the outermost surface of the particle will be examined. In the worst case, the presence of contaminant films on particles can prevent analysis of the underlying particles. Only with the recent development of micro-XPS instruments has the method been used for individual particle analysis. Combining small analytical areas with the traditional ability of XPS to examine any type of sample and obtain quantitative elemental analysis along with chemical bonding it becomes obvious that it is an especially powerful technique. This is clearly demonstrated in the analysis of unknown particles on a plastic film as shown in Fig. 1. Analysis of the substrate film revealed that it contained carbon and oxygen, and a trace of silicon (Fig. 2a). Moreover, the carbon spectra (Fig. 2b) and oxygen spectra (not shown) are consistent with a polyester, most likely poly(ethylene terephthalate) (PET). Analysis

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of the large particle revealed that it contained carbon and fluorine, and traces of oxygen and silicon. The carbon and fluorine spectra indicated that the large particle consisted of poly(tetrafluoroethylene) (PTFE). A map of the fluorine distribution on the sample (not shown) revealed that the two small 10-20 µm particles located to the right of the large particle did not contain fluorine. Point analysis of these particles found carbon, oxygen, nitrogen, silicon, and zinc suggesting that several compounds were present (Fig. 2c). Based on the knowledge of compounds likely to be found in PET, one can guess that zinc might be attributed to zinc stearate. Although imaging clearly showed the location of the small particles and elemental analysis revealed the approximate concentration of the elements, the fact that several compounds were detected at the same time limited the ability of XPS to determine the elemental and chemical composition of each component.

Figure 1. X-ray induced secondary electron (SXI) image of a plastic film showing the presence of an approx. 300 µm2 large particle and two smaller 10-20 µm diameter particles.

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Figure 2. (a) XPS survey spectra and (b) high resolution carbon spectra of the large particle (top) and the plastic film substrate (bottom) regions defined in the SXI image in Fig. 1. (c) XPS survey spectrum of the small particles shown in Fig. 1.

2.2. Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) XPS has been shown to be a quantitative method that provides elemental composition and chemical bonding but not unambiguous compound identification. In contrast, TOF-SIMS is often able to make unambiguous compound identifications, but it is difficult to perform quantitative analysis, particularly for particle analysis. Thus, these two surface analysis methods complement each other. TOFSIMS is a specialized form of secondary ion mass spectrometry. As the name implies, a mass spectrum of the surface is obtained by bombarding the surface with high energy ions which cause secondary ions to be ejected. These secondary ions are ionized molecules and fragments of surface compounds. In the case of TOFSIMS the mass analysis is performed by measuring the time required for an ion to fly from the sample surface to the detector. Because a TOF-SIMS instrument operates as a mass analyzer rather than a mass filter, a complete mass spectrum is obtained for each incident primary ion bombardment. By operating the primary ion gun at low current the method can be performed in the static mode where the masses generated are independent of analysis time. In the static mode all ions originate from unsputtered material and hence all detected ions are characteristic of the original surface. When operated in the static mode, all ions come from the outermost 1-3 monolayers. Thus TOF-SIMS, performed in the static mode, provides mass spectra of compounds in the first few monolayers of the sample. The use of a finely focused primary ion beam permits analysis of regions as small as ~ 2 µm2 for organic compound identification or 0.1 µm in diameter for elemental analysis. Moreover, most instruments can display the intensity of emitted ions as a function of X-Y location on the surface. This provides a means for imaging the distribution of distinct chemical compounds on a surface with spatial resolution on the order 2 to 0.1 µm. An excellent detailed overview of TOF-SIMS can be found in Ref. [2].

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The compound specificity of TOF-SIMS is readily demonstrated in a study of contaminants on a magnetic disk recording medium. Optical inspection of the disk surface revealed a series of deposits each roughly 2-5 µm in diameter. The location of the deposits was readily apparent in the total positive ion image of the sample (see Fig. 3a). In this pseudo-color image the deposits appear as dark spots indicating a lower total ion yield from the deposits compared to the disk substrate. Positive mass spectra from these dark spots and from the substrate indicated that the spots were a hydrocarbon-based material, whereas the substrate consisted of a fluorocarbon. The fluorocarbon most certainly originated from a fluoro-lubricant coating on the disk. Hydrocarbons were not expected on the disk, but a hydrocarbon grease was used in adjacent components of the drive assembly. As is shown in Fig. 4, the positive ion spectrum of the grease is an excellent match for the deposits. Images of intense ions in the grease spectrum (27, 41, 55, 113, 127, 371, 483 and 497 m/z) (Fig. 3b) and from the fluoro-lubricant (12, 31, 47 and 50 m/z) (Fig. 3c) document the grease and lubricant distributions on the disk. These mass spectra and ion images clearly showed that the deposits were droplets of the hydrocarbon grease. Both XPS and TOF-SIMS are surface analysis methods which detect only those elements in the outer few monolayers. This surface sensitivity can be problematic during particle analysis if surface contaminants are present. Micro-FT-IR and micro-Raman spectroscopies, that can have very large sampling depths, are alternative choices. These methods provide chemical bonding information but are not element specific, and, therefore, cannot provide elemental composition. In both FT-IR and Raman spectroscopies, molecular vibrations within the material are probed by exposing the sample to light. In the case of micro-FT-IR spectroscopy, a broad band infrared light is passed through or reflected from the sample and the amount of transmitted or reflected light is recorded. In micro-Raman

Figure 3. Positive ion TOF-SIMS pseudo-color images showing the relative intensity of (a) all ions (0-1000 m/z), (b) characteristic ions from the deposits (27, 41, 55, 113, 127, 371, 483 and 497 m/z) and (c) characteristic ions from the substrate (12, 31, 47 and 50 m/z) from a magnetic disk recording medium having optically visible deposits on the surface.

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Figure 4. Positive ion TOF-SIMS spectra of (a) the grease droplets and (b) a reference grease used in the magnetic disk drive assembly.

spectroscopy the sample is irradiated with a single wavelength of light and the energy of the scattered light is modified through interactions with molecular vibrations. Although the methods by which the vibrational modes are probed differ between FT-IR and Raman spectroscopies, the information content is similar. Both methods have found extensive use in organic compound identification due to the presence of functional group vibration modes generally found above 1500 cm–1 and “finger print” composite vibration modes generally found below 1500 cm–1. Spectra from inorganic compounds are generally less informative, hence there are fewer applications of FT-IR and Raman spectroscopies in inorganic compound analysis. In both methods the sample is analyzed under ambient or dry nitrogen conditions. This greatly expands the utility and ease of use of micro-FT-IR and micro-Raman spectroscopies over the surface analytical methods XPS, TOFSIMS and AES, that require high vacuum conditions. 2.3. Micro-Fourier Transform Infrared Spectroscopy (micro-FT-IR) Far-field traveling-wave infrared spectrometers have been available for over 60 years, and high-speed Fourier transform spectrometers for the past 25 years. During this long development, vast libraries of IR reference spectra have been compiled. These libraries are invaluable for spectral interpretation and are often used for exact identification of unknown materials. Particle analysis is generally performed using instruments equipped with a microscope permitting analysis of areas as small as 10 µm in diameter. A convenient sample preparation method is to deposit the particle on a silicon wafer. The wafer, being transparent to infrared ra-

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diation, permits the particle to be analyzed in transmission mode. Secondary benefits of silicon wafer substrates are that they are hard and shiny making it easy to deposit and locate particles. The ability to analyze organic particles as small as 10 µm finds applications in a wide variety of industries [3-5]. The example discussed here is taken from the electronics industry. The optical photograph given in Fig. 5 shows the presence of a fine powdery substance on metal connector pins. The sample was prepared by carefully scraping the residue from the pins and depositing it on a silicon wafer. The transmission spectrum shown in Fig. 6a contains distinct bands corresponding to OH, CHx and COO vibrations. A search of the spectral library produced the reference spectrum of solder flux (Fig. 6b), which although not an exact match is sufficiently close as to identify the unknown powder as a solder flux residue. The use of group band vibrations for functional group identification and spectral library matching for specific compound identification is quite common. 2.4. Micro-Raman Spectroscopy Both Raman and FT-IR spectroscopies examine molecular composition through interaction of incident light with molecular vibrations. There are, however, three important properties that differentiate the methods. First, micro-Raman spectros-

Figure 5. Optical photo showing a powdery substance on connector pins.

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Figure 6. FT-IR spectra of powdery substance on connector pins (a) and reference spectrum of solder flux (b).

copy can use a finely focused light source that permits analysis of particles as small as 0.5 µm, provided the particles have large scattering cross sections. Second, the intensities of Raman absorptions are quite different from those in FT-IR. Third, because the intensity of scattered light is very weak, fluorescence can completely overwhelm the spectrum. Fortunately, there are many common light sources such as the visible 488 nm (blue) and 515 nm (green) lines of an argon ion laser and 633 nm (red) of HeNe laser, that can be utilized when fluorescence occurs. Huong [6] and Jimenez-Sandoval [7] present overviews of applications of micro-Raman spectroscopy in the biomaterial, composites, optoelectronics, pharmaceutical, and semiconductor industries. Because of the vast differences in the intensities of Raman and FT-IR vibrations, Raman spectroscopy is uniquely capable of identifying certain materials. Take for example proteins, which are high-molecular-weight polyamides made from 20 naturally occurring amino acids. To a large degree the FT-IR spectra of proteins are indistinguishable from synthetic polyamides. However, the Raman spectra of proteins contain five features that permit the distinction between proteins and synthetic polyamides. Four of these features are distinct bands: (1) the S–S in cystine, (2) hydrogen-bonding in tyrosine (TYR), (3) aromatic ring breathing and (4) aromatic C–H stretching. The fifth feature is that the three bands between 1300 and 1700 cm–1 (A-III, CH2 scissoring and A-I) are much broader in proteins due to the wide variety of amino acids in the protein chain. The presence of these five features in proteins and their absence in synthetic aliphatic polyamides is demonstrated in the top two spectra in Fig. 7. The presence of these features in the spectrum of an unknown particle is convincing evidence for biological contamination as shown in the bottom spectrum in Fig. 7.

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Figure 7. Raman spectra of albumin protein (top), polyamide (middle) and an unknown particle of biological origin (bottom).

2.5. Near-Field FT-IR and Near-Field Raman microscopies and spectroscopies Spatial resolution in traditional optical, infrared and Raman microscopies and spectroscopies is constrained by diffraction to approximately half the wavelength of the light being used. Using traditional optics, light propagates from the source to the sample and finally to a detector. Since the sample, source and detector are positioned far from each other and light must propagate from each location, the measurement is performed under far-field conditions. Conversely near-field conditions exist when the light interacting with the sample is a nonpropagating evanescent wave and the optics is near the sample. Although there are many ways to achieve near-field conditions, a popular method uses an optical fiber probe or source. The optical fiber source or probe is fabricated by heating and drawing the fiber to a small (sub-wavelength) diameter. All but the tip of the fiber is then coated with metal, thereby producing a small aperture at the end of a light tube. The fiber position (X, Y, Z) is controlled by nano-positioning hardware. Once the tip is brought within a few nanometers of the surface, an image can be obtained by raster scanning the fiber while keeping the sample to tip distance constant. The widest use of near-field conditions is in scanning near-field optical microscopy (SNOM) sometimes called near-field scanning optical microscopy (NSOM).

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In the context of this paper, SNOM does not fulfill the requirements for particle characterization since it simply provides an image of the particle. However, if the incident source is infrared light, scanning near-field infrared microscopy can be performed [8-10]. If a single wavelength laser is used, scanning near-field Raman microscopy can be performed [11-13]. In either case some of the image contrast is based on the interaction of the light with sample vibrations. Hence, true chemical images can be generated. A more complex system is required to obtain IR or Raman vibrational spectra under near-field conditions. Although the feasibility of obtaining near-field IR and Raman spectra have been demonstrated, much work remains, particularly in near-field IR, before they can be used for routine analysis of unknown particles [14-18]. 2.6. Energy Dispersive X-ray Spectroscopy (EDS) EDS is undoubtedly one of the most widely used analytical methods for determining the elemental composition of micrometer- and submicrometer-sized particles. The dominant reason for its wide acceptance is that it can quantitatively detect all elements above lithium provided the concentration is above the minimum detection limit, approx. 0.1 wt% for elements above fluorine. A second reason is that EDS instruments are typically attached to electron microscopes such that one can readily select individual particles for analysis and document particle morphologies. The technique is based on the fact that atoms ionized by high-energy electron bombardment exhibit spontaneous emission of X-rays. Thus, when a high energy electron removes an inner shell electron, an electron from a higher energy outer shell drops down to fill the inner shell vacancy and in the process releases energy equivalent to the difference in energies between the inner and outer shells. This energy is dissipated by spontaneous X-ray emission as in EDS, or by ejection of a second electron from an outer shell as in AES. By measuring the number and energy of emitted X-rays one can determine the concentration and identity of near-surface atoms. The quantitative accuracy of EDS during particle analysis is somewhat limited due to surface topography and in the case of sub-micrometer particles, due to detection of the surrounding substrate. Sampling depth and analysis volume depend on the sample composition and incident electron beam energy and angle. Sampling depths are generally >0.2 µm and lateral analysis area is generally 0.5 µm diameter or the rastered area, whichever is larger [19]. X-ray emission occurs for all materials and is only limited by the fact that it is difficult, if not impossible, to steer incident high-energy electrons to specific locations on insulating surfaces. Fortunately, insulating surfaces can be examined in lowvacuum systems or coated with thin conducing layers such as carbon, aluminum, or chromium and still obtain meaningful EDS data. Because of the ease with which EDS can be used to examine all types of solid samples and the large installed instrument base, it is an excellent “first look” tool. With appropriate software, particle analysis by EDS can be automated. Particles that are airborne or in liquids must first be captured on a suitable substrate such as

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a polymer membrane filter. This is often done by gravitational settling or vacuum filtration. For particles on solid surfaces the sample can be ultrasonically dispersed in an appropriate solvent and the resultant solution vacuum filtered. Conversely, the solid surface can be examined in the as-received state. The particles are often located by inspection of secondary electron or back-scatter electron micrographs. The process can be automated such that whenever a bright feature (having an atomic number greater than carbon) is detected by the back-scatter electron detector an EDS spectrum is recorded along with the analysis position. By scanning the electron beam and the sample stage the entire sample can be inspected. This method can become very time consuming if the particles are very small and few in number. This is often the case for wafer surfaces in semiconductor manufacturing. In this industry, particles and defects are often identified on silicon wafers by light scattering techniques [20]. Custom systems have been developed that use particle maps generated by light scattering techniques to position wafers within SEM/EDS instruments. These instruments are capable of analyzing whole 200 mm and 300 mm wafers. Great care must be used to ensure that the

Figure 8. Backscattered-electron image showing the locations of particles on a polymer membrane filter disk after exposure to a laboratory environment for several days.

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wafer is oriented equivalently in both the light scattering and SEM/EDS instruments [21]. In the example presented here, a study of airborne particles was initiated by placing a polymer membrane filter disk on a laboratory table for several days. Fig. 8 shows the backscattered electron micrograph of the membrane. Note that the dark background is due to the organic membrane and the bright spots are particles containing elements heavier than carbon. Automated analysis of the particles was stopped after detection of 10 particles. The particles were then characterized in terms of the chemical classification (defined by the analyst and based on elemental composition), the substrate area obscured by the particle, and lateral aspect ratio of the particle (maximum length/maximum width). These results are given in Table 2. Not surprising, most of the particles are silicates or clays. In this particular study the analysis time was approx. 0.5 h; however, quite often it can take several hours and hundreds of particles are processed. Table 2. Characteristics of airborne particles captured on a polymer membrane filter disk Particle

Classification

Area (µm2)

Aspect ratio

1 2 3 4 5 6 7 8 9 10

AlCaSiO AlCaSiO AlSiO AlSiO CaSiO CuZn Fe SiO2 SiO2 Zr

0.60 0.73 0.64 7.28 0.49 15.4 1.24 0.49 0.69 0.81

1.96 2.82 1.91 19.9 1.39 2.41 1.65 1.39 2.19 1.36

Classification: user selectable, based on elemental composition. Area: lateral area of the substrate obscured by the particle. Aspect ratio: ratio of maximum length to maximum width.

2.7. Auger Electron Spectroscopy (AES) Fundamentally AES has many features of EDS and XPS. Like EDS, AES instruments are capable of secondary electron imaging and provide quantitative analysis of all elements above helium with detection limits of 0.1-1 atom%. Thus, locating individual particles, documenting particle morphology and determining elemental composition are all generally straightforward. In contrast to EDS, the detected species are electrons rather than X-rays. Recall that high-energy electron radiation removes inner shell electrons. Loss of the first electron leaves the atom in an excited ionized state that undergoes relaxation whereby a second electron from an outer shell drops down to fill the inner shell vacancy and in the process

Surface and micro-analytical methods for particle identification

43

releases energy equivalent to the difference in energies between the inner and outer shells. The excess energy results in X-ray emission as in EDS or ejection of a third electron as in AES. Since the only relaxation methods are Auger electron emission and X-ray emission, the Auger electron yield is inversely proportional to the X-ray yield. The Auger electron yield from 1s shell vacancies is effectively unity for lithium and decreases with increasing atomic number. Thus, AES is much more sensitive for light elements than EDS. Above sodium, multiple electron cascades are possible such that AES has good sensitivity for all elements LiU. As a general rule, AES requires conducting or semi-conducting samples. Unlike EDS, insulating samples cannot be coated with a conducting layer since the thickness of the conducting layer would be on the order of the AES sampling depth. Fortunately, submicrometer insulating particles on conducting substrates behave like conductors such that analysis is possible. AES sampling depths are typically less than 10 nm. The sampling volume is then given roughly by the sampling depth times either the electron beam diameter or the area over which the electron beam is rastered. The extremely small sampling volume of AES makes it a viable alternative to EDS.

Figure 9. (a) SEM image and (b) AES spectrum of a 50 nm particle on a silicon wafer. (c) AES map showing the distribution of aluminum.

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The shape of the AES sampling volume is ideal for examining thin, plate-like particles. The small sampling depth assures that the substrate is not detected and the ability to scan the probe electron beam limits analysis to the particle. For particles <100 nm, the probe beam is not rastered and analysis is confined to the beam diameter. Electron scattering within the particle can cause the primary beam or high energy secondary electrons to strike the substrate, thereby producing Auger electrons from both the particle and the substrate. This is clearly shown in case of a 50 nm particle resting on a silicon wafer (see Fig. 9a). Even though an electron beam <30 nm diameter was used, the AES spectrum contained a significant contribution from the silicon substrate as shown in Fig. 9b. However, the map depicting the intensity of aluminum Auger electrons (Fig. 9c), clearly shows that aluminum is confined to the particle. Electron scattering has no effect on the signal from the 50 nm particle but rather adds signal from the substrate.

Figure 10. (a, b) SEM images showing the FIB cross section through a buried particle on a patterned silicon wafer. (c) AES map showing the distribution of oxidized silicon, elemental silicon and tungsten metal.

Surface and micro-analytical methods for particle identification

45

Point mode analysis has the advantage of maximizing signal intensity from the particle of interest. However, particles of this size can be very difficult to locate particularly when the particle density is low. Another consideration for extremely small particles is the requirement that the sample should not be contaminated with extraneous particles during handling and sample preparation. These restrictions dictate the design of instruments tailored to specific industries. Similar to EDS, custom instruments have been introduced to handle whole 200 mm and 300 mm wafers in class-1 environments. Semi-automated analysis is possible when these tools are integrated with optical defect detection systems such that particle locations are known. In such instances particles as small as the beam diameter can be analyzed. In some instances, particles are buried below the surface. This can happen during IC fabrication when particle contamination takes place during an intermediate step and is covered by subsequent processing. In these situations the particles can be exposed by ion milling a large area from the top down, or micro-milling a particle in cross section with a focused ion-beam (FIB) tool. If available, the latter method is preferred, since a greater amount of information is retained. Determining the particle composition, as well as the number and composition of overlayers, increases the likelihood of identifying the exact cause and production step where contamination occurred. For example, Fig. 10a, b shows the FIB cross section of a 1-µm3 particle on a patterned silicon wafer [22]. Exposure of the particle interior permitted AES analysis that showed that the core particle consisted of oxidized silicon. Moreover, maps showing the distribution of oxidized silicon, elemental silicon and tungsten revealed that the silicon dioxide particle was encapsulated first by elemental silicon and then by tungsten (see Fig. 10c). Thus, AES analysis not only determined the composition of the particle but showed that it was deposited before or during the deposition of poly-silicon. 3. CONCLUSIONS

No single analytical method provides elemental composition, chemical bonding and exact compound identification of organic, inorganic, and metallic particles. However, methods do exist that fulfill some of these requirements for specific particle sizes. Table 1 summarizes six properties that often dictate which technique, XPS, TOF-SIMS, FT-IR, Raman, EDS or AES, is most appropriate for analysis of a given particle. Organic particles are best analyzed by XPS, TOFSIMS, FT-IR and Raman techniques, since they all provide chemical bonding information. These methods can also be used to analyze inorganic particles with varying degrees of success. XPS offers chemical bonding and quantitative elemental composition but only for relatively large non-volatile particles. The only method capable of unambiguously determining exact chemical structures is TOFSIMS. Because of the extremely shallow sampling depth of TOF-SIMS, care must be taken to prevent surface contamination that could mask the underlying particle. FT-IR and Raman spectroscopies provide chemical bonding information on most

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materials, even those that are volatile. Moreover when operated under near-field conditions, they can be used to examine particles as small as 50 nm. Qualitative or semi-quantitative elemental analysis of submicrometer particles is best performed by EDS or AES. Both EDS and AES operate in conjunction with electron microscopes, thereby also providing particle morphology. EDS analysis is easy to perform on a wide variety of samples and is widely available due to the large installed instrument base. AES is a viable alternative to EDS, particularly for thin plate-like particles. Being a more specialized technique with far fewer installed instruments, AES usage trails that for EDS. REFERENCES 1. D. Briggs and M.P. Seah (Eds.), Practical Surface Analysis – Second Edition, Volume 1 – Auger and X-ray Photoelectron Spectroscopy, John Wiley & Sons, New York, NY (1990). 2. J.C. Vickerman and D. Briggs (Eds.), ToF-SIMS: Surface Analysis by Mass Spectrometry, IM Publications, Chichester (2001). 3. N. Berro, J.P.D. Cook, S. Ungrey, T. Lester, F.R. Shepard, R. Surridge and W.D. Westwood, J. IES 36(6), 15 (1993). 4. P. Fletcher, P.V. Coveney, T.L. Hughes and C.M. Metheven, J. Petroleum Technol. 47(2), 129 (1995). 5. H.U. Grenlich and B. Yan, Infrared and Raman Spectroscopy of Biological Materials, Marcel Dekker, New York, NY (2001). 6. P.V. Huong, Vibrational Spectrosc. 11(1), 17 (1996). 7. S. Jimenez-Sandoval, Microelectr. J. 31(6), 419 (2000). 8. E. Betzig and J.K. Trautman, Science 257, 189 (1992). 9. A. Piednoir and F. Creuzet, Micron 27(5), 335 (1996). 10. B. Dragnea and S.R. Leone, Int. Rev. Phys. Chem. 20(1), 59 (2001). 11. D.A. Smith, S. Webster, M. Ayad, S.D. Evans, D. Fogherty and D. Batchelder, Ultramicroscopy 61(1), 247 (1995). 12. S. Webster, D.A. Smith and D.N. Batchelder, Vibrational Spectrosc. 18(1), 51 (1998). 13. E.J. Ayars, C.L. Jahncke, M.A. Paesler and H.D. Hallen, J. Microsc. 202(1), 142 (2001). 14. H.M. Pollock and D.A.M. Smith, in: Handbook of Vibrational Spectroscopy, J.M. Chalmers and P.R. Griffiths (Eds.), Vol. 2, John Wiley & Sons, New York, NY (2002). 15. A. Piednoir, F. Creuzet, C. Licoppe and J.M. Ortega, Ultramicroscopy 57(2), 282 (1995). 16. R.M. Stockle, V. Deckert, C. Fokas, D. Zeisel and R. Zenobi, Vibrational Spectrosc. 22(1), 39 (2000). 17. S. Webster, D.A. Smith, D.N. Batchelder and S. Karlin, Synthetic Metals 102(1), 1425 (1999). 18. Y. Narita, T. Tadokoro, T. Ikeda, T. Saiki, S. Mononobe and M. Ohtsu, Appl. Spectroscopy 52(9), 1141 (1998). 19. J. Goldstein, D.E. Newbury, P. Echlin, D.C. Joy, A.D. Romig Jr., C.E. Lyman, C. Fiori and E. Lifshin, Scanning Electron Microscopy and X-ray Microanalysis, Plenum Press, New York, NY (1992). 20. P.-F. Huang, Y.S. Uritsky and C.R. Brundle, in: Handbook of Silicon Semiconductor Metrology, A.C. Diebold (Ed.), pp. 515-546, Marcel Dekker, New York, NY (2001). 21. C.R. Brundle and Y.S. Uritsky, in: Handbook of Silicon Semiconductor Metrology, A.C. Diebold (Ed.), pp. 547-582, Marcel Dekker, New York, NY (2001). 22. K.D. Childs, D. Narum, L.A. LaVanier, P.M. Lindley, B.W. Schueler, G. Mulholland and A.C. Diebold, J. Vac. Sci. Technol. A 14, 2392 (1996).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 47–62 Ed. K.L. Mittal © VSP 2003

The haze of a wafer: A new approach to monitor nano-sized particles K. XU,∗,1 R. VOS,1 G. VEREECKE,1 M. LUX,1 W. FYEN,1 F. HOLSTEYNS,1 K. KENIS,1 P.W. MERTENS,1 M.M. HEYNS1 and C. VINCKIER2 1

IMEC vzw, Kapeldreef 75, B-3001 Leuven, Belgium Chemistry Department, KULeuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium

2

Abstract—The deposition behavior of the nano-sized SiO2 particles on substrates (nitride and silicon) is investigated and the particle number deposited per unit area is found to be proportional to the particle concentration in the contamination solution. A diffusion model is developed to estimate the particle surface concentration deposited based on the diffusing ability of the particle in the solution. When the particle surface concentration is very high, the light-point defect signal measured by lightscattering instruments does not increase proportionally with the particle surface concentration deposited. On the contrary, the haze starts to increase dramatically. Also, it is shown that the added haze is proportional to the particle surface concentration deposited on the surface. The bigger the particle, the more effect the particle has on the haze increase. A model is developed to describe the added haze as a function of the particle size, the particle surface concentration on the wafer, and the refractive index of the particle material. Consequently, by measuring the haze, the particle surface concentration after high-level contamination can be quantified. This allows determining particle surface concentration for sizes smaller than the size limit of the state-of-the-art light scattering instruments. Keywords: LPD; contamination; haze.

1. INTRODUCTION

Surface cleaning techniques have been successfully used for integrated circuit (IC) manufacturing for more than 30 years. With shrinking dimensions of IC structures, the impact of particles on device yield becomes more and more important. The critical particle size needs to be lowered proportionally to the technology node. The concerns about the critical particle size measurements that are needed for sub-100-nm technology have already been expressed on several occasions, e.g., see the 2001 update International Technology Roadmap for Semiconductors (ITRS). Consequently, smaller defects (such as nano-sized particles) need ∗

To whom all correspondence should be addressed. Phone: (32-16) 288-276, Fax: (32-16) 281-315, E-mail: [email protected]

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to be monitored and removed. However, counting nano-sized particles deposited on substrates is a big challenge because the state-of-the-art light scattering instruments allow inspection of particles down to only 65 nm (KLA-Tencor SP1TBI) or 50 nm (SP1DLS) for wafers with extremely low surface roughness. In order to study particles smaller than 50 nm, an approach for quantifying the particle-count deposited on a substrate becomes necessary. At very high contamination levels, the surface concentration of particles deposited on substrates could reach such a high level that is beyond the limit of SP1. In such a case, SP1 cannot measure the particle surface concentration accurately and the surface concentration of light point defects (LPDs) measured by SP1 will be different from the actual surface concentration of particles deposited on substrates. As known, the average haze of a wafer is a manifestation of the roughness of the substrate surface. The roughness of the wafer will increase when the wafer is contaminated, which results in an added average haze. It has been reported that the haze signal might be used to monitor high particle surface concentration on a wafer surface [1]. For instance, this is especially important because in most chemical mechanical polishing applications sub-micrometer-sized particles are being used and the contamination level is very high (~ 1013 #/m2). In this study, different sized SiO2 particles deposited on silicon (O3-last) and nitride (HF-last) substrates were chosen. The deposition behavior of the nano-sized particles is studied and the particle surface concentration deposited on substrates after controlled contamination is measured using the SP1. A model is developed to estimate the particle surface concentration deposited on substrates after a controlled contamination as a function of the particle concentration in the contamination bath and the contamination time. This paper investigates the correlation between the added haze of a wafer and the particle surface concentration deposited on the wafer. A model is developed to describe the added haze as a function of the particle size, the particle surface concentration on the wafer and the refractive index of the particle material. Finally, an example is given to show that the particle removal efficiency calculated using the haze signal coincides well with the one calculated using the LPDs signal. 2. EXPERIMENTAL

The silicon wafers were 200 mm, p-type. The nitride wafers had a 150-nm nitride layer deposited on 15 nm pad-oxide. Before use, the wafers were cleaned using an IMEC-clean [2] in a STEAG automated wet-bench. Nitride wafers received an additional diluted HF-dip + over flow rinse + Marangoni drying in the manual wet bench. The deposition of SiO2 colloidal particles with different sizes on two different substrates (nitride and bare silicon) with different zeta-potentials (see Fig. 1) was investigated in this study. Clearly, both particles and substrates are negatively

The haze of a wafer: A new approach to monitor nano-sized particles

49

Figure 1. Zeta-potential measurements (Nicomp PSS ZW380) on the particles (a) and streaming potential measurements on the substrates (b) used in the current study.

charged at neutral pH. In order to exclude long-range electrostatic repulsive forces, all controlled contamination was done at low pH, such as pH ~ 0. Controlled contamination of wafers was done using an immersion-based contamination procedure, i.e., wafers were immersed in a particle-contaminated bath at pH ~ 0 followed by overflow rinse and Marangoni drying. The final LPD surface concentration and average added haze of wafers were determined by light scattering measurements using a KLA Tencor SP1TBI or SP1DLS instrument with dark field, wide and narrow collection angles and oblique incident beam (Fig. 2). Scanning Electron Microscopy (SEM) measurements were carried out in order to determine exactly how many particles had deposited on a unit area of the sub-

Figure 2. A schematic overview of KLA-Tencor SP1TBI or SP1DLS.

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strate after extremely high level contamination. For this purpose, the pieces of both silicon and nitride wafers were dipped in small beakers containing particlecontaminated solutions using the same conditions as in the contamination bath. After the dip, the pieces of wafers were rinsed and blown dry with a N2 gun. The surface concentration of particles was determined with SEM pictures by counting the particles within a unit area. 3. THEORY

In order to estimate the particle surface concentration, a diffusion model was developed based on established theories and known parameters [3]. Since the particle contamination was carried out at pH ~ 0, the electrostatic double layers of both particles and substrates are greatly compressed at such a high ionic strength and thus the electrostatic forces between particles and substrates can be neglected [4]. The dominant force left is the attractive van der Waals force, which works only at a very short distance (~ 3 nm). Hence, all the particles traveling by diffusion and colliding with the wafer surface can be considered as deposited particles on the surface i.e., at time t, the particle concentration c = 0 at the distance from the wafer x = 0. The particle concentration in the contamination bath is c0 at time t = 0. The particle concentration in the contamination bath will change as a function of the time and the distance from the wafer surface when the wafer is dipped in the contamination bath as a result of adsorption (Fig. 3). According to Fick’s second law, the rate of the change of particle concentration in the contamination bath ∂c ∂t is determined by the following equation:

Figure 3. Effect of diffusion along a wafer surface. The evolution of concentration profiles after three time intervals is shown (t1 < t2 < t3).

The haze of a wafer: A new approach to monitor nano-sized particles

∂ c ( x, t ) ∂ 2 c ( x, t ) =D ∂t ∂x 2

51

(1)

where D is the diffusion coefficient, determined by the Stokes–Einstein equation D = kT / 6πη r , r the effective hydrodynamic radius of a spherical particle, k the Boltzmann constant, η the solution viscosity and T the temperature. When the above-mentioned equation assumes the following initial and boundary conditions, at x = 0, at t = 0, at x → ∞,

c = 0, c = c 0, c = c0,

for t for x > 0 for t

the solution of equation (1) via integration is given as: c = c0 × erf

x

(2)

4 Dt

Consequently, the number of particles Ndip that deposit on a surface A at time t can be evaluated if we count the total amount of particles disappeared from the contamination bath per unit time.

Ndip, t = A ⋅

D1/ 2 ⋅ c0 π 1/ 2 ⋅ t1/ 2

(3)

where A is the area of the full wafer. Equation (3) is actually the Conttrell Equation [3], which applies only when no steady-state of particle concentration by the wafer surface has been reached and is characterized by the dependence on square root of time. The number of particles deposited during a dip time t is given as: t =t

2

t =0

π

Ndip = ò Ndip, t =

⋅ A ⋅ c0 ⋅ ( Dt )

1/2

(4)

The concentration gradient as a function of the dip time and the distance from the wafer surface calculated using equation (4) for 80-nm SiO2 particles is given in Fig. 4. At a fixed dip time, the shape of the concentration profile should be the same for each particle concentration in the carry-over layer and the actual concentration in the carry-over layer depends only on the initial concentration. Since some of the particles attached loosely to the substrates can be rinsed off during the neutral pH rinse, the particle-count after rinse could be much less than just after dip [6, 7] (Fig. 5). Therefore, the total number of particles Ntotal deposited during contamination at a fixed dip time can be determined by the following expression:

Ntotal = frinse ⋅

2

π

⋅ A ⋅ c0 ⋅ Dt

(5)

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Figure 4. The concentration (c) profiles of 80-nm SiO2 particles as a function of the dip time and the distance from the wafer surface.

Figure 5. Particle surface concentration deposited on substrates after immersion-based contamination as a function of overflow rinse time [7].

where frinse is the rinse coefficient, which varies with different substrates and the rinse time. At rinse time 0 the frinse is equal to 1, and the frinse at rinse time t can be simply determined by

The haze of a wafer: A new approach to monitor nano-sized particles

f rinse =

N total (t = t ) N total (t = 0)

53

(6)

where t is the rinse time. If the total number of particles deposited on a full wafer is described as the particle surface concentration deposited ( σ total , the particle count per unit area, #/m2), equation (5) can be written as:

σ total = f rinse ⋅

2

π

⋅ c0 ⋅ Dt

(7)

4. RESULTS AND DISCUSSION

The particle sizes of 30 nm, 80 nm and 140 nm SiO2 were measured by SEM. The size distribution is reported in the form of percentage: the number of particles which lie in a size range of 10 nm are counted and the results are depicted as a function of the particle size (see the data points in Fig. 6). The Gaussian distribution of the particle size was calculated based on the SEM-measured particle average diameter and standard deviation and is also depicted in Fig. 6 (the curves). Obviously, the actual particle size distribution is very close to a Gaussian distribution. The surface concentration of 80-nm SiO2 particles deposited on both silicon and nitride substrates after immersion-based contamination was measured with SP1 and SEM, and the results are shown in Fig. 7 as a function of the particle concentration in the contamination bath. The dip time of the wafers in the contamination bath was fixed at 2 min and the rinse time was 4 min at pH 6. A linear fit is observed only for the SP1 data. As far as the SEM results are concerned, the first 4–5 points perfectly coincide with the SP1 linear fit while at higher particle concentrations, the points deviate more and more from the straight line. This can be explained by a large fraction of the surface covered by particles at the high particle concentration. At a bath concentration of 4 × 1013 #/ml, the number of deposited particles will completely cover the wafer surface and some particles will also deposit on top of other particles, considering the total area covered by the deposited particles (see Fig. 8a). However, Fig. 8b shows that this is not the case: there are almost no particles which deposit on top of each other at higher contamination. Therefore, the total particle surface concentration deposited on substrates will be much less than expected in the case of high particle concentration in the contamination bath. The same work was done with 140-nm SiO2 particles on silicon substrates. Figure 9 shows that the linear fit of SP1 data coincides very well with SEM data. Therefore, it can be concluded clearly that the number of particles deposited on both substrates is proportional to the particle concentration in the contamination bath over several orders of magnitude.

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Figure 6. Particle size distribution presented in the form of the percentage of the number of particles in size ranges (measured in 10 nm size intervals with SEM) fitted to a Gaussian distribution of the particles calculated based on the SEM measured average particle diameter and the standard deviation.

Figure 7. Surface concentration of 80-nm SiO2 particles deposited on both (a) silicon and (b) nitride substrates after immersion-based contamination as a function of the particle concentration in the contamination bath. Linear fit is shown only for SP1 data.

The haze of a wafer: A new approach to monitor nano-sized particles

(a)

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(b)

Figure 8. SEM pictures of 80-nm particles on nitride substrates.

Figure 9. Surface concentration of 140-nm SiO2 particles deposited on silicon substrates as a function of the particle concentration in contamination bath. Linear fit is only given for SP1 data.

The particle surface concentration during the contamination as a function of the dip time is shown in Fig. 10. The curve based on the diffusion model (equation (7)) is given as well. Obviously, the experimental data points fit well with the diffusion model as a function of dip time. The particle surface concentration deposited during the contamination is calculated using equation (7) and the results are depicted in Fig. 11 for all particles on both substrates. Obviously, for 80-nm and 140-nm particles on both substrates, the results from the diffusion model coincide very well with the SP1 and SEM results.

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Figure 10. Variation of particle surface concentration deposited during contamination with the dip time for 140-nm SiO2 particles deposited on silicon and nitride substrates.

As far as to the SEM data points for 30-nm particles on both substrates, are concerned, they coincide well with the particle surface concentration determined by the diffusion model. The last 1–2 SEM data points in Fig. 11e and Fig. 11f should be considered with caution because of extremely high level of contamination. Clearly, the diffusion model (equation (7)) is well acceptable as an approach to quantify the particle surface concentration as a function of particle concentration in the contamination bath. As the contamination level increases, the number of particles deposited on substrates could be very high and might exceed the maximum number of particles the SP1 can count. This threshold is below approx. 70 000 LPDs per wafer. Assuming a uniform deposition on the complete wafer surface and by measuring a limited surface area on the wafer (i.e., large exclusions), higher densities of particles on the wafer surface can be detected as LPD counts. In order to determine the correlation between the particle surface concentration on the wafer and the measured signals (LPDs or haze by the SP1), 80-nm SiO2 particles deposited on silicon substrates were chosen. In Fig. 12, the LPD surface concentration and the haze measured by SP1 as a function of the surface concentration of particles deposited (quantified using the diffusion model) are given. The solid grey curve is a one-toone curve, i.e., one particle corresponds to one defect during the measurement. Obviously, the first several SP1 LPD data points with low contamination levels fit well with the one-to-one curve. However, the LPD surface concentration deviates considerably from this linear line and reaches saturation at high-level contamination. This saturation is regarded as the upper-limit of the particle surface concentration detection by the light scattering system of SP1, which is 109 #/m2 for 80nm particles. On the other hand, the added haze starts to increase proportionally to

The haze of a wafer: A new approach to monitor nano-sized particles

(a)

(b)

(c)

(d)

(e)

(f)

57

Figure 11. Particle surface concentration calculated using the diffusion model as a function of the particle concentration in the contamination bath for three particle sizes on silicon and nitride substrates.

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Figure 12. Surface concentration of the added defects (LPDs), the added haze measured by SP1 and the surface concentration of particles determined by SEM as a function of the surface concentration of particles estimated using the Diffusion Model.

the particle surface concentration deposited on the wafer. Hence, we can conclude that there is a saturation of the LPD signal on the wafer with a high particle surface concentration. In this case, SP1 cannot recognize the particles any more and the particle signals contribute to the average added haze of the wafer. In other words, LPDs are more associated with a low particle concentration surface and the haze signal is more associated with a high particle concentration surface. The average added haze of the silicon and nitride wafers contaminated with 140-nm, 80-nm and 30-nm SiO2 particles as a function of the particle surface concentration deposited is depicted in Fig. 13. The particle surface concentration on the wafers is calculated using the Diffusion Model. The added average haze seems to be proportional to the particle surface concentration deposited on substrates. Clearly, the bigger the particle size, the larger the haze signal measured for the same particle surface concentration. Based on Rayleigh approximation, a model is developed to describe the haze of a wafer ηsc contaminated with particles: 4

ηsc − ηbg =

2æd ö Ω 2 d 2σ n − 1) ç ÷ ( Ω0 è λ ø cosθ i

(8)

where ηbg is the background haze, i.e., the haze of a clean substrate in absence of particles; Ω the solid angle of collection, which is a constant for each detector; d the particle diameter; n the refractive index of the particle material (e.g., 1.46 for SiO2); λ the wavelength of the laser light (488 nm); θ i the incident angle which is 70º for oblique illumination in the KLA-Tencor SP1 and (ηsc – ηbg) the haze added by the particle contamination to the substrate. There is only one fit parame-

The haze of a wafer: A new approach to monitor nano-sized particles

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ter, Ω0. If the light scattering is isotropic, the value of Ω0 should be the same for both narrow and wide detectors. All the data points in Fig. 13 are used to determine Ω0 and the fitted curves are also shown in Fig. 13. Despite its simplicity, equation (8) describes the relationship between the added haze of a substrate, the particle diameter and the particle surface concentration deposited remarkably well. Also when haze measurements were done using the narrow detector channel, similar results were obtained (Fig. 14). Ω0 is calculated for both substrates and for both narrow and wide detector angles and the values of Ω0 are summarized in Table 1. On a silicon substrate the particles seem to scatter more light than on a Si3N4 substrate. It also appears

Figure 13. The added haze of the wafer (dark field, wide detector) as a function of particle surface concentration deposited on the wafer. The particle surface concentration in the graphs is calculated using the Diffusion Model.

Figure 14. The added haze of the wafer (dark field, narrow detector) as a function of particle surface concentration deposited on the substrate. The particle surface concentration in the graphs is calculated using the Diffusion Model.

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Table 1. Ω0 values for SiO2 particles using oblique illumination in combination with the wide and narrow detectors of SP1 Detector

Si substrate

Si3N4 substrate

Wide

0.8 ± 0.3

1.6 ± 0.3

Narrow

0.31 ± 0.03

1.8 ± 0.4

that for the Si substrate the light is not scattered isotropically but more light is scattered in the directions covered by the narrow detector. For the nitride substrate, the Ω0 values for the two detectors are practically identical. This may be an indication that the light scattered from the SiO2 particles on the nitride substrate under study is isotropic. Experimentally, we can easily measure the haze value from 0.01 ppm to 100 ppm (corresponding to 109–1013 #/m2) for 80-nm particles on silicon substrates while we can only measure the particle surface concentration as the LPD surface concentration less than 109 #/m2. This proportionality between the added haze and the particle surface concentration can be used to quantify the particle surface concentration after extremely high level of the contamination instead of LPD measurements. As an example of using the haze method for the evaluation of removal of particles, the removal of 80-nm SiO2 particles with a low contamination level (107 #/m2) and a high contamination level (1012 #/m2) on a silicon substrate was investigated (Table 2). The wafers were processed using megasonic cleaning systems A and B. For the low-level contaminated wafers, the LPD surface concentration was used to calculate the removal efficiency. For the high-level contaminated wafers, the added haze was used to calculate the removal efficiency. According to Table 2, the removal efficiency calculated using LPD surface concentration is almost the same as the one calculated using the haze value for both cleaning systems. Another example is to use the haze method for the evaluation of removal of particles below the current size detection limit. For instance, the removal of 30-nm SiO2 particles (d = 34.3 ± 5.9 nm) using brush scrubber cleaning is shown in Fig. 15. It can be observed that the particle removal efficiency decreases drastiTable 2. The removal efficiency calculated using LPD surface concentration and the haze Cleaning tool

Contamination

Measured signal

Removal (%)

System A

Low

LPDs

99.9 ± 0.1

System B

High Low High

Haze LPDs Haze

100 ± 0.1 74.7 ± 9.2 77.7 ± 2.5

The haze of a wafer: A new approach to monitor nano-sized particles

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Figure 15. Effect of the number of wafers processed on the particle removal efficiency for wafers highly contaminated with SiO2 particles after brush scrubber cleaning using ultra-pure water. PRE (particle removal efficiency) is the PRE calculated for the particles in the size range 0.2–2.0 µm.

cally with the number of wafers processed because of the brush loading with particles. Obviously, by monitoring the added haze instead of individual LPDs, this effect is more pronounced and allows to monitor the actual behavior of these nano-sized particles. 5. CONCLUSIONS

The particle surface concentration deposited on substrates from the immersionbased contamination is proportional to the particle concentration in the contamination bath for a fixed contamination condition. The surface concentration of particles deposited on both silicon and nitride substrates from immersion-based contamination could be well estimated by the diffusion model if the particle concentration in the contamination bath was known. This model was verified by varying the particle concentration in the bath and the dip time of contamination. Using light-scattering measurements, light-point defects are found to be more associated with the low-particle-concentration surface and the haze signal is more associated with the high-particle-concentration surface. When the particle surface concentration on the wafer is very high, the light-point defects signal does not increase proportionally with the surface concentration of particles deposited. The haze equation can well describe the relationship between the added haze of a substrate, the particle diameter and the particle concentration deposited with only one fit coefficient. For the nitride substrate, a single fit coefficient applies well for both wide and narrow detectors. By measuring the haze signal, the parti-

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cle surface concentration after extremely high-level contamination can be investigated, including the surface concentration of nano-sized particles smaller than the current size detection limit of the state-of-the-art light-scattering equipment. REFERENCES 1. S.H. Yoo, J. Sun, N. Narayanswami and G. Thomes, Proceedings of Ultra Clean Processing of Silicon Surfaces 2000, M. Heyns, P. Mertens and M. Meuris, pp. 259-262, Scitec Publications, Uetikon-Zürich, Switzerland (2001). 2. M. Meuris, P.W. Mertens, A. Opdebeeck, H.F. Schmidt, M. Depas, G. Vereecke, M.M. Heyns and A. Philipossian, Solid State Technol., 109-114 (July 1995). 3. G.M. Barrow, Physical Chemistry, 4th Edition, McGraw-Hill, New York, NY (1983). 4. J. Israelachvili, Intermolecular and Surface Forces, 2nd edition, Academic Press, London (1991). 5. A.J. Bard and L.R. Faulkner, Electrochemical Methods: Fundamentals and Applications, John Wiley, New York, NY (2001). 6. R.K. Iler, The Chemistry of Silica, John Wiley, New York, NY (1979). 7. W. Fyen, J. Van Steenbergen, K. Xu, R. Vos, P.W. Mertens and M.M. Heyns, to be published in the Proceedings of Ultra Clean Processing of Silicon Surfaces 2002, 16-18 September 2002; Ostend, Belgium.

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 63–76 Ed. K.L. Mittal © VSP 2003

Particle transport and adhesion in an ultra-clean ion-beam sputter deposition process C.C. WALTON,1,∗ D.J. RADER,2 J.A. FOLTA1 and D.W. SWEENEY1 1

Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA Sandia National Laboratory, PO Box 5800, Albuquerque, NM 87185, USA

2

Abstract—The transport and adhesion of submicrometer particles have been studied in an ion-beam sputter-coating chamber, to improve ultra-clean coating technology for Extreme Ultraviolet Lithography (EUVL). EUVL is an extension of optical lithography to λ = 13.4 nm using reflective optics. For enhanced reflectivity, the EUVL mask and optics must be coated with an 81-layer, 280 nm total thickness Mo/Si multilayer coating. The reflectance of the multilayer is highly sensitive to particle defects, so the particle level on the mask must be reduced to a total areal density below 0.003 particles/cm2. Current ion-beam sputter coating technology can achieve a median level of 0.04 added particles/cm2 (i.e., 10 added particles 90 nm or larger on a 200 mm Si-wafer test substrate), but this must be reduced by about 10 times to meet mask cost requirements for EUVL. In order to understand the sources of particle defects on the masks, transport and adhesion of particles in ion-beam coating conditions have been studied, using test particles and particles native to the coating process. At process pressure near 1×10–4 Torr, gas drag is negligible for particles larger than 10 nm, so particles travel ballistically until they hit a surface. Particle bounce appeared to contribute to transport in many experiments. Test particles introduced at a velocity V ~ 300 m/s reached remote surfaces with no line-of-sight to the particle source, consistent with multiple bounces within the chamber. The ion beam has sufficient momentum to entrain slower particles and accelerate them toward the sputter target, where some can bounce to the substrate. A model of particle entrainment by the ion beam is presented, and the relationship of beam entrainment to particle bounce is assessed. Keywords: Particles; defects; optical coatings; EUVL; lithography; bounce; transport; ion drag; ionbeam; sputtering.

1. INTRODUCTION

Extreme Ultraviolet Lithography (EUVL) is the favored technology by the IC industry for the 45 nm critical-dimension node and beyond [1]. Compared to lithography in current production, EUVL represents a 10-times wavelength decrease to λ = 13.4 nm, i.e., in the soft X-ray or extreme ultraviolet regime. Since all lens ∗

To whom all correspondence should be addressed. Phone: (1-925) 423-2834, Fax: (1-925) 423-1488, E-mail: [email protected]

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materials absorb at this wavelength, EUVL is based on reflective optical surfaces, which are coated with an 81-layer Mo/Si quarter-wave stack for enhanced reflectivity. Most of these surfaces are not on an image plane of the EUVL lithographic stepper, such as, for example, the condenser optics in the illuminator or the reducing optics after the reticle. These surfaces away from the image plane are not sensitive to modest levels of particle contamination, provided that the flare, or total intensity scattered by the particles, is negligible. But the EUVL reticle, which is also reflective and coated with the Mo/Si multilayer, is imaged directly onto the wafer. Therefore, any particles in the reticle coating that are larger than the resolution of the optical system will be imaged as well. For this reason, a coating process with unprecedented cleanliness is required to apply the multilayer coating to the reticle. The multilayer coating is highly conformal, and is, therefore, sensitive to buried particles originating on the substrate or particles landing on the growing films during multilayer deposition. The critical particle size (the smallest particle that will print as a fatal defect on the wafer) is approximately 40-60 nm. Only one particle above this size, at most, can be accommodated by positioning it over a noncritical area of the device pattern. Therefore, the EUVL mask must be coated with at most 1 particle over the 11 cm × 13 cm active area. A clean ion-beam sputtering process has been developed with a median added particle level of 0.04 particles/cm2, or about 5 particles in the active area, using a dedicated ion-beam sputtering (IBS) coating tool at LLNL. A further improvement of 5-10 times is required to achieve a useful 60% yield of clean masks. In order to reduce particle contamination further, the authors have investigated the basic mechanisms of particle transport in the IBS environment. Groundbreaking particle-contamination work in other thin-film coating environments has been performed by several groups [2–5]. Roth et al. used laser light scattering (LLS) to observe trapping of particles at plasma sheath edges in a silane discharge [4]. Selwyn et al. expanded the use of LLS into etching chambers [6] and magnetron sputter-coaters [7], and found that particles could be trapped at the plasma sheath edge by a balance of electrostatic forces. When the plasma is switched off, the trapped particles are released and become a major source of contamination on the wafer. Various commercial devices (in situ particle monitors (ISPMs)) are intended to monitor particles in pump lines and gas supply lines to control contamination (Particle Measurement Systems (PMS); Pacific Scientific Instruments (formerly High Yield Technologies (HYT)). But this approach has a weakness: the level of particle contamination in the pump lines is often poorly correlated to that on the wafer. An “above-wafer” ISPM has been developed by one supplier (Process Metrix, Inc., San Ramon, CA, USA) that claims to surmount this problem. Extensive investigations have also been done of particle movement at higher pressures in chemical vapor deposition (CVD) processes [8–15], and in particlebearing plasmas (“dusty plasmas”) in other situations, such as the science of interplanetary dust behavior [16–18]. Brown et al. have studied particle entrapment

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and transport in high-energy ion beams in ion implanters [19]. However, few studies have been published on particle transport in ion-beam sputtering. Because of the highly directional ion beam, the substrate located far from the plasma, and the typical low operating pressure, ion-beam sputtering is physically different from CVD or magnetron sputtering. This paper presents preliminary work on basic particle transport mechanisms during ion-beam sputtering. 2. EXPERIMENTAL

Four experiments were performed, the first with “native” particles intrinsic to the process, and the rest with test particles introduced under controlled conditions. The experiments were performed in an 80-cm-diameter spherical test chamber used as a model system. The chamber has a horizontal, perforated metal floor (about 5 cm below the sphere equator) where the coating is deposited. A single 1500 L/s cryopump achieves a base pressure of about 5 × 10–7 Torr. A DC ion gun (Ion Tech Inc., Ft. Collins, CO, USA) with two graphite grids and a 3 cm beam diameter is mounted on a moveable base that can be positioned anywhere in the chamber. Typical ion beam operating conditions were an ion energy of 750 eV, and a beam current of 35 mA with an accelerator-grid current of 5 mA. There are 10 ports available for feed-throughs or observation windows. Three particle sources were used to introduce test particles into the chamber. Source I was the cluster sprinkler, which produced clusters of particles. It consisted of a small canister with a fine perforated metal screen on the bottom. When the canister was vibrated through a mechanical feed-through, clusters of test particles (in this case 1.5 µm SiO2 spheres) fell through the screen by gravity. This provided a simple source, but produced clusters of particles with a wide size distribution. Particle direction and velocity were determined by gravity, and the particles may have acquired some charge from friction with each other and with the screen. Source II (the “shaker”) consisted of a small piece of woven cleanroom wiper cloth impregnated with test particles and stretched over the ends of a U-shaped elastic steel strip. An electric motor with an off-center weight was attached to one arm of the U. When the motor was turned on, its vibration from the off-center weight shook the steel strip and vibrated the “U” like a tuning fork, thereby stretching the cloth and causing test particles to be emitted, presumably by chafing of the cloth fibers. The device was contained in a 6-cm-diameter cylindrical casing, closed except for a 1.5-cm-diameter aperture at one end. The device was placed in the casing such that the cloth was about 5 cm from the aperture, through which particles could escape while the motor was running. This arrangement produced individual particles and allowed control of the particle direction, since particles can only escape through the aperture. But the velocity was unknown and the particles might have been charged. From some simple gravity experiments emitting particles horizontally and measuring their distance to fall to the floor, the shaker appears to emit particles in a wide range of velocities from about 2 to 20 m/s.

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Source III was a commercial aerosol generation system (TSI Inc., St. Paul, MN, USA) consisting of a liquid reservoir (containing a suspension of test particles in DI water), an atomizer (model 3076), two diffusion drying cells, and a charge neutralizer. The suspension was atomized into droplets by a flow of clean nitrogen across a nozzle in the atomizer. The flow made a 90° turn in front of an impaction plate, where larger droplets escaped the gas flow, struck the plate, and dripped back to the reservoir. Smaller droplets (mean diameter below about 0.3 µm) were carried along with the gas flow to the dryers. The water in the droplets was removed by diffusion as the gas flow passed over silica-gel beads in the dryers, leaving free-floating single particles (and some smaller residue particles from any impurities in the liquid). The particles continued into the charge neutralizer, which uses a sealed 85Kr β-radiation source to establish a Boltzmann charge equilibrium. This reduced the charge of each particle to less than 10 elementary charges (positive or negative), with the charge magnitude depending on the particle size. The particles were then injected into the chamber through a 25 µm orifice in a thin plate (Small Parts, Inc., Miami Lakes, FL, USA) on the end of a flexible copper tube. The gas flow rate through the orifice was 12 ± 0.5 sccm, decreasing to about 8 sccm over ~ 2 h of use. For the concentration of particles used in the suspension, the total particle flow into the chamber was about 1000 test particles/min. The aerosol particle source produced individual particles with a known direction and velocity and only a small charge. However, their velocity was much higher than for the other sources (about 300 m/s vs. 2-20 m/s), as discussed below. Test particles for all three injection systems were 0.5-1.5 µm SiO2 or polystyrene latex (PSL) spheres (Duke Scientific, Palo Alto, CA, USA). Experiments were run at pressure P = 1 × 10–4 Torr except as noted. Particles were collected on 200 mm Si wafers at various points in the chamber, and counted with a Tencor 6420 optical wafer inspection tool. The Tencor instrument detects particles by off-normal incidence laser light scattering (at λ = 488 nm) and has a particledetection sensitivity limit of 0.12 µm (measured against PSL reference spheres). The Tencor 6420 sized the 0.5 µm test spheres at 0.25–0.33 µm. This apparent discrepancy occurred because the tool was calibrated for scatter by latex spheres on Si substrates, while most experiments were done with SiO2 spheres, sometimes on Si substrates that had been previously coated with the Mo/Si multilayer. The scattered intensity measured by the tool is strongly dependent on the index of refraction of the particle material and the roughness of the substrate. The Si wafers were held vertically by 12 cm posts, to which they were held at their edges by spring clips. The wafers were 200 mm epitaxial Si (Wacker Siltronic), coated with an 81-layer periodic Mo/Si multilayer with a 6.7 nm-period and a 280 nm total thickness. We used wafers coated with the Mo/Si multilayer to simulate conditions of particle adhesion during deposition of the multilayer on an EUVL lithographic mask. The wafers placed directly in the ion beam as sputter targets were uncoated Si. The vacuum chamber was not in a cleanroom, but a local low-particle environment was established around the loading port using a

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1.5 m × 1.5 m enclosure and laminar-flow air filters (High-Efficiency Particle Arresting, or HEPA type). With careful wafer handling (using clean tweezers and fresh latex gloves) and a protocol of slow pumping and venting of the chamber (~ 1 Torr/s with no sudden starts), the background count (particles added by all handling and pumping) was typically 20-30 particles/wafer. During normal deposition of a Mo/Si multilayer, the sputter targets are 1-2 cm thick disks of Mo or Si. But if a clean Si wafer is used as a sputter target for a short experiment (typically 3 min), it remains smooth enough to be optically inspected after the experiment. In this way, the sputter target is also a witness wafer for particles traveling in the ion beam itself. 3. RESULTS

The first tests were conducted to understand the transport of particles intrinsic to the ion-beam sputter process (i.e., without the deliberate introduction of any test particles). Three clean wafers were used as witnesses to collect particles at various positions in the chamber (see Fig. 1). The first wafer is in the ion beam where the sputter target would be in normal coating operation, and is labeled “target”. The second wafer is in the position of the mask blank being coated, and is labeled as “mask”. The third wafer is at the other side of the chamber, facing the wall, to measure particle circulation away from the ion beam and sputtered material, and is labeled “hide”. Fig. 1 shows the experimental setup, approximately to scale. Typical optical particle maps for the target and mask wafers are shown in Fig. 1. The target wafer shows a spot of high particle density where the beam strikes it, and the spot corresponds in size to the apparent width of the beam. The mask wafer shows about 30-times fewer particles, evenly distributed over the surface. The average value of this ratio over about 10 similar experiments was 10. The hide wafer, in turn, is typically 5-10-times cleaner than the mask wafer. Wafers experiencing only handling, pumping and venting are cleaner still, showing that a process related to operating the ion gun, rather than the handling and pumping procedures, is responsible for most of the particles. Particle levels from these tests are summarized in Fig. 2. While the overall particle level varies with time (tending to get cleaner with repeated experiments after the chamber had sat idle), the particle level ratios among the various wafers are approximately constant. An example of this is the wafers in Fig. 1, where the target and mask wafers have a 30:1 particle density ratio, but are cleaner than the average target and mask particle densities given in Fig. 2. To verify that the ion beam was playing a role in the transport of particles, a simple experiment was made with the particle sprinkler (Source I). The sprinkler produced clusters of 1.5 µm SiO2 test spheres, which were deflected by the ion beam and collected on a test wafer below (Fig. 3). The size of the clusters varied with position – the smallest clusters had the highest deflection angle. The size dependence of the deflection angle is shown in the graph.

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Figure 1. (a) Configuration of ion beam experiments in test chamber (top view). Ion beam impinges on target wafer at 30° from normal, sputtering atoms of target material off target and onto mask to be coated. The hide wafer is mostly out of the path of sputtered material from the target and facing wall. Arrows give the direction of the polished side of the test wafers. (b) Particle maps of target and mask, taken with Tencor 6420 optical scanning tool. Below the particle maps are histograms of particle sizes (as measured by scattered intensity).

Figure 2. Typical particle density for wafers in various positions in the chamber. The particle density changed with chamber conditions from experiment to experiment, but the ratio of particle density from target wafer to mask wafer to hide wafer remained approximately constant. Digits below labels are numbers of wafers averaged to give the result; error bars are ± 1 σ. Definitions: Target, Mask, Hide are wafers placed as shown in Fig. 1; Walk wafers go through all the pump and vent steps but see no deposition; Witness wafers are left in the box, exposed only to box opening, closing and transportation.

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Figure 3. Experimental data and model prediction of deflection angle θ (as labeled in diagram) of clusters of test particles by the ion beam. Test particles (1.5 µm SiO2 spheres) were dropped into the ion beam from above using the cluster sprinkler (Source I) and collected on a wafer below. The particles were in clusters ranging from 2-3 particles to a few hundred particles. The smaller clusters were deflected the most. The model (described in the text) explains the trend in the experimental result, but with an error of about 2-times in cluster size.

To experiment further with the ion beam’s effect on particles, the “shaker” source (Source II) was used to inject individual particles into the ion beam from the side during coating. The shaker produces a stream of individual particles (no doublet or triplet peaks were found in the size histogram) and has a fairly low background of other particles (the background level in the size histogram is about 20-times lower than the peak for the test particles). The shaker was used to inject test spheres directly into the ion beam as shown in Fig. 4. While test particles were found on all three test wafers, running the ion gun greatly increased the particle density on the target (by about 10-fold) and on the coated wafer (by about 2fold), while decreasing the particle density on the hide wafer (by about 2-fold). The particle areal densities are shown in the chart. To investigate bounce of particles with known velocity in the absence of the ion beam, the commercial aerosol system (Source III) was used. The aerosol particle source was used to produce a flow of dry Ar gas bearing 0.5 µm SiO2 spheres, and the gas was leaked directly into vacuum (P ~ 4 × 10–4 Torr) through a 25 µm orifice. The particle jet leaving the orifice was aimed directly at the main wafer, with a “hide” wafer facing away, as shown in Fig. 5. The particle density was found to be uniform and equal over both wafers. When the chamber pressure was turned up to decrease the stopping distance for the test particles, the article densities on the two wafers diverged, with the main wafer density going up about 30-fold, and the hide wafer density going down by the same factor (Fig. 6).

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Figure 4. (a) Experimental setup for particle injection experiment. Test particles (0.5 µm SiO2 spheres) were injected directly into the ion beam using the “shaker” source (Source II). Comparing particle levels with ion beam on vs. ion beam off, the particle level on the target increased 10-fold, on the mask increased 2-fold and on the hide wafer decreased 2-fold. (b) The areal particle densities found on the wafers.

Figure 5. (a) Experimental configuration for particle bounce experiment (Particle source III, top view). The test wafers are held vertically, with polished surfaces facing as shown by arrows. A jet of test particles (0.5 µm SiO2 spheres) is introduced from the orifice at the end of the tube at about 300 m/s, and the pressure in the chamber is (5 ± 1) × 10–4 Torr. (b) Optical particle maps of the main wafer and hide wafer, showing test particles only. In addition to the test particles, there was a comparable number of residue particles from the aerosol system, also nearly evenly distributed.

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Figure 6. Effect of chamber pressure on particle counts on the two wafers in Fig. 5. Both wafers had equal counts at a typical sputtering pressure of 5 × 10–4 Torr. At higher pressure, the particle count on the main wafer increased about 45-fold, and that on the hide wafer dropped to a background level of a few particles, consistent with background pressure slowing particles down and increasing sticking at the first surface (the main wafer). The stopping distance at each pressure (calculated from standard results for viscous drag in the free-molecular limit [32]) is shown along the lower axis. At the highest pressure, the stopping distance is comparable to the distance from the particle jet to the main wafer (about 0.1 m), so they are slowed by drag to a low velocity before hitting the wafer and stick immediately. At the lowest pressure, the stopping distance is much greater than the diameter of the chamber (about 0.8 m), so the particles take a long path with many bounces. At all pressures used here Reynolds numbers are low (below 0.01), so inertial drag is negligible compared to viscous drag.

4. DISCUSSION

The first experiments clearly show that the ion beam is capable of strongly accelerating micrometer-size particles in the beam direction – the deflection is directly observed in Fig. 3, and Fig. 1 suggests the ion beam is carrying a stream of particles with it when it impacts the target. Similar entrainment of micrometer-size particles was observed (but at much higher ion energy and current density) by Brown et al. [19]. Particle motion in plasmas can result from many forces, including ion drag, neutral drag, electrostatics, thermophoresis, and gravity. These forces have been studied by several authors [15, 20–23], and some have developed quantitative transport models including all these forces. The majority of work in this field has been for chemical vapor-deposition (CVD) or magnetron sputter plasmas. CVD plasmas typically have ion energies of a few eV or less, reducing the importance of ion drag. In magnetron plasmas, ion energies are typically a few hundred eV, but the sputter target is one electrode of the discharge. Because of the voltage drop, the target forms a sheath, and ion drag can be balanced by the electrostatic force at the sheath boundary, trapping particles there as observed by Selwyn et al. [6]. But in ion-beam sputtering, the

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plasma is extracted through the gun grids and charge-neutralized before reaching the target. Therefore, a strong electric field is not expected along the length of the beam, and, furthermore, the long beam (typically 20–40 cm) gives a longer distance to accelerate particles than in a magnetron system, where the typical targetsubstrate distance is 10 cm. Therefore, it is plausible for ion drag to dominate electrostatics in ion-beam sputtering in determining particle motion. On the hypothesis that ion drag would dominate other terms, we made a simple model of the momentum and compared to the experiment (Fig. 3). The model assumes: (1) that the cross section of the particle for ion collisions is its physical cross section, (2) that the ion-particle collision is totally inelastic (the ion is embedded in the particle, and all its momentum is transferred to the particle), (3) that the ions do not significantly shrink the particle by sputtering and (4) that clusters of particles do not break up while in the beam. If the particle enters perpendicular to the beam traveling at a velocity V⊥, the deflection angle can be approximated as θ = arctan(U||/V⊥), where V|| is the velocity the particle acquires parallel to the beam due to ion drag. For ion energy EAr, the impulse given to the particle by each ion is ∆p = 2mAr EAr , where mAr is the mass of an argon atom. The force on the particle in the beam direction is then F= dp/dt = N ∆p, where N is the number of ions striking the particle per unit time. The ion beam has current density J (ions per unit area per unit time), which is assumed to be uniform over the beam width w. Then if the cross section of the particle is its physical cross section, N = πrp2J if rp is the particle radius. We can then write the acceleration of the particle, a, along the beam direction as a = F/mp, where mp = 4πrp3 ρp/3 is the particle mass, and ρp is the particle density. Now V|| = a∆t, where ∆t = w/V⊥ is the time the particle spends in the beam. Combining, this gives:

θ = arctan(

3wJ 2mAr EAr 4 r ρν ⊥ 2

)

Using this model, and the additional acceleration due to gravity since the test particles entered the beam from above, the theory fits the data with an error of about a factor of 1.5 in the particle size or about 10° in the deflection angle (Fig. 3). The error could be explained by a number of factors, such as a tendency for clusters to break up in the beam, loss of some ion energy to particle heating rather than particle kinetic energy, or a difference between the ion-particle scatter cross section and the physical cross section [22]. The model could be improved by taking these factors into account and writing the full equation of motion, but since the experiments themselves were limited by the rather crude particle sources, we have reserved this for future work. Nevertheless, the result shows that particle entrainment by the ion beam can be understood quantitatively (at least for these particle cluster sizes) in terms of ion drag and gravity. The largest force not taken into account in this model is probably electrostatics. The background gas pressure is too low (1 × 10–4 Torr) for a strong contribution

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of neutral drag, and the temperature gradients in the chamber are too weak (the experiments are too short for the target to heat to more than ~ 50°C) for a strong contribution due to thermophoresis. The electrostatic force is the most difficult to model, because both the electric field and the charge on the particle must be known, but both are difficult to measure or estimate in a plasma environment. A charge of 104e on a 0.5 µm particle would give a force comparable to the ion drag force (~ 5 × 10–14 N) if a field of 10 V/m was present. A detailed model of electrostatics and ion drag [21] for micrometer-size particles trapped in a highpressure glow-discharge plasma (about 500-times higher pressure than that in our experiments) finds that particles settle in traps where ion drag balances the electrostatic force. A similar model comparing ion drag to electrostatics in highdensity ECR plasmas finds that ion drag dominates electrostatics by a factor of 100, even for a particle charge of 300e, because of the high ion flux in ECR systems. Since the ion-beam deposition chamber is designed to maximize ion flux, and uses an electron source to neutralize the ion beam and to lower the electric field, it is plausible that ion drag dominates in this case as well. But to adapt these models to the conditions of this study requires knowledge of the plasma conditions beyond the scope of this work. A study by Poppe et al. [24] on charging of micrometer-size particles during collisions with hard surfaces found that charging was approximately proportional to the kinetic energy of the particles at impact, and a few hundred elementary charges could be acquired at velocities of 1020 m/s. Thus electrostatic forces from collision charging are not expected to be larger than those already present from charging by the plasma. By this model, ion drag would accelerate a 0.5 µm particle to V ≈ 10 m/s before it reaches the target, if it originates at the ion source with zero starting velocity. Particle bounce has been observed at 0.4-2 m/s by numerous authors [25–30] and reviews of bounce and adhesion models have been given by John [30] and Busnaina [31]. For a given particle material and size, there is a critical velocity above which a spherical particle will probably bounce. For non-spherical particles, this velocity boundary is less sharp, with the probability of bounce tending to a constant value independent of velocity [27]. For 0.5 µm SiO2 spheres striking smooth Si, the critical velocity has been measured at 1-3 m/s by Poppe et al. [27]. Therefore, the test particles in this experiment have sufficient velocity to bounce off the target wafer toward the mask wafer. This gives an explanation of the results in Fig. 4 – with the ion beam on, test particles crossing the beam were swept toward the target wafer, and a fraction bounced to the mask wafer. Meanwhile, with the beam on, fewer particles were able to cross the beam axis and reach the “hide” surface by other bounce routes across the region behind the particle seeder. A more detailed model is needed to test whether these particle levels are consistent with a reasonable initial velocity distribution from the shaker source, and also whether the particle distribution on the test wafers is consistent with particle motion determined only by momentum entrainment and bounce. Work on this is in progress.

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More evidence of bounce is found in the aerosol injection experiments (Fig. 5). At the orifice the gas bearing the test particles in suspension passes from atmospheric pressure to a vacuum of 4 × 10-4 Torr. It is well known that with such a large pressure drop, gas flow at the orifice is choked. In a choke flow, the flow rate is limited by gas momentum transfer, and the gas velocity reaches Mach 1, or about 320 m/s for argon. The pressure in the orifice throat is ~ 1 atm. The viscous-drag stopping distance [32] for a 0.5 µm particle in Ar at 1 atm is ~ 0.6 mm, comparable with the thickness of the orifice plate. Since the stopping distance is also the distance needed to accelerate an initially-stationary particle to the surrounding gas velocity, we can expect the particles to accelerate to the full velocity of the gas in the orifice, and enter the chamber at V ~ 320 m/s. When the particles strike the target wafer, their velocities far exceed the critical velocity and they will certainly bounce. The particles are almost unimpeded by the surrounding gas, since the stopping distance at the chamber pressure of 5 × 10–4 Torr is ~ 300 m. Based on measurements by Poppe et al. [27] of the fraction of kinetic energy retained after bounce for similar spheres hitting a silicon wafer, we can stimate that a 300 m/s particle will make at least 5 bounces before it slows down to about 1 m/s and sticks. The number of bounces will be higher if some impacts are at glancing incidence (less than 30° from the surface), since the particle retains more of its energy in this case [28]. After many bounces, particles are at random positions around the chamber, and are striking all chamber surfaces like molecules of an ideal gas. The even distribution of particles throughout the chamber is also supported by the particle density found on the Si wafers. If the particles end up randomly distributed over the inner surface of the chamber, the particle density on the wafer should be reduced by the ratio of the total surface area of the chamber to the area of the wafer, or about 60-fold. The experimental result was a particle density about 45-times lower than the value expected from the known output of the aerosol generator. The discrepancy may result from a tendency of slower particle to settle on horizontal surfaces under the force of gravity. No horizontal test wafers were used in the experiment. When the pressure is raised, the surrounding gas slows down the particles, and the stopping distance becomes comparable with the chamber dimensions. For illustration, stopping distances at the four pressures used are shown in Fig. 6 along the horizontal axis. With the short stopping distance, the particles are slowed to near the sticking velocity before they impact the main wafer. Under such conditions, the particle density is 45-times higher on the main wafer (indicating that almost all the particles stick there) and only a few particles are found on the hide wafer. The test particles in Fig. 5, which are known to be traveling at about 300 m/s, make at least 5 bounces. But the same test particles injected into the ion beam at lower velocity (and “native” particles as well) stop mostly on the first surface (the target wafer), with only 3-10% bouncing off the target wafer, then sticking to the second surface (the mask wafer). This implies that the particles in the ion beam are travelling much slower than 300 m/s, and our model of entrainment by the

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beam predicts velocities near 10 m/s. However, an improved experiment (with more controlled particle injection) and a more complete model are needed in concert to fully understand particle transport in ion beam sputtering. It is also important to conduct similar injection experiments with non-spherical particles, since the sticking probability and energy retained were found to be very different for spheres and non-spheres by Poppe et al. [27]. 5. CONCLUSIONS

We have measured particle transport by ion beams in sputter coating chambers by collecting process-produced particles on clean Si wafers, and found that the ion beam carried a stream of particles with it that deposited on the sputter target. Test spheres injected deliberately into the beam were either deflected along the beam direction or were fully entrained in the beam, depending on their size and initial velocity. Some of these spheres apparently reflected from the target and reached other surfaces in the chamber. A model of particle transport including the momentum of the ion beam and gravity reasonably explains the results for 5-50 µm clusters of 1.5 µm test particles, and is qualitatively consistent with results for 0.5 µm particles. The results suggest that the ion beam itself is a key actor in particle transport in ion-beam sputter systems, and this effect must be considered in any effort to build a low-particle IBS process tool. Particles traveling hundreds of meters/s will bounce many times from chamber walls in a low-pressure (~ 10–4 Torr) environment, and can reach any point in the chamber. Slower particles stick on the first or second impact, as predicted by existing theory of particle bounce. Measuring particle counts on witness wafers placed in the ion beam and around the chamber can be a valuable diagnostic for understanding particle motion. Very simple particle seeding methods can allow initial diagnosis of basic transport paths, though a sophisticated particle source allowing control of particle velocity is needed for a rigorous experiment. REFERENCES 1. J. Canning, in: Attendee Survey. Next Generation Lithography Workshop, International Sematech, August 28-30, 2001, Pasadena, CA. pp. 6-10 at: http://www.sematech.org/public/resources/litho/ngl/ng10901/2001%20WS%20Final%20Report%202.pdf

2. 3. 4. 5. 6. 7.

(2001). W.J. Yoo and C. Steinbruchel, Appl. Phys. Lett. 60, 1073-1075 (1992). G.S. Selwyn, C.A. Weiss, F. Sequeda and C. Huang, J. Vac. Sci. Technol. A 15, 2023-2028 (1997). R.M. Roth, K.G. Spears, G.D. Stein and G. Wong, Appl. Phys. Lett. 46, 253-255 (1985). G.M. Jellum, J.E. Daugherty and D.B. Graves, J. Appl. Phys. 69, 6923-6934 (1991). G.S. Selwyn, K.L. Haller and E.F. Patterson, J. Vac. Sci. Technol. A 11, 1132-1135 (1993). G.S. Selwyn, C.A. Weiss, F. Sequeda and C. Huang, Thin Solid Films 317, 85-92 (1998).

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8. T. Fujimoto, K. Okuyama, M. Shimada, Y. Fujishige, M. Adachi and I. Matsui, J. Appl. Phys. 88, 3047-3052 (2000). 9. S.G. Geha, R.N. Carlile, J.F. O’Hanlon and G.S. Selwyn, J. Appl. Phys. 72, 374-383 (1992). 10. B.M. Jelenkovic and A. Gallagher, J. Appl. Phys. 82, 1546-1553 (1997). 11. K.S. Kim and M. Ikegawa, Plasma Sources Sci. Technol. 5, 311-322 (1996). 12. M. Shiratani, T. Fukuzawa and Y. Watanabe, IEEE Trans. Plasma Sci. 22, 103-109 (1994). 13. S.J. Choi, D.J. Rader and A.S. Geller, J. Vac. Sci. Technol. A 14, 660-665 (1996). 14. T.J. Sommerer, M.S. Barnes, J.H. Keller, M.J. McCaughey and M.J. Kushner, Appl. Phys. Lett. 59, 638-640 (1991). 15. H.C. Kim and V.I. Manousiouthakis, J. Appl. Phys. 89, 34-41 (2001). 16. P. Bliokh, V. Sinitsin and V. Yaroshenko, Dusty and Self-Gravitational Plasmas in Space, Kluwer Academic Publishers, Dordrecht (1995). 17. P.K. Shukla, Phys. Plasmas 8, 1791-1803 (2001). 18. D. Winske, Revista Mexicana de Astronomia y Astrofisica 7, 1-6 (1998). 19. D.A. Brown, P. Sferlazzo, S.E. Beck and J.F. O’Hanlon, J. Appl. Phys. 71, 2937-2944 (1992). 20. D.J. Rader and A.S. Geller, Particle Transport in Parallel-Plate Reactors, Sandia National Laboratory, Report # SAND99-1539 (1999). 21. J.E. Daugherty and D.B. Graves, J. Appl. Phys. 78, 2279-2287 (1995). 22. M.D. Kilgore, J.E. Daugherty, R.K. Porteous and D.B. Graves, J. Vac. Sci. Technol. B 12, 486493 (1994). 23. M.S. Barnes, J.H. Keller, J.C. Forster, J.A. O’Neill and D.K. Coultas, Phys. Rev. Lett. 68, 313316 (1992). 24. T. Poppe, J. Blum and T. Henning, Astrophys. J. 533, 472-480 (2000). 25. S. Wall, W. John, H.C. Wang and S.L. Goren, Aerosol Sci. Technol. 12, 926-946 (1990). 26. B. Dahneke, J. Colloid Interface Sci. 51, 58-65 (1975). 27. T. Poppe, J. Blum and T. Henning, Astrophys. J. 533, 454-471 (2000). 28. R.M. Brach, P.F. Dunn and X.Y. Li, J. Adhesion 74, 227-282 (2000). 29. L.N. Rogers and J. Reed, J. Phys. D: Appl. Phys. 17, 677-689 (1984). 30. W. John, Aerosol Sci. Technol. 23, 2-24 (1995). 31. A.A. Busnaina, J. Adhesion 51, 167-180 (1995). 32. W.C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles, Wiley, New York, NY (1999).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 77–128 Ed. K.L. Mittal  VSP 2003

Particle deposition from a carry-over layer during immersion rinsing WIM FYEN, ∗,† KAIDONG XU, RITA VOS, GUY VEREECKE, PAUL MERTENS and MARC HEYNS IMEC, Kapeldreef 75, B-3001 Leuven, Belgium

Abstract—In this work the deposition of submicrometer-sized particles from a carry-over layer onto a substrate being rinsed is investigated. The particles used are 80 nm spherical colloidal silica particles, the substrates are thermal oxide, chemical oxide on silicon and silicon nitride. This paper focusses only on stagnant solutions. Two mechanisms are proposed by which particles can deposit: (i) adsorption during immersion and (ii) evaporative deposition during drying. The latter is caused by the evaporation of liquid, leaving the particles on the surface as a drying residue. In a first series of tests the particle deposition after immersion in a stagnant particle suspension is determined. When the net particle–substrate interaction is strongly repulsive at the pH of this suspension, only evaporative deposition takes place. In the opposite case, i.e., when the particle–substrate interaction is strongly attractive, diffusion limited adsorption takes place. By comparing the experimental data with theoretical models for both extreme conditions we can determine the pH regions where attraction or repulsion between the particles and the surface is dominant. In a second series of tests, the immersion in a particle suspension is followed by a stagnant rinsing step. In that case particle adsorption can also take place during immersion in the rinsing liquid. If the pH values of the particle suspension and rinsing liquid are different, the pH in the vicinity of the substrate (inside the carry-over layer) changes during the rinsing step from the pH of the particle suspension until the pH of the rinsing liquid is obtained. This process is denoted as the pH shock, and an analytical model to calculate it is derived in this paper. Using the relation between particle–substrate interactions and pH (obtained in the first series of tests) together with the calculation of the pH shock, a model is developed to predict particle adsorption during stagnant rinsing. This is done for each substrate separately. The resulting models are experimentally verified by performing tests where a particle-adsorption step at very low pH (0.2) is followed by a rinsing step in neutral water. For all three substrates, a satisfactory agreement between experimental results and theoretical models is observed. Keywords: Diffusion; adsorption; evaporation; particle; rinsing; immersion.

1. INTRODUCTION

The adhesion and removal of small particles on substrates is extremely important in many industrial applications [1, 2]. In some cases adhesion is desired (e.g., ∗ To whom all correspondence should be addressed. Phone: +32(0)16281530,

Fax: +32(0)16281315, E-mail: [email protected] † Also part of the Electrical Engineering Dept. of the Catholic University Leuven, Belgium.

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copiers, filtration units, coatings), but for many applications particles are considered to be contaminants that must be removed in order to improve process yield and performance. Removal of particles is generally performed in a liquid medium. This is due to the fact that in a liquid the adhesion force between the particles and the surface is significantly lower than in vacuo or air and, hence, removal is likely to be easier. A consequence of working in a liquid medium, however, is that the cleaning liquid must be removed from the substrate. This is done in a rinsing step where the process liquid is replaced with another, more dilute, rinsing liquid. The latter is eventually removed from the substrate in a drying step. Although much effort is typically spent on the optimization of the actual cleaning step, little effort is put into the rinsing step. Often one simply assumes the rinsing step to be particleneutral, i.e., neither adding or removing extra particles. We shall show that this is not necessarily the case. For critical applications — where final particle levels on the surface must be kept minimal — it is, therefore, crucial that the rinsing step is optimized together with the cleaning step. One of these critical applications is the manufacturing of integrated circuits. Because the typical dimension of their smallest components is of the order of 70 nm, unwanted particles — even as small as a few tens of nanometers — can result in device failure. In this work we have investigated the rinse process in detail for a few substrates commonly used in the semiconductor industry. We focus on the case of particle deposition during rinsing as a result of liquid carry-over from the process tank. Because we are interested in obtaining analytical models that can help in process optimization, all tests have been performed in stagnant liquids. Because for a flowing suspension a boundary layer close to the surface will develop, all phenomena that take place within this boundary layer will not deviate much from the tests in stagnant liquids. As such, the resulting models describing particle deposition can also be used in a qualitative manner for systems of relatively low flow velocity (in the order of mm/s). This is not the case for the pH shock calculations, because the typical diffusion length of the H+ -ions can become comparable to the thickness of the boundary layer and, hence, the velocity profile can significantly influence the pH variation. In Section 2 we will describe the experimental procedure and present details on the materials and process tools used in the course of the experiments. Because the pH of the suspension is the most important parameter determining the particle–substrate interaction we will investigate how the pH correlates with particle adsorption. This will be done in Section 4 by comparing analytical models for particle adsorption and experimental data. Once this correlation is known, we can investigate particle adsorption under transient pH conditions, which can take place during rinsing. First, we will calculate how fast the pH will change as a function of rinse time. Next, we will use the correlation between pH and deposition rate to predict particle deposition in the transient pH case. It will be shown that depending on the way the interaction energy changes with pH, different types of behaviors are possible. Theoretical

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models of the different possibilities will be given and compared with experimental results.

2. EXPERIMENTAL

2.1. Dip tests 2.1.1. General description A schematic description of the procedure used in this work is depicted in Fig. 1. Samples were first dipped in a suspension containing a certain concentration C0 of submicrometer-sized particles. After a given time they were transferred to a tank containing rinsing liquid (note that in some tests the rinse step was omitted). Although no particles were deliberately added to the rinsing liquid they could enter the rinse tank via the so-called carry-over layer. This is a thin layer of processing liquid that is entrained with the substrate as it leaves the processing tank. Typical thickness values of this layer are on the order of 20 µm for aqueous suspensions [3]. In practice this value depends on withdrawal speed and post-withdrawal drainage [4, 5] but from rinse tests we can derive that for our experimental system the thickness was of the order of 23-26 µm (see Section 4.2.3). In the next step, the substrates were removed from the rinsing tank and dried. Finally, the surface concentration of particles was determined by an appropriate inspection technique. 2.1.2. Details of the procedure Silicon wafers (covered with a surface layer of interest, see Section 2.2) were manually cut to obtain rectangular pieces of approximately 2 cm by 3 cm. These pieces were attached to a PFA (perfluoro alkoxy) holder and dipped in 100 ml beakers containing either the particle suspension or the rinsing liquid. During immersion into and withdrawal from the particle suspension or rinsing solution the sample was held vertically. When the substrate was fully immersed in the liquid,

Figure 1. Schematic description of the experimental procedure used in this work.

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the holder was fixed to a laboratory stand to keep the sample in the same position in the beaker. The drying step consisted of a nitrogen blow dry. This was done by holding a nitrogen gun at an angle of approximately 45 degrees and blowing in a single pass from one edge of the sample to the other. The total drying time for this procedure was a few seconds. After this step residual droplets at the edge of the sample (coming from the sample backside or from the contact points with the tweezers) were evaporated by directing the nitrogen gun perpendicularly at the center of the wafer piece. In this way the nitrogen flow from the center of the piece to the edge prevented these residual droplets from reaching the center of the piece. 2.1.3. Surface inspection The particle-surface concentration was determined from Scanning Electron Microscope (SEM) micrographs using a manual counting procedure. As the SEM inspection contains information only on a very local scale (in the order of a few µm2 ) a statistical averaging procedure was used. First of all, for each sample four SEM micrographs were taken in the central region, separated by a few mm, which is significantly larger than the field of view of the SEM. Furthermore, particles were counted on four different locations on each micrograph. The final particle surface density was calculated as the average of these 16 values. After an extensive study on multiple samples it was found that the relative standard deviation of this averaging procedure was always below 10%, provided that the total surface concentration remained within a certain range (roughly between 0.25 and 50 particles/µm2 ). When total particle levels are too low, there are not enough particles within each field of view of the SEM micrographs and consequently the error bars increase significantly. For particle levels approaching monolayer coverage the counting procedure becomes too unreliable and, furthermore, inter-particle effects are likely to influence the process. The particle dilution was, therefore, optimized to yield a final surface concentration within the proposed range. 2.1.4. Particle dilution All particle suspensions were prepared the day of use, in order to avoid aging effects. This procedure consisted of diluting the necessary amounts of concentrated stock suspension (containing approximately 6.5×1014 particles/cm3 , see Section 2.2.2). Because relatively small volumes were used in each test — typically 1001000 µl of stock suspension — deviations in the actual particle concentration can arise. Possible causes are uncertainties in the calibration of the micro-pipettes or inaccuracies in the pipetting procedure. Moreover, the actual particle concentration in the stock suspension itself was based on indirect measurements (see Section 2.2.2). In a repeatability study it was indeed found that the results from dip tests performed in the same suspension agreed better with each other than from tests performed in different suspensions. To minimize this effect, dip tests belonging to the same type of experiment were grouped together and performed in the same suspension. In this way, variations related to the actual particle concentration will be

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systematic for the entire series of tests performed in that dilution. Furthermore, each experimental graph was normalized. This was done by including a test condition where the particle–substrate interaction was expected to be strongly attractive as a reference. For this reference test condition particle adsorption followed a diffusion limited behavior. By fitting an appropriate analytical model (see Section 4.1.2) to experimental results of the reference condition the actual particle concentration could be extracted. This concentration was used to normalize all data points obtained from tests performed in the same particle suspension. It was found that the variation related to the concentration was of the order of 10%, which was still comparable to the variation resulting from the SEM counting procedure. For tests where this procedure could not be used we could still draw qualitative conclusions reliably. 2.2. Characterization of materials 2.2.1. Chemicals The water used in all experiments was ultrapure water (UPW) with a conductivity of 0.055 µS/m (or resistivity of 18.2 M
· cm). The pH of the solutions was adjusted with 37% ultrapure hydrochloric acid (HCl) from Ashland Chemical with a purity of 1 ppb of metals. 2.2.2. Silica spheres Spherical colloidal silica (SiO2 ) particles of 80 nm nominal diameter were obtained from H.C. Starck (Leverkusen, Germany). They were delivered in a stock suspension of approximately 30 w% at a pH of 1.8. An SEM micrograph of these particles is shown in Fig. 2. From this micrograph (and from other micrographs that are not shown in this report) the size distribution was determined by measuring the diameter of several tens of particles. The average value and standard deviation were 78.4 ± 9.7 µm [59]. By a gravimetric method the solids content was measured to be 32.1 w%. Taking the density of SiO2 as 1.96 g/cm3 we calculated the parti-

Figure 2. SEM micrograph of 80 nm spherical silica particles.

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cle concentration (assuming a monodisperse distribution) as 6.5×1014 particles/cm3 [59]. 2.2.3. Substrates The wafer pieces were cut from 200 mm <100> silicon wafers (Wacker Siltronic) covered with a layer of silicon nitride or silicon dioxide. Before each experiment the substrates were precleaned using the IMEC-Clean procedure [6]. This procedure consists of an oxidizing step (H2 O2 /H2 SO4 at 90◦ C) to remove organic contamination, followed by a dilute HF etch step to remove particulate contaminants and a low-pH HCl rinse to reduce metallic contamination. The wafers were then rinsed in water saturated with ozone (O3 , 10 ppm) and dried in a Marangoni dryer. The entire preclean procedure was performed in an automated wetbench (Steag/Microtech). Silicon nitride. Silicon nitride (Si3 N4 ) was deposited using a Low Pressure Chemical Vapor Deposition (LPCVD) step using silane and ammonia as precursor gases. The thickness of this layer was around 150 nm. To avoid interfacial stress between the nitride layer and silicon substrate — due to a mismatch in lattice constants — a thin pad (10 nm) oxide was deposited before nitride deposition. Thermal oxide. Thermal oxide layers were grown on the silicon wafers using a wet oxidizing step (i.e., using H2 O as the source of oxygen) at temperatures between 900 and 1000◦ C. During the experiments wafers from two different batches (100 nm and 500 nm thickness) were used. CVD oxide. Chemical Vapor Deposited (CVD) oxide layers were obtained using tetraethyl orthosilicate (TEOS) as a precursor. Densified TEOS wafers were prepared by subjecting the wafers to a thermal treatment at 300◦ C for 10 min. Wafers from batches containing 100 nm and 200 nm TEOS were used in the experiments. Chemical oxide. A chemical oxide was obtained on bare silicon wafers by performing the IMEC-clean sequence [6]. During the ozonized rinse a thin oxide layer (thickness between 5 and 10 Å [7]) is grown on the silicon surface. These surfaces are commonly denoted as “ozone-last” surfaces, referring to the final contact with ozone. 2.2.4. Electrokinetic potentials For the particles the zeta potential was measured by electrophoretic light scattering, performed in a PSS Nicomp zeta potential analyzer (Model 370) using a 632 nm HeNe laser. The sample volume was 2.8 ml. For the substrates the streaming potential was measured in 10−2 M KNO3 . The pH of the solutions was adjusted by adding appropriate amounts of HCl and KOH. The corresponding electrokinetic potentials are plotted as a function of the pH of the solution in Fig. 3. For the particles one can see that the isoelectric point (IEP) is below 3 (since at pH 3 the surface is still negatively charged). For the SiO2 surfaces the IEPs are in the range

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Figure 3. Electrokinetic potential for SiO2 particles, chemical and thermal oxide surfaces, and silicon nitride surface.

2-4, which is typical for silica surfaces [8]. For the silicon nitride the IEP is around 5, in agreement with previous studies on nitride surfaces [9].

3. THEORETICAL BACKGROUND

3.1. Surface forces When two surfaces come into close proximity, they will exert different types of forces on each other. These forces are commonly referred to as surface forces [10]. The two most extensively studied surface forces are the electrostatic and the van der Waals forces. They form the basis of the well-known DLVO theory. With this theory the stability of many colloidal systems can be described. Experimental evidence exists that for some surfaces, such as silica, additional short range forces must be taken into account [8, 10– 12]. Because the experimental results from this work do not allow a quantitative description of these surface forces we shall not investigate them in great detail. However, because in this work the pH is considered to be an important variable it is instructive to discuss the possible effects of pH on these surface forces. 3.1.1. Electrostatic interactions Origin. Electrostatic interactions arise due to the overlap of the double layers of ions surrounding charged surfaces. The surface charge can be the result of (i) dissociation of surface groups, or (ii) specific adsorption of ions from solution [11]. The potential in the double layer decays exponentionally with the distance from the surface: Ψ (x) ≈ Ψ0 e−κx ,

(1)

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Table 1. Debye–Hückel inverse double layer constant (κ −1 in nm) for different concentrations (M) of a 1-1 electrolyte Concentration (M)

κ −1 (nm)

10−7 10−5 10−3 10−1

951 95.1 9.51 0.95

where Ψ (x) is the potential at a distance x, Ψ0 the surface potential and κ the inverse Debye–Hückel length defined as
kT −1 , (2) κ = 8π e2 I where  is the liquid permittivity, k the Boltzmann constant, T the absolute temperature, e the elementary charge and I the ionic strength of the solution. The calculation of the interaction energy between two bodies requires the solution of the non-linear Poisson–Boltzmann equation, which can only be done numerically for a spherical particle and a flat substrate [13]. Various approximate solutions exist, derived for cases of low surface potential [14– 17]. However, for this study it suffices to know that κ −1 is a characteristic distance over which electrostatic forces operate. Effect of pH. A first effect of the pH on electrostatic interactions is due to the change in ionic strength of the solution. From equation (2) one can see that κ −1 will decrease with increasing ionic strength. Some values of κ −1 for different values of the ionic strength of a 1-1 electrolyte are given in Table 1. One can see that in aqueous solutions the influence of the electrostatic forces can range as far as 1 µm. Increasing the ionic strength of the solution will significantly reduce this distance. A second effect of pH is due to the change in surface potential of the surfaces involved in the interaction. As shown in the electrokinetic potential results in Section 2.2.4, the surface potential for the materials used in this study increases as the pH of the solution is lowered. At very low pH, the surfaces are positively charged while at very high pH the surfaces bear a net negative charge. At the extreme end of the pH ranges electrostatic repulsion is, therefore, expected. In intermediate pH ranges — when two different materials are oppositely charged — electrostatic attraction is expected. 3.1.2. Van der Waals interactions Origin. In contrast to the electrostatic interactions, van der Waals interactions can be described as electrodynamic interactions. They arise from the overlap of electromagnetic fields surrounding each molecule. The origin of these electromag-

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netic fields lies in the transitory fluctuations in charge that are the result of thermal agitation or uncertainties in the positions and momenta of electrons and atomic nuclei [18]. Between two molecules the interaction evdW is found to decay with the inverse of the sixth power of the distance C (3) r6 where C is a constant containing the necessary molecular physical parameters describing dipole–dipole (=Keesom), dipole–induced dipole (=Debye) and induced dipole–induced dipole (=London) interactions. For macroscopic bodies the combined effect of all electrodynamic interactions between their constituent molecules can extend up to distances significantly longer than molecular dimensions (on the order of 100 nm). In the microscopic approach — due to Hamaker [19] — these interactions are assumed to be pairwise additive. By integration one can calculate the total interaction energy for arbitrary bodies. However, for larger separation distances ( 10 nm) retardation effects become important and equation (3) tends to an inverse seventh-power relationship. As a result various equations have been proposed for specific geometric constraints. For our purpose it suffices to know that the total interaction energy between a sphere and a flat plate is inversely proportional to the distance for small separations and tends to an inverse square dependence for larger separations. This is illustrated by the approximate equation proposed by Gregory [20], giving the van der Waals interaction energy for a sphere of radius R at a distance of closest approach h from a flat surface as: evdW = −

EvdW,ret = −

A132 R 1 6h (1 + 14 λh ) ret

(4)

where λret is a characteristic length when retardation becomes important, typically taken to be approximately 100 nm and A132 is the Hamaker constant for materials 1 and 2 interacting across a medium 3. In the additive approach A132 can be calculated from the density of the materials. For dense bodies the assumption of pairwise additivity is not valid. In the so-called macroscopic approach — initially due to Lifshitz — quantum field techniques were used to solve Maxwell’s equations for a system of infinite slabs separated by vacuum. This approach was later refined by Dzyaloshinskii, Lifshitz and Pitaevskii (DLP) to include the effect of non-vacuum interlayers [21]. In this way all information for the electrodynamic fluctuation fields is taken from the dielectric frequency spectrum of the materials, (ω). The complicated mathematics involved, however, makes this approach useful for studying planar geometries only. Because most of the uncertainty in the microscopic approach is due to the calculation of the Hamaker constants [22], one often resorts to a hybrid approach. The Hamaker constant is then calculated using the macroscopic approach and used in the expressions obtained by pairwise addition to account for the system’s

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Table 2. Non-retarded Hamaker constants A132 for different dielectric materials, interacting across vacuum (A1V2 ) and water (A1W2 ) in 10−20 J Material 1: Material 2: SiO2

Si3 N4

A1V2

SiO2 A1W2

A1V2

Si3 N4 A1W2

7.59a 6.55b 6.5c

0.63a 0.849b 0.83c

12.1a 10.8a

2.07a 1.17a

17.3a

5.13a

a From Bergstrom [23]; b from Hough and White [24]; c from Israelachvili [11].

geometrical configuration. In this way the Hamaker constant is calculated as an infinite sum of different frequency contributions, based on full spectral data of the constituing materials. In a slightly simplified form this can be written as   ∞  3kT   1 (iξn ) − 3 (iξn ) 2 (iξn ) − 3 (iξn ) (1 + rn ) · e−rn (5) A132 (h) ≈ 2 n=0 1 (iξn ) + 3 (iξn ) 2 (iξn ) + 3 (iξn ) where the prime denotes that the (n = 0) term must be divided by a factor of two. Furthermore ξn = (2π kT /h¯ )n (with h¯ Planck’s constant divided by 2π ) and rn is the ratio of travel time of a signal √ of frequency ξn across a distance h and back to the period of the signal: rn = 2h 3 (ξn )ξn /c. As an illustration, Table 2 gives a list of non-retarded Hamaker constants for two dielectric materials interacting in vacuo (A1V2 ) and in water (A1W2 ), calculated from their full spectral data [11, 23– 25]. The observed differences can be attributed to (i) the use of different sources of spectral data, (ii) differences in the mathematical equations used to solve the original Lifshitz equations and (iii) differences in the crystallography of the materials listed (e.g., SiO2 may refer to fused silica, amorphous silica or quartz, since the table serves as an indication only we refer to the original papers for details). Because the Hamaker constant is calculated as a difference of dielectric susceptibilities the van der Waals interaction is largely reduced when water is used as an interlayer instead of air or vacuum, as evidenced in Table 2. Effect of pH. According to the microscopic approach the pH does not influence the van der Waals interaction, because the Hamaker constant is not affected by a change in pH. In the macroscopic approach, however, the pH will have an effect through a change in ionic strength. Similar to the electrostatic interaction energy, the (n = 0) term in equation (5) will be screened by the ions in the solution (the higher frequencies are not screened because the ionic species cannot respond to high frequencies [11]). This corresponds to setting r0 equal to 2κh in equation (5) [22, 26]. Equation (5) can then be written as A132,nonret ≈ Aν=0 (1 + 2κh)e−2κh + Aν>0

(6)

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Table 3. Contribution of 34 kT to the total Hamaker constants A132 from Table 2 (in %). This is a good estimate of the contribution from the (n = 0) term in equation (5) Material 1: Material 2: SiO2 Si3 N4

with Aν=0

3kT = 4



SiO2 A1W2, ν=0 (%) A1W2

Si3 N4 A1W2, ν=0 A1W2 (%)

≈ 35-48 ≈ 14-26

≈ 14-26 ≈6

1 (0) − 3 (0) 1 (0) + 3 (0)



2 (0) − 3 (0) 2 (0) + 3 (0)



the contribution due to Keesom and Debye interactions, and   ∞  3kT  1 (iξn ) − 3 (iξn ) 2 (iξn ) − 3 (iξn ) Aν>0 = 2 n=1 1 (iξn ) + 3 (iξn ) 2 (iξn ) + 3 (iξn )

(7)

(8)

the contribution due to London dispersion forces. Equation (7) shows that the maximum contribution due to the zero-frequency term is 3kT , which is about 4 −21 J at room temperature. For vacuum systems this contribution can, 3 × 10 therefore, be neglected, but for aqueous systems where typical Hamaker constants are of the order of 1 × 10−20 J [27] (see, e.g., Table 2) the ionic strength of the solution will have a significant effect on the van der Waals attraction, since the static term is a large contributor to the total interaction. Because the static dielectric constants for the dielectrics listed in Table 2 are significantly smaller than the dielectric constant of water (SiO2 ≈ 3.82, Si3 N4 ≈ 7.4, H2 O ≈ 78 [23]) the static contribution is nearly 34 kT . Table 3 lists the contribution of 34 kT to the total Hamaker constant for the material combinations from Table 2. One can see that for the systems involving silica the contribution of the static terms is of the order of 30-50%. For example, for a high ionic strength solution the total van der Waals interaction for the silica/water/silica system is reduced by 50%. 3.1.3. Short range interactions Origin. Nowadays it is widely accepted that besides the electrostatic and van der Waals interactions other types of interaction can be important [10–12, 25, 28– 32]. Initially these interactions were denoted by the term “non-DLVO” interactions, because they had to be proposed in order to bring experimental results in agreement with the DLVO theory. With the introduction of sensitive techniques (such as the surface force apparatus and atomic force microcsope) these interactions could be measured directly. On molecularly smooth surfaces (such as cleaved mica) an oscillating force was observed with a period of 0.22-0.26 nm — approximately the diameter of a water molecule — superimposed on an exponentially decreasing force. On rougher surfaces short range repulsive interactions with an exponential

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decay length of 1 nm or less have been measured. Over the last decades some theoretical models have appeared that can explain this behavior [33– 36]. However, there is still no consensus on what the underlying mechanisms are. One hypothesis is that the polar water molecules are strongly oriented at surfaces that can form hydrogen bonds with them (such as silica). The possibility of this has been confirmed by Monte Carlo simulations. These also show that this effect can extend up to several (around 10) molecular diameters in the bulk liquid. When two surfaces approach each other, the disturbance of this oriented layer will result in a repulsive force, denoted as a structural force. A second hypothesis is related to ion-ion interactions when hydrated ions adsorb onto the solid surface and is often referred to as a hydration force. In spite of this difference in approach, literature agrees on the fact that the short range repulsive interaction energy (between two infinite plates) can be written as an exponentially decreasing function ESRR, = KE e

−λ

h SRR

(9)

where the pre-exponential factor KE is given in J/m2 and the decay length λSRR is given in m. Some authors have also suggested that the two mechanisms are quite different and both can operate simultaneously. In this case the expression for the SRR interaction will contain two exponential terms ESRR, = KE0 e

−λ

h SRR0

+ KE1 e

−λ

h SRR1

(10)

where λSRR0 is of the order of the diameter of a water molecule (0.17-0.3 nm [28]) and λSRR1 is of the order of 1 nm. Equations (9) and (10) are also often reported as an interaction force (instead of interaction energy). A simple integration then yields the corresponding pre-exponential terms: KFi = λi KEi with KFi in N/m2 . Table 4 summarizes reported values of the pre-exponential factors and decay lengths. To allow comparison we have converted the pre-exponential terms into Table 4. Literature results of parameters used in the equation describing short range interactions (equations (9) and (10) with KEi = KFi /λi ) Condition

KF0 (N/m2 )

λ0 (nm)

KF1 (N/m2 )

λ1 (nm)

water film on quartza (θ ≈ 0) water film on quartzb (fully hydroxylated) water film on quartzb (θ ≈ 10-20◦ ) force between glass and quartz rodsc water film on quartzd water interlayer between quartze AFM, between SiO2 sphere and surfacef

– – – – – – (2-3.5) ×108

– – – – – – 0.17-0.3

(1-2) ×106 2 × 108 1 × 107 1 × 105 9.94 × 106 1.4 × 106 (0.86-1) ×106

1 1.5 2 1 2.32 0.85 1.8-2.1

a Churaev and Derjaguin [30]; b Churaev [29]; c Derjaguin and Churaev [31]; d Derjaguin [10], p. 273; e Derjaguin [10], p. 277; f Dedeloudis [28].

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dimensions compatible with force interactions (i.e., in N/m2 ). Because the preexponential terms and decay lengths are based on experimental data from various origins (force–distance curves, disjoining pressure isotherms, etc.) there is quite a spread in the reported values. They clearly indicate, however, that the SRR effect can extend up to several nm into the bulk of the liquid and prevent the surfaces to come into real contact. Mathematically speaking, these interactions, therefore, define a distance of minimum approach H0 . Because the van der Waals attraction is inversely proportional to the distance, even a small increase in H0 will significantly reduce the attractive interactions between the particle and the substrate. Effect of pH. Literature data on the influence of liquid composition on short range interactions are scarce, and, moreover, often contradictory in nature. This controversy results from different authors proposing different mechanisms driving these short range interactions. In the papers where these interactions are correlated with the removal of the hydration layer of ions in the liquid interlayer, the repulsive interactions are predicted to increase with ionic concentration [37– 40]. In models where these interactions are correlated with the structuring of water molecules at the interface, a decrease of the repulsive interactions with ionic content [33] is predicted. This is because the presence of ions is believed to interfere with the formation of an oriented water structure. In reality both mechanisms may be acting simultaneously. Some models have indeed predicted both a decrease and an increase in short range repulsive forces with ionic strength, depending on the particular system under study [12, 35, 36]. Based on these observations it is, therefore, not possible to predict a priori how the pre-exponential constants KEi (and hence KFi ) and the decay lengths λi from equations (9) and (10) will change with the pH of the liquid. It is, however, possible that a change in pH will affect the short-range repulsive interactions [12]. 3.1.4. Total particle–surface interaction A plot of the interaction energy between a particle and a substrate as function of separation distance is given in Fig. 4 for a system of identically charged surfaces |Ψ | = 25 mV and Hamaker constant of 1 × 10−20 J, using KF = 1.5 × 106 N/m2 and λ = 0.8 nm. The ionic strength varies between 10−6 and 10−1 M. At low ionic strength, the electrostatic interaction dominates at large separation and creates an electrostatic barrier. It is well known that the height of this barrier determines the rate at which particles will deposit on the surface. At high ionic strength (and also at small separations) the SRR interactions and van der Waals interactions result in the presence of a primary minimum. The depth of this minimum will determine whether the particles are irreversibly bound to the surface or not. The exact shape of the curve — and also the depths and heights of the minimum and maximum — depends on the different parameters discussed in Sections 3.1.1, 3.1.2 and 3.1.3. These can only be determined reliably from direct force measurements. From indirect techniques such as monitoring the particle adsorption with time — which has been used in this work — one can only derive qualitative information regarding

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Figure 4. Plot of the interaction energy (in kT -units) between a spherical particle and a flat surface as function of the separation distance for different values of the ionic strength (between 10−6 and 10−1 M). Parameters used are: |Ψ | = 25 mV, A132 = 1 × 10−20 J, KF = 1.5 × 106 N/m2 and λ = 0.8 nm.

the interaction curve, such as the presence or absence of a minimum or barrier, and whether it is shallow or high. 3.2. Particle diffusion in the vicinity of a flat plate 3.2.1. Mathematical description Consider an infinite flat plate immersed in a liquid containing particles of radius R. → → If C(− r , t) represents the concentration of particles at position − r we can calculate the behavior of the ensemble of particles from the convective diffusion equation [41]   → → ∂C(− r , t) − DC(− r , t) − → → − → − → + v · ∇C( r , t) = ∇ · D∇C( r , t) − K (11) ∂t kT → − → where − v is the liquid velocity, D the particle diffusion constant and K the interaction force field acting on the particle which in our case can be written as − → K = −∇Φ

(12)

where Φ contains contributions from van der Waals interactions, electrostatic interactions and short-range interactions, as discussed in Section 3.1. We can calculate the average diffusion length x of the particles in a time-frame t as [42]:
Dt x = (13) π

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Using the Stokes–Einstein equation to calculate the diffusion constant D=

kT 6π Rη

(14)

we can see that for colloidal particles (of the order of a few tenths of a micrometer) x is significantly larger than the length scale over which the potential field operates (∝ κ −1 ). It has been shown that in this case equation (11) reduces to the Smoluchowski–Levich approximation [16] → ∂C(− r , t) − → → +→ v · ∇C(− r , t) = ∇ · (D∇C(− r , t)) (15) ∂t − → where the force field K is now included in the boundary conditions at the surface of the plate [16, 41, 43]. Since all our tests are performed in a stagnant solution the → → convective term − v · ∇C(− r , t) cancels. Equation (15) therefore reduces to Fick’s second law of diffusion which can be written in 1-dimensional form (because the dimension of the substrates used in this test is significantly larger than x ): ∂ 2 C(x, t) ∂C(x, t) =D ∂t ∂x 2

(16)

with x the distance perpendicular to the plate. Note that in our treatment we have assumed that the diffusion constant D is independent of position and concentration. 3.2.2. Mechanisms for deposition We can distinguish two different mechanisms by which particles present in a suspension can end up on an immersed substrate [44]: (i) as a result of adsorption during the immersion in the liquid and (ii) as a result of the drying step. The first contribution is a result of attractive interactions between the particle and the surface. The corresponding surface concentration due to adsorption can be written as σadsorption(t) where t denotes that particle adsorption is a function of time. The second contribution arises when the substrate is withdrawn from the suspension and dried. When liquid evaporation takes place during the drying step all non-volatile species present in the evaporated volume of liquid (such as suspended particles) will deposit on the substrate. This amount can be written as C evap (t)δevap with δevap the thickness of the liquid film that evaporates and C evap (t) the average concentration of particles in this film. Note that the value of this average concentration can vary with time as a result of rinsing. This contribution is referred to as evaporative deposition. The total surface concentration of particles σ (t) can then be written as the sum of both contributions [44], i.e., σ (t) = σadsorption(t) + C evap (t)δevap

(17)

If the concentration profile of particles C(x, t) is known we can easily calculate the contribution from the immersion step and from the drying step.

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Calculation of adsorption. The amount of particles (per unit area) that adsorbs during the contact with the suspension of particles can be calculated by integrating the particle flux J (x, t) at the surface over time:  t J (0, t  )dt  (18) σadsorption(t) = 0

where the flux J is defined as

 ∂C(x, t)  J (y, t) = −D · ∂x x=y

(19)

and where C(x, t) is the concentration profile of the particles. Calculation of evaporative deposition. The amount of particles (per unit area) that deposits as a result of liquid evaporation is given as C evap (t)δevap with C evap (t) the average concentration in the zone [0  x  δevap ]. This can be calculated as  δevap C evap (t)δevap = C(x, t)dx (20) 0

Although the right-hand side of equation (20) is mathematically more straightforward, we use the expression on the left hand side as the starting point because it reflects better the physical mechanism that is responsible for particle deposition. 3.2.3. Analogy between diffusion and heat conduction In order to obtain an analytical expression for C(x, t) we must solve Fick’s law of diffusion (equation (16)) for a variety of boundary conditions. Mathematically, this equation is equivalent to the equation of heat conduction ∂T (21) ∂t where T is the temperature and κtherm the thermal conductivity. For this equation many analytical solutions for a variety of boundary conditions are readily available [45, 46]. For 1-dimensional problems of heat conduction in infinite and semi-infinite media we can, therefore, easily extend the solutions to the field of particle diffusion problems by simply associating T (x, t) with C(x, t) and κtherm with D. κtherm ∇ 2 T =

4. PARTICLE DEPOSITION AFTER IMMERSION IN A STAGNANT LIQUID

In this section we investigate the deposition of particles onto a substrate immersed into a stagnant liquid. It has been shown that in the presence of electrostatic and van der Waals interactions particle adsorption can be mathematically described as a first-order irreversible reaction of rate constant kdep at the surface of the substrate [16, 41, 43]. This approach will be used in our theoretical treatment to calculate the amount of particles that adsorbs during immersion, σadsorption, for systems with

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very high, intermediate or no electrostatic barrier. For a correct interpretation of experimental data we must also calculate particle deposition as a result of the drying step used in the experimental procedure, i.e., C evap (t)δevap . In the first series of tests particle deposition on a surface for different pH values was determined. From a comparison between experimental and theoretical results we could distinguish pH ranges where the particle and the surface repelled or attracted each other. In the next series of tests a short rinse followed the deposition step. In this way we could check whether the particles were irreversibly bound after their adsorption to the surface. This will give us information on the depth of the primary minimum and provide us with indirect evidence of short-range repulsive forces. 4.1. Theoretical models for particle adsorption and evaporative deposition 4.1.1. Case of a very high electrostatic barrier In the case of very strongly repulsive interactions (typically for barrier heights larger than 10kT [43]) it has been found that the particle adsorption is so strongly reduced that it can no longer be measured experimentally. For these conditions we will, therefore, assume that no adsorption occurs, hence the concentration profile will be C(x, t) = C0 (t > 0)

(22)

Calculation of adsorption. Evidently, equation (22) implies that the flux is zero at all times, hence for this case we can write σadsorption(t) = 0 (t > 0) Calculation of evaporative deposition. tion (20) yields:

(23)

Substitution of equation (22) into equa-

σevaporation(t) = C0 δevap (t > 0)

(24)

Equation (24) permits us to calculate the thickness of the evaporated liquid film during nitrogen blow off. 4.1.2. Case of negligible electrostatic barrier This case corresponds to (i) strongly screened electrostatic interactions, (ii) attractive electrostatic interactions, or (iii) no electrostatic interactions at all (e.g., surface is at its IEP). In his fast coagulation theory Smoluchowski [47] solved this case by assuming the rate constant for adsorption to be infinitely high. Correspondingly all particles that reach the surface become irreversibly bound to it, hence C(0, t) = 0 (t > 0)

(25)

In the literature this is often known as the perfect sink boundary condition. In order to solve equation (16) together with equation (25) we use the approach described in Section 3.2.3 based on the heat conduction equation. From the temperature profile

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Figure 5. Normalized concentration profiles C(x, t)/C0 of a particle with diffusion constant of 5.4 × 10−12 m2 /s irreversibly adsorbed on a surface at x = 0, calculated from equation (26).

in a semi-infinite plate at initial temperature T0 with its boundary at x = 0 kept at zero we can calculate the corresponding particle concentration profiles as [45, 46]   x (26) C(x, t) = C0 erf √ 4Dt with erf(x) the error function defined as 2 erf(x) = √ π



x

e−y dy 2

(27)

0

To illustrate the diffusion process we have plotted the concentration profiles from equation (26) for a 80 nm particle (with diffusion constant of 5.4 × 10−12 m2 /s calculated from equation (14)) in Fig. 5 for different time intervals. Note that the concentration profiles are normalized with respect to the initial concentration, i.e., C(x, t)/C0 . Calculation of adsorption. Because the rate constant for adsorption is infinity, diffusion of particles to the surface is the rate limiting step. The flux of particles to the surface can, therefore, be calculated by the Cottrell equation, describing the limiting current to a planar electrode under diffusion control [48].
D (28) J (0, t) = C0 πt The same equation has been obtained for diffusion of small particles to flat collector surfaces [16]. Integrating equation (28) with respect to time we obtain
Dt (29) σadsorption(t) = 2C0 π Equation (29) shows that under diffusion limitations the particle surface concentration increases with the square root of time. Note that we have assumed that the already adsorbed particles exert no influence on the diffusion process. This is

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true only for low particle surface densities, i.e., significantly lower than monolayer coverage. For larger surface concentrations more elaborate models taking into consideration surface blocking effects must be used [16]. Calculation of evaporative deposition. From equation (20) we can calculate σevaporation(t) by integrating equation (26) over the evaporated thickness:    δevap x dx (30) σevaporation(t) = C0 erf √ 4Dt 0 which can be solved to give 

δevap σevaporation(t) = C0 δevap erf √ 4Dt




 + C0

4Dt π

 e

2 −δevap 4Dt

 −1

(31)

Physically equation (31) corresponds to the triangular area below the concentration profile between x = 0 and x = δevap . For δevap of the order of a few µm (see Fig. 7) we can see that for a diffusion limited process the amount of particles that deposit as a result of liquid evaporation during nitrogen blow off rapidly decreases with immersion time. For long times we can linearize the error function in equation (31) around small values of its argument, i.e., 2 erf(y) ∼ √ y (y  1) π

(32)

and hence we can estimate σevaporation(t) as 2 C0 δevap δevap for √ 1 σevaporation(t)  √ 4π Dt 4Dt

(33)

Assuming δevap ≈ 2 µm and D = 5.4 × 10−12 m2 /s this approximation holds for t > 1 s. 4.1.3. Case of an intermediate electrostatic barrier For the sake of completeness we also include the general case of an electrostatic barrier height that is of the order of a few kT units. It has been shown that in this case the effect of an electrostatic barrier can be expressed as a first-order rate reaction at the surface [41, 49, 50]. The corresponding rate constant kdep can be calculated from the particle–substrate interaction potential Φ as [41, 49, 50] kdep = with

 δΦ ≈

δf

D δΦ

Φ

e kT dx 0

(34)

(35)

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where δf is the distance over which the interaction potential becomes negligibly small. Equation (35) can be further approximated using a Taylor series expansion [41, 49, 50]. As a result the rate constant kdep can be approximated by

2 

−d Φ   dx 2 x Φxmax max − kT kdep ≈ D (36) e 2π kT where xmax is the position where the potential Φ is maximal. The particle concentration profile is then obtained by solving equation (16) together with the following boundary condition: D

∂C(x, t) = kdep C(x, t) (x = 0) ∂x

(37)

This problem resembles the evaporation of moisture from a wet, porous solid into a flow of passing air (the boundary condition for evaporation can be written analogously to equation (37), see also p. 34 in Ref. [45]). The solution of this problem — where we have already made the necessary substitutions — is     2 kdep kdep kdep √ x x x+ t D erf C(x, t) = C0 erf √ +e D √ + Dt (38) D 2 Dt 2 Dt Calculation of adsorption. Similar to the two previous cases we can calculate the surface concentration of adsorbed particles by integrating the flux at the plane (x = 0). This calculation has already been performed for equation (38) (p. 34 in Ref. [45]) yielding 2

  kdep kdep √ C0 D 2 kdep √ t σadsorption(t) = e D erfc Dt + √ Dt − 1 (39) kdep D π D Calculation of evaporative deposition. The amount of particles that will deposit during the blow off procedure can be calculated from equation (20):      δevap 2 kdep kdep kdep √ x x x+ t D erfc erf √ Dt dx σevaporation(t) = C0 + +e D √ D 2 Dt 2 Dt 0 (40) which cannot be solved analytically. If kdep is large, we can estimate σadsorption(t) from the solution of a diffusion limited process (i.e., equation (31)). If kdep is small, we can use equation (24) as an upper limit for σadsorption(t). It is also interesting to note that since 2

lim ez erfc(z) = 0

z→∞

equation (39) reduces to equation (29) for large values of kdep .

(41)

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4.2. Experimental results and discussion 4.2.1. Deposition as function of time Deposition at near-neutral pH. First, the deposition of 80 nm SiO2 particles onto three different substrates, silicon nitride, silicon with chemical oxide and thermal oxide, was investigated. Theoretically the suspension contained 6.5 × 1011 particles/cm3 . It had a pH of 5.04, a result of the initial low pH of the stock suspension and the 1:1000 dilution step with ultrapure water. The normalized surface concentration (i.e., σadsorption/C0 ) is plotted in Fig. 6. The normalized

Figure 6. Normalized surface concentration of 80 nm SiO2 particles at pH 5.04 as function of immersion time. Substrates are silicon nitride, silicon with chemical oxide and thermal oxide. The solid line represents diffusion limited adsorption (calculated from equations (29) and (31)). The dashed line represents the case of no adsorption (calculated from equations (23) and (24)). The parameters used in the fits are D = 5.4 × 10−12 m2 /s and C0 = 6.5 × 1011 particles/cm3 .

Figure 7. Histogram of experimental values of δevap based on normalized surface concentration values of 80 nm SiO2 particles on thermal oxide, TEOS and densified TEOS.

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concentration has the dimension of m (on the y-axis it is plotted as µm) and gives the length of the diffusion boundary layer, i.e., a characteristic distance over which diffusion takes place in the time frame under study. The vertical error bars correspond to the standard deviation calculated from the different SEM counting procedures for each condition (16 in total). The horizontal error bars are taken at 5 s, representing the uncertainty in handling and blow drying. Because this uncertainty is primarily due to transfer delays, which result in an increased contact time of the substrate with the liquid, the error bars are only plotted to the right. The solid line is the solution for barrierless, i.e., diffusion-limited, adsorption. It is calculated from equations (29) and (31) and normalized by C0 . The dashed line represents the case of no adsorption, i.e., equations (23) and (24). The corresponding parameters used in the fits are D = 5.4 × 10−12 m2 /s (diffusion constant of a 80nm spherical particle using equation (14)) and C0 = 6.5 × 1011 particles/cm3 , which corresponds to the theoretical particle concentration. For the nitride substrate we observe a good agreement between the experimental points and the theoretical model, indicating that diffusion limited deposition takes place. For both oxide substrates (thermal oxide and chemical oxide) no increase of deposition is observed with time. Because the nitride surface is almost electroneutral at the pH under study (see Section 2.2), no electrostatic barrier exists, which is in agreement with the observed adsorption behavior. For the oxide surfaces an apparently high electrostatic barrier prevents the particles from adsorbing in the time frame under investigation. The measured surface concentration is entirely due to the withdrawal and blow off procedure, i.e., equation (24). This means that the normalized surface concentration plotted on the graph corresponds to the evaporated thickness δevap . In Fig. 7 we summarize all the normalized surface concentration values for those tests where no increase with time was observed (including other experiments described later in this paper). The corresponding mean and standard deviation are 1.56 and 0.52 µm, respectively. These values can be used in equation (20) to estimate the contribution from the drying step. In practice, however, it can be neglected in most cases, except when there is almost no adsorption of particles. Deposition at low pH. A similar test was also performed at very low pH (0.2 as measured), obtained by addition of HCl to a suspension of C0 = 3.25 × 1012 particles/cm3 . The resulting normalized surface concentration is represented in Fig. 8. Similar to Fig. 6 the solid line represents the case of diffusion limited adsorption and the dashed line is the case without adsorption. For these tests the actual particle concentration used in the normalization was C0 = 2.93 × 1012 particles/cm3 . When using the theoretically predicted concentration all data points are systematically 10% above the diffusion-limited curve. As explained in Section 2.1 this can be attributed to the dilution procedure. As the solid line represents the maximum amount of particles that can deposit in the given time (i.e., the diffusion limit) it would be physically unrealistic to observe higher deposition rates. Note that this correction is only justified when the theoretical limit lies below the experimental values, such as in this case. When the experimental values are below the diffusion

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Figure 8. Normalized surface concentration of 80 nm SiO2 particles at pH 0.2 as function of immersion time. Substrates are silicon nitride, silicon with chemical oxide and thermal oxide. The solid line represents diffusion limited adsorption (calculated from equations (29) and (31)). The dashed line represents the case of no adsorption (calculated from equations (23) and (24)). The parameters used in the fits are D = 5.4 × 10−12 m2 /s and C0 = 2.93 × 1012 particles/cm3 .

limit this correction cannot be made because such a behavior can be the result of the presence of an electrostatic barrier (see Section 4.1.3). For the nitride substrate we also observe in this experiment that adsorption follows the diffusion limited rate. The two types of oxides, however, show completely opposite behavior. Adsorption on the chemical oxide substrate follows the diffusion limited conditions, while no adsorption is observed on the thermal oxide. Because of the very high ionic strength of the suspension, electrostatic interactions are completely screened (e.g., see Table 1 and Fig. 4). Instead, van der Waals and SRR interactions are expected for this experimental system. For nitride substrates no evidence of SRR interactions has been reported in literature so far. However, for both types of proposed models (water layer structuring or hydration of ions) it is likely that some SRR interactions are present, even in the case of nitride substrates. The fact that the observed adsorption follows the diffusion limited case indicates that SRR interactions are either very small, or even completely absent on nitride surfaces. In either case, a rather deep potential minimum (∼ several kT or larger) must be present. The different behaviors observed for the two oxide surfaces indicate that the SRR interactions between the particles and the thermal oxide surface are different from those with the chemical oxide. Tables 2 and 3 show that for the silica/water/silica system at high ionic strength, the Hamaker constant is only about 4 × 10−21 J, hence attractive forces are rather small. The way how SRR interactions are influenced by the presence of high concentrations of HCl (∼ 1 M) will, therefore, determine if the primary minimum is sufficiently deep to keep the particles adsorbed. From the experimental data available we can only conclude that the SRR interactions

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Figure 9. Normalized surface concentration of 80 nm SiO2 particles from a suspension at pH 0.22 (by adding HCl) as function of immersion time. Substrates are TEOS (as deposited and densified) and thermal oxide.

are strong enough to prevent adsorption onto thermal oxide while they are not on the chemical oxide. To investigate this phenomenon further, two other types of SiO2 — commonly used in the microelectronics industry — were investigated in a similar test with a particle concentration of 6.4×1011 /cm3 . The substrates were TEOS, as deposited and with extra densification step of 10 s at 300◦ C. The resulting normalized surface concentration is given in Fig. 9 including the previous results from a thermal oxide substrate. Note that the y-axis is on a different scale than in the previous graphs. Also, on these oxide surfaces there is no evidence of particle deposition over the time of the experiment. Because these oxides were grown at elevated temperatures ( 300◦ C) their structure is likely to be different from the chemical oxide which is formed at room temperature. The literature indeed shows that such a chemical (ozone-grown) oxide has a lower density than thermally grown oxides [7]. Although there is a clear indication of the presence of SRR interactions from the tests reported here, a correlation with the structuring of water layers, the pH of the solution, the ionic strength or the presence of Cl− -ions cannot be derived from these data. However, the data clearly show that a chemical oxide behaves differently with respect to particle adsorption than oxides grown at elevated temperatures. 4.2.2. Effect of pH on deposition To investigate how the pH of the suspension influences the particle–substrate interactions similar tests were performed for suspensions of different pH values. By selecting a fixed deposition time, the results can be quantitatively compared with each other. From the theoretical fits included in Figs 6 and 8 we can see that for a two minute immersion time the diffusion-limited adsorption is more than 10-times higher than evaporative deposition. This means even if adsorption is rather low, a 2-min immersion readily allows us to distinguish adsorption from evaporative deposition. Figure 10 represents the normalized surface concentration

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Figure 10. Normalized surface concentration of 80 nm SiO2 particles as function of pH (adjusted with HCl). Immersion time is 2 min, substrates are silicon nitride, silicon with chemical oxide and thermal oxide. Manually drawn lines are included to guide the eye. The arrows indicate theoretical diffusion limited adsorption (top arrow) and evaporative deposition (bottom arrow).

(after a 2-min immersion) for the same substrates as in Fig. 8. The theoretical concentration of SiO2 particles was 6.5 × 1011 particles/cm3 . The pH was adjusted by adding appropriate amounts of HCl. Because these tests were performed in different particle suspensions we have used the theoretical value of C0 to normalize the experimental data. To account for the uncertainty in the dilution procedure, the error bars are taken 50% larger than obtained from the standard deviation of the SEM counting procedure. The arrows on the right hand side of the figure represent the theoretical adsorption diffusion limit after 2-min immersion, obtained from Fig. 8, and the evaporative deposition obtained from Fig. 7. Smooth curves are drawn through the experimental points to guide the reader. For the thermal oxide substrate we observe that for all pH values tested the normalized surface concentration is comparable to the evaporated thickness. This indicates that no significant adsorption occurs over the time frame of the test. For the chemical oxide surface a different behavior is observed. We can distinguish two pH ranges in which clearly distinct processes take place. For a pH of the suspension below 1.5, the adsorption rate corresponds to the diffusion-limited case, while for pH values larger than 1.5 no adsorption is observed. For the nitride substrates the adsorption corresponds to the diffusion limit for pH values above 1.5. At a pH of 1.5 the normalized surface concentration drops to a minimum value — about half of the diffusion limit — and increases back slowly as the pH decreases until the diffusion limit is obtained again at a pH of 0.2 (corresponding to the results from Fig. 8). The fact that for the three different substrates the deposition behavior changes around pH 1.5 suggests that this effect is related to the particles. One hypothesis is that the particle’s IEP occurs at this pH. This can explain the large deposition onto the nitride substrates above pH 1.5, since both surfaces are oppositely charged in this

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region (based on the streaming potential data from Fig. 3 for the nitride substrate that show that the IEP of nitride lies at a pH value of around 5). However, for the chemical oxide surfaces (which according to Fig. 3 have an IEP between pH 2 and 3) SRR interactions must be assumed to explain the measured particle deposition. Since we know neither the extent of the structural interactions, nor the effect of pH on them, no additional information is gained from an extensive theoretical analysis of surface forces. We, therefore, accept the results from Fig. 10 as a given and use the corresponding adsorption rates in our later analysis of the rinsing process. 4.2.3. Reversibility of the adsorption process From the previous results there is ample evidence that SRR interactions must be taken into account for the experimental system we are investigating. In Section 3.1 it was already mentioned that they will shift the distance of minimum approach to higher values, and hence will decrease the depth of the primary minimum. If this minimum is sufficiently shallow reversible detachment of the particles from the substrates is possible [30]. This has important consequences for the rinsing process because it means that particles can be removed from the surface by choosing appropriate conditions that induce particle detachment. Experimental results. The reversibility of the particle–substrate interaction was investigated by monitoring the amount of particles left on the surface after a rinsing step that was performed directly after the particle deposition step (without an intermediate drying step). The deposition step consisted of a 2-min immersion in a suspension containing theoretically 6.5 × 1011 particles/cm3 at pH 0.2. The rinsing step was performed in a dilute HCl solution (with pH between 0.2 and 4.0). Experimental results from this series of experiments are shown in Fig. 11 for the

Figure 11. Normalized surface concentration of 80 nm SiO2 particles as a function of rinse pH (adjusted with HCl). Initial deposition was 2 min at pH 0.2 (see Fig. 8) followed by static rinse in dilute HCl for 2 min. Substrates are silicon nitride, silicon with chemical oxide and thermal oxide. Manually drawn lines are included to guide the eye. The arrows indicate theoretical diffusion limited adsorption (top arrow) and evaporative deposition (bottom arrow).

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same substrates as used in previous tests. The theoretical value of C0 was used to normalize the data points. The arrows on the right hand side of the figure represent the theoretical diffusion limited adsorption after 2-min immersion, obtained from Fig. 8, and the evaporative deposition, obtained from Fig. 7. Smooth curves are drawn through the experimental points to guide the reader. Each marker represents a different sample. In order not to overload the graph, the individual error bars are omitted. In interpreting Fig. 11 it is important to realize that the effect of the additional rinse step is represented by the difference between the initial and final particle levels. For the chemical oxide and nitride surfaces the initial levels correspond to the upper arrow (diffusion-limited adsorption), while for the thermal oxide the initial level is practically zero, but a certain amount of particles is carried over from the deposition step to the rinse step. By comparing Fig. 11 with Fig. 10 one can see a remarkable resemblance between the two graphs. For pH values where particle adsorption is low, a large amount of particles is also removed from the surface during the rinse step. For pH values where the diffusion-limited adsorption occurs no detachment is observed. In other words: (i) particle detachment is possible by varying the pH of the solution and (ii) the pH effect on particle detachment can be correlated with the pH effect on particle adsorption. Estimation of carry-over layer thickness. Figure 11 also provides an indirect means to estimate the thickness of the carry-over layer thickness. Indeed, when the rinsing step is performed in a pH range where attraction is dominant, all particles present within the carry-over layer will deposit during the rinse step. Similar tests performed at longer times (not shown here) indicated that within 2 min practically all of these particles deposited on the surface. As can be seen in Fig. 11 the fraction of particles coming from the carry-over layer (COL) with thickness δCOL constitutes approximately 20-25% of the amount of particles that is deposited during the contact with the particle suspension. Knowing that σadsorption is given by equation (29) and the amount of particles in the carry-over layer is obtained by integrating the concentration profile given in equation (26) we can write    δCOL x √ C erf dx 0 0 4Dt  ≈ 20-25% (42) 2C0 Dt π Solving equation (42) for δCOL by a trial and error method we find that δCOL ≈ 23-26 µm, in very good agreement with our initial guess of 20 µm. A more detailed description of the rinsing process will be given in Section 5. Consequences of reversibility. If particles can detach from the surface, the assumptions used in Section 4.1.3 are not valid. Indeed, the use of an irreversible first-order reaction to describe particle–substrate interactions has been derived for the case of DLVO interactions, i.e., when only van der Waals and electrostatic interactions are present. In that case the primary minimum is deep enough to

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irreversibly trap the adsorbed particles. The fact that particles can detach from the surface suggests that the depth of the primary minimum is of the order of kT and indicates the presence of additional short-range repulsive forces. The equations of Section 4.1.3 should, therefore, be modified by a detachment reaction with rate constant kdetach . In this work we will not investigate the case of simultaneous adsorption and detachment. However, we will derive a model for rate-limited detachment in Section 5.2.4, assuming that adsorption can be neglected.

5. PARTICLE DEPOSITION FROM A CARRY-OVER LAYER UNDER TRANSIENT PH CONDITIONS

In Section 4 we have established a correlation between the pH of the suspension and the interaction of the particles with the surface. This was done by examining the deposition of particles onto the substrate. In practical cleaning situations, however, most of the particles enter the rinsing tank due to carry-over from the processing liquid. As normally the pH values of the process liquid (i.e., the liquid in the carryover layer) and the rinsing liquid differ, the pH close to the wafer surface changes during the rinse step. This phenomenon has been called the pH shock. In Section 3.1 we have seen that as the pH changes, the interactions between the particles and the substrate also change. This effect will be investigated in this section. First we will calculate the pH shock, i.e., how quickly the pH changes as a function of time. Next, we present the procedure that was used to investigate particle adsorption experimentally during transient pH conditions. In a following section we will derive models to describe particle deposition under transient pH conditions for the experimental system described in Section 4. They will be based on the correlation between pH and particle–substrate interactions — established in Section 4.2.2 — together with the calculations of the pH shock. Given the complex mathematics involved analytical models can only be obtained for some idealized cases. In the experimental section we will then compare the predictions with experimental data and evaluate the validity of these models. 5.1. Calculation of the pH shock 5.1.1. Description of the model system A schematic description of the idealized system for which we want to calculate the pH is given in Fig. 12. A flat plate taking a carry-over layer of thickness δCOL of concentration CCOL is immersed into a rinse tank of concentration Crinse . For mathematical purposes we shall only treat the case of a stagnant rinsing liquid. The pH during rinsing is calculated from the concentration profile C(x, t) of H+ -ions. In this model, only the H+ -ions are considered and it is assumed that Crinse and CCOL are acidic (or neutral). To calculate the H+ concentration profile we must solve equation (16). The initial conditions corresponding to the model from Fig. 12 are C(x, t) = CCOL

(0  x  δCOL , t = 0)

(43)

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Figure 12. Schematic representation of a flat substrate taking a carry-over layer of concentration CCOL into a rinse tank of concentration Crinse . The average thickness of the carry-over layer is δCOL .

C(x, t) = Crinse

(δCOL < x < ∞, t = 0)

(44)

Furthermore, we assume that the H+ -ions do not interact with the wafer surface, hence we can consider the wafer surface as an impermeable wall: ∂C(x, t) = 0 (x = 0, t > 0) (45) ∂x Under the assumption that the bulk is infinitely large compared to the carry-over layer volume we can write for a static rinse process C(x, t) = Crinse (x → ∞, t > 0)

(46)

Note that this approach is equally valid for a single tank system where the first liquid is drained and subsequently is being replaced with the second liquid. Furthermore, we assume that neither of the liquids is buffered. It should also be noted that in the models we neglect turbulences in the liquid during immersion and withdrawal of the substrates. 5.1.2. Solution method The solution to equation (16) with initial conditions (43) and (44) and boundary conditions (45) and (46) can be obtained using the methodology described in Section 3.2.3, i.e., from a similar problem of heat conduction. Unfortunately, the corresponding analogous problems describing the temperature profile in a plate have only been solved for systems corresponding to the case where the right hand sides of equations (44) and (46) are zero [46]. For the concentration problem this means that Crinse = 0. To overcome this problem we make use of the fact that if C(x, t) is a solution to equation (16) C ∗ (x, t) = [C(x, t)+ constant] is also a solution. If we set the constant equal to −Crinse the problem can be transformed into ∂C ∗ (x, t) ∂ 2 C ∗ (x, t) = DH + ∂t ∂x 2

(47)

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where we have explicitly specified that we are focussing on the concentration profile of H+ -ions. The corresponding initial and boundary conditions are: C ∗ (x, t) = CCOL − Crinse 0 C ∗ (x, t) = ∂C ∗ (x, t) = 0 ∂x C ∗ (x, t) = 0

(0  x  δCOL , t = 0) (δCOL < x < ∞, t = 0)

(48) (49)

(x = 0, t > 0)

(50)

(x → ∞)

(51)

where we have implicitly assumed that Crinse < CCOL . After a solution for C ∗ (x, t) is found the solution to the initial problem can be written as: C(x, t) = C ∗ (x, t) + Crinse

(52)

Knowing the final concentration profile C(x, t) we can calculate the pH at the surface pHsurf (t) as pHsurf (t) = − log [C(0, t)]

(53)

5.1.3. Concentrated carry-over layer rinsed in a dilute liquid The solution to the problem described by equations (48), (49), (50) and (51) can be readily taken from the temperature profile calculated for an isolated infinite plate with initial temperature T0 for |x| < δCOL and zero for |x| > δCOL (see p. 56 in Ref. [46]). Upon transformation the latter into concentration-related units we obtain      CCOL − Crinse δCOL + x δCOL − x ∗ C (x, t) = + erf √ (54) erf √ 2 2 DH + t 2 DH + t and after applying equation (52) we obtain      CCOL − Crinse δCOL + x δCOL − x + erf √ erf √ C(x, t) = Crinse + 2 2 DH + t 2 DH + t

(55)

Using equation (53) we can calculate the pH at the surface during a static rinsing process as    δCOL (56) pHsurf (t) = − log Crinse + (CCOL − Crinse ) erf √ 2 DH + t The calculated surface pH (equation (56)) is represented in Fig. 13 for a 20 µm carry-over layer of a 1 M acid solution immersed in a neutral rinsing liquid. In Fig. 13a we observe that the pH rises very fast initially (about 1 pH unit in the first second) and levels off at longer times. When looking at equation (56) one can see that for times longer than 1 second the error function can be linearized using equation (32) yielding   δCOL C(0, t) ≈ Crinse + (CCOL − Crinse ) √ for t > 1s (57) π DH + t

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a)

b)

Figure 13. Calculated surface pH vs. time for a 20 µm carry-over layer of 1 M acid immersed in neutral liquid according to equation (56). (a) On a linear scale (b) on a logarithmic scale.

When the pH values of the carry-over layer and the rinse solution differ more than about two units (i.e., CCOL  Crinse ) we obtain 

δCOL pH(t) ≈ pHCOL − log √ π DH +

 +

1 log(t) for t > 1s 2

(58)

where pHCOL is the initial pH of the carry-over layer. Equation (58) shows that the slope of the pH vs. time (on a logarithmic scale) is 0.5, indicating that two decades of rinse time are needed for each further increase of one pH unit. This is shown in Fig. 13b which plots the surface pH vs. time on a logarithmic scale. An important finding is also that the point where the pH is 1.5 occurs after about 15 s rinsing. Depending on the assumptions for δCOL this point may shift somewhat, but in practice the pH range 1.5 ± 0.1 occurs somewhere within 10-20 s, 15 s being a good estimate. 5.1.4. Dilute carry-over layer rinsed in a concentrated liquid For completeness we can mention that the complementary problem (i.e., when the rinsing liquid is more concentrated than the carry-over liquid) can be solved in the same manner. The H+ concentration profile in a system, as depicted in Fig. 12,

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where Crinse > CCOL is given as:

     Crinse − CCOL δCOL + x δCOL − x + erfc √ (59) C(x, t) = CCOL + erfc √ 2 2 DH + t 2 DH + t

with erfc(x) = 1 − erf(x). The corresponding concentration of H+ -ions at the surface is given by   δCOL (60) C(0, t) = CCOL + (Crinse − CCOL )erfc √ 4DH + t The erfc-function on the right hand side of equation (60) will be almost equal to 1 when its argument is of the order of 2-3. For typical values of δCOL (≈ 20 µm) and DH + (= 9.31 × 10−9 m2 /s) this occurs for times t less than a few tenths of a second. This is not surprising because this is the approximate time that an H+ -ion needs to cross the distance of the carry-over layer thickness δCOL . In practice this means that a wafer which is rinsed in a solution of lower pH will attain the pH of the rinsing liquid in less than a second. For alkaline solutions a similar conclusion holds. 5.2. Theoretical models for particle deposition from a carry-over layer immersed in a stagnant rinsing liquid A mathematical model describing particle deposition from a carry-over layer that is being rinsed requires the solution of the transient diffusion equation (equation (16)). The results presented in Section 4.2.2 indicate that over the pH range 0-4 the particle–substrate interactions can range from very repulsive to very attractive and are different for each substrate. As a consequence, the boundary conditions needed to describe the diffusion process depend on the type of substrate used and the pH range covered during the rinsing step. Therefore, different models describing particle diffusion during the rinse step will have to be developed, each covering a certain type of behavior that is related to the way how particle–substrate interactions vary with pH. Similar to the deposition models derived in Section 4 the concentration profile of the particles during the rinse step will be calculated for each condition. From these profiles the amount of adsorbed particles and the evaporative deposition can be calculated using equations (18) and (20). 5.2.1. Choice of rinse pH In order to investigate the deposition of particles from a carry-over layer under transient pH conditions, samples were dipped first in a particle suspension and subsequently in a rinsing liquid (as already described in Section 2.1). To induce a transient pH, the pH of the rinsing liquid was chosen differently from the pH of the particle suspension. Based on the pH shock calculations we know that when the rinsing liquid is more acidic than the particle suspension the pH drop occurs in less than a second — a time-scale which is experimentally not accessible. Therefore, we will focus on the opposite case, i.e., with the rinsing liquid being less acidic than

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the particle suspension. This case is also more representative of a real rinsing step where the rinsing fluid is generally neutral water or slightly acidified water [6]. To allow comparison between different tests, the pH of the particle suspension was kept constant at 0.2 (this value was experimentally measured after addition of 1 M HCl to the particle suspension). The largest pH shock covered in this work was obtained by using neutral rinse water (with a pH of approximately 6, due to adsorption of CO2 from the atmosphere). From Fig. 13 we know that a significant change in pH occurs within the first 2 min. For longer times the pH will only slowly increase with time. In the experiments the first 2 min of the rinsing step will, therefore, be investigated in detail. 5.2.2. Initial condition The initial condition for the rinsing step is given as: C(x, 0) = δ(x)σsuspension,adsorption(tdep ) + Csuspension(x, tdep )

(61)

where δ(x) is the Dirac function and tdep is the immersion time in the particle suspension. Csuspension(x, t) represents the concentration profile of particles during immersion in the particle suspension, i.e., equation (22), equation (26) or equation (38), and σsuspension,adsorption(t) represents the surface concentration of adsorbed particles given by equation (23), equation (29) or equation (39). Note that in this section we shall use the notation t to refer to the immersion time in the rinsing liquid. Physically equation (61) means that two types of particles are carried over to the rinsing tank: adsorbed particles and suspended particles. The first type are particles that have adsorbed on the surface during the immersion in the particle suspension. They are located at the (x = 0) plane at the start of the rinsing step. The second-type of particles are suspended in the carry-over layer. Thermal oxide substrates. For the thermal oxide samples no adsorption was observed at pH 0.2. This means that the particle concentration profile in the carryover layer is the same as before the sample entered the particle suspension (i.e., C0 ). The initial condition can, therefore, be written as C(x, 0) = C0 (∀x)

(62)

Chemical oxide and nitride substrates. For the nitride and chemical oxide substrates the deposition at pH 0.2 followed the diffusion rate-limited model as described by equation (29). The initial concentration profile (equation (61)) can be obtained from equations (26) and (29) to yield:  
Dtdep x (63) + erf  C(x, 0) = C0 δ(x)2 π 4Dtdep

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Figure 14. Normalized concentration profile of 80 nm particles (with diffusion coefficient of 5.4 × 10−12 m2 /s) after 2 min of deposition and subsequent immersion in rinse liquid.

From equation (63) we can calculate the ratio of particles in the carry-over layer (Ncarry−over ) to the adsorbed particles (Nadsorbed) as    δCOL   √x 2 C erf dx 0 −δCOL 0 Ncarry−over 1 x 4Dt  + e 4Dt − 1 (64) = = √ erf  Dtdep Nadsorbed π 4Dtdep 2C 0

π

which is a function that monotonously decreases with time. From equation (64) we can calculate that for a deposition time of 2 min the fraction of particles in the carry-over layer is less than 20-25% of the particles in the adsorbed state (assuming 80 nm particles with D = 5.4 × 10−12 m2 /s and a carry-over layer thickness of 23-26 µm, see Section 4.2.3). For mathematical simplicity we will assume that on the nitride and chemical oxide surfaces all particles are initially present at the surface. Although this may seem a rather crude approximation, it is important to realize that most particles are located at the outer edge of the carry-over layer (see, e.g., the concentration profile in Fig. 5 after 2 min deposition). The corresponding profile of particles in the carry-over layer after immersion in the rinse tank (which contains no particles) is given in Fig. 14. It is clear that because the concentration gradient towards the bulk is significantly larger than the concentration gradient towards the substrate, more particles will diffuse towards the bulk of the liquid. For the experimental conditions used in these tests the amount of these particles that will end up on the substrate surface will, therefore, be small compared to the initial amount of particles on the substrate surface, which is 4–5-times larger than the total number of particles suspended in the carry-over layer. 5.2.3. Type 1: Diffusion from a carry-over layer into the rinsing liquid A first model is derived for a system where particles do not interact with the surface during the entire time frame under study. An example is the system consisting of the colloidal silica particles from our tests with a thermal oxide substrate. For this system no particle adsorption over the entire pH range of interest has been observed.

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During the rinsing step, the particles will, therefore, not deposit on the surface, but rather diffuse into the bulk of the rinsing liquid. Initial and boundary conditions. Initially (i.e., at the start of the rinsing step) the carry-over layer (with thickness δCOL ) contains a uniform concentration (C0 ) of particles while the rinse liquid contains no particles, i.e., C(x, t) = C0 (0  x  δCOL , t = 0) 0 (δCOL < x  ∞, t = 0)

(65)

As no adsorption on the substrate surface takes place we can consider the surface to be an impermeable wall, i.e., ∂C(x, t) = 0 (x = 0, t > 0) (66) ∂x Furthermore, we assume the bulk to be infinitely large compared to the dimensions of the carry-over layer, hence C(x, t) = 0 (x → ∞, t > 0)

(67)

Calculation of particle concentration profile. This problem is similar to the calculation of the pH during a static rinsing process (see Section 5.1.3). The corresponding solution is given by equation (55) with Crinse = 0 and CCOL = C0 :      C0 δCOL − x δCOL + x erf + erf (68) √ √ C(x, t) = 2 2 Dt 2 Dt Calculation of adsorption. As no adsorption will take place during the rinsing step (see equation (66)), we have σadsorption(t) = 0

(69)

Calculation of evaporative deposition. The contribution from the drying step can then be calculated using equation (20). Physically this represents the area below C(x, t) between x = 0 and x = δevap :       C0 δevap δCOL − x δCOL + x erf + erf dx (70) √ √ σevaporation(t) = 2 0 2 Dt 2 Dt This equation can be solved using the identity (see p. 304 in Ref. [51]).  1 2 erf(x)dx = xerf(x) + √ e−x (71) π After some rearrangements we obtain    δCOL + δevap  C0 σevaporation(t) = erf δCOL + δevap √ 2 4Dt    δCOL − δevap  C0 − erf δCOL − δevap √ 2 4Dt

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+C0

  −(δCOL −δevap )2 Dt −(δCOL +δevap )2 4Dt 4Dt −e e π

(72)

If δevap is a few times thinner than δCOL (which is typically the case) we can see that for very short times (on the order of a few seconds) the concentration of particles in the region (0 < x < δevap ) will still be equal to C0 , hence σevaporation(t) ≈ C0 δevap (t → 0)

(73)

while for long times (on the order of minutes) the argument of the error function in equation (70) can be linearized using equation (32). Upon integration we obtain δCOL (t → ∞) σevaporation(t) ≈ C0 δevap √ π Dt

(74)

5.2.4. Type 2: Particle detachment from the adsorbed state A second model is derived for a system where a certain amount of initially adsorbed particles are released into the rinsing liquid. A representative case for this system are the colloidal silica particles used in this study and a chemical oxide surface. The experimental results in Section 4.2.3 suggest that the adsorbed particles are only loosely bound to the surface and can be released from the surface under proper pH conditions (i.e., if the pH is higher than 1.5). The literature shows that spontaneous detachment of particles from a surface is indeed possible, provided that shortrange repulsive forces are present [52– 58]. According to theoretical models, the rate of detachment is extremely dependent on the electrostatic interactions at close separation [58]. In this range the simple interaction model presented in Section 3.1.1 is not valid — instead more elaborate models should be employed [58]. However, even these more complicated models also rely on certain approximations with regard to the rate of detachment. In a simple case the detachment process is often assumed to follow first-order kinetics described by a rate constant kdetach . Various other models — including a distribution of rate constants — have been proposed [54]. The experimental systems reported so far, however, are significantly different from the experimental system studied in this work. First of all, the reported data show that the detachment process takes place over several hours while for our experimental systems this effect is observed within a few minutes. Moreover, the reported data also show that the fraction of particles removed within the course of the experiment seldom exceeds 20-30%, while the results in Fig. 11 indicate that for chemical oxide more than 50% of the particles are removed within 2 min. Finally, the experimental conditions in this work were chosen in the low pH range where electrostatic forces are almost completely screened. Instead of using elaborate models — that must be numerically solved for each set of parameters — we will develop a simple analytical model that can be directly used. Initial and boundary conditions. As discussed in Section 5.2.2, the adsorption process during the immersion in the particle suspension depletes the zone close to the surface of the substrate. Neglecting the particles in the depleted zone with

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respect to the adsorbed particles we can approximate the initial concentration profile as: C(x, t) ≈ σ0 δ(x) (t = 0)

(75)

where the initial surface concentration σ0 can be calculated from equation (29). Furthermore, we assume that a fraction ffix of the adsorbed particles remains immobilized on the surface and that a fraction 1 − ffix is released into the bulk at a rate described by a first-order rate constant kdetach . This represents an idealized version of simultaneous detachment at two different rates where it is assumed that within the time frame of the experiment the process of the lowest detachment rate can be neglected compared to the faster one. Such a behavior has been confirmed experimentally and has been ascribed to surface heterogeneities [52]. Mathematically we can express this condition by imposing a given flux on the surface of the wafer:  ∂C(x, t)  = kdetach σadsorption(t) (76) −D ∂x x=0 where σadsorption(0) = σ0

(77)

Note that the experimental evidence in Fig. 11 indicates that detachment of the particles does not start until the pH is higher than 1.5. From Fig. 13 one can see that this will be after about 15 s. Furthermore, we consider an infinite bulk, hence C(x, t) = 0 (x → ∞, t > 0)

(78)

Calculation of concentration profile. The solution to our problem can be obtained using the method of integration of continuous plane sources developed in the field of heat conduction (p. 262 in Ref. [46]). The corresponding concentration profile requires the solution of the following integral kdetach σ0 e−kdetach t C(x, t) = √ 2 πD



t

0

x2

ekdetach y− 4Dy dy √ y

(79)

which cannot be readily solved analytically. We, therefore, limit our calculations to the case where the rate constant kdetach is infinitely large. This corresponds to the well known diffusion problem of an initial number of species (σ0 ) present at (x = 0) that diffuse freely into a semi-infinite plane, which has the following solution [42]: x2

e− 4Dt C(x, t) = σ0 √ π Dt

(80)

Calculation of adsorption. Although there is no analytical solution to equation (79) we can calculate the adsorption of particles on the wafer surface by writing a

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mass balance of the particle flux at the surface:  dσadsorption(t) ∂C(x, t)  = D  ∂x dt x=0

(81)

Combining equation (81) with equation (76) we can write dσadsorption(t) = −kdetach σadsorption(t) dt

(82)

σadsorption(t) = σ0 e−kdetach t

(83)

to yield

which represents the surface concentration of adsorbed particles that are detaching according to a first-order reaction with rate constant kdetach . In case a fraction of particles ffix is immobilized on the surface, equation (83) can be modified into   (84) σadsorption(t) = σ0 ffix + (1 − ffix )e−kdetach t In case the detachment process occurs instantaneously (i.e., kdetach = ∞), we obtain σadsorption(t) = σ0 ffix (t > 0)

(85)

which can also be calculated by substituting the concentration profile from equation (80) into equation (18), while making use of equation (19). Calculation of evaporative deposition. Evaporative deposition is calculated using equation (20) and equation (80) as  δevap x2 e− 4Dt dx (86) σ0 √ σevaporation(t) = π Dt 0 which can be solved to give

  δevap σevaporation(t) = σ0 erf √ 4Dt

(87)

In the case a fraction ffix of particles remains adsorbed on the surface during the course of the experiments, equation (87) can be transformed into   δevap (88) σevaporation(t) = σ0 (1 − ffix )erf √ 4Dt 5.2.5. Type 3: Particle detachment from the adsorbed state followed by re-adsorption A third model is developed for cases where the particle–substrate interaction is initially repulsive, but becomes attractive after a certain time. This type of behavior is often encountered in cleaning processes because the cleaning chemistry is optimized towards removal of contaminants (i.e., inducing repulsive interactions), while the subsequent rinsing step often is performed in neutral water. In case of

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the pH reaching a point where the electrostatic forces become attractive, particles can re-adsorb during the rinse. Experimentally this corresponds to the behavior observed on nitride substrates. The pH shock calculations indeed show that within a few seconds the pH is in the range 1-1.5 which corresponds to the point where adsorption on the nitride surface is minimal. At higher pH values (> 1.5) the interactions are mainly attractive, as evidenced in Fig. 10. A complete mathematical model needs to take simultaneous detachment and adsorption into account. Furthermore, the corresponding rate constants kdetach and kdep will be a function of time (because the pH varies with time during the rinse). For mathematical simplicity we assume that the process consists of two consecutive steps: a repulsive step of time trep and an attractive step of time tattr . During the first step, particles are released from the surface and diffuse into the rinsing liquid. During the second step particles that come close to the surface as a result of diffusion can get adsorbed on it. Furthermore, we assume that the corresponding rate constants are infinite, i.e., particles are immediately released during the repulsive step and deposit irreversibly during the adsorption step. Initial and boundary conditions. The initial conditions for the nitride substrates are approximated in the same way as for the chemical oxide, i.e., C(x, t) ≈ σ0 δ(x) (t = 0)

(89)

with σ0 given by equation (29). The first boundary condition assumes that the bulk can be considered infinitely large, hence C(x, t) = 0 (x → ∞, t > 0)

(90)

The other boundary condition — at the surface of the wafer — consists of two parts. In the first phase of the rinsing process (0 < t  trep ) the particle–substrate interaction is strongly repulsive, and the initially adsorbed particles are assumed to detach infinitely fast. The duration of this “repulsive” time is denoted as trep . In the remainder of the rinsing process (t > trep ) the particle–substrate interaction is strongly attractive, and the wafer surface is approximated by a perfect sink, hence  ∂C(x, t)  −D = 0 (x = 0, 0 < t  trep ) (91) ∂x x=0 (92) C(x, t) = 0 (x = 0, t > trep ) Calculation of concentration profile. For t  trep we have the same boundary conditions as for the infinitely fast detachment of particles from a chemical oxide, hence C(x, t) is given by equation (80). For t > trep we can rely on the same method that is used to calculate the temperature profile in a semi-infinite solid with a given initial temperature profile whose surface temperature (at x = 0) is kept at zero (p. 58 in Ref. [46]). Upon transforming the temperature variables into concentration

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variables we obtain 1 C(x, tattr ) = √ 2 π Dtattr



∞

   )2 (x+x  )2 − (x−x − f (x ) e 4Dtattr − e 4Dtattr dx  

(93)

0

where f (x  ) represents the initial concentration profile at the start of boundary condition (92) and x  is a dummy integration variable. f (x  ) can be calculated from equation (80) for t = trep : 2

x − 4Dt rep

e f (x  ) = σ0 

(94)

π Dtrep

For convenience we have expressed the concentration profile as C(x, tattr ) where tattr = t − trep is a new time variable that starts when the attractive particle–surface interactions start. A general solution can be obtained by substituting equation (94) into equation (93) and solving the integral. As this is a tedious calculation the details are grouped in Appendix A.2. The corresponding result is   −x 2 4D(trep +tattr ) σ0 e x  C(x, tattr ) =  (95) erf   t attr π D(trep + tattr ) 4D (trep + tattr ) trep

Calculation of re-adsorption. By taking a closer look at the first term of the right hand side of equation (95), i.e., the fraction, we can see that this corresponds to the concentration profile for a system that is fully repulsive during the entire time t, i.e., given by equation (80) with t = trep + tattr . This means that we can interpret the second term of the right hand side of equation (95), i.e., the error function, as a correction term to account for re-adsorption during the rinsing step. The most important parameters in this correction function are the total process time t and the ratio ttattr . To visualize the effect of particle re-adsorption we plot in Fig. 15 rep the normalized concentration profile (C0 /σ0 from equation (95)) for a particle with diffusion constant of 5.4×10−12 m2 /s and a total rinsing time of 30 s, while changing : 0 (curve a); 1/4 (curve b); 1/2 (curve c); 1 (curve d); 2 (curve e) and the ratio ttattr rep 4 (curve f). It is important to realize that in this way the normalized concentration profile is not dimensionless, but has the dimension of an inverse length. Figure 15 shows that the concentration profiles in case of attraction deviate significantly from =0). The amount of the case without an attractive step (given by curve a with ttattr rep re-adsorption can be calculated using equation (18). Because of the tedious nature of this procedure we only present the result here. Details can be found in Appendix A.3.   2 tattr (96) σadsorption(tattr ) = σ0 arctan π trep

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Figure 15. Normalized concentration profiles C(x, t)/σ0 of particles initially adsorbed on the surface at x = 0, diffusing into the rinsing liquid for a time trep and re-adsorbing for t > trep . The profiles are calculated from equation (95) with D = 5.4 × 10−12 m2 /s, δCOL = 23 µm, trep + tattr = 30 s for : 0 (curve a), 1/4 (curve b), 1/2 (curve c), 1 (curve d), 2 (curve e) and 4 (curve f). different ratios of ttattr rep

Figure 16. Fraction of re-adsorbed particles fredep as function of ttattr ratio, calculated from equation rep (97).

hence the fraction of initially adsorbed particles that re-adsorbs during the attractive part of the rinse step fredep can be calculated as   2 tattr (97) fredep = arctan π trep We can see that only one parameter is needed to describe re-adsorption of particles during rinsing: the ratio of the attractive time to the repulsive time. Equation (97) is . This figure shows that most of the re-adsorption plotted in Fig. 16 as function of ttattr rep occurs at the earliest stages of the attractive phase of the rinsing step. This is not surprising because at the beginning of the attractive phase the concentration of particles close to the surface is still significantly higher than far into the bulk.

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Similarly to the model from Section 5.2.4 we can also assume that a fraction of particles ffix does not detach from the surface (during the repulsive phase of the process). In that case equation (96) can be modified to   tattr 2 σadsorption(tattr ) = σ0 ffix + (1 − ffix ) arctan (98) π trep Calculation of evaporative deposition. The amount of particles that deposits during the drying step cannot be readily calculated analytically. From the concentration profiles in Fig. 15 we can see that this amount can be neglected compared to the amount of re-adsorbed particles. Indeed, the amount of re-adsorbed particles for a given rinsing process is represented in Fig. 15 by the area between curve a and the corresponding re-adsorption profile, while the amount of evaporatively deposited particles is given by the area below the re-adsorption profile from x = 0 to is very small, e.g., at the very start of the attractive x ≈ 3 µm. Except when ttattr rep phase, this assumption is reasonable. 5.3. Experimental results and discussion As we have seen, the behavior of the thermal oxide, chemical oxide and silicon nitride substrates is described by different mathematical models. The corresponding results will, therefore, be treated separately. All tests reported here were performed in a particle suspension of theoretical concentration of 6.5 × 1011 particles/cm3 . In each series of dip tests a sample without additional rinse was included for normalization. Two parameters that are used in all theoretical models in this section are the thickness of the evaporated layer δevap and the thickness of the carry-over layer δCOL . Calculations are performed for the average values of δevap and δCOL that have been determined empirically: δevap ≈ 1.6 µm (see Fig. 7) and δCOL ≈ 23 µm (see Section 4.2.3). Where needed, the influence of small variations in these parameters will be shown. It is important to realize, however, that these values are not arbitrary fitting parameters, but have a well-defined physical meaning. 5.3.1. Thermal oxide: diffusion into the rinsing liquid The results of a neutral rinse of a thermal oxide surface, following a 2-min immersion in a particle suspension containing 1 M HCl (pH ≈ 0.2) are given in Fig. 17 on a log scale. The calculations from equation (72) are included for three sets of δevap and δCOL : (i) 2 µm and 25 µm (ii) 1.6 µm and 23 µm (iii) 1.0 µm and 20 µm. The middle curve represents the average values of both parameters. The other curves are calculated for values at the high, respectively low, end of the experimental range. As the particle surface concentration is entirely due to evaporative deposition (δevap ) which also depends on how many particles are carried over into the rinse tank (δCOL ), any errors in δevap and δCOL will have a significant effect on the results. Good agreement is observed between the experimental results and the theoretical model for reasonable values of δCOL and δevap .

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Figure 17. Normalized surface concentration of 80 nm SiO2 particles on thermal oxide rinsed in neutral water, following a 2-min immersion in a particle suspension at pH 0.2. The theoretical curves are calculated from equation (72) with three combinations of δevap and δCOL : (i) 2 µm and 25 µm (ii) 1.6 µm and 23 µm (iii) 1.0 µm and 20 µm.

5.3.2. Chemical oxide: detachment from the surface The model describing detachment from a surface is given by the sum of equations (84) and (88) where kdetach and ffix show up as the two parameters describing the detachment process. Unlike the values of δevap and δCOL which are merely parameters related to the experimental procedure, kdetach and ffix must be fitted to the experimental results. The results of a neutral rinse following a 2-min immersion in a particle suspension containing 1 M HCl (pH ≈ 0.2) are given in Fig. 18. Theoretical fitting curves (assuming δCOL = 23 µm and δevap = 1.6 µm) are calculated for the two cases discussed in Section 5.2.4. As the rinse tests in Fig. 11 show that no detachment is observed when the pH is below 1.5 we have shifted the start of the detachment process to 15 s (which, according to Section 5.1.3, corresponds to the time where the pH rises above 1.5). The first model corresponds to rate-limited detachment (i.e., equation (84) without correction for the drying step, because there is no simple analytical solution for this case). The second case corresponds to infinitely fast detachment (i.e., equation (85) with contribution from drying step from equation (88)). Good fits are obtained using ffix = 0.25 and kdetach = 0.1 s−1 . From the figure it is clear that both models correspond equally well to the experimental data. For simplicity we, therefore, propose the case of infinitely fast detachment, which leaves us with only one fitting parameter, i.e., the fraction of particles fixed to the surface ffix , which is found to be 0.25. The reason why some particles are not removed cannot be deduced from these simple experiments. One hypothesis is that the surface contains heterogeneities and hence some particles are bound more strongly. Alternatively, a fraction of 25% of the particles may have somewhat different properties (size, surface chemistry, density, etc.) which make them adsorb more strongly to the surface.

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Figure 18. Normalized surface concentration of 80 nm SiO2 particles on chemical oxide rinsed in neutral water, following a 2-min immersion in a particle suspension at pH 0.2. Fitted curves are calculated using δCOL = 23 µm and δevap = 1.6 µm and ffix = 0.25. The dashed line corresponds to kdetach = 0.1 s−1 (from equation (84)) and the solid line corresponds to kdetach = ∞ (from the sum of equation (85) and equation (88)).

5.3.3. Nitride: detachment and re-adsorption Because the particle adsorption (or detachment) depends on whether the pH is below or above 1.5, separate tests were performed with the nitride substrates. First, particle detachment was investigated during a rinse at pH 1.5, following a 2-min immersion in a particle suspension containing 1 M HCl (pH ≈ 0.2). The normalized surface concentration is represented in Fig. 19. The theoretical fitting curves are calculated for the case of instantaneous detachment and for first-order detachment. In both cases ffix is set equal to 0.3. Figure 19 shows that instantaneous detachment (kdetach = ∞) does not occur, but rather a slow detachment takes place that can be well described by kdetach = 0.03 s−1 . One should realize, however, that in practice re-adsorption will occur. This is evidenced by the deposition curves from Fig. 10 in the pH range below 1.5. Because this effect is not taken into account in the model the actual rate constant for detachment will be somewhat higher. Moreover, the actual detachment rate constant will be time dependent because the pH during the detachment process is not constant. Nevertheless, the results from this figure clearly show that after 15 s of rinsing there is still a significant amount of particles on the surface (in this case approximately 60%). In a next series of tests, the re-adsorption of particles on nitride substrates during a rinsing step in liquid with a pH higher than 1.5 was investigated. The experimental results are summarized in Fig. 20. The samples were first immersed for 2 min in a particle suspension containing 1M HCl (pH ≈ 0.2) and subsequently rinsed in liquid at pH3 and near-neutral pH (around 6). As only 10 min of rinsing were investigated, the increase of pH with time is expected to be similar for the two cases. Therefore, no significant difference is expected. This is evident from the markers in Fig. 20. The theoretical curves are calculated using δCOL = 23 µm and δevap = 1.6 µm. The dashed line corresponds to equation (96) (i.e., with ffix = 0) and the solid line

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Figure 19. Normalized surface concentration of 80 nm SiO2 particles on nitride rinsed at pH 1.5, following a 2-min immersion in a particle suspension at pH 0.2. Theoretical curves are calculated using δCOL = 23 µm and δevap = 1.6 µm and ffix = 0.3. The dashed line corresponds to kdetach = 0.03 s−1 (from equation (84)) and the solid line corresponds to kdetach = ∞ (from the sum of equation (85) and equation (88)).

Figure 20. Normalized surface concentration of 80 nm SiO2 particles on nitride rinsed in pH 3 and 6, following a 2-min immersion in a particle suspension at pH 0.2. Theoretical curves are calculated using δCOL = 23 µm and δevap = 1.6 µm. The dashed line corresponds to ffix = 0 (from equation (96)), the solid line corresponds to ffix = 0.3 (from equation (98)).

corresponds to equation (98) with ffix = 0.3. The value has been taken from Fig. 19 after 15 s of rinsing, i.e., when the pH at the surface is expected to be approximately 1.5. This value is lower than after 15 s of rinsing at pH 1.5 (see Fig. 19). The reason is that the when the pH of the rinsing liquid is higher than 1.5, the pH will rise quickly towards 1-1.5 which is the pH range where adsorption of particles on nitride is minimal (as shown in Fig. 10). Consequently, the detachment of particles during the first seconds of rinsing at pH 3 or 6 will be faster than for the rinsing process at pH 1.5. The fact that in the models depicted in Figs 19 and 20 ffix is chosen to be 0.3 is merely coincidental. For the rinsing tests at pH 3 and 6 the parameter ffix can,

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therefore, best be interpreted as the fraction of particles that have not detached from the surface at the start of the attractive phase of rinsing. Because the re-adsorption process occurs very rapidly in the first seconds of the attractive phase of rinsing, as indicated by the initial slope of the re-adsorption curves in Fig. 16, the difference between the two fits (with ffix = 0 and ffix = 0.3) in Fig. 20 is quite small and both curves fit the experimental data rather well. The fact that the experimental data points are in both cases somewhat above the theoretical curves is attributed to the presence of additional particles in the carry-over layer, which have been neglected in the model (see also the discussion in Section 5.2.2).

6. SUMMARY AND CONCLUSIONS

In this work the interaction between silica spheres and silicon wafers — covered with a layer of silicon nitride, thermal oxide or chemical oxide — has been investigated during immersion in stagnant aqueous particle suspensions and rinsing liquids. First we have presented an overview of the different surface forces that are believed to play a role in the interaction between the particles and the surface. It was made clear that various parameters needed to be established in order to obtain an accurate description of the interaction energy. The most important features of the interaction energy vs. distance curve are an electrostatic barrier and a primary minimum. The first one is important for low ionic strengths and large distances and determines the rate of particle adsorption. The primary minimum depends on the van der Waals interactions and additional short range interactions and determines particle detachment from the surface. In a first series of tests, the deposition of particles as a function of immersion time was determined for different pH values. Analytical models have been presented for different heights of the electrostatic barrier. The necessary corrections for the drying step used in the experimental procedure were also included. From the experimental results the pH range where attractive, respectively repulsive, interactions are dominant could be derived by comparing them with the theoretical models. It was found that the three substrates used in the test followed completely different behaviors. For the thermal oxide substrates there was never evidence of adsorption. This was attributed to the presence of short-range repulsive forces, strong enough to prevent adsorption. For the chemical oxide surfaces particle adsorption was observed for pH values below 1.5. Various explanations are possible to explain this behavior, but they all suggest that the short-range interactions on chemical oxide are affected differently by the change in pH than those on a thermal oxide surface, hence both oxides should be treated as being different materials. For the nitride substrates adsorption was minimal at pH 1.5 and increased as the pH shifted to lower or higher values. It was also shown that in some cases particle adsorption on some of the surfaces was reversible, i.e., particles could detach from the surface under proper pH conditions.

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In a next series of tests, particle deposition from a carry-over layer was investigated. It is representative of a surface cleaning procedure where a contaminated processing liquid is being rinsed off. If processing liquid and rinsing liquid have different pH values, a sudden change in pH (pH shock) at the start of the rinsing step will occur. Mathematical expressions to calculate the pH shock have been presented. Knowing the effect of pH on particle–substrate interactions, it could be calculated at what time during the rinsing step attractive or repulsive interactions would be dominant. For each of the three substrates an analytical model was presented that calculated the particle deposition during the rinse step. In the model for the thermal oxide surfaces it was assumed that particles diffused from the carryover layer into the bulk of the rinsing liquid. For the chemical oxide surface it was assumed that a certain fraction of particles remained irreversibly bound to the surface, while the other particles detached from the surface according to first-order rate kinetics. For the nitride substrates it was assumed that initially particles detached from the surface but after a certain time the detached particles could re-adsorb on the surface. For all three systems a good agreement with the experimental data was obtained. For flowing rinsing systems, viscous forces will significantly reduce the liquid velocity in the region close to the solid surface (the so-called boundary layer). The models presented in this work can, therefore, also be used qualitatively to describe flowing systems for immersion times small enough for particles to remain close to the surface.

Acknowledgements The authors gratefully acknowledge support from Sophia Arnauts in sample preparations and pre-cleanings and from Nausikaä Van Hoornick with the illustrations and bibliography in this manuscript. Much gratitude is also extended to the peer reviewers of this paper for their constructive remarks.

APPENDIX A. CALCULATION OF PARTICLE RE-ADSORPTION DURING RINSING

In this Appendix diffusion equation (16) is solved for a system where (i) an initial amount of particles (per area) σ0 is located on the surface, (ii) a first phase of repulsive interactions releases the particles from the surface so they can freely diffuse into an infinite bulk for a time trep and (iii) a second phase of attractive interactions traps all particles that reach the surface for times longer than trep .

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A.1. Initial and boundary conditions The mathematical notation of the initial and boundary conditions describing the model system is: C(x, t) = σ0 δ(x) C(x, t) = 0  ∂C(x, t)  = 0 −D ∂x x=0 C(x, t) = 0

(t = 0) (x → ∞, t > 0)

(99) (100)

(t  trep )

(101)

(x = 0, t > trep )

(102)

where δ(x) is the Dirac function. A.2. Calculation of the particle concentration profiles A.2.1. Phase of repulsive interactions The solution to the diffusion problem during the first phase (0 < t  trep ) has been reported previously [45, 46] (see also equation (80)) and is given as: −x 2

e 4Dt C(x, t) = σ0 √ π Dt

(103)

A.2.2. Phase of attractive interactions Using the approach described in Section 3.2.3 we can find a solution to the diffusion problem by using the method to find the temperature in an infinite rod (x ∈ [0, ∞]) with initial temperature distribution f(x), whose surface (x = 0) is held at zero temperature. The general solution can be written as [46, p. 59]    ∞  )2  )2 1 − (x−x − (x+x  4Dt 4Dt attr attr dx  f (x ) e −e (104) C(x, tattr ) = √ 2 π Dtattr 0 where we have already substituted the variables from the field of heat conduction into their equivalents from the field of diffusion. For convenience we have shifted the origin of the time axis to the start of the phase of attractive interactions, with a new time variable tattr , hence tattr = t − trep . The initial concentration profile f (x) can be calculated from equation (103) at t = trep : −x 2

e 4Dtrep f (x) = σ0  π Dtrep

(105)

After substituting equation (105) into equation (104) we can calculate the concentration profile during the phase of attractive interactions as    ∞  )2  )2 −x  2 σ0 − (x−x − (x+x 4Dtrep 4Dt 4Dt attr attr e dx  C(x, tattr ) = e −e (106) √ 2π D tattr trep 0

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Upon expanding the exponential terms we obtain after some rearrangements:  ∞  2  2  C(x, tattr ) = A (107) e−ax +bx − e−ax −bx dx  0

where the pre-integral terms of equation (106) are grouped in the constant A −x 2

σ0 e 4Dtattr A= √ 2π D tattr trep and a=

1 1 + 4Dtattr 4Dtrep b=

2x  4Dtattr

The two exponential terms in the integral of equation (107) can be solved analytically as follows [51]:
   1 π b2 2ax − b −ax 2 +bx 4a (108) e erf √ = e 2 a 2 a and

 e

−ax 2 −bx

1 = 2




  π b2 2ax + b 4a e erf √ a 2 a

(109)

where erf(x) is the error function defined in equation (27). The general solution (equation (106)) can, therefore, be written as:
      1 π b2 2ax  − b 2ax  + b x →∞ 4a erf − erf e √ √ (110) C(x, tattr ) = A 2 a 2 a 2 a x  →0 where the sub- and superscripts on the right square bracket signify that the difference must be taken between the bracketed terms evaluated at x  tending to infinity and x  tending to zero, respectively. Making use of the properties of the error function (erf(0) = 0 and erf(∞) = 1), equation (110) simplifies to:
   1 π b2 b e 4a 2 erf √ (111) C(x, tattr ) = A 2 a 2 a and the final solution can now be obtained by substituting the equations for A, a and b back into equation (111). After some further rearrangements we arrive at:   −x 2 4D(trep +tattr ) σ0 e x  erf   (112) C(x, tattr ) =  t attr π D(trep + tattr ) 4D (trep + tattr ) trep

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A.3. Calculation of particle re-adsorption The amount of particles that re-adsorbs in time tattr can be calculated from equation (18). Using equation (19) we can calculate the flux J (x, tattr ) as J (x, tattr ) = −D

∂C(x, tattr ) ∂x

(113)

Using the expression for C(x, tattr ) from equation (112) into equation (113) we can calculate the flux as   −x 2 σ0 x e 4D(trep +tattr ) x  erf   J (x, tattr ) =  2 π D(trep + tattr ) trep + tattr trep D tattr (trep + tattr ) trep

−

σ0 e π

−x 2 4D(trep +tattr )

e

−x 2 trep 4Dtattr (trep +tattr )

1

 (trep + tattr ) ttattr rep

(114)

Using equation (114) in equation (18) we can calculate the surface concentration of re-adsorbed particles as  tattr 1 σ0   dt  (115) σadsorption(tattr ) = t π  0 (t + t ) rep trep This can be solved using the identity [51]  √ 1 √ dx = 2Arctan( x) (1 + x) x giving us: 2σ0 σadsorption(tattr ) = Arctan π



tattr trep

(116)

 (117)

and the fraction of particles that re-adsorbs during the attractive part of the rinse step fredep can be calculated as   σattr (trep , tattr ) 2 tattr (118) fredep = = Arctan σ0 π trep

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 129–139 Ed. K.L. Mittal © VSP 2003

The use of surfactants to reduce particulate contamination on surfaces MICHAEL L. FREE∗ Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112-0114, USA

Abstract—Reducing particulate contamination on surfaces is critical to many different technologies, and surfactants can play an important role in reducing residual particulate contamination in processes that utilize fine particles. The behavior of surfactants in solution under a variety of conditions will be presented in the context of adsorption and aggregation. The effects of surfactant hydrocarbon chain length and solution ionic strength will be analyzed. Surface forces between particles and surfaces will be discussed, and the important role the surfactant molecules can play in altering such forces as it relates to reducing residual particulate contamination will be presented. Keywords: Surfactant; particle removal; interfacial forces; adsorption; decontamination.

1. INTRODUCTION

The removal of particles from surfaces is a critical aspect of cleaning in many modern manufacturing processes. Failure to remove particles adequately from microelectronic circuits during the fabrication process leads to circuit failure and accompanying low wafer yields. Incomplete removal of radioactive or toxic particles in industrial systems results in unnecessary residual contamination. Inadequate removal of particles from polished optical components reduces their performance quality. Thus, it is clear that improved removal of particles from surfaces is an important goal in many modern cleaning applications, and many studies have been performed to understand and improve particle removal technology [1-17]. The removal of particles from surfaces is the result of applying a removal force that is greater than the adhesion force. The adhesion force between the particle and the substrate is affected by inherent particle properties, the medium between the particle and the surface, and other factors. The key to enhanced particle removal is to apply either a larger removal force, which may also lead to surface damage, or reduce the adhesion force. Surfactant molecules can be useful in reducing the adhesion force between particles and substrate surfaces, thereby enhancing particle removal without increasing the removal force to potentially damaging levels. ∗

Phone: (1-801) 585-9798, Fax: (1-801) 581-4937, E-mail: [email protected]

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2. SURFACTANT PHENOMENA RELATED TO ENHANCED PARTICLE REMOVAL

2.1. Surfactant aggregation and adsorption In order to comprehend how surfactants can modify adhesion forces, it is useful to understand what surfactants are and how surfactants behave in aqueous environments. Surfactants are amphiphilic molecules that have a hydrophilic functional group, such as sulfate, sulfonate, amine, carboxylate, phosphate, or other related chemical entity, and a hydrophobic tail, which often consists of a straight alkyl segment of consecutive CH2 units from 6 to 18 units in length. The hydrophilic group facilitates solubility in aqueous media, and the hydrophobic group reduces solubility in aqueous media and provides an entropy-driven force for aggregation and/or adsorption of the surfactant molecules. As the surfactant concentration in an aqueous medium rises, the hydrophobic portion of the molecules drives surfactant molecules to assemble in greater concentration at surfaces and interfaces. This phenomenon occurs because the molecules can reduce their energy by associating their hydrophobic entities with each other, rather than with water molecules. As surfactant molecules assemble and concentrate at the air–water interface with increasing concentration above a threshold level, the surface tension at that interface decreases as illustrated in Fig. 1. Further increases

Figure 1. Relation between surface tension and surfactant concentration as well as depictions of general associated aggregation phenomena.

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in surfactant concentration lead to increased molecular packing at the air–water interface, as well as enhanced adsorption at solid–liquid interfaces, such as particle and substrate surfaces in contact with solution. However, if the concentration is sufficient, the packing at interfaces reaches a maximum level and further increases in surfactant concentration force the surfactant molecules to form aggregate structures in solution known as micelles (see Fig. 1). Micelles are often spherical structures that in aqueous media contain the hydrophobic entities in the structure interior and the hydrophilic entities in the outer portion of the structure. The concentration at which micelles form is known as the critical micelle concentration (cmc). 2.2. Importance of the cmc As the surfactant concentration approaches and exceeds the critical micelle concentration, multi-layers of surfactant can form on surfaces. As shown in Fig. 2 for cetyl pyridinium chloride (CPC) in an acidic chloride medium, the level of adsorption of surfactant molecules stays below or near the monolayer level until the cmc is approached and surpassed. Above the cmc, multi-layers of surfactant are present on the surface, as shown in Fig. 2.

Figure 2. The effect of CPC concentration in 0.02 M NaCl solution on surface tension and adsorption density. (Data adapted from Ref. [18]). The surface tension data were acquired using a balance with 0.0001 g resolution. The adsorption density measurements were made using an Elchema EQCN 400B oscillator and a Labview (version 5.0) data acquisition and control system.

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The cmc is clearly an important indicator of the ability of a surfactant to aggregate and/or adsorb at surfaces. Adsorption takes place at significant levels only when the concentration is somewhat near the cmc (usually within two orders of magnitude). Multiple layers of adsorbed surfactant are possible above the cmc. Moreover, the cmc provides an important transition between submonolayer coverage and multilayer coverage, as well as a relative indicator of the tendency of surfactant molecules to aggregate. Thus, the cmc provides important information that is relevant to surface modification and enhanced particle removal using surfactants. 2.3. Calculation of the cmc The critical micelle concentration is influenced significantly by both ionic strength and hydrocarbon chain length. In fact, changes in these factors can account for changes in critical micelle concentrations that range over several orders of magnitude. An equation that has been developed to predict the cmc of surfactant molecules under a variety of chain length and ionic strength scenarios can be expressed as [19]:

cmc ≅ exp(

1 o + k ( L − 6) RT ln(γ )]) [( L − 6)∆Gc.l. + ∆Gother RT

(1)

in which R is the gas constant, T is the absolute temperature, L is the total number of consecutive CH2 units in the surfactant molecule, ∆Gc.l. is the free energy increment for each CH2 unit (–1500 J/mol is a good estimate for some surfactants [20]), ∆Goother is the residual free energy not accounted for by the L–6 term (–2000 J/mol is a reasonable estimate for some surfactants [20]), k is a solvent polarity factor (usually near 1.5 for surfactants for which L is 12 to 18 [20]) and γ is the activity coefficient determined using an ionic activity coefficient equation, such as the Davies equation, which can be expressed as [21]:

γ =10

−0.5083 z 2 (

I −0.2 I ) 1+ I

(2)

at 25oC, where z is the charge of the surfactant ion (usually 1) and I is the ionic strength [21]: n

I = 0.5å m j z j

2

(3)

j=1

where m is the dimensionless molality, and j = 1 to n represents all positively and negatively charged species in solution. The validity of the cmc prediction equation is illustrated in Fig. 3. The data in Fig. 3 show that there is a very good correlation between the measured cmc values and those predicted using this equation.

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Figure 3. Comparison of cmc predicted by Eq. (1) and the measured cmc. The letter S at the beginning represents sodium and the S at the end represents sulfate. The letter C and the accompanying number indicate the number of carbon atoms in the hydrophobic tail portion of the surfactant molecule, all of which are alkyl or consecutive chain CH2 units. The letter C at the end of the legend indicates chloride. The letter P represents pyridinium. The numbers in parentheses indicate the ionic strength of the solution.

2.4. Interfacial forces The adsorption of surfactant molecules on particle and substrate surfaces alters the interaction forces between the particle and the substrate. The overall interaction force involves primarily van der Waals, electrostatic and hydrophobic force components. The van der Waals force between a spherical particle and a flat plate can be expressed as [16]:

FvdW (h ) =

AR 6h

2

(4)

in which FvdW is the van der Waals force, which is nearly always negative (i.e., attractive), A is the Hamaker constant, R is the radius of the particle and h is the separation distance between the exposed surfaces of the particle and the substrate. For systems involving two surfaces covered by thin films, such as generally occurs for particle-substrate adhesion systems, an expression for the van der Waals

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force, which has been adapted from Israelachvili [20] for particle–surface interaction using the Derjaguin approximation, is expressed as [16]:

A A A A A121 A545 R A FvdW (h ) = [ 432 − 545 323 − 121 343 + ] 2 2 2 2 6 h ( h + tp ) (h + ts ) (h + tp + ts )

(5)

where 1 is the surface of the substrate, 2 is the coating on the substrate surface, 3 is the medium separating the surfaces, 4 is the coating on the particle, 5 is the surface of the particle, h is the distance between the coated surfaces, ts is the thickness of the coating on the substrate surface and tp is the thickness of the coating on the particle surface. Using the Derjaguin approximation to determine the interaction force between a particle and a surface, it can be shown that the electrostatic interaction force is given as [16]:

Fel (h ) =

128π R ρ ∞ kT γ particleγ surface

χ

where

γ = tanh(

zeΨo ), 4kT

exp( − χ h )

(6)

(7)

and

χ =(

2000e 2 IN A 1/2 ) ε oε mkT

(8)

in which z is the ion valence, e is the electrical charge, ρ∞ is the bulk dissolved ion concentration, Ψo is the surface potential, which in this study was assumed to be approximately equal to the measured zeta potential. I is the ionic strength (0.5åz2p∞ for all positive and negative ions), NA is Avogadro’s number, εo is the dielectric permittivity of vacuum and εm is the dielectric constant of the medium between the two surfaces. The hydrophobic force is much more difficult to define and is only relevant when both surfaces are hydrophobic. Hydrophobic forces are typically only significant below the critical micelle concentration in aqueous media when the surfaces on which adsorption occurs are hydrophilic prior to exposure to surfactant molecules. If the surfaces are hydrophobic prior to surfactant adsorption, submonolayer coverage would be desirable to reduce the hydrophobic attraction between surfaces in aqueous media. The overall interaction force is the sum of the van der Waals, electrostatic and hydrophobic forces. Often, however, only the van der Waals and electrostatic forces are considered. The use of the van der Waals and electrostatic forces to determine the overall interaction force was proposed by Derjaguin and Landau [22],

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and Verwey and Overbeek [23] several decades ago and is known as the DLVO theory. The overall interaction forces often dominate the adhesion forces and thereby determine the forces that are necessary to remove particles from surfaces. 2.5. Modification of interfacial forces and enhancement of particle removal using surfactants The foregoing discussion shows that the electrostatic, hydrophobic/hydrophilic and surface properties of the particles and substrate determine the adhesion force between the entities. The previous information about surfactants shows that surfactants can adsorb at interfaces. It is also apparent that the adsorption of ionic or charged surfactant molecules on a solid hydrophilic surface in aqueous media will likely alter the hydrophobicity, charge, and general surface properties of the substrate. Consequently, it is not surprising that the adsorption of surfactant molecules can significantly alter the interaction forces between the particles and the substrate. Calculation of the DLVO particle–surface interaction force between 1 µm diameter quartz particles and a quartz substrate with and without CPC leads to the data shown in Fig. 4. As illustrated in Fig. 4 the interaction force is positive or re-

Figure 4. Force divided by particle radius plotted versus the separation distance between a spherical particle and the substrate surface.

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M.L. Free

pulsive in both cases until the particles approach within a few nanometers. However, as the particles approach the surface the interaction force for the case when surfactant is present is positive or repulsive, whereas the interaction force is negative for the case in which surfactant was not present. Thus, it is apparent that the addition of surfactant significantly alters the interaction force between the particles and the substrate. The same type of approach can be used to predict interaction forces under a wide variety of conditions. Most often the use of surfactant molecules reduces the adhesion force between the particles and the substrate. 3. EXPERIMENTAL PROCEDURES

The particle deposition experiments were performed by polishing and rinsing in deionized water. Alumina particles with an average diameter of 1 µm (Sumitomo) were deposited onto chemical-vapor-deposited tungsten coated silicon wafer pieces (2 cm × 3 cm × 0.1 cm) during polishing. Polishing was performed manually for one minute using CRIC1000-5 polishing pads (Rodel) and a slurry consisting of 20 wt% alumina particles in a 0.1 M ferric nitrate solution containing the specified level of reagent-grade cetyl pyridinium chloride (CPC) obtained from Aldrich. Wafer pieces were rinsed using double-distilled water for 10 s at a flow velocity of approx. 1 m/s. Wafer pieces were then placed in a near-vertical position for residual water drainage and drying. The residual particle density was determined by microscopic examination at multiple random locations on each wafer piece. The accuracy of the residual particle density determination was approx. ± 30%. Surface tension measurements were made using a microbalance (0.1 mg resolution) and a platinum Wilhelmy plate. All experiments were performed at 27-31oC. 4. RESULTS AND DISCUSSION

The effectiveness of surfactant molecules in reducing the number density of residual particles is readily observed from residual particle density measurements that follow substrate surface exposure to particles in a deposition slurry containing surfactant and subsequent rinsing in deionized water. Data in Fig. 5 show that the number of residual particles decreases slowly as the surfactant concentration increases below the cmc. However, the residual particle density decreases rapidly as the surfactant concentration exceeds the cmc level. This observation indicates that surfactant molecules are effective in reducing residual particle contamination, although the effectiveness is minimal unless the concentration of surfactant exceeds the cmc. Similar results for particle removal are presented in Ref. [16] for the quartz-alumina system.

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Figure 5. Residual 1 µm (diameter) alumina particle density on a tungsten surface as a function of cetyl pyridinium chloride (CPC) concentration.

The general explanation for the effect of the cmc in the enhanced removal of particles using a surfactant is that the surfactant reduces the attractive van der Waals forces as well as creates or enhances electrostatic repulsion. However, such an explanation also implies that surfactant adsorption below the cmc should enhance particle removal significantly, but it does not. The explanation for the reduced performance below the cmc is not entirely clear. However, the surfactant adsorbed at surfactant concentrations below the cmc is at or below the monolayer level. Consequently, for hydrophilic surfaces such as quartz, alumina and metals the hydrophobic tail is oriented away from the surface, thereby creating a hydrophobic surface. Because the opposite surface is also coated at or below the monolayer level below the cmc, the opposite surface is also hydrophobic, resulting in an attractive hydrophobic force between the two surfaces. The attractive hydrophobic force that is present below the cmc may offset the positive removal effects of adsorbed surfactant, leading to a minimal overall reduction in adhesion forces. The effects of adsorbed surfactant above and below the cmc are illustrated schematically in Fig. 6. Thus, it is apparent that the effectiveness of surfactants in enhancing particle removal from surfaces is most pronounced above the cmc where multiple layers of adsorbed surfactant are present.

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Figure 6. Schematic illustration showing surfactant adsorption on both particle and substrate surfaces as a function of surfactant concentration (note that the water molecules between the surfaces and surfactant molecules have been omitted to retain clarity).

5. CONCLUSIONS

The presence of a surfactant in solution can reduce the adhesion forces between particles and substrates and thereby enhance particle removal. Surfactants are most effective in reducing adhesion forces when the surfactant concentration exceeds the supernatant solution cmc. Below the cmc the surfactant adsorption tends to lead to hydrophobic surfaces and associated attractive hydrophobic forces that can reduce the effectiveness of surfactant molecules in enhancing particle removal. Consequently, the use of surfactants in reducing residual particle contamination is most effective when the available surfactant concentration exceeds the cmc. Acknowledgements The laboratory assistance of Justin Fuller is gratefully acknowledged along with financial support for the cmc prediction aspect of the project provided by the National Science Foundation (DMR-9983945). REFERENCES 1. F. Zhang, A. Busnaina and G. Ahmadi, J. Electrochem. Soc. 146, 2665 (1999). 2. R. Vos, K. Xu, M. Lux, W. Fyen, R. Singh, Z. Chen, P. Mertens, Z. Hatcher and M. Heyns, in: Ultra Clean Processing of Silicon Surfaces, 2000, M. Heyns, P. Mertens and M. Meuris (Eds.), p. 263, Scitec Publications, Wetikon-Zürich (2001).

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3. A. Iqbal, S.R. Roy, G.B. Shinn, S. Raghavan, R. Shah and S. Peterman, Microcontamination, 45 (October 1994). 4. M. Itano, F.W. Kern Jr., M. Miyashita and T. Ohmi, IEEE Trans. Semiconductor Manufact. 6, 258 (1993). 5. S. Verhaverbeke, R. Messoussi, H. Morinaga and T. Ohmi, in: Ultraclean Semiconductor Processing Technology and Surface Chemical Cleaning and Passivation, M. Liehr, M. Heyns, M. Hirose and H. Parks (Eds.), pp. 3-12, Materials Research Society, Pittsburgh, PA (1995). 6. W.C. Krusell, J.M. de Larios and J. Zhang, Solid State Technol., 38 (June 1995). 7. T.H. Kuehn, D.B. Kittelson, Y. Wu and R. Gouk, J. Aerosol Sci., 27, S427 (1996). 8. G. Gale, A. Busnaina, F. Dai and I. Kashkoush, Semiconductor Int., 19(9), 4 (1996). 9. J.M. Lee, K.G. Watkins and W.M. Steen, Appl. Phys. A, 71, 671 (2000). 10. Y.F. Lu, W.D. Song, B.W. Ang, M.H. Hong, D.S.H. Chan and T.S. Low, Appl. Phys. A, 65, 9 (1997). 11. Y. Otani, N. Namiki and H. Emi, Aerosol Sci. Technol., 23, 665 (1995). 12. S.K. Das, R.S. Schechter and M.M. Sharma, J. Colloid Interf. Sci., 164, 63 (1994). 13. M.A. Hubbe, Colloids Surf., 12, 151 (1984). 14. M.L. Free and D.O. Shah, J. Colloid Interf. Sci., 208, 104 (1998). 15. M.L. Free and D.O. Shah, Micro, 29 (May 1998). 16. M.L. Free and D.O. Shah, in: Particles on Surfaces 5&6: Detection, Adhesion and Removal, K.L. Mittal (Ed.), p. 95, VSP, Utrecht (1999). 17. M.L. Free and D.O. Shah, in: Particles on Surfaces 7: Detection, Adhesion, and Removal, K. Mittal (Ed.), p. 405, VSP, Utrecht (2002). 18. R.Y. Dong and M.L. Free, J. Colloid Interface Sci., in press. 19. M.L. Free, Corrosion, 58, 1025 (2002). 20. J.N. Israelachvili, Intermolecular and Surface Forces, 2nd edition, Academic Press, San Diego, CA (1992). 21. J.N. Butler and D.R. Cogley, Ionic Equilibrium, John Wiley, New York (1998). 22. B.V. Derjaguin and L. Landau, Acta Physicochem., 14, 633 (1941). 23. E.J.W. Verwey and J.Th.G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam (1948).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 141–151 Ed. K.L. Mittal © VSP 2003

The use of rectangular jets for surface decontamination E.S. GESKIN∗ and B. GOLDENBERG Department of Mechanical Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102-1982, USA

Abstract—Surface processing by a rectangular jet with a wide range of precisely controlled aspect ratio was investigated. Several versions of the slot nozzle to generate a rectangular jet were constructed and tested in NJIT’s Waterjet Laboratory. The principal advantage of these nozzles was the possibility to vary the jet width and thickness over a wide range. This enabled us to increase the rate of surface processing (cleaning, decoating) and to reduce water consumption. The fabrication and the restoration of the nozzles were simple and inexpensive. The nozzles were successfully used for metal depainting, derusting and graffiti removal. The tests showed significant effectiveness of the slot nozzle, even at the early stage of its design. Particularly, the water consumption per square meter of the treated surface by the developed nozzle was significantly less than using comparable commercial nozzles. The experiments performed clearly demonstrated that the rectangular jets constituted a more effective surface processing tool than the commonly used round jets. Keywords: Cleaning; rectangular jets; surface processing.

1. INTRODUCTION

In recent years, high-speed fluid and slurry jets have become one of the major tools in manufacturing, maintenance of civil structures and environment protection [1]. A number of new non-traditional applications are emerging in mining, medicine and defense. Applications of jets range from demolition of buildings and breakage of stones to eye surgery to precision machining. The most important jet application, however, is surface decontamination, including cleaning, decoating, degreasing, derusting, etc. Currently, the most common cleaning technniques involve the use of various cleansers, detergents, degreasers, etc. In most cases, however, environmental consequences of chemical treatment are damaging and in some cases they are unacceptable. In order to be effective, a cleanser is expected to form a stable solution with the debris. This solution, unfortunately, constitutes a stable pollution stream. Besides, as the requirements for surface cleanliness increase, so does the cost of chemical treatment. ∗

To whom all correspondence should be addressed. Phone: (1-973) 596-3338, Fax: (1-973) 642-4282, E-mail: [email protected]

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E.S. Geskin and B. Goldenberg

There are a number of alternative cleaning techniques such as laser, low temperature plasma, ultrasound, mechanical scrubbing, etc, which enable us to decontaminate desired surfaces with no environmental damage [2]. But only the water and slurry jets impact has the potential to become a leading surface decontamination technique. The water jets are able to remove most deposits at an acceptable rate and cost. The debris and water are readily separable and, thus, can be recycled. However, the water consumption in the course of jet cleaning is high and the equipment (pump) is expensive. In order to expand the use of jet cleaning it is necessary to simplify the needed equipment, to reduce water consumption and to enhance process efficiency. These objectives can be met by improving the design of the water nozzle. Existing nozzles constitute an opening in a solid metal or ceramic body. Practically, all nozzles have a round orifice as it is much easier to generate a round opening than any other geometry. Besides, the round jet has minimal surface friction, i.e., minimal head loss per unit mass. The round geometry has, however, significant shortcomings. A rectangular tool geometry, in general, is much more effective than a cylindrical one in the course of material separation (knife, saw) or surface processing (brush, scrubber). The method of cleaning developed here involves formation of high-speed jets of a controllable geometry by expelling a fluid from the high-pressure chamber through a specially designed rectangular port [3]. In the final analysis the nozzle developed eliminates some of the geometrical limitations impeding the applications of high-energy fluid jets. A variety of new machining tools and dies should emerge from such a development. In this study, however, we will focus on its application in surface cleaning. There is an urgent need for such services as graffiti removal, street cleaning, etc. We expect that the invented nozzle will next be used for processing of large (bridges, roads, airports, etc.) and very large (beaches, etc.) surfaces. At the other extreme the rectangular nozzle can be used for ultraprecision cleaning. The principal advantage of the invented nozzle is the possibility to vary over a wide range the width and the thickness of the jet. This enables us to increase the rate of cleaning and to reduce water consumption in the course of surface processing (cleaning, decoating) and machining. Several versions of the invented nozzle were constructed and tested in NJIT’s Waterjet Laboratory. The nozzles were successfully used for metal depainting, derusting and graffiti removal. Special experiments were carried out in order to compare the performance of the invented nozzle and a commercial one. The tests showed significant superiority of the NJIT nozzle even at an early stage of its design. Particularly, the specific water consumption by the invented nozzle was significantly less than that using a comparable commercial nozzle. A device for graffiti removal based on the use of the invented nozzle was constructed and is available for preliminary field demonstration.

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2. DEFFICIENCY OF ROUND JETS

Figure 1 illustrates the interaction between a round jet and the substrate. As it is shown in this figure, the substrate A is subjected to the treatment (cleaning, decoating, etc.) by the jet B moving with speed V in the direction of the arrow. The treatment is due to the energy delivered to the substrate A by the jet B. The section “a” is a part of the substrate A, while the section “b” is a part of the jet B. In the course of treatment the section “a” is impacted by the section “b” of the jet B. Because the widths w of the sections “a” and “b” are equal, the section “a” of the substrate is treated by the section “b” of the jet. The length of the section “b”, l determines the duration of the interaction between the jet B and the section “a”. F Here l = b is average length of the chord of the section “b” and Fb is the area w of the section “b”. The energy which the section “a” receives from the jet B, while the jet is impacting the substrate A, is delivered only by the section “b”. The energy of the rest of the jet does not affect the section “a”. The amount of the energy delivered to the section “a” by the jet B is proportional to the duration of the “a”– “b” interaction (residence time), i.e., the length l of the section “b”. Let us assume that the kinetic energy is evenly distributed across the jet B and that the kinetic energy of water is completely transferred to the substrate A in the course of the water impact on the substrate surface. Thus, the energy E absorbed

Figure 1. Schematic of cleaning the substrate “A” by the jet “B” moving with speed V. Section “b” is a part of the jet B impacting the section “a” of the substrate A.

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by the section “a” in the course of the jet-surface interaction is [4, 5]: E=

lFa e V

(1)

where Fa is area of the section “a”, e is the energy delivered by the jet to a unit of the substrate surface per unit of time and V is traverse rate of the nozzle. Because the values of Fa , e and V can be assumed to be constant for given operational conditions, the amount of energy delivered to the substrate is E = kl ,

(2)

where k is a constant. Thus, at the given jet energy and traverse rate the amount of energy delivered to a substrate is a function of l . The energy needed for the surface treatment E0 is given by the equation: E0 = k l 0

(3)

Here l 0 is the length of the section which delivers the required amount of energy to the section “a” at given process conditions. Let us discuss the treatment of the substrate A by the moving jet B (Fig. 2). In this case the sections a', a0 and a'' are subjected to the impacts of the sections b', b0

Figure 2. Schematic of cleaning sections a', a" and ao of the substrate A by the moving jet B. Note the different durations of cleaning sections a', a" and ao, determined by the length of the chord l.

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145

and b'' characterized by the lengths l ', l 0 and l '' where l '< l 0 < l ''. The section b0 delivers the required amount of energy to the section a0. On the other hand, the section a' does not acquire a sufficient amount of energy and should be treated again, while the section a'' gains an excessive amount of energy. The insufficient and excessive energy supplies result in energy loss. The section a'' might be damaged by the extra energy delivered in the course of treatment. The section a' also might gain extra energy and be damaged during the additional treatment. Let us now discuss the total energy utilization in the course of the surface treatment by a moving jet. Let us assume that at given operational conditions the length of the chord AB is equal to l 0 . Then the part of the substrate impacted by the segment ABCDEF (Fig. 3) will obtain excessive energy, while areas treated by the segments AGB and EHD will gain insufficient amounts of energy. The amount of the excessive energy delivered to the surface of the substrate is proportional to the areas of the segments BCD and AFE and this energy is lost. The energy delivered to the substrate by the AGB and EHD segments is also lost, because the substrate surface subjected to treatment by these parts of the jet has to be treated again. The useful energy, i.e., the energy necessary and sufficient for the surface treatment is proportional to the area of the square ABDE. An optimal energy utilization is attained if the ratio of the area ABDE to the cross-sectional area of the jet is maximal. This is attained if l = d where l is the length of the 2 chords AB and BD and d is the jet diameter. At this condition the area of the square ABDE occupies 64% of the cross-sectional area of the jet. Because the energy delivered by the jet’s segments AGB, BCD, EHD and EFA is lost, the minimum energy loss experienced in the course of the use of the round jet constitutes 36% of the energy supplied.

Figure 3. Schematic of the water utilization in the course of cleaning by a round jet moving with speed V. A part of the stream energy proportional to the area ABDE (AB = l 0 ) is utilized. The part of the stream energy proportional to the shaded area is lost.

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Figure 4. Utilization of the energy of the rectangular and round jets. Note: at AB =

l0 the part of 0

the energy of the round jet proportional to the shaded area is lost.

Let us assume now that a section “a” is treated by a rectangular jet ABCD (Fig. 4). Let us also assume that the length of the edge AB assures the delivery of energy to the substrate A required for surface treatment. The width of the jet, which is equal to the segment BC, determines the width of the strip swept, i.e., the rate of surface treatment. If the same rate of treatment is attained by the round jet, the energy delivered by the shaded areas of the jet cross-section is lost. Thus, the use of a round nozzle for surface treatment necessarily results in energy losses which might constitute a significant part of the available jet energy. 3. PERFORMANCE OF THE NJIT NOZZLE

The Waterjet Laboratory at NJIT investigated the use of high pressure (up to 400 MPa) rectangular jets for surface cleaning. The sweeping width of the jet is variable and can exceed 50 mm. The general form of the jet developed is shown in Fig. 5. Note the extremely high aspect ratio and the stability of the generated jet. The streams generated by a commercial and an NJIT nozzle are shown in Fig. 6. Although the water consumption by the commercial nozzle is more than that by the NJIT nozzle, the width of the jet generated by the NJIT nozzle is more than that of the conventional one. In further experiments the performance of the commercial and NJIT nozzles was compared under similar conditions. The commercial (Fig. 7a) and NJIT (Fig. 7b) nozzles were used to remove paint from a car body. The results presented show significant advantage of the new nozzle. Table 1 compares results from the use of commercial and NJIT nozzles. The experiments performed demonstrate that the rate of cleaning by the NJIT nozzle can exceed 18 times that by a commercial nozzle.

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Figure 5. Water stream of NJIT nozzle at a pressure of 138 MPa and flow rate 17.0 l/min.

Figure 6. Water stream generated by the commercial and NJIT nozzles. (a) Commercial round nozzle, ID=0.66 mm, pressure P=86 MPa, flow rate F=3.6 l/min. (b) NJIT nozzle, pressure P=93 MPa, flow rate F=2.9 l/min.

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Figure 7. Comparison of speed and quality of cleaning the surface of a car body using a commercial nozzle (a) and the new NJIT nozzle (b).

Table 1. Comparison of the cleaning efficiency of the different nozzles Kind of nozzle

Kind of deposit

S (mm2)

P (MPa)

F (l/min)

D Rate of cleaning (mm) (cm2/min)

Commercial nozzle (Fig. 6a) NJIT nozzle (Fig. 6b)

Hard paint from a car body Hard paint from a car body

0.34

86

1.0

10.0

3.2

0.48

93

0.8

10.0

58.0

S, cross-sectional area of the nozzle opening; P, water pressure; F, water flow rate; D, standoff distance.

The NJIT nozzle was used in various cleaning operations such as removing an oxide film from aluminum screen (Fig. 8), graffiti from marble (Fig. 9) and brick (Fig. 10). The experimental results presented show the feasibility and effectiveness of using the plane stream for a wide variety of cleaning applications. Moreover, the replacement of the round nozzle by the rectangular one was simple and did not involve any difficulties. It can be suggested that in the most or at least in some of cleaning operations the slot nozzle should replace the existing round one. In the experiments performed the thickness of the jet was determined by the conditions of the nozzle fabrication and, in principle, can be reduced even further. The width of the stream was maximal and was determined by the available pump flow rate. The nozzle traverse rate was selected so that the cleanliness of the generated surface complied with process specification. At a given geometry (the width and

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Figure 8. The surface of an aluminum screen before removal of high-temperature oxide film and after decoating by the NJIT nozzle.

Figure 9. Removal of graffiti using NJIT nozzle at a water pressure of 69 MPa and a flow rate of 6.4 l/min. (a) Prior to cleaning, (b) in process.

thickness) of the jet and the water pressure the jet traverse rate was selected so that a desired surface cleanliness was obtained. Optimization of the jet geometry will enable us to increase further the rate of the treatment.

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Figure 10. A view of the rectangular jet. The jet was used to remove paint from the edge of the brick. Process duration was 50 s.

4. CONCLUSIONS

The common sense, existing practice and available scientific data evidently demonstrate that water blasting has a potential for becoming a principal cleaning technique. However, the process of blasting must be improved in order to utilize this potential. The main avenue for such an improvement is to increase the efficiency of energy utilization in the course of the jet cleaning. The energy efficiency is the ratio of the energy utilized for deposit removal and the total jet energy. The experiments performed in this study demonstrated that a mere change in the geometry of the impingement zone enabled us to improve the energy utilization dramatically. It is possible that a variation of the aspect ratio might increase the process rate still further. Moreover, it is also possible that the rectangular jet geometry is not optimal. It is obvious that other improvements in the process conditions will increase the cleaning rate still further. For example the use of a pulse jet [6] produced significant increase of the rate of cleaning. The experiments performed in this work show that the use of rectangular jets constitutes an effective way of improving the cleaning technique. REFERENCES 1. D. Summers, Waterjetting Technology, E&FN Spon, London (1995). 2. K.L. Mittal (Ed.), Surface Contamination and Cleaning, Vol. 1, VSP, Utrecht (2003).

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3. E.S. Geskin and B. Goldenberg, US Patent (pending) “Method of the Jet Formation and Apparatus for the Same”, Application 10-119/777 (April 11, 2002). 4. E.S. Geskin, in Waterjet in Civil Engineering, A. Momber (Ed.), A.A. Balkema, Rotterdam (1988). 5. M.C Leu, P. Meng, E.S. Geskin and L. Tismenetskiy, ASME Trans. J. Manuf. Sci. Eng., 120, 571-577 (1998). 6. P. Meng, M.C. Leu and E.S. Geskin, ASME Trans. J. Manuf. Sci. Eng., 120, 578-589 (1998). 7. W. Yan, A. Tieu, M. Vijayand and A. Makomaski, in Water Jetting, P. Lake (Ed.), BHR Group, Cranfield (2002).

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Ice-air blast cleaning: Case studies D. SHISHKIN, E. GESKIN,∗ B. GOLDENBERG and O. PETRENKO New Jersey Institute of Technology, Department of Mechanical Engineering, Newark, NJ 07102-1982, USA

Abstract—Ice blasting constitutes one of the most promising emerging cleaning techniques. The ice-air blasting generates minimal waste materials, requires portable, comparatively inexpensive facilities and most of all there is virtually no substrate damage in the course of blasting. This paper discusses the results of an experimental study on ice cleaning. Different techniques for ice powder production are analyzed and the conceptual designs of various ice blasting systems are discussed. Special attention is paid to the current and potential applications of ice-based cleaning. The case studies involve decontamination of electronic devices, precision mechanical parts, soft plastics, biological materials, etc. Derusting and depainting of steel and graffiti removal were also explored. The analysis performed enables us to identify the potential applications of the ice blasting in industry, civil engineering and medicine. Keywords: Ice-air blasting; ice particle production; derusting; depainting; graffiti removal; biomedical applications.

1. INTRODUCTION

Surface decontamination is, without question, one of the most important technological processes. Ranging from workpiece degreasing to surface preparation of spacecraft parts, cleaning technology is necessary for an infinite number of diverse applications. De-icing of airplane surfaces, sterilization of healthcare equipment and devices, and decontamination of pharmaceutical and food processing facilities are a matter of public safety. One of the emerging cleaning techniques is ice-air blasting. A number of studies indicated that ice particles could be used as an abrasive medium [1-4]. The principal advantage of ice abrasives is that only pure water is used in their production, which is available at low cost. There is no need to deliver and store ice. The only sources needed for fabrication of ice particles are water and electricity. The use of an ice-air jet (IAJ) prevents environmental pollution and practically eliminates substrate contamination. The need

∗

To whom all correspondence should be addressed. Phone: (1-973) 596-3338, Fax: (1-973) 642-4282, E-mail: [email protected]

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for “green” cleaning techniques is rapidly growing and it is safe to predict that IAJ will find important practical applications. Despite enormous technological advantages, the use of the ice blasting is practically non-existent. The most important problem, which actually impedes adoption of the ice-jet technology, is the difficulties in the generation and handling of ice abrasives. Regular abrasives are stable in all practical ranges of operational conditions, while ice particles can exist only at subzero temperature. Maintaining such a temperature within the nozzle and within the jet is an extremely difficult task. Ice particles tend to pack and clog the supply lines. The adhesion between the particles increases dramatically as the temperature approaches 0ºC. Thus prior to entrance in the nozzle ice particles should be maintained at a low temperature. These and some other problems prevent adoption of the ice blasting by the industry. In order to find acceptance of this technology it is necessary to develop a practical technique for formation of ice particles and particles entrainment by a high-speed air stream. Although the use of ice blasting has been suggested by a number of inventors, the practical application is much more limited. The use of air-ice blasting for steel derusting is reported by Liu [5]. The following operational conditions were maintained during blasting: air pressure: 0.2-0.76 MPa; grain diameter: below 2.5 mm; ice temperature: –50°C; traverse rate: 90 mm/min; and stand-off distance: 50 mm. Under these conditions the rate of derusting ranged from 290 mm2/min at an air pressure of 0.2 MPa to 1110 mm2/min at an air pressure of 0.76 MPa. The quality of the treated surface complied with ISO 8501-1. A successful application of IAJ was recently reported (J. Shlossberg, personal communication). A reported proprietary technology was used to freeze water droplets in a refrigerated space with subsequence entrainment of the generated particles by the air stream. According to Shlossberg (personal communication) the stream developed was successfully used for on-site cleaning and derusting metal parts. Another approach to ice particles formation was used in a study by the NJIT’s Waterjet laboratory [6-10]. In this study ice particles were generated by crushing ice in the course of water freezing or grinding of ice particles. Both approaches, freezing the water droplets and crushing the solid ice, have comparative advantages and the areas of their applications will be determined in the course of future research. 2. ICE PROPERTIES

Solid particles, regardless of their properties, are able to erode a material at the impingement site. The erosion of substrates by impinging particles is due to stress waves generated in the course of impact. The strength and duration of these waves depend on mechanical properties of the impinging particles. The behavior of ice particles in the course of impact is determined by ice elasticity. In the temperature range of –3°C to –40°C ice behaves as an almost perfect elastic body.

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The dynamic elastic properties of ice [9-12] at –5°C are given as: Young’s modulus (E) = 8.9-9.9 GPa, rigidity modulus (G) = 3.4-3.8 GPa, bulk modulus (K) =8.3-11.3 GPa and Poisson’s ratio (ν) = 0.31-0.36. For comparison, for aluminum alloy 1100-H14, E = 70 GPa and G= 26 GPa, and for silica glass E = 70 GPa. Thus, the elastic characteristics of conventional abrasives are superior to that of ice and, thus, these abrasives are much more effective in machining. Despite a lower cleaning efficiency, the use of water ice will be readily acceptable by industries where the contamination of the substrate constitutes the primary concern of the users. 3. POTENTIAL APPLICATIONS OF ICE BLASTING

Ice blasting consists of three unit operations: formation of blasting medium, medium acceleration and impacting the workpiece. The media (particles, pellets, slugs) can be generated by freezing water droplets from a moving or still fluid, freezing the moving or still water contained in an enclosure, and fragmentation (crushing, grinding) of lumped ice. Media acceleration can be attained by the entrainment of ice particles by the air, steam, water or supercritical CO2. The necessary condition for the adoption of ice jets by the industry is the development of a reliable and inexpensive technology for generation of ice particles. The process should be reasonably simple and one should be able to vary the velocity, size and temperature of ice particles over a wide range. One of the main issues in the use of the ice powder is sintering of ice particles and their adhesion to the surface of the enclosure. The strength of adhesion of ice particles depends on the ice temperature. It is necessary to maintain the ice temperature below –30°C to prevent sintering of the particles. Sintering is also determined by the duration of the particles’ contact. The moisture contained in the atmosphere in the course of ice transportation will bring about adhesion of the ice to walls, or sintering of ice particles. Both phenomena result in the formation of a plug and clogging of the conduits. Thus, in sites of particle production and transportation, the temperature must be below –30°C and the moisture content of the atmosphere must be minimal. 4. FORMATION OF ICE PARTICLES

We investigated various techniques for ice particles formation. The simplest technique consisted in entrainment of water droplets by cold air and submerging the water droplets into liquid nitrogen. A crushing system for ice particles formation was designed (Figs 1 and 2). The system operates as follows. Ice and dry ice are supplied into the first stage of crushing. Here piston 2 moves ice to the rotating knives 3. The coarse particles obtained are supplied to the screw conveyer of the second stage. This conveyer

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Figure 1. Schematic of the system for ice particles formation. 1, First stage of crushing; 2, piston; 3, driver for the first stage of crushing; 4, piston motor; 5, second (precise) stage for crushing; 6, driver for the second stage of crushing; 7, spring vibrator for the second stage of crushing; 8, intermediate supply bunker No. 1; 9, spring vibrator for the intermediate supply bunker No. 1; 10, electromagnetic vibrator; 11, intermediate supply bunker No. 2; 12, spring vibrator for the intermediate supply bunker No. 2; 13, intermediate supply line; 14, electric heater; 15, insulation enclosure for the intermediate supply line; 16, variable vibrator; 17, vibration transfer stainless steel rods.

delivers particles to the rotating knives, which generate fine particles. These particles are supplied to bunker 8 and then to vibrator 10. The vibrating metal rod 9 assures continuity of flow through bunker 9. The vibrator 10 supplies particles to bunker 12 and then transporting conduit 13. The suction created by the water nozzle assures delivery of the particles to the nozzle head. The heater 14 prevents clogging of the entrance port. Vibration of the crushers, bunkers and intermediate lines assures continuity of powder flow. The rate of vibration, as well as operations of both stages of crushing are controlled by a PC-based microprocessor system MP. The crusher bunkers and vibrator 10 are located within the insulated en-

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Figure 2. Photograph of the system for ice particle formation (general view).

closure. The supply line 13 is also located in the enclosure. The air at a temperature of –70ºC is supplied into the enclosures. The continuous ice particles flow was attained by this system. The experimental study of crushing the ice block by rotating knives involves monitoring the torque applied to the knife, stresses in the blades, temperature of the ice surface and the size distribution of the generated ice particles. Another system combined water freezing and particle formation. The system operates as follows. City water flows through a steel pipe. The walls of the pipe are cooled by a refrigerant or liquid nitrogen. The water within the pipe is driven by an auger. The operational conditions (rates of water and refrigerant supplies, and refrigerant flow rate) assure formation of ice particles at a desired rate. The size and the temperature of the particles are also controlled. It was found that the stream generated consisted of almost homogeneous ice particles. The machine, a general view of which is shown in Fig. 3, consists of the following functionally separated blocks: – an ice-making block which includes the evaporator, auger, auger driver and TurboJet cooling apparatus, which provides the refrigerant; – an ice-unloading mechanism which includes the driver for traverse movement, drivers for feeder springs, flexible tubing and nozzle block support; and – a nozzle block which includes two parallel nozzles with focusing tubes and focusing device.

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Figure 3. Schematic of auger-type icemaker. 1, evaporator; 2, refrigerant coils; 3, insulation; 4, auger; 5, ice reloading device; 6, air gun; 7, air supply port; 8, water supply port; 9, port for liquid refrigerant; 10, thermocouples; A, air flow rate gauge; B, water flow rate gauge; C, flow rate gauge for liquid refrigerant; D, thermocouples.

The parts for the ice-making block were manufactured by Hoshizaki of America, Inc. [13]. The other blocks were designed and manufactured in our laboratory. The Hoshizaki flaker series evaporator has a maximum ice output of 8.4 kg/h and produces ice powder in the temperature range from –20°C in high water flow rate regime to –60°C in low water flow rate regime. The TurboJet cooling apparatus supplies the refrigerant with an average flow rate of 9.8 l/min at a stable temperature of –72°C and pressure of about 150 kPa. Water flow rate is controlled precisely by the valve. The ice-unloading mechanism works as an automatic feeder and transports ice particles to the nozzle. The nozzle block consists of two nozzles and special focusing device. In our experiments we used nozzles of three distinct diameters and optimal nozzle-to-focusing tube ratio 1:2. Ice is supplied to the nozzles through flexible plastic tubes, which remain elastic under the low temperature (Fig. 4). City water was adequate for system operation. The experiments performed were carried out in the following ranges of water flow rates: – from 0 to 150 ml/min for coolant medium; – from 0 to 200 ml/min for liquid nitrogen coolant medium.

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Figure 4. Schematic of the nozzle block. 1, precisely controlled spring feeder drivers; 2, spring feeder; 3, traverse motion driver; 4, focusing tube unit; 5, high pressure air compressor; 6, CPUcontrolled valves; 7, CPU-controlled spring feeders; A, direction of ice flow movement; B, CPU; C, feedback to CPU from spring feeder drivers.

The dimensions of the auger, heat exchanger, water supply port, etc., were determined by the design of the commercial ice maker. The rate of supply of the cooling medium was 9.8 l/min and the rate of supply of liquid nitrogen was controlled by a precise valve. The water flow rate was varied from 0 to 200 ml/min. We also increased the torque on the auger driver in order to prevent jamming of the icemaker. In the final set of experiments, we were able to generate the desired kinds of particles by proper selection of the water flow rate under the given cooling conditions. The attempts to improve ice production by increasing the water pressure or controlling the supply of the cooling medium were unsuccessful. It was determined, however, that it was necessary to eliminate any obstructions to the ice flow in order to prevent jamming of the heat exchanger.

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5. ICE-AIR JET (IAJ)

A number of applications of the IAJ for surface cleaning was investigated. It was shown that in the optimal range of process conditions this jet constituted a precision tool for selective material removal operations. A number of experiments were carried out in order to demonstrate this ability of the ice-air jet. Various electronic devices (computers, calculators, electronic games and watches) were

(a)

(b) Figure 5. (a) The electronic watches were disassembled and covered by a mixture of lithium grease and copper powder. After this the watches were disabled. Then all components of watches including microchips, conduits and LC displays were decontaminated and (b) after IAJ cleaning the watches performed normally.

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disassembled and the electronic boards were contaminated by a mixture of grease and metal powder. Then the boards were cleaned and reassembled. After cleaning, the computers, calculators and watches worked normally (Fig. 5). Other experiments involved degreasing; depainting and deicing of liquid crystals matrix, polished metals, optical glass, and fabrics; removal of emulsion from a photofilm; removal of glue residue; and removal of graffiti, etc (Figs 6-12).

Figure 6. Photograph of the solar panel element of a calculator containing electronic matrix and conduits. The solar panel was contaminated by a heavy layer of Rust-Oleum gloss protective enamel and then decontaminated by IAJ. After cleaning the calculator and solar panel performed normally.

Figure 7. Photograph of a variable resistor. The moving contacts were contaminated by a mixture of grease and conductive copper powder. After IAJ cleaning device performed normally.

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Figure 8. Photograph of a strip of soft plastic covered by Rust-Oleum gloss protective enamel. The paint was partially removed by IAJ from the plastic surface. No surface damage was observed. The feasibility of restoration and fabrication of plastic parts was demonstrated.

Figure 9. Photograph of rough aluminum surface partially cleaned by IAJ. The aluminum surface was covered by a layer of Rust-Oleum gloss protective enamel. No surface damage was noticed.

The feasibility of damage-free and pollution-free decontamination of highly sensitive surfaces was demonstrated. Because our system was designed to produce fine ice particles, it was not applicable for removal of heavy deposits, for example, rust. A generic environmentally-friendly surface processing technology is emerging as a result of the above experiments.

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(a)

(b) Figure 10. Photograph of (a) rusted carbon steel plate before the IAJ treatment and (b) the same plate after treatment.

6. CONCLUSIONS

One of the most promising avenues in surface cleaning technology is ice blasting. The addition of ice particles or pellets into air or water streams eliminates the use of chemicals and abrasives, dramatically reduces water consumption and helps to create new cleaning and etching technologies. Non-damaging character of ice cleaning makes it possible to use this technology for the maintenance of elec-

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(a)

(b) Figure 11. (a) Epoxy glue was used to create a joint between plastic and rubber surfaces. Notice the highly adhesive character of the glue and (b) the glue residue was removed by IAJ cleaning. No surface damage was noticed.

tronic and precision mechanical parts, food processing units, etc. Low cost and availability of ice abrasive particles determines their applications for cleaning of buildings and de-icing of roads, among others. Damage-free cleaning of discarded parts will improve materials reuse and recycling. The availability of ice particles offers potential applications of ice blasting for such surface processing operations as decoating, polishing, deburring and grinding in such remote areas as deserts, Arctic, etc.

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(a)

(b) Figure 12. (a) Graffiti was removed with conventional IAJ. Note that discoloration occurred in the treated region and (b) that the surface was decontaminated by IAJ. No damage to the underlying paint layer occurred.

REFERENCES 1. 2. 3. 4. 5.

I. Harima, Japanese Patent 04360766 A (1992). H. Shinichi, Japanese Patent 09225830 A (1997). J. Huffman, R. Petersen, M. Henning, G. Stettes and F. Newkirk, US Patent 6,301,908 (2001). S. Vissisouk, US Patent 5,367,838 (1994). B. Liu, in: Jetting Technology, H. Louis (Ed.), pp. 203-211, Professional Engineering Publishing, London (1998).

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6. D. Shishkin, E.S. Geskin, B. Goldenberg and K. Babets, in: Surface Contamination and Cleaning, K.L. Mittal (Ed.), Vol. 1, VSP, Utrecht (2003). 7. D. Shishkin, E.S. Geskin and B. Goldenberg, in: Surface Contamination and Cleaning, K.L. Mittal (Ed.), Vol. 1, VSP, Utrecht (2003). 8. D. Shishkin, E.S. Geskin and B. Goldenberg, Cleaner Times, 27, 17 (2001). 9. T.J. Sanderson, Ice Mechanics: Risks to Offshore Structures, Graham & Trotman, London (1988). 10. B. Michael, Ice Mechanics, Les Presses de l’University of Laval, Quebec, Canada (1978). 11. P.V. Hobbs, Ice Physics, Clarendon Press, Oxford (1974). 12. N.H. Fletcher, The Chemical Physics of Ice, Cambridge University Press, Cambridge (1970). 13. Hoshizaki America, Inc., “Ice Maker Manual Instructions”, Peachtree City, GA (1998).

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Development of a technique for glass cleaning in the course of demanufacturing of electronic products E.S. GESKIN,∗ B. GOLDENBERG and R. CAUDILL New Jersey Institute of Technique, Department of Mechanical Engineering, Newark, NJ 07102-1982, USA

Abstract—The primary objective of this exploratory study was to determine the technical feasibility of a fluidized-bed-based technique for cleaning CRT glass cullet. A laboratory-scale experimental setup was constructed and tested. A range of process characteristics was examined with the objective of producing visually clean cullet without undue reduction in the cullet size. As a result, preliminary process characteristics for the experimental bed were determined and a conceptual process design was suggested. It was shown that the fluidized bed approach could handle any size cullet, whereas traditional cleaning systems are limited to larger cullet sizes. It was also shown in the course of our experiments that fluidized bed cleaning resulted in generation of fine glass powder, which is a high value product. Keywords: Fluidized bed; cleaning; glass; fragments.

1. INTRODUCTION

This project is a part of the larger effort undertaken to develop and demonstrate techniques to efficiently recover end-of-life (EOL) cathode ray tube (CRT) glass [1, 2]. The primary objective of this study was to determine the technical feasibility of a fluidized-bed-based technique for cleaning CRT glass cullet. During the CRT production process, layers of phosphor and other coatings are applied to the interior surface of the CRT. These materials plus any dirt or other contaminants must be removed before the glass can be used as recycled cullet for the CRT glass industry. A recent survey of the major CRT glass manufacturers indicates that a significant market exists for disposed CRT glass cullet provided that it is acceptably clean, sorted and attractively priced. Consequently, an efficient and effective CRT glass cleaning process is critical in achieving high rates of recovery and recycle of computer monitors and televisions. The system developed should provide those involved in CRT recycling a practical means for glass decontamination. ∗

To whom all correspondence should be addressed. Phone: (1-973) 596-3338, Fax: (1-973) 642-4282, E-mail: [email protected]

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Glass cleaning in the course of CRT demanufacturing constitutes a complex engineering problem. It is necessary to decontaminate brittle fragments having a wide range of sizes and unpredictable geometry. Each individual fragment needs to be cleaned while the size reduction due to collisions with other fragments and the reactor wall should be limited. The size of the fragments varies over a wide range. The cost of cleaning must be affordable to a small business, and the equipment must not require complex maintenance and complex process control. Concerns have been raised regarding the viability of current cleaning techniques; consequently, this study was undertaken to examine an innovative approach to CRT glass cleaning which has the potential to provide the required glass cleanliness at low cost. Although improvements in existing cleaning techniques might produce positive results, it was suggested by the authors that the fluidized bed technique might provide a high-throughput, low-cost solution for cleaning of CRT glass cullet. However, this technique had not been demonstrated or evaluated for this application. Such a demonstration is the main objective of the presented study. The feasibility of fluidized bed cleaning of CRT glass cullet was demonstrated during the first stage of this work. It was shown that stirring a water bath containing submerged glass fragments resulted in surface decontamination, while glass fracturing and subsequent size reduction did not exceed an acceptable level. In order to evaluate and demonstrate fluidized bed cleaning, it was necessary to determine an effective design of the reactor as well as conditions of its operation. It was also necessary to determine the change in the size distribution of fragments in the course of cleaning. A laboratory-scale setup was constructed during the second stage of the work in order to address the issues above. This setup was used for glass cleaning which involved decontamination of solid fragments submerged into a water bath stirred by the rising gas (air) bubbles. One of the results of erosion glass cleaning is the formation of fine glass particles. It was clear that commercialization of fine glass particles might enhance the competitiveness of the CRTs recycling, if, of course, users of such particles were identified. To this end, the Multi Life Cycle Engineering Research Center (MERC) at NJIT initiated a study of the use of glass fine powder for fabrication of commercial plastic and ceramic products. The preliminary experiments demonstrated the potential of such an application. 2. EXISTING GLASS CLEANING TECHNIQUES

Currently three basic routes are available for removing coatings and other contaminants from the CRT glass: ● Crush–Separate–Clean–Sort ● Sort–Separate–Clean–Crush ● Sort–Separate–Crush–Clean

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In the first option, the CRT is crushed; glass is separated from metals and electronics and other components; glass from the faceplate (panel) along with the funnel is cleaned; and the fragments of the faceplate and funnel are separated. The other two scenarios begin by sorting into leaded/unleaded CRTs; CRT is cut to separate the funnel from the faceplate and remove all other parts; and the funnel and faceplate glass are separately cleaned and crushed. Scenario 2 assumes that the funnel and faceplate are cleaned prior to crushing, whereas the last scenario (followed here) keeps the funnel glass separate from the faceplate glass but crushes both the faceplates and the funnels before cleaning. In general, the cost of cleaning is proportional to the surface area of the parts to be processed. Crushing dramatically increases the surface area of glass and thus the cost of cleaning. At the same time, there are a number of obstacles in cleaning unbroken faceplates and especially funnels. It is extremely difficult to clean fragile parts of a complex shape. The blasting techniques, for example, hot water spray, dry abrasive blasting, waterjet or abrasive waterjet, are, in principle, capable of performing such operation. However, due to the complex geometry of CRTs expensive and sophisticated equipment would be needed for nozzle guiding. In addition, the funnel is extremely fragile and prone to breakage, thus its handling constitutes a problem in itself. Because of this, at this stage cleaning of crushed glass was selected as the most viable option. At the same time the use of a guided waterjet could be considered if an affordable nozzle guiding system were available. One of the most efficient batch-cleaning techniques is the use of chemicals; for example, the caustic bath. Environmental concerns make this approach unpleasant. Another efficient existing technique for cleaning a glass batch is tumbling. In this case no chemicals are needed and the energy is consumed for fragment acceleration only. An advantage of tumbling over blasting techniques is that the fluidized bed approach can handle any size cullet, whereas traditional non-chemical cleaning systems are limited to larger sizes. Devices needed for such operation are commercially available. However, the possible crushing of fragments and, thus, reduction of the cullet size limits the use of these techniques. An alternative method for cleaning a glass batch is to bring the glass cullet into intimate contact with a fluid using a fluidized bed reactor. In this case the fluid environment softens the glass–glass interaction. In our experiment it was noticed that forces generated in the course of fragment impacts were sufficient for surface erosion, but did not cause glass fracturing. Thus, it was necessary to evaluate comparative advantages and disadvantages of these two techniques. However, no commercial device for fluidized bed cleaning is currently available. In order to compare the fluidized bed and other cleaning techniques it was necessary to design and construct the fluidized bed reactor and to investigate its operation. Such an investigation will enable us to design a technology for cleaning of CRT fragments.

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3. FLUIDIZED BED TECHNIQUE

An objective of this work was to show the feasibility and determine the conditions for blasting of a lump of CRT fragments (cullet), which secure the intense bath behavior shown in Fig. 1a. The conditions sought include the geometry of the reactor, batch size and the kind of fluid (air or water) needed for the fluidization of the glass cullet. The use of the fluidized bed for material processing is a wellestablished technique. Presently, however, the use of this technique is limited to treatment of small particles. There is no known application of the fluidized bed for processing of brittle fragments, like CRT glass cullet. A fluid bath used for fragments cleaning constitutes a three-phase fluidized bed. This system has been extensively studied by a number of researchers [3–5]. However, both literature and patent sources provide no information about the treatment of brittle fragments. Moreover, the feasibility of such a technique has been far from obvious. Fluidized bed cleaning of glass offers substantial advantages but has disadvantages too. The glass hardness dramatically enhances surface erosion and, thus, deposits removal. The erosion occurs in the course of fragment–wall and especially fragment–fragment collisions. However, the collision of brittle fragments results in their fracturing, i.e., size reduction. This reduces the output of the recyclable glass and increases glass losses. Both surface cleaning and size reduction are directly proportional to the process duration. Thus, the possibility of fluidized bed application to CRT glass recycling depends on the feasibility to reduce surface

Figure 1. Schematics of the fluid beds: (A) fluidized bed; (B) channeling bed; (C) spouting bed.

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contamination without unacceptable size reduction. The objective of this work was to evaluate destruction of glass in the course of the fluidized bed cleaning. Another objective of this work was to gain basic knowledge needed for the design and operation of the fluidized bed cleaning system suitable for CRT glass recovery in the course of demanufacturing of electronic devices. 4. FEASIBILITY STUDY

After a preliminary investigation of the cleaning of lump systems, an experimental laboratory setup for glass cleaning was constructed and glass decontamination was investigated. Cleaning was achieved by stirring the water bath containing glass fragments at various bath geometries and fluid injection conditions. The device was comparatively simple and its design allowed variation of the blasting conditions, as well as extraction of the fragments at any stage of cleaning. The blasting was carried out by injection of water or air into the water bath containing a load of glass fragments. In the course of blasting, the motion of the fragments, color of the bath, water level and distribution of air bubbles were visually observed. The rate of glass cleaning was characterized by the change of water color in the bath. When no such change was observed, blasting was stopped. After completion of blasting, the glass cullet was removed from the reactor and the cleanliness of the glass was evaluated visually. Cleanliness was considered acceptable if no deposit was observed at the glass surface. Finally, the size distribution of fragments prior to and after cleaning was determined via screening. The size distribution of the fine particles was determined using a Beckman–Coulter LC particle size analyzer. During the first stage of this work, the conceptual design of the cleaning system was completed. According to this design the fluidized bed reactors will be located near the conveyor which transports CRTs through the cutting/separation process. After separation, the funnels and faceplates are introduced into two different reactors so that different kinds of glasses are processed separately. Each reactor (Fig. 2) consists of three sections separated by screens. At the upper section the funnels and faceplates are impacted by a set of spikes. At impact the glass fractures and decomposes into an array of fragments (cullet) (Fig. 2). Small fragments pass through the screen and accumulate at the middle section of the reactor while the larger ones remain on the screen and are crushed by new CRT sections supplied into the reactor. It is possible that additional shaking of the screen and crushing of glass will be necessary to prevent glass accumulation in the upper section of the reactor. Small fragments accumulated in the middle section of the reactor are submerged in a water bath. The water filling the two lower sections is supplied via a nozzle located at the bottom section, and is removed via a port at the top of the middle section. The water bath containing glass fragments is stirred by the air injected in the reactor via nozzles located at the bottom section. While passing

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Figure 2. Conceptual design of the fluidized bed reactor for glass cleaning.

Figure 3. Fluidized bed generated in the course of glass cleaning.

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through the water bath, air forms evenly distributed bubbles at the reactor crosssection. As a result, the stream shown in Fig. 1a develops. This stream induces an intense circulation of the fragments. The collisions between the fragments and between the fragments and the wall result in erosion cleaning of the glass surface. This process is continued until the desired cleanliness of the glass is attained. The glass is then removed from the reactor. The large fragments accumulated in the top section are further crushed. Further filtering and processing of the sludge removed from the bottom section yields valuable glass fines, which potentially have viable secondary uses as by-products. The cullet collected in the middle section has dimensions required by the glass industry and constitute the primary output of the reactor. A laboratory-scale prototype simulating the operations above (Figs 3 and 4) was constructed and tested. A sequence of experiments were carried out in order to demonstrate the feasibility of using the fluidized bed for glass cleaning and to evaluate design and operational parameters of the reactor. It was determined that if an intense and stable circulation of fragments was maintained the process resulted in acceptable surface decontamination. It was also found that the process comprised three distinct periods. Initially (2–3 min after process initiation), blasting did not force agitation of the fragments. Then the fluidized bed started to form and fragments started to circulate. The water color changed indicating that the deposit was being removed from the glass surface. At some point in time the change in color ends; this indicates completion of cleaning. The representative experiments are presented below. Experiment 1. A glass tube with an internal diameter (ID) of 15 cm and a length of 1 m was filled with 5.7 l water. The glass from a separated CRT was dumped in the water. The total weight of the glass was 2 kg and the size of fragments was about 5–10 mm. At the bottom of the tube a water nozzle with ID 1.55 mm was installed and water at a pressure of 3.4 MPa was injected into the tube. It was observed that the water stream was not able to form the fluidized bed and cycle the glass fragments, which remained at the bottom of the tube as a lump. The experiment was not successful. Experiment 2. In order to increase the kinetic energy of the water, the nozzle diameter was reduced to 1.25 mm and the water pressure was increased to 13.5 MPa. The size of the pipe was not altered. Still no glass circulation was attained. Experiment 3. The nozzle ID was reduced to 0.75 mm. The water pressure prior to the nozzle reached 40.8 MPa. The fragments moved in the water bath chaotically. However, the velocity of the fragments was not sufficient and practically no collisions occurred. Again the results of the experiments were negative. Experiment 4. The ID of the tube was reduced to 75 mm. The length of the tube was 1 m. One kg of glass cullet was loaded into 7.6 l water. The size of fragments in this case did not exceed 50 mm, because larger fragments could not move freely in the tube. Water was injected into the tube via a nozzle with ID 0.75 mm at a pressure of 41 MPa. Under these conditions a fluidized bed was formed and

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Figure 4. Size distribution of screen and funnel fragments after cleaning in a fluidized bed.

Figure 5. Size distribution of the fragments of the faceplate before and after cleaning.

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the desired glass circulation was attained. After the blasting was stopped, the glass was separated from the water and its cleanliness was evaluated visually. It was found that when the duration of blasting exceeded 15 min, acceptable glass cleanliness was attained. However, because the level of the bath during blasting increased and water flowed out of the tube, the experiment was ended. Experiment 5. Experiment 4 was repeated. In order to prevent the water overflow during the injection, a number of openings were formed in the tube wall to allow the extra water to flow out from the tube. In order to prevent glass from escaping, the openings were protected by screens. As a result the glass fragments were successfully decontaminated. Experiments 1–5 demonstrated the feasibility of using water blasting for glass decontamination. However, the use of the medium-pressure, high-flow rate pump increased the cost of the facilities. In addition, special provisions are needed to remove and recycle the blasting water. Because of these shortcomings, water was replaced by air as a blasting medium. The air blasting was studied in the course of the following experiments. Experiment 6. The experiment involved the use of air as a blasting medium. In the course of this experiment fragments of the faceplate were loaded into a glass tube with an ID of 88 mm and a length of 2 m and containing about 5.7 l water. Air at a pressure of 0.4–0.6 MPa and a flow rate of 0.0085 m3/s was injected into the tube via a single nozzle. The nozzle diameter was 6 mm. The duration of blasting was 8 min. A visually acceptable cleanliness of glass was attained. Experiment 7. In order to increase the rate of cleaning Experiment 6 was repeated at a nozzle diameter of 3 mm. At this condition, the air stream was not decomposed into bubbles and continuous gas streams in the liquid were developed. The experiment showed that at the process conditions the minimal nozzle diameter which prevented formation of continuous streams was 6 mm. At the nozzle diameter of 6 mm and more, the injected air formed bubbles which stirred the bath. Experiment 8. The blasting conditions were identical to those in Experiment 6. The funnel glass having “black” deposit (composition unknown) was used. Process duration was 10 min. The final glass cleanliness was acceptable. Experiment 9. The blasting conditions were identical to those in Experiment 8. The funnel glass having “white” deposit (the composition unknown) was loaded. Process duration was 10 min. The result was negative; the glass cleanliness was unacceptable. Experiment 10. The conditions for blasting of the fragments of the funnel glass having the “white” deposit were identical to those of Experiment 9. Process duration was 25 min. The glass cleanliness was acceptable. Experiment 11. The conditions for cleaning funnel fragments having the “white” deposit were identical to those of Experiment 10. Process duration was 15 min. The glass cleanliness was acceptable. Other experiments involved the use of various tube materials (glass, plexiglas, metal). It was found that any of these materials could be used for reactor construc-

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tion. Blasting with air at various tube lengths was also explored. It was shown that the length of the tube was acceptable as long as water was contained in the tube. Another part of the study involved investigation of fragments size reduction in the course of blasting. The fragments of the faceplate and the funnel were separated by a screen and then by a particle size analyzer. Thus, fragments size distribution was determined. The results are shown in Figs 4 and 5. 5. EXPERIMENTAL RESULTS

The experiments conducted demonstrated the feasibility of fluidized bed decontamination of CRT fragments. As the glass decontamination was attained only at intense circulation and, thus, collision of the fragments, the conclusion was that deposit removal was due to mechanical interaction between fragments. Chemical processes played a secondary, if any, role in glass cleaning in the above experiments. It was found that the water blasting was an unstable process. The channeltype flow is readily formed in the course of water injection. Special provision for water removal is required. Conversely, air blasting results in the formation of a steady stream of bubbles, which occupies practically the entire volume of the bath. This brings about complete decontamination of the glass. Indeed, no contaminated fragments were found in a number of experiments involving air blasting. Thus, the most efficient way of glass cleaning is air blasting of the water bath containing glass fragments. The results of cleaning, however, are determined by the conditions of blasting (nozzle diameter, airflow rate), as well as by the reactor geometry (diameter, height). If the amount of air or its velocity is not sufficient the deposit is not removed. If, however, the velocity of the blasting medium is excessive or the flow rate per unit bath cross section is too high the blasting medium forms channels in the bath. In this case at least a part of the bath is not involved in the circulation, and thus cleaning of the glass will be incomplete. In order to assure glass cleaning, it is necessary to prevent formation of an air jet in the water bath. This goal is attained if the dynamic air pressure at the entrance of the bath is comparable to static pressure of the water. If the static pressure exceeds the dynamic pressure of the air, the nozzle will be locked and air will not be able to enter the bath. If, on the other hand, the dynamic pressure significantly exceeds the static pressure of the water, a jet is formed at the exit of the nozzle. This jet might decompose into bubbles within the bath in the region where the energy dissipation at the gas-liquid interface results in a significant loss of the jet kinetic energy. Of course, such mode of bubble formation is highly inefficient. It should be noted that if the air stream decomposes into an array of bubbles, as shown in Fig. 3, the formation of a channel flow becomes impossible. Decontamination of fragments is due to forces generated at the glass surface in the course of collisions. In order to accomplish surface decontamination, the fragment velocity must be adequate. The source of kinetic energy for the fragments is the potential energy of the emerging bubbles. While emerging, the bub-

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bles accelerate the water in the bath and water accelerates the submerged particles. A part of the bubble energy is lost due to the dissipative processes in the bath. The potential energy of air bubbles at their formation is equal to the sum of the kinetic energy of the emerging bubbles and the energy dissipated in the bath and is determined by the air flow rate and the water level. These variables determine the rate of energy supply into the bath. The required energy, i.e., the energy needed for removal of the deposit, depends on the deposit adhesion to the glass surface. The stronger the adhesion, the higher the fragment velocity needed and the longer the process duration. For complete cleaning, the available energy must exceed, or at least be equal to, the required energy. The collision of glass fragments facilitates surface cleaning but causes fracturing leading to cullet size reduction. It was found that cullet size was reduced by 17% for the faceplate and by 40% for the funnel. At the same time, the fraction of fine particles increased by 9% and 21%, respectively. It is necessary to optimize the conditions and duration of cleaning in order to reduce glass fracturing while producing clean cullet and fine powder. In order to attain complete decontamination of the glass batch the emerging bubbles must be evenly distributed across the bath. No still regions or channels should develop. A uniform bubble distribution will be achieved if the velocity of the emerging bubbles is equal to volumetric flow rate of the air at the entrance of the bath divided by the cross-sectional area of the bath. The thermodynamic considerations (conditions of bubble formation and distribution, potential energy of the bubbles) enable us to use the dimensionless equations, which determine the basic dimensions of the bath and constitute the basis for the reactor design. It was shown that the material of the tube did not affect decontamination. Various tube materials were used to construct the reactor and no change in process conditions was noticed. It appears that the dominant mechanism for the deposit removal is the particle collision. The information acquired enables us to suggest that the fluidized bed cleaning occurs as follows. In the beginning, the air bubbles entering or generated in the bath emerge to the surface and induce water circulation. The kinetic energy of the water increases due to the transfer of the energy from bubbles to the water. Due to the friction between the water and fragments, tangential forces are developed at the solid–liquid interface. These forces, however, are insufficient to overcome inertial and gravitational forces acting on the fragments as well as the frictional forces at the solid–solid interface. Consequently, during this stage of the process, water circulates with increasing speed, while glass fragments remain motionless. As the water speed increases, so do the drag forces at the solid–liquid interface. Eventually the drag becomes sufficient to entrain glass particles into the water stream. Energy transfer from the bubbles accelerates the water, while the energy transfer from the water accelerates the fragments. Both the water and glass cullet move with increasing speed. This, however, results in an increased energy dissipation within the water, as well as at the gas–water and water–solid interfaces.

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Figure 6. Size distribution of the fragments of the funnel before and after cleaning.

The energy dissipation reduces the acceleration of both water and particles. Eventually both water and glass attain equilibrium conditions and move at constant velocity. As the moving particles collide, the collisions result in surface erosion and subsequent decontamination. The process continues until the deposit is removed completely. These phenomena constitute the second stage of cleaning. After decoating of fragments, collisions result only in further cullet fracturing. This is the third stage of the fluidized bed glass cleaning. In order to optimize process results it is necessary to minimize the duration of the first stage, precisely maintain the required fluidized bed parameters during the second stage and eliminate the third stage. The experiments performed showed that the desired results were attained at a reactor diameter of 88 mm, height of 2 m, charge of 1 kg, blast air flow of 0.0085 m3/sec and pressure of 0.4–0.6 MPa. At these conditions the process duration was 10 min. The effect of the fluidized bed cleaning on the size of glass fragments is shown in Figs 4–6. It follows from these figures that the funnel glass is more susceptible to fracturing than faceplate. These figures also show that after cleaning the glass consists of both very fine and large fragments. The percentage of intermediate size fragments is comparatively small. Additional process analysis is needed to explain these phenomena.

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6. CONCLUSIONS

The study performed involved an experimental investigation of decontamination of broken glass generated in the course of CRT recovery. The experiments involved cleaning of fragments submerged into a water bath and blasted by air. It was found that blasting resulted in acceptable cleaning of the fragments. Thus, the work demonstrated the feasibility of the use of the fluidized bed. This is the main outcome of the study performed. Additional research is needed, however, to elaborate the process mechanism and to optimize the reactor parameters. It is possible that in addition to the mechanical deposit removal a chemical decontamination is also taking place. It is also possible that this mode of decontamination can be enhanced by the addition of chemicals; for example, surface-active agents or by the increase of bath temperature. Cleaning caused reduction of the fragments size which negatively affects the value of the recycled glass. However, the fluidized bed cleaning resulted in the formation of fine glass powder, which has commercial value on its own. Currently, only comparatively large cullet has found commercial application as a charge for smelting furnaces. It is expected that new studies will identify the users of fine particles. It is also expected that the market value of these particles will be quite high. The utilization of the fine powder, which currently is disposed, will reduce cost of glass recycling. Acknowledgements This work was accomplished as a subcontract to the Demanufacturing of Electronic Equipment for Reuse and Recycling (DEER2) task of the National Defense Center for Environmental Excellence (NDCEE), a Department of Defense (DOD) program. The authors express deep appreciation for the assistance of R. Cooper, C. Yourkievitz and G. Yourkievitz in planning of this study and for evaluation of its results. The contribution of T. Schachinger in the preparation of this manuscript is acknowledged. REFERENCES 1. E.S. Geskin, B. Goldenberg and R.J. Caudill, Proceedings of the 2002 IEEE International Symposium on Electronics and the Environment, pp. 240-253 (2002). 2. E.S. Geskin, B. Goldenberg and R.J. Caudill, in Water Jetting, P. Lake (Ed.), BHR Group, Cranfield (2002). 3. L.S. Fan, Gas-Liquid-Solid Fluidization Engineering, Butterworth, Oxford (1989). 4. L.S. Fan and K. Tsuchiya, Wake Dynamics in Liquids and Liquid-Solid Suspensions, Butterworth, Oxford (1990). 5. C. Growe, M. Sommerfeld and Y. Tsuji, Multiphase Flow with Droplets and Particles. CRC Press, Boca Raton, FL (1997).

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Part 2 Particle Adhesion and Removal

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 183–229 Ed. K.L. Mittal © VSP 2003

Mechanics of nanoparticle adhesion — A continuum approach JÜRGEN TOMAS∗ Mechanical Process Engineering, Department of Process Engineering and Systems Engineering, Otto-von-Guericke-University, Universitätsplatz 2, D-39106 Magdeburg, Germany

Abstract—The fundamentals of particle-particle adhesion are presented using continuum mechanics approaches. The models for elastic (Hertz, Huber, Cattaneo, Mindlin and Deresiewicz), elasticadhesion (Derjagin, Bradley, Johnson), plastic-adhesion (Krupp, Molerus, Johnson, Maugis and Pollock) contact deformation response of a single, normal or tangential loaded, isotropic, smooth contact of two spheres are discussed. The force-displacement behaviors of elastic–plastic (Schubert, Thornton), elastic–dissipative (Sadd), plastic–dissipative (Walton) and viscoplastic–adhesion (Rumpf) contacts are also shown. Based on these theories, a general approach for the time and deformation rate dependent and combined viscoelastic, plastic, viscoplastic, adhesion and dissipative behaviors of a spherical particle contact is derived and explained. The decreasing contact stiffness with decreasing particle diameter is the major reason for adhesion effects at nanoscale. Using the model “stiff particles with soft contacts”, the combined influence of elastic-plastic and viscoplastic repulsions in a characteristic (averaged) particle contact is shown. The attractive particle adhesion term is described by a sphere–sphere model for van der Waals forces without any contact deformation and a plate–plate model for this micro-contact flattening is presented. Various contact deformation paths for loading, unloading, reloading and contact detachment are discussed. Thus, the varying adhesion forces between particles depend directly on this “frozen” irreversible deformation, the socalled contact pre-consolidation history. Finally, for colliding particles the correlation between particle impact velocity and contact deformation response is obtained using energy balance. This constitutive model approach is generally applicable for solid micro- or nanocontacts but has been shown here for dry titania nanoparticles. Keywords: Powder; particle mechanics; contact behavior; constitutive models; adhesion force; nanoparticles.

1. INTRODUCTION

In terms of particle processing and product handling, the well-known flow problems of cohesive powders in storage and transportation containers, conveyors or process apparatuses include bridging, channeling and oscillating mass flow rates. In addition, flow problems are related to particle characteristics associated with ∗

Phone: (49-391) 67-18783, Fax: (49-391) 67-11160, E-mail: [email protected]

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feeding and dosing, as well as undesired effects such as widely spread residence time distribution, time consolidation or caking, chemical conversions and deterioration of bioparticles. Finally, insufficient apparatus and system reliability of powder processing plants are also related to these flow problems. The rapid increasing production of cohesive to very cohesive nanopowders, e.g., very adhering pigment particles, micro-carriers in biotechnology or medicine, auxiliary materials in catalysis, chromatography or silicon wafer polishing, make these problems much serious. Taking into account this list of technical problems and hazards, it is essential to deal with the fundamentals of particle adhesion, powder consolidation and flow, i.e. to develop a reasonable combination of particle and continuum mechanics. The well-known failure hypotheses of Tresca, Coulomb and Mohr and Drucker and Prager (in Refs. [1, 2]), the yield locus concept of Jenike [3, 4] and Schwedes [5], the Warren–Spring equations [6–10], and the approach by Tüzün [12], etc., were supplemented by Molerus [13–16] to describe the cohesive, steady-state flow criterion. Nedderman [17, 18], Jenkins [19] and others discussed the rapid and collisional flow of non-adhering particles, as well as Tardos [20] discussed the frictional flow for compressible powders without any cohesion from the fluid mechanics point of view. Additionally, the simulation of particle dynamics of free flowing granular media is increasingly used, see, e.g., Cundall [21], Campbell [22], Walton [23, 24], Herrmann [25] and Thornton [26]. Additionally, particle adhesion effects are related to undesired powder blocking at conveyer transfer chutes or in pneumatic pipe bends [27] in powder handling and transportation, to desired particle cake formation on filter media [28, 29], to wear effects of adhering solid surfaces [30, 31], fouling in membrane filtration, fine particle deposition in lungs, formulation of particulate products [32–35] or to surface cleaning of silicon wafers [36–40, 133], etc. The force–displacement behaviors of elastic, elastic–adhesion, plastic– adhesion, elastic–plastic, elastic–dissipative, plastic–dissipative and viscoplastic– adhesion contacts are shown. Based on these individual theories, a general approach for the time and deformation rate dependent and combined viscoelastic, plastic, viscoplastic, adhesion and dissipative behaviors of a spherical particle contact is derived and explained. 2. PARTICLE CONTACT CONSTITUTIVE MODELS

In terms of particle technology, powder processing and handling, Molerus [13, 14] explained the consolidation and non-rapid flow of dry, fine and cohesive powders (particle diameter d < 10 µm) in terms of the adhesion forces at particle contacts. In principle, there are four essential mechanical deformation effects in particle–surface contacts and their force–response (stress-strain) behavior can be explained as follows (Table 1):

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(1) elastic contact deformation (Hertz [41], Huber [42], Derjaguin [43], Bradley [44, 45], Cattaneo [46], Mindlin [47], Sperling [48], Krupp [49], Greenwood [50], Johnson [51], Dahneke [52], Thornton [53, 54], Sadd [55]), which is reversible, independent of deformation rate and consolidation time effects and valid for all particulate solids; (2) plastic contact deformation with adhesion (Derjaguin [43], Krupp [56], Schubert [57], Molerus [13, 14], Maugis [58], Walton [59] and Thornton [60]), which is irreversible, deformation rate and consolidation time independent, e.g. mineral powders; (3) viscoelastic contact deformation (Yang [61], Krupp [49], Rumpf et al. [62] and Sadd [55]), which is reversible and dependent on deformation rate and consolidation time, e.g., bio-particles; (4) viscoplastic contact deformation (Rumpf et al. [62]), which is irreversible and dependent on deformation rate and consolidation time, e.g., nanoparticles fusion. This paper is intended to focus on a characteristic, soft contact of two isotropic, stiff, linear elastic, smooth, mono-disperse spherical particles. Thus, this soft or compliant contact displacement is assumed to be small (hK/d << 1) compared to the diameter of the stiff particle. The contact area consists of a representative number of molecules. Hence, continuum approaches are only used here to describe the force-displacement behavior in terms of nanomechanics. The microscopic particle shape remains invariant during the dynamic stressing and contact deformation at this nanoscale. In powder processing, these particles are manufactured from uniform material in the bulk phase. These prerequisites are assumed to be suitable for the mechanics of dry nanoparticle contacts in many cases of industrial practice. 2.1. Elastic, plastic and viscoplastic contact deformations 2.1.1. Elastic contact displacement For a single elastic contact of two spheres 1 and 2 with a maximum contact circle radius rK,el but small compared with the particle diameter d1 or d2, an elliptic pressure distribution pel(rK) is assumed, Hertz [41]: 2

æ rK ö æ pel ö çp ÷ =1– ç r ÷ è max ø è K ,el ø

2

(1)

With the maximum pressure p(rK = 0) = pmax in the center of contact circle at depth z = 0, pmax =

3 ⋅ FN 2 ⋅ π ⋅ rK ,el 2

(2)

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Mechanics of nanoparticle adhesion — A continuum approach 189

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and the median particle radius r1,2 (characteristic radius of contact surface curvature) (Fig. 1), æ ö r1,2 = ç 1 + 1 ÷ è r1 r2 ø

–1

(3)

and the average material stiffness (E, modulus of elasticity; ν, Poisson ratio) æ 1 −ν 2 1 −ν 2 1 2 E = 2⋅ç + ç E1 E2 è *

ö ÷ ÷ ø

−1

(4)

one can calculate the correlation between normal force FN and maximum contact radius rK,el: rK3 ,el =

3 ⋅ r1,2 ⋅ FN

(5)

*

2⋅ E

Considering surface displacement out of the contact zone (for details, see Huber [42]) the so-called particle center approach or height of overlap of both particles hK is [41]: 2

hK = rK ,el / r1,2

(6)

Substitution of Eq. (6) in Eq. (5) results in a non-linear relation between elastic contact force and deformation [41] (Fig. 1): * 3 FN = 2 ⋅ E ⋅ r1,2 ⋅ hK 3

(7)

Eq. (7) is shown as the dashed curve marked Hertz. The maximum pressure 2 pmax, Eq. (2), is 1.5 times the average pressure FN / (π ⋅ rK ,el ) on the contact area

and lies below the micro-yield strength pf. Because of surface bending and, consequently, the opportunity for unconfined yield at the surface perimeter outside of the contact circle rK ≥ rK,el (Fig. 1b), a maximum tensile stress is found [42] σ t ,max ≈ −0.15 ⋅ pmax (here negative because of positive pressures in powder mechanics):

σt pmax

2

rK ≥ rK ,el

r = − 1 − 2 ⋅ν ⋅ 2K 3 rK ,el

(8)

This critical stress for cracking of a brittle particle material with low tensile strength is smaller than the maximum shear stress τ max ≈ 0.31 ⋅ pmax according to Eq. (11) which is found at the top of a virtual stressing cone below the contact

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Figure 1. Characteristic spherical particle contact deformation. (a) Approach and (b) elastic contact deformation (titania, primary particles d = 20–300 nm, surface diameter dS = 200 nm, median particle diameter d50,3 = 610 nm, specific surface area AS,m = 12 m²/g, solid density ρs = 3870 kg/m3, surface moisture XW = 0.4%, temperature θ = 20°C) [148]. Pressure and compression are defined as positive but tension and extension are negative. The origin of this diagram (hK = 0) is equivalent to the characteristic adhesion separation for direct contact (atomic center to center distance), and can be estimated for a molecular force equilibrium a = a0 = aF=0. After approaching from an infinite distance –∞ to this minimum separation aF=0 the sphere–sphere contact without any contact deformation is formed by the attractive adhesion force FH0 (the so-called “jump in”). Then the contact may be loaded FH0 – Y and, as a response, is elastically deformed with an approximate circular contact area due to the curve marked with Hertz (panel b). The tensile contribution of principal stresses according to Huber [42] at the perimeter of contact circle is neglected for the elliptic pressure distribution, drawn below panel b.

Mechanics of nanoparticle adhesion — A continuum approach 2

2

193

2

area on the principal axis rK = x + y = 0 in the depth of z ≈ rK,el/2. Combining the major principal stress distribution, Eq. (9), σ1 = σz(z) at contact radius rK = 0 2

r σ z (z) = 2 K ,el 2 , pmax r + z

(9)

K ,el

and the minor principal stress, Eq. (10), σ2 = σy = σt(z) [42]

σ t ( z) pmax r

2

K ≤ rK ,el

r r ù é = − 1 ⋅ 2 K ,el 2 + (1 + ν ) ⋅ ê1 − z ⋅ arctan K ,el ú , 2 r +z r z û K ,el ë K ,el

(10)

the maximum shear stress inside a particle contact rK ≤ rK,el is obtained using the Tresca hypothesis for plastic failure τ max = ( σ 1 − σ 2 ) 2 [1]:

τ ( z) pmax

2

rK ≤ rK ,el

r = 3 ⋅ 2 K ,el 2 − 1 + ν 4 r +z 2 K ,el

r ù é ⋅ ê1 − z ⋅ arctan K ,el ú z û ë rK ,el

(11)

This internal shear stress distribution becomes more and more critical for ductile or soft solids with a small transition to yield point, and consequently, plastic contact deformation like nanoparticles with very low stiffness, see Section 2.3. Due to the parabolic curvature FN(hK), the particle contact becomes stiffer with increasing diameter r1,2, contact radius rK or displacement hK (kN is the contact stiffness in normal direction): kN =

dFN * * = E ⋅ r1,2 ⋅ hK = E ⋅ rK dhK

(12)

The influence of a tangential force in a normal loaded spherical contact was considered by Cattaneo [46] and Mindlin [47, 63]. About this and complementary theories as well as loading, unloading and reloading hysteresis effects, one can find a detailed discussion by Thornton [53]. He has expressed this tangential contact force as [53, 54]: FT = 4 ⋅ψ ⋅ G* ⋅ r1,2 ⋅ hK ⋅ ∆δ ± (1 − ψ ) ⋅ tanϕ i ⋅ ∆FN

(13)

Here ∆δ is the tangential contact displacement, ψ the loading parameter dependent on loading, unloading and reloading, ϕi the angle of internal friction, G = E 2 (1 + ν ) the shear modulus, and the averaged shear modulus is given as: æ 2 – ν1 2 – ν 2 ö + G = 2⋅ç G2 ÷ø è G1 *

–1

(14)

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Thus, with ψ = 1 the ratio of the initial tangential stiffness kT =

dFT * = 4 ⋅ G ⋅ rK dδ

(15)

to the initial normal stiffness according to Eq. (12) is: kT 2 ⋅ ( 1 − ν ) = kN 2 −ν

(16)

Hence this ratio ranges from unity, for ν = 0, to 2/3, for ν = 0.5 [63], which is different from the common linear elastic behavior of a cylindrical rod. 2.1.2. Elastic displacement of an adhesion contact The adhesion in the normal loaded contact of spheres with elastic displacement will be additionally shown. For fine and stiff particles, the Derjaguin, Muller and Toporov (DMT) model [43, 65, 66] predicts that half of the interaction force FH,DMT/2 occurs outside in the annular area which is located at the perimeter closed by the contact, Eq. (17). This is in contrast to the Johnson, Kendall and Roberts (JKR) model [67], which assumes that all the interactions occur within the contact radius of the particles. The median adhesion force FH,DMT (index H,DMT) of a direct spherical contact can be expressed in terms of the work of adhesion WA, conventional surface energy γA or surface tension σsls as WA = 2 ⋅ γ A = 2 ⋅ σ sls . The index sls means particle surface-adsorption layers (with liquid equivalent mechanical behavior) – particle surface interaction. If only molecular interactions with separations near the contact contribute to the adhesion force then the so-called Derjaguin approximation [43] is valid FH ,DMT = 4 ⋅ π ⋅ σ sls ⋅ r1,2 ,

(17)

which corresponds to Bradley’s formula [44]. This surface tension σsls equals half the energy needed to separate two flat surfaces from an equilibrium contact distance aF=0 to infinity [75]: ∞

σ sls

=− 1⋅ 2

ò

pVdW (a ) da =

aF =0

CH ,sls 24 ⋅ π ⋅ aF =0 2

(18)

The adhesion force per unit planar surface area or attractive pressure pVdW which is used here to describe the van der Waals interactions at contact is equivalent to a theoretical bond strength and can simply calculated as [75] (e.g., pVdW ≈ 3–600 MPa): pVdW =

CH ,sls 6 ⋅π

⋅ aF3 =0

=

4 ⋅ σ sls aF =0

(19)

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Using this and for a comparison of the adhesion or bond strength, a dimensionless ratio of adhesion displacement (extension at contact detachment), expressed as height of “neck” hN,T around the contact zone, to minimum molecular center separation aF=0 can be defined as 2 hN ,T æ 4 ⋅ r1,2 ⋅ σ sls ç = ΦT = aF = 0 ç * 2 3 è E ⋅ aF =0

1/ 3

ö ÷ ÷ ø

,

(20)

which was first introduced by Tabor [74] and later modified and discussed by Muller [66] and Maugis [76]. The DMT model works for very small and stiff particles ΦT < 0.1 [66, 76, 82]. For separating a stiff, non-deformed spherical point contact, the DMT theory [65] predicts a necessary pull-off force FN,Z equivalent to the adhesion reaction force expressed by Eq. (17). Compared with the stronger covalent, ionic, metallic or hydrogen bonds, these particle interactions are comparatively weak. From Eq. (18) the surface tension is about σsls = 0.25–50 mJ/m2 or the Hamaker constant according to the Lifshitz continuum theory amounts to CH,sls = (0.2–40)⋅10–20 J [70, 75]. Notice here, the particle interactions depend greatly on the applied load, which is experimentally confirmed by atomic force microscopy [78, 79, 98]. A balance of stored elastic energy, mechanical potential energy and surface energy delivers the contact radius of the two spheres [51], expressed here with a constant adhesion force FH,JKR from Eq. (23): rK3 =

3 ⋅ r1,2 2⋅ E

*

(

⋅ FN + FH ,JKR + 2 ⋅ FH ,JKR ⋅ FN + FH2,JKR

)

(21)

Eq. (21) indicates a contact radius enhancement with increasing work of adhesion. The contact force-displacement relation is obtained from Eqs. (6) and (21) and can be compared with the Hertz relation Eq. (7) by the curves in Fig. 2 marked with Hertz and JKR: * 4 ⋅ E* ⋅ FH,JKR 3 3 2 ⋅ E FN = ⋅ r1,2 ⋅ hK − ⋅ r1,2 ⋅ hK 3 3

(22)

For small contact deformation the so-called JKR limit [51] is half of the constant adhesion force FH,JKR. This JKR model can be applied for higher bond strengths ΦT > 5 [76, 82–84]. It is valid for comparatively larger and softer particles than the DMT model predicts [115]: FN ,Z ,JKR =

FH ,JKR = 3 ⋅ π ⋅ σ sls ⋅ r1,2 2

Thus the contact radius for zero load FN = 0,

(23)

196

J. Tomas

Figure 2. Characteristic particle contact deformation. (c) Elastic–plastic compression [148]. The dominant linear elastic–plastic deformation range between pressure levels of powder mechanics [4] is demonstrated here. If the maximum pressure in the contact center reaches the micro-yield strength pmax = pf at the yield point Y then the contact starts with plastic yielding which is intensified by mobile adsorption layers. Next, the combined elastic–plastic yield boundary of the partial plate–plate contact is achieved as given in Eq. (58). This displacement is expressed with the annular elastic Ael (thickness rK,el) and circular plastic Apl (radius rK,pl) contact area, shown below panel c.

Mechanics of nanoparticle adhesion — A continuum approach

197

3 ⋅ r1,2 ⋅ FH ,JKR

rK ,0 = 3

(24)

E*

is reduced to the pull-off contact radius, i.e., rK ,pull-off = rK ,0 / 3 4 .

(25)

Additionally, with applying an increasing tangential force FT, the contact radius rK is reduced by the last term within the square root: 3

rK =

3 ⋅ r1,2 æ FT2 ⋅ E* 2 çF +F ⋅ + 2 ⋅ F ⋅ F + F − N H ,JKR H ,JKR N H ,JKR 2 ⋅ E* ç 4 ⋅ G* è

ö ÷, ÷ ø

(26)

When the square root in Eq. (26) disappears to zero, a critical value FT,crit is obtained, the so-called “peeling” of contact surfaces [64, 88]: FT ,crit = 2 ⋅

(2⋅ F

H ,JKR

)

⋅ FN + FH2,JKR ⋅ G* E*

(27)

An effective or net normal force (FN + FH,JKR) remains additionally in the contact [54]. Considering FT > FT,crit, i.e., contact failure by sliding (see Mindlin [63]), the tangential force limit is expressed as FT = tanϕi ⋅ ( FN + FH0 ) . The adhesion force FH0 (index H0) is constant during contact failure and the coefficient (or angle) of internal friction µi = tanϕi is also assumed to be constant for a multi-asperity contact [50, 81, 82]. This constant friction was often confirmed for rough surfaces in both elastic and plastic regimes [50, 81, 84], but not for a single-asperity contact with nonlinear dependence of friction force on normal load [82, 84]. Rearranging Eq. (26), the extended contact force–displacement relation shows a reduction of the Hertz (first square-root) and JKR contributions to normal load FN which is needed to obtain a given displacement hK: *

* 4 ⋅ E ⋅ FH ,JKR F 2 ⋅ E* 3 3 ⋅ r1,2 ⋅ hK − T * FN = 2 ⋅ E ⋅ r1,2 ⋅ hK − 3 3 4⋅G

(28)

However in terms of small particles (d < 10 µm), the increase of contact area with elastic deformation does not lead to a significant increase of attractive adhesion forces because of a practically too small magnitude of van der Waals energy of adhesion (Eq. (18)). The reversible elastic repulsion restitutes always the initial contact configuration during unloading. Consequently, the increase of adhesion by compression, e.g., forming a snow ball, the well-known cohesive consolidation of a powder or the particle interac-

J. Tomas

198

tion and remaining strength after tabletting must be influenced by irreversible contact deformations, which are shown for a small stress level in a powder bulk in Figs 2 and 3. If the maximum pressure pmax = pf in the center of the contact circle reaches the micro-yield strength, the contact starts with irreversible plastic yielding (index f). From Eqs. (2) and (5) the transition radius rK,f and from Eq. (6) the center approach hK,f are calculated as: rK ,f =

hK ,f =

π ⋅ r1,2 ⋅ pf

(29)

*

E

π 2 ⋅ r1,2 ⋅ pf2 E*

(30)

2

Figure 2 demonstrates the dominant irreversible deformation over a wide range of contact forces. This transition point Y for plastic yielding is essentially shifted towards smaller normal stresses because of particle adhesion influence. Rumpf et al. [62] and Molerus [13, 14] introduced this philosophy in powder mechanics and the JKR theory was the basis of adhesion mechanics [58, 67, 76, 85, 86, 90]. 2.1.3. Perfect plastic and viscoplastic contact displacement Actually, assuming perfect contact plasticity, one can neglect the surface deformation outside of the contact zone and obtain with the following geometrical relation of a sphere

(

rK2 = r12 − r1 − hK ,1

)

2

= 2 ⋅ r1 ⋅ hK ,1 − hK2 ,1 ≈ d1 ⋅ hK ,1

(31)

the total particle center approach of the two spheres: 2

hK = hK ,1 + hK ,2 =

2

2

rK rK r + = K d1 d 2 2 ⋅ r1,2

(32)

Because of this, a linear force–displacement relation is found for small spherical particle contacts. The repulsive force as a resistance against plastic deformation is given as: FN ,pl = pf ⋅ AK = π ⋅ d1,2 ⋅ pf ⋅ hK

(33)

Thus, the contact stiffness is constant for perfect plastic yielding behavior, but decreases with smaller particle diameter d1,2 especially for cohesive fine powders and nanoparticles: k N ,pl =

dFN = π ⋅ d1,2 ⋅ pf dhK

(34)

Mechanics of nanoparticle adhesion — A continuum approach

199

Figure 3. Characteristic particle contact deformation. (d) Elastic unloading and reloading with dissipation (titania) [148]. After unloading U – E the contact recovers elastically in the compression mode and remains with a perfect plastic displacement hK,E. Below point E on the axis the tension mode begins. Between the points U – E – A the contact recovers elastically according to Eq. (64) to a displacement hK,A. The reloading curve runs from point A to U to the displacement hK,U, Eq. (65).

200

J. Tomas

Additionally, the rate-dependent, perfect viscoplastic deformation (at the point of yielding) expressed by contact viscosity ηK times indentation rate h&K is assumed to be equivalent to yield strength pf multiplied by indentation height increment hK pf ⋅ hK = η K ⋅ h&K

(35)

and one obtains again a linear model regarding strain rate: FN ,vis = ηK ⋅ A& K = π ⋅ d1,2 ⋅ηK ⋅ h&K

(36)

An attractive viscous force is observed, e.g., for capillary numbers Ca = ηK ⋅ h&K / σ lg > 1 when comparatively strong bonds of (low-viscous) liquid bridges are extended with negative velocity –h&K [71–73]. Consequently, the particle material parameters: contact micro-yield strength pf and viscosity ηK are measures of irreversible particle contact stiffness or softness. Both plastic and viscous contact yield effects were intensified by mobile adsorption layers on the surfaces. The sum of deformation increments results in the energy dissipation. For larger particle contact areas AK, the conventional linear elastic and constant plastic behavior is expected. Now, what are the consequences of small contact flattening with respect to a varying, i.e., load or pre-history-dependent adhesion? 2.2. Particle contact consolidation by varying adhesion force Krupp [49] and Sperling [48, 56] developed a model for the increase of adhesion force FH (index H) of the contact. This considerable effect is called here as “consolidation” and is expressed as the sum of adhesion force FH0 according to Eq. (17) plus an attractive/repulsive force contribution due to irreversible plastic flattening of the spheres (pf is the repulsive “microhardness” or micro-yield strength of the softer contact material of the two particles, σss/a0 is the attractive contact pressure, index ss represents solid–vacuum–solid interaction): 2 ⋅ σ ss ö æ FH = 4 ⋅ π ⋅ r1,2 ⋅ σ ss ⋅ ç 1 + ÷ è a0 ⋅ pf ø

(37)

Dahneke [52] modified this adhesion model by the van der Waals force without any contact deformation FH0 plus an attractive van der Waals pressure (force per unit surface) pVdW contribution due to partially increasing flattening of the spheres which form a circular contact area AK (CH is the Hamaker constant based on interacting molecule pair additivity [69, 75]):

Mechanics of nanoparticle adhesion — A continuum approach

FH = FH0 + AK ⋅ pVdW =

CH ⋅ r1,2 æ 2 ⋅ hK ö ⋅ ç1+ a0 ÷ø 6 ⋅ a02 è

201

(38)

The distance a0 denotes a characteristic adhesion separation. If stiff molecular interactions are provided (no compression of electron sheath), this separation a0 was assumed to be constant during contact loading. By addition the elastic repulsion of the solid material according to Hertz, Eq. (7), to this attraction force, Eq. (38), and by deriving the total force Ftot with respect to hK, the maximum adhesion force was obtained as absolute value FH ,max

CH ⋅ r1,2 æ 2 ⋅ CH2 ⋅ r1,2 ç = ⋅ 1+ 2 2 6 ⋅ a0 ç 27 ⋅ E* ⋅ a 7 0 è

ö ÷, ÷ ø

(39)

which occurs at the center approach of the spheres [52]: 2

hK ,max =

CH ⋅ r1,2 *2

(40)

6

9 ⋅ E ⋅ a0

But as mentioned before, this increase of contact area with elastic deformation does not lead to a significant increase of attractive adhesion force. The reversible elastic repulsion restitutes always the initial contact configuration. The practical experience with the mechanical behavior of fine powders shows that an increase of adhesion force is influenced by an irreversible or “frozen” contact flattening which depends on the external force FN [57]. Generally, if this external compressive normal force FN is acting at a single soft contact of two isotropic, stiff, smooth, mono-disperse spheres the previous contact point is deformed to a contact area, Fig. 1a to Fig. 2c, and the adhesion force between these two partners increases, see in Fig. 3 the so-called “adhesion boundary” for incipient contact detachment. During this surface stressing the rigid particle is not so much deformed that it undergoes a certain change of the particle shape. In contrast, soft particle matter such as biological cells or macromolecular organic material do not behave so. For soft contacts Rumpf et al. [62] have developed a constitutive model approach to describe the linear increase of adhesion force FH, mainly for plastic contact deformation: p æ FH = ç 1 + VdW pf è

pVdW ö ÷ ⋅ FH0 + p ⋅ FN = 1 + κ p ⋅ FH0 + κ p ⋅ FN f ø

(

)

(41)

With analogous prerequisites and derivation, Molerus [14] obtained an equivalent expression:

J. Tomas

202

FH = FH0 +

pVdW ⋅ FN = FH0 + κ p ⋅ FN pf

(42)

The adhesion force FH0 without additional consolidation (FN = 0) can be approached as a single rigid sphere–sphere contact (Fig. 1a). But, if this particle contact is soft enough the contact is flattened by an external normal force FN to a plate–plate contact (Fig. 2c). The coefficient κp describes a dimensionless ratio of attractive van der Waals pressure pVdW for a plate–plate model, Eq. (19), to repulsive particle micro-hardness pf which is temperature sensitive:

κp =

CH,sls pVdW = pf 6 ⋅ π ⋅ aF3 =0 ⋅ pf

(43)

This is referred to here as a plastic repulsion coefficient. The Hamaker constant CH,sls for solid–liquid–solid interaction (index sls) according to Lifshitz’ theory [70] is related to continuous media which depends on their permittivities (dielectric constants) and refractive indices [75]. The characteristic adhesion separation for a direct contact is of a molecular scale (atomic center-to-center distance) and can be estimated for a molecular force equilibrium (a = aF=0) or interaction potential minimum [75, 76, 91]. Its magnitude is about aF=0 ≈ 0.3–0.4 nm. This separation depends mainly on the properties of liquid-equivalent packed adsorbed water layers. This particle contact behavior is influenced by mobile adsorption layers due to molecular rearrangement. The minimum separation aF=0 is assumed to be constant during loading and unloading for technologically relevant powder pressures σ < 100 kPa (Fig. 2c). For a very hard contact this plastic repulsion coefficient is infinitely small, i.e., κp ≈ 0, and for a soft contact κp → 1. If the contact circle radius rK is small compared to the particle diameter d, the elastic and plastic contact displacements can be combined and expressed with the annular elastic Ael and circular plastic Apl contact area ratio [57]: FH = FH0 +

pVdW æ A pf ⋅ çç 1 + 2 ⋅ el 3 Apl è

ö ÷÷ ø

⋅ FN

(44)

For a perfect plastic contact displacement Ael → 0 and one obtains again Eq. (42): FH ≈ FH0 + κ p ⋅ FN

(45)

This linear enhancement of adhesion force FH with increasing preconsolidation force FN, Eqs. (41), (42) and (45), was experimentally confirmed for micrometer sized particles, e.g., by Schütz [94, 95] (κp = 0.3 for limestone) and Newton [96] (κp = 0.333 for poly(ethylene glycol), κp = 0.076 for starch, κp =

Mechanics of nanoparticle adhesion — A continuum approach

203

0.017 for lactose, κp = 0.016 for CaCO3) with centrifuge tests [92] as well as by Singh et al. [97] (κp = 0.12 for poly(methylmethacrylate), κp ≈ 0 for very hard sapphire, α-Al2O3) with an Atomic Force Microscope (AFM). The two methods are compared with rigid and rough glass spheres (d = 0.1–10 µm), without any contact deformation, by Hoffmann et al. [98]. Additionally, using the isostatic tensile strength σ0 determined by powder shear tests [91, 122, 147, 149, 151], this adhesion level is of the same order of magnitude as the average of centrifuge tests (see Spindler et al. [99]). The enhancement of adhesion force FH due to pre-consolidation was confirmed by Tabor [30], Maugis [85, 86] and Visser [110]. Also, Maugis and Pollock [58] found that separation was always brittle (index br) with a small initial slope of pull-off force, dFN,Z,br/dFN (FN,Z,br ≈ – FH), for a comparatively small surface energy σss of the rigid sphere–gold plate contact (index ss). In contrast, a pull-off force FN,Z,br proportional to FN was obtained from the JKR theory [58] for the full plastic range of high loading and brittle separation of the contact (Table 1): FN,Z,br = −σ ss ⋅ E ⋅ *

FN

π ⋅ pf3

(46)

Additionally, a load-dependent adhesion force was also experimentally confirmed in wet environment of the particle contact by Butt and co-workers [78, 79] and Higashitani and co-workers [87] with AFM measurements. The dominant plastic contact deformation of surface asperities during the chemical–mechanical polishing process of silicon wafers was also recognized, e.g., by Rimai and Busnaina [111] and Ahmadi and Xia [141]. These particlesurface contacts and, consequently, asperity stressing by simultaneous normal pressure and shearing, contact deformation, microcrack initiation and propagation, and microfracture of brittle silicon asperity peaks affect directly the polishing performance. Thus the Coulomb friction becomes dominant also in a wet environment. 2.3. Variation in adhesion due to non-elastic contact consolidation 2.3.1. Elastic–plastic force–displacement model All interparticle forces can be expressed in terms of a single potential function Fi = ±∂U i (hi ) / ∂hi and thus are superposed. This is valid only for a conservative system in which the work done by the force Fi versus distance hi is not dissipated as heat, but remains in the form of mechanical energy, simply in terms of irreversible deformation, e.g., initiation of nanoscale distortions, dislocations or lattice stacking faults. The overall potential function may be written as the sum of the potential energies of a single contact i and all particle pairs j. Minimizing this potential function å å ∂U ij / ∂hij = 0 one obtains the potential-force balance. i

j

J. Tomas

204

Thus, the elastic–plastic force–displacement models introduced by Schubert et al. [57], Eq. (44), and Thornton [60] Eq. (47)

(

FN = π ⋅ pf ⋅ r1,2 ⋅ hK − hK,f / 3

)

(47)

should be supplemented here with a complete attractive force contribution due to contact flattening described before. Taking into account Eqs. (41), (42) and (44), the particle contact force equilibrium between attraction (-) and elastic plus, si* multaneously, plastic repulsion (+) is given by ( rK represents the coordinate of annular elastic contact area): 2 å F = 0 = − FH0 − pVdW ⋅ π ⋅ rK2 − FN + pf ⋅ π ⋅ rK,pl

(48)

rK

+ 2 ⋅π ⋅

ò

* * pel (rK ) ⋅ rK

* drK

rK ,pl

2 2 ⋅ π ⋅ pmax ⋅ rK é æ rK,pl 2 2 ⋅ ê1 − çç FN + FH0 + pVdW ⋅ π ⋅ rK = pf ⋅ π ⋅ rK,pl + 3 ê è rK ë

ö ÷÷ ø

2 ù3 / 2

ú ú û

(49)

At the yield point rK = rK,pl the maximum contact pressure reaches the yield strength pel = pf. 2 2 é 2 ⋅ π ⋅ rK æ pf ö ù 2 2 FN + FH0 + pVdW ⋅ π ⋅ rK = pf ⋅ êπ ⋅ rK,pl + ⋅ç ÷ ú 3 êë è pmax ø úû

(50)

Because of plastic yielding, a pressure higher than pf is absolutely not possible and thus, the fictitious contact pressure pmax is eliminated by Eq. (1): FN + FH0 + pVdW ⋅ π

⋅ rK2

2 2 é 2 ⋅ π ⋅ rK æ rK,pl 2 = pf ⋅ êπ ⋅ rK,pl + ⋅ç1− 2 3 ç ê rK è ë

öù ÷ú ÷ú øû

(51)

Finally, the contact force equilibrium 2 é rK,pl ù 2 FN + FH0 + pVdW ⋅ AK = π ⋅ pf ⋅ rK ⋅ ê 2 + 1 ⋅ 2 ú ê 3 3 rK ú ë û

Apl ù é = pf ⋅ AK ⋅ ê 2 + 1 ⋅ 3 3 AK úú ëê û

and the total contact area AK are obtained:

(52)

Mechanics of nanoparticle adhesion — A continuum approach

AK =

FN + FH0 Apl ö æ − pVdW pf ⋅ çç 2 + 1 ⋅ 3 3 AK ÷÷ è ø

205

(53)

Next, the elastic–plastic contact area coefficient κA is introduced. This dimensionless coefficient represents the ratio of plastic particle contact deformation area Apl to total contact deformation area AK = Apl + Ael and includes a certain elastic displacement: A κ A = 2 + 1 ⋅ pl 3 3 AK

(54)

The solely elastic contact deformation Apl = 0, κA = 2/3, has only minor relevance for cohesive powders in loading (Fig. 2), but for the complete plastic contact deformation (Apl = AK) the coefficient κA = 1 is obtained. From Eqs. (43), (53) and (54) the sum of contact normal forces is obtained as:

(

FN + FH0 = π ⋅ rK ⋅ pf ⋅ κ A − κ p 2

)

(55)

From Eq. (5) the transition radius of elastic-plastic model rK,f,el-pl (index el-pl) and from Eq. (6) the particle center approach of the two particles hK,f,el-pl are calculated as: rK,f ,el − pl =

(

3 ⋅ π ⋅ r1,2 ⋅ pf ⋅ κ A − κ p 2⋅ E

hK,f ,el− pl =

(

9 ⋅ π ⋅ r1,2 ⋅ pf ⋅ κ A − κ p 2

2

4⋅ E

)

(56)

*

*2

)

2

(57)

Checking this model, Eq. (56), with pure elastic contact deformation, i.e., κp → 0 and κA = 2/3, the elastic transition radius rK,f, Eq. (29), is also obtained. For example, nanodisperse titania particles (d50,3 = 610 nm is the median diameter on mass basis (index 3), E = 50 kN/mm2 modulus of elasticity, ν = 0.28 Poisson ratio, pf = 400 N/mm2 micro-yield strength, κA ≈ 5/6 contact area ratio, κp = 0.44 plastic repulsion coefficient) a contact radius of rK,f,el-pl = 2.1 nm and, from Eq. (57), a homeopathic center approach of only hK,f,el-pl = 0.03 nm are obtained. This is a very small indentation calculated, in principle, by means of a continuum approach. The contact deformation is equivalent to a microscopic force FN = 2.1 nN or to a small macroscopic pressure level of about σ = 1.4 kPa (porosity ε = 0.8) in powder handling and processing.

J. Tomas

206

Introducing the particle center approach of the two particles Eq. (6) in Eq. (55), a very useful linear force–displacement model approach is obtained again for κA ≈ constant:

(

)

FN + FH0 = π ⋅ r1,2 ⋅ pf ⋅ κ A − κ p ⋅ hK

(58)

But if one considers the contact area ratio of Eq. (63), a slightly nonlinear (progressively increasing) curve is obtained. Using the elastic–plastic contact consolidation coefficient κ due to definition (Eq. (71)) one can also write: FN + FH0 =

π ⋅ r1,2 ⋅ pf ⋅ κ A ⋅ hK 1+ κ

(59)

The curve of this model is shown in Fig. 2 for titania powder which was recalculated from material data and shear test data [147, 149]. The slope of this plastic curve is a measure of irreversible particle contact stiffness or softness, Eq. (34). Because of particle adhesion impact, the transition point for plastic yielding Y is shifted to the left compared with the rough calculation of the displacement limit hK,f by Eq. (30). The previous contact model may be supplemented by viscoplastic stress-strain behavior, i.e., strain-rate dependence on initial yield stress. For elastic–viscoplastic contact, one obtains deformation with Eqs. (36) and (58) (κA ≈ constant):

(

)

FN + FH0 = π ⋅ r1,2 ⋅ηK ⋅ κ A − κ p,t ⋅ h&K

(60)

A dimensionless viscoplastic contact repulsion coefficient κp,t is introduced as the ratio of the van der Waals attraction to viscoplastic repulsion effects which are additionally acting in the contact after attaining the maximum pressure for yielding.

κ p,t =

pVdW η ⋅ h& K

(61)

K

The consequences for the variation in adhesion force are discussed in Section 2.3.3 [147]. 2.3.2. Unloading and reloading hysteresis and contact detachment Between the points U – E (see Fig. 3), the contact recovers elastically along an extended Hertzian parabolic curve, Eq. (7), down to the perfect plastic displacement, hK,E, obtained in combination with Eq. (58): 2

hK,E = hK,U − 3 hK,f ⋅ hK,U

(62)

Mechanics of nanoparticle adhesion — A continuum approach

207

Thus, the contact area ratio κA is expressed more in detail with Eqs. (6) and (54) for elastic κA = 2/3 and perfect plastic contact deformation, κA = 1 if hK,U → ∞: h h κ A = 2 + K,E = 1 − 1 ⋅ 3 K,f 3 3 ⋅ hK,U 3 hK,U

(63)

Beyond point E to point A, the same curve runs down to the intersection with the adhesion boundary, Eq. (67), to the displacement hK,A:

(

* FN,unload = 2 ⋅ E ⋅ r1,2 ⋅ hK − hK,A 3

)

3

− FH,A

(64)

Consequently, the reloading runs along the symmetric curve

(

FN,reload = − 2 ⋅ E ⋅ r1,2 ⋅ hK,U − hK 3 *

)

3

+ FN,U

(65)

from point A to point U to the displacement hK,U as well (Fig. 3). The displacement hK,A at point A of contact detachment is calculated from Eqs. (57), (58), (64) and (67) as an implied function (index (0) for the beginning of iterations) of the displacement history point hK,U:

(

hK,A,(1) = hK,U − 3 hK,f ,el-pl ⋅ hK,U + κ ⋅ hK,A,(0)

)

2

(66)

If one replaces FN in Eq. (72) (see Section 2.3.4), by the normal force– displacement relation, Eq. (58), additionally one obtains a plausible adhesion force–displacement relation which shows the increased pull-off force level after contact flattening, hK = hK,A compared with Eq. (38) and point A in the diagram of Fig. 4: FH,A = FH0 + π ⋅ r1,2 ⋅ pVdW ⋅ hK,A

(67)

The unloading and reloading hysteresis for an adhesion contact takes place between the two characteristic straight-lines for compression, the elastic–plastic yield boundary Eq. (58), and for tension, the remaining adhesion (pull-off) boundary Eq. (67) and Fig. 3. At this so-called adhesion (failure) boundary the contact microplates fail and detach with the increasing distance a = aF =0 + hK,A − hK . The actual particle separation a can be used by a long-range hyperbolic adhesion force curve FN,Z ∝ a −3 with the van der Waals pressure pVdW as given in Eq. (19) and the displacement hK,A for incipient contact detachment by Eq. (66):

208

J. Tomas

Figure 4. Characteristic particle contact deformation. (e) Contact detachment [148]. Again, if one applies a certain pull-off force FN,Z = –FH,A as given in Eq. (67) but here negative, the adhesion boundary line at failure point A is reached and the contact plates fail and detach with the increasing distance a = aF =0 + hK ,A − hK . This actual particle separation is considered for the calculation by a hyperbolic adhesion force curve FN,Z = –FH ,A ∝ a −3 of the plate–plate model Eq. (68).

Mechanics of nanoparticle adhesion — A continuum approach

209

Figure 5. Characteristic particle contact deformation. The complete survey of loading, unloading, reloading, dissipation and detachment behaviors of titania [148]. This hysteresis behavior could be shifted along the elastic–plastic boundary and depends on the pre-loading, or in other words, preconsolidation level. Thus, the variation in adhesion forces between particles depends directly on this frozen irreversible deformation, the so-called contact pre-consolidation history.

FN,Z (hK ) = −

FH0 + π ⋅ r1,2 ⋅ pVdW ⋅ hK,A hK,A æ h ö − K ÷ ç1+ a aF = 0 ø F =0 è

3

(68)

These generalized functions in Fig. 3 for the combination of elastic-plastic, adhesion and dissipative force–displacement behaviors of a spherical particle contact were derived on the basis of the theories of Krupp [49], Molerus [13], Maugis

J. Tomas

210

[58], Sadd [55] and, especially, Thornton [53, 60]. A complete survey of loading, unloading, reloading, dissipation and detachment behaviors of titania is shown in Fig. 5 as a combination of Fig. 1a to Fig. 4e. This approach may be expressed here in terms of engineering mechanics of macroscopic continua [1, 2] as the history-dependent contact behavior. 2.3.3. Viscoplastic contact behavior and time dependent consolidation An elastic-plastic contact may be additionally deformed during the indentation time, e.g., by viscoplastic flow (Section 2.1.3). Thus, the adhesion force increases with interaction time [32, 49, 77, 128]. This time-dependent consolidation behavior (index t) of particle contacts in a powder bulk was previously described by a parallel series (summation) of adhesion forces, see Table 1, last line marked with Tomas [122–125, 146–149]. This method refers more to incipient sintering or contact fusion of a thermally-sensitive particle material [62] without interstitial adsorption layers. This micro-process is very temperature sensitive [122, 124, 125, 146]. Additionally, the increasing adhesion may be considered in terms of a sequence of rheological models as the sum of resistances due to plastic and viscoplastic repulsion κp + κp,t, line 5 in Table 2. Hence the repulsion effect of “cold” viscous flow of comparatively strongly-bonded adsorption layers on the particle surface is taken into consideration. This rheological model is valid only for a short-term in-

Table 2. Material parameters for characteristic adhesion force functions FH(FN) in Fig. 8 Instantaneous contact consolidation

Time-dependent consolidation

Constitutive model of contact deformation Repulsion coefficient

plastic

viscoplastic

Constitutive models of combined contact deformation Contact area ratio

elastic–plastic

elastic–plastic and viscoplastic

Apl κA = 2 + 3 3⋅ A + A pl el

Apl + Avis κ A ,t = 2 + 3 3⋅ A + A + A pl vis el

κp =

CH ,sls pVdW = 3 pf 6 ⋅ π ⋅ aF =0 ⋅ pf

(

)

κp κA −κp

Contact consolidation coefficient

κ=

Intersection with FN-axis (abscissa)

FN ,Z ≈ −π ⋅ aF =0 ⋅ hr ⋅ pf

(

)

pVdW ⋅t ηK

(

κ vis = 1 ,2

≠ f CH ,sls

κ p ,t =

κ p + κ p ,t κ A ,t − κ p − κ p ,t

FN ,Z ,tot ≈ −

π ⋅ aF =0 ⋅ hr ⋅ pf 1 ,2

1 + pf ⋅ t / ηK

(

≠ f CH ,sls

)

)

Mechanics of nanoparticle adhesion — A continuum approach

211

Figure 6. Characteristic elastic–plastic, viscoelastic–viscoplastic particle contact deformations (titania, primary particles d = 20–300 nm, surface diameter dS = 200 nm, median particle diameter d50,3 = 610 nm, specific surface area AS,m = 12 m2/g, solid density ρs = 3870 kg/m3, surface moisture XW = 0.4%, temperature θ = 20°C, loading time t = 24 h). The material data, modulus of elasticity E = 50 kN/mm2, modulus of relaxation E∞ = 25 kN/mm2, relaxation time trelax = 24 h, plastic microyield strength pf = 400 N/mm2, contact viscosity ηK = 1.8·1014 Pa·s, Poisson ratio ν = 0.28, Hamaker constant CH,sls = 12.6·10-20 J, equilibrium separation for dipole interaction aF=0 = 0.336 nm, contact area ratio κA = 5/6 are assumed as appropriate for the characteristic contact properties. The plastic repulsion coefficient κp = 0.44 and viscoplastic repulsion coefficient κp,t = 0.09 are recalculated from shear-test data in a powder continuum [147, 149].

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Figure 7. Constitutive models of contact deformation of smooth spherical particles in normal direction without (only compression +) and with adhesion (tension –). The basic models for elastic behavior were derived by Hertz [41], for constant adhesion by Yang [61], for constant adhesion by Johnson et al. [51], for plastic behavior by Thornton and Ning [60] and Walton and Braun [59], and for plasticity with variation in adhesion by Molerus [13] and Schubert et al. [57]. This has been expanded stepwise to include nonlinear plastic contact hardening and softening equivalent to shearthickening and shear-thinning in suspension rheology [91]. Energy dissipation was considered by Sadd et al. [55] and time-dependent viscoplasticity by Rumpf et al. [62]. Considering all these theories, one obtains a general contact model for time- and rate-dependent viscoelastic, plastic, viscoplastic, adhesion and dissipative behaviors [91, 146–148, 151].

Mechanics of nanoparticle adhesion — A continuum approach

213

dentation t < ηK / ( κ ⋅ pf ) , e.g., t < 5 d for the titania used as a very cohesive

powder (specific surface area AS,m = 12 m2/g, with a certain water adsorption capacity). All the material parameters are collected in Table 2. A viscoelastic relaxation in the particle contact may be added as a timedependent function of the average modulus of elasticity E*, Yang [61] and Krupp [49] (trelax is the characteristic relaxation time): æ 1 = 1 ç * 1 + − 1* * * E E∞ (t → ∞) çè E0 (t = 0) E∞

ö ÷ ⋅ exp ( − t trelax ) ÷ ø

(69)

The slopes of the elastic–plastic, viscoelastic–viscoplastic yield and adhesion boundaries as well as the unloading and reloading curves, which include a certain relaxation effect, are influenced by the increasing softness or compliance of the spherical particle contact with loading time (Fig. 6). This model system includes all the essential constitutive functions of the authors named before [41, 55, 57, 60, 61]. A survey of the essential contact force-displacement models is given in Fig. 7 and Table 1. Obviously, contact deformation and adhesion forces are stochastically distributed material functions. Usually one may focus here only on the characteristic or averaged values of these constitutive functions. 2.3.4. Adhesion force model Starting with all these force-displacement functions one turns to an adhesion and normal force correlation to find out the physical basis of strength-stress relations in continuum mechanics [13, 14, 122, 149]. Replacing the contact area in Eq. (38), the following force–force relation is directly obtained: FH = FH0 + pVdW ⋅ AK = FH0 +

pVdW FH0 + FN ⋅ pf 2 + 1 ⋅ Apl − pVdW pf 3 3 AK

(70)

Therefore, with a so-called elastic–plastic contact consolidation coefficient κ,

κ=

κp κA −κp

(71)

a linear model for the adhesion force FH as function of normal force FN is obtained (Fig. 8): FH =

κp κA ⋅ FH0 + ⋅ F = (1 + κ ) ⋅ FH0 + κ ⋅ FN κA −κp κA −κp N

(72)

The dimensionless strain characteristic κ is given by the slope of adhesion force FH which is influenced by predominant plastic contact failure. It is a meas-

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214

Figure 8. Particle contact forces for titania powder (median particle diameter d50,3 = 610 nm, specific surface area AS,m = 12 m2/g, surface moisture XW = 0.4%, temperature = 20°C) according to the linear model Eq. (72), non-linear model Eq. (79) for instantaneous consolidation t = 0 and the linear model for time consolidation t = 24 h (Eq. (73)). The powder surface moisture XW = 0.4% is accurately analyzed with Karl–Fischer titration. This is equivalent to an idealized mono-molecular adsorption layer being in equilibrium with an ambient air temperature of 20°C and 50% humidity.

ure of irreversible particle contact stiffness or softness. A shallow slope designates a low adhesion level FH ≈ FH0 because of stiff particle contacts, but a large slope means soft contacts, or consequently, a cohesive powder flow behavior [91, 147, 149]. The contact flattening may be additionally dependent on time or displacement rate (Section 2.1.3). Thus, the contact reacts softer and, consequently, the adhesion level is higher than before. This new adhesion force slope κvis is modified by the viscoplastic contact repulsion coefficient κp,t, which includes certain viscoplastic microflow at the contact (Table 2 and Fig. 8), FH ,tot =

κ p + κ p ,t κ A ,t ⋅ FH0 + ⋅F κ A ,t − κ p − κ p ,t κ A ,t − κ p − κ p ,t N

(73)

= (1 + κ vis ) ⋅ FH0 + κ vis ⋅ FN

with the so-called total viscoplastic contact consolidation coefficient κvis that includes the elastic-plastic κp and the viscoplastic contributions κp,t of contact flattening,

Mechanics of nanoparticle adhesion — A continuum approach

κ vis =

κ p + κ p,t κ A,t − κ p − κ p,t

215

(74)

Eqs. (72) and (73) consider also the flattening response of soft particle contacts at normal force FN = 0 caused by the adhesion force κ⋅FH0 (Krupp [56]) and κvis⋅FH0. Hence, the adhesion force FH0 represents the sphere–sphere contact without any contact deformation at minimum particle–surface separation aF=0. This initial adhesion force FH0 may also include a characteristic nanometer-sized height or radius of a rigid spherical asperity aF =0 < hr << r1,2 with its center lo1,2

cated at an average radius of the spherical particle, Krupp [49], Rumpf et al. [33] and Schubert et al. [34]:

FH0 =

CH,sls ⋅ hr

1,2

2 6 ⋅ aF =0

é r1,2 / hr ê 1,2 ⋅ ê1 + ê 1 + 2 ⋅ hr / aF = 0 1,2 ëê

(

)

ù ú CH,sls ⋅ hr1,2 ≈ 2ú 2 6 ⋅ aF = 0 ú ûú

(75)

This rigid adhesion force contribution FH0, see also the fundamentals [44, 69] and supplements [32, 49, 56, 67, 98–112], is valid only for perfect stiff contacts. Additionally, for mono-sized spheres d = 4 ⋅ r1,2 an averaged asperity height hr = 2 ⋅ hr

1,2

(

can be used with hr = 1 / hr + 1 / hr 1,2

1

2

)

−1

. When the asperity height is

not too far from the averaged sphere radius hr < r1,2 , then the adhesion force can 1,2

be calculated as, see Hoffmann (index Ho) [98]: FH0 ,Ho =

≈

CH ,sls ⋅ hr

1 ,2

6 ⋅ aF2 =0

é r1,2 / hr ê 1 ,2 1 ⋅ê + 1 + hr / r1,2 1 ,2 1 + 2 ⋅ hr / aF =0 ê 1 ,2 ë

(

CH ,sls ⋅ hr 6⋅a

2 F =0

(

1 ,2

⋅ 1 + hr / r1,2 1 ,2

)

ù ú 2 ú ú û

(76)

)

If the radius of the roughness exceeds the minimum separation of the sphere– plate system in order of magnitudes (hr >> aF=0), the contribution of the plate, second term in Eq. (76), can be neglected and the adhesion force may be described as the sphere-sphere contact [98]. Rabinovich and co-workers [113–115] have used the root mean square (RMS) roughness from AFM measurements and the average peak-to-peak distance between these asperities λr to calculate the interaction between a smooth sphere and a surface with nanoscale roughness profile (index Ra):

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216

FH0,Ra =

ù CH,sls ⋅ r1,2 é 1 1 ê ú (77) ⋅ + 2 2 2 6 ⋅ aF =0 ê 1 + 58.14 ⋅ r1,2 ⋅ RMS / λr (1 + 1.817 ⋅ RMS / a ) ú F =0 ë û

The first term in brackets represents the contact interaction of the particle with an asperity and the second term accounts for the non-contact interaction of the particle with an average surface plane. This approach describes stiff nanoscale roughness as caps of asperities with their centers located far below the surface. For example, RMS roughness of only 1 or 2 nm is significant enough to reduce the theoretical adhesion force FH0 by an order of magnitude or more [115]. Greenwood [50, 80, 81] and Johnson [67] described the elastic and plastic deformations of random surface asperities of contacts by the standard deviation of roughness and mean pressure. The intersection of function (72) with abscissa (FH = 0) in the negative of consolidation force FN (Fig. 8), is surprisingly independent of the Hamaker constant CH,sls:

FN ,Z

é r1,2 / hr ê 1 ,2 = −π ⋅ aF =0 ⋅ hr ⋅ pf ⋅ κ A ⋅ ê1 + 1 ,2 1 + 2 ⋅ hr / aF =0 ê 1 ,2 ë

(

)

ù ú 2 ú ú û

(78)

≈ −π ⋅ aF =0 ⋅ hr ⋅ pf 1 ,2

This minimum normal (tensile or pull-off) force limit FN,Z for nearly brittle contact failure combines the influences of the particle contact hardness pf ≈ (3– 15)⋅σf (σf = yield strength in tension, details in Ghadiri [117]) for a confined plastic micro-stress field in indentation [116] and the particle separation distribution, which is characterized here by the mean particle roughness height hr , and 1,2

the molecular center separation aF=0. Obviously, this value characterizes also the contact softness with respect to a small asperity height hr as well, see Eq. (34). This elastic–plastic model (Eq. (72)) can be interpreted as a general linear constitutive contact model concerning loading pre-history-dependent particle adhesion, i.e., linear in forces and stresses, but non-linear regarding material characteristics. But if one eliminates the center approach hK of the loading and unloading functions, Eqs. (58) and (64), an implied non-linear function between the contact pulloff force FH,A = – FN,Z at the detachment point A is obtained for the normal force at the unloading point FN = FN,U:

Mechanics of nanoparticle adhesion — A continuum approach

217

FH ,A ,(1) = FH0 + κ ⋅ ( FN + FH0 ) é 3 ⋅ ( FN + FH0 ) æ F − FH0 − π ⋅ r ⋅ κ p ⋅ pf ⋅ ê ⋅ çç 1 + H ,A ,(0) 2 * FN + FH0 è ëê 2 ⋅ r1,2 ⋅ E 2 1,2

öù ÷÷ ú ø ûú

2/3

(79)

This unloading point U is stored in the memory of the contact as preconsolidation history. This general non-linear adhesion model (dashed curve in Fig. 8) implies the dimensionless, elastic-plastic contact consolidation coefficient κ and, additionally, the influence of adhesion, stiffness, average particle radius r1,2, average modulus of elasticity E* in the last term of the equation. The slope of the adhesion force is reduced with increasing radius of surface curvature r1,2. Generally, the linearised adhesion force (Eq. (72)) is used first to demonstrate comfortably the correlation between the adhesion forces of microscopic particles and the macroscopic stresses in powders [91, 146, 147]. Additionally, one can obtain a direct correlation between the micromechanical elastic-plastic particle contact consolidation and the macro-mechanical powder flowability expressed by the semi-empirical flow function ffc according to Jenike [4]. It should be pointed out here that the adhesion force level in Fig. 8 is approximately 105–106 times the particle weight for fine and very cohesive particles. This means, in other words, that one has to apply these large values as acceleration ratios a/g with respect to gravity to separate these pre-consolidated contacts or to remove mechanically such adhered particles from surfaces. For a moist particle packing, the liquid-bridge-bonding forces caused by capillary pressure of interstitial pores and surface tension contribution of the free liquid surface additionally determine the strength [118–122]. Attraction by capillary pressure and increasing van der Waals forces by contact flattening due to normal load (application of an external pressure) are also acting in particle contacts of compressed water-saturated filter cakes or wet-mass powders [91, 144, 145, 150]. 2.4. Energy absorption in a contact with dissipative behavior If one assumes a single elastic–plastic particle contact as a conservative mechanical system without heat dissipation, the energy absorption equals the lens-shaped area between the unloading and reloading curves from point U to A as shown in Fig. 3: hK ,U

Wdiss =

ò

hK ,A

hK ,U

FN,reload (hK ) dhK −

ò

FN,unload (hK ) dhK

hK ,A

from Eqs. (64), (67) for FH,A and (65), (58) for FN,U, one obtains finally:

(80)

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218

Wdiss = − 8 ⋅ E 15

(

*

r1,2 ⋅ hK ,U − hK ,A

)

5

(

) (

+ π ⋅ r1,2 ⋅ pf ⋅ éκ A ⋅ hK ,U − κ p ⋅ hK ,U − hK ,A ù ⋅ hK ,U − hK ,A ë û

)

(81)

Additionally, the specific or mass-related energy absorption includes the aver3 age particle mass mP = 4 / 3 ⋅ πr1,2 ρs a characteristic contact number in the bulk

powder (coordination number k ≈ π/ε [13]) and the dissipative work Wm,diss = k ⋅ Wdiss / mP : = −E 20 ⋅ ε ⋅ ρs *

Wm ,diss

+

æ h −h ö ⋅ ç K ,U K ,A ÷ r1,2 è ø

(

3 ⋅ π ⋅ pf ⋅ hK ,U − hK ,A 32 ⋅ r12,2 ⋅ ε ⋅ ρs

5/ 2

) ⋅ éκ ë

(82) A

(

)

⋅ hK ,U − κ p ⋅ hK ,U − hK ,A ù û

A specific energy absorption of 3 to 85 µJ/g was dissipated during a single unloading–reloading cycle in the titania bulk powder with an average pressure of only σM,st = 2 to 18 kPa (or major principal stress σ1 = 4 to 33 kPa) [147, 149]. 3. PARTICLE IMPACT AND CONTACT DISPLACEMENT RESPONSE

In a shear zone, when two particles (particle 2 is assumed to be fixed) come into contact and collide, the velocity of particle 1 is reduced gradually. Part of the initial kinetic energy is radiated into both particles as elastic waves. Now the contact force reaches a maximum value (maximum de-acceleration) and the particle velocity is reduced to zero. hK * Wel = 2 ⋅ E ò 3 0

3 * 5 r1,2 ⋅ hK dhK = 4 ⋅ E r1,2 ⋅ hK 15

(83)

With the particle mass m1,2 = ρs ⋅ 4 ⋅ π ⋅ r1,2 , the correlation between particle ve3 locity v1 and center approach hK is obtained: 3

* æh ö v = E ⋅ K 3 ⋅ π ⋅ ρs çè r1,2 ÷ø 2 1

5/ 2

(84)

In the recovery stage the stored elastic energy is released and converted into kinetic energy and the particle moves with the rebound velocity v1,R into the opposite direction.

Mechanics of nanoparticle adhesion — A continuum approach

219

The so-called impact number or coefficient of restitution e = Fˆ1,R / Fˆ1 indicates the impact force ratio of the contact decompression phase after impact and the contact compression phase during impact, e = 0 for perfect plastic, 0 < e < 1 for elastic–plastic, e = 1 for perfect elastic behavior, see examples in Refs. [29, 126, 130, 132]. Thus e2 < 1 characterizes the energy dissipation (Wdiss is the inelastic deformation work of particle contact, Ekin,1 = mP ⋅ v12 / 2 is the kinetic energy of particle 1 before impact): 2

e =

Ekin,1 − Wdiss Ekin,1

(85)

In terms of a certain probability of particle adhesion inside of the contact zone a critical velocity (index H) as the stick/bounce criterion was derived by Thornton (index Th) [60] who used the JKR model: v1,H,Th

2 1.871 ⋅ FH,JKR æ 3 ⋅ FH,JKR = ⋅ç mP ç d ⋅ E* 2 è

1/ 3

ö ÷ ÷ ø

(86)

For an impact velocity v1 > v1,H particle bounce occurs and the coefficient of restitution is obtained as [60]: 2

v1,R

e=

2

v1

2

= 1−

v1,H 2

v1

(87)

Even if the impact velocity v1 is 10-times higher than the critical sticking velocity v1,H,Th the coefficient of restitution is 0.995 [60]. But in terms of combined elastic–plastic deformation the kinetic energy is mainly dissipated. If one uses the center approach hK,f of Eq. (30) the critical impact velocity v1,f for incipient plastic yield (index f) is calculated from Eq. (84) as [131–133]: 2

v1,f

pf æπ ⋅p ö =ç *f ÷ ⋅ 3 ⋅ ρs è E ø

(88)

The critical velocity v1,H to stick or to adhere the particles with a plastic contact deformation was derived by Hiller (Index HL) [126]:

(1 − e ) =

2 1/ 2

v1,H,HL

e

2

⋅1⋅ d π ⋅ a2

CH,sls

F =0 ⋅ 6 ⋅ ρs ⋅ pf

(89)

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Figure 9. Recalculated plastic contact deformation and sticking/bounce at central impact stressing using data from Fig. 6. Two particles approach with velocities v1 and v2, impact and the contact is elastic–plastically deformed (top panel). The inelastic deformation energy is dissipated into the contact. This is equivalent to the areas (gray tones) between the elastic–plastic boundary and adhesion boundary of the force–displacement lines which are obtained by integration (Eq. (91)). If the kinetic energy of these particles would be large enough, these particles can detach with rebound velocities v1R and v2R. The critical impact velocity for incipient yield of the contact is shown (Eq. (88)). Above this value, the two particles adhere or stick in practice, i.e., v1R = 0. From this, the critical impact velocity v1,H follows and is shown in the bottom panel versus particle center approach or displacement hK,U. The model of Hiller/Löffler predicts a constant velocity (Eq. (90)). However, practical experience shows us that the faster the particles move and impact, the larger the contact displacement, and consequently, the higher the tendency to stick. This is demonstrated by the curve of Eq. (93) in the bottom panel versus displacement hK,U.

Mechanics of nanoparticle adhesion — A continuum approach

221

This can be rearranged if one uses the dimensionless plastic repulsion coefficient κp according to Eq. (43) to obtain the following simple expression:

(1 − e ) =

2 1/ 2

v1,H,HL

e

⋅

2

aF = 0 6 ⋅ pf ⋅κ p ⋅ d ρs

(90)

Unfortunately, Eq. (90) does not include the increase of “soft” contact flattening response hK by increasing particle impact velocity v1. Now this dominant energy absorption Wdiss during particle impact stressing, beginning at any unloading point U, is considered approximately as a trapezium-shaped area between elastic– plastic yield boundary and adhesion boundary for the contact of particles 1 and 2 in the force–displacement diagram of Fig. 9. With the contribution of the work of adhesion WA to separate this contact from equilibrium separation aF=0 to infinity, the energy balance gives (AK is the contact area): m1,2 2 2 ⋅ v1 − v1,R = 2

(

hK ,U

) ò

hK ,U

ò

FN (hK ) dhK +

hK ,f

− FN ,Z (hK ) dhK

hK ,f ∞

+ AK ⋅

ò

(91)

− pVdW (a ) da

a F =0

2 = v12 − v1,R

3 ⋅ pf 2 4 ⋅ ρs ⋅ r1,2

(

)

2 2 ⋅ éκ A ⋅ hK,U − hK,f + κ p ⋅ hK,U ⋅ aF =0 ù ë û

(92)

The difference in characteristic impact velocities results directly in a center approach, hK,U, expressed by the unloading point U. The response of this contact displacement hK,U is a consolidation force, FN,U. Additionally, a certain preconsolidation level, FN,U, in a shear zone may affect the sticking/bounce probability. If the rebound velocity v1,R = 0 the two particles will adhere. Consequently, the critical sticking velocity v1,H is obtained without any additional losses, e.g., due to elastic wave propagation: v1,H =

3 ⋅ pf 2 4 ⋅ ρs ⋅ r1,2

(

)

2 2 ⋅ éκ A ⋅ hK,U − hK,f + κ p ⋅ hK,U ⋅ aF =0 ù ë û

(93)

For example using data from Refs. [147, 149], this critical sticking velocity lies between 0.2 and 1 m/s for titania, curve in the sticking velocity–displacement diagram in Fig. 9, which is equivalent to an average pressure level σM,st = 2 to 18 kPa (or major principal stress σ1 = 4 to 33 kPa) [151]. These calculation results of particle adhesion are in agreement with the practical experiences in powder handling and transportation, e.g., undesired powder blocking at conveyer transfer chutes. In terms of powder flow the behavior after multiple stressing of soft de-

222

J. Tomas

forming contacts in the nanoscale of center approach hK, may be described as “healing contacts”. To demonstrate this enormous adhesion potential, 1-µm silica particles were completely removed from a 100-mesh woven metal screen (147 µm wide) with 40 m/s air velocity [127] and 32-µm glass beads from glass surface with more than 117 m/s [129]. Air velocities of 10 to 20 m/s were necessary to blow off about 50% of quartz particles (d = 5–15 µm) which had adhered to filter media after impact velocities of about 0.28 to 0.84 m/s [28, 29]. These fundamentals of particle adhesion dynamics may also be important to chemically clean silicon wafers [36, 134–141] or mechanical tool surfaces by jet pressures up to 2 MPa and CO2-ice particle velocities up to 280 m/s [135]. 4. CONCLUSIONS

The models for elastic (Hertz, Huber, Cattaneo, Mindlin and Deresiewicz), elastic–adhesion (Derjaguin, Johnson), plastic–adhesion (Derjaguin, Krupp, Molerus, Johnson, Maugis and Pollock) contact deformation response of a single, normal or tangential loaded, isotropic, smooth contact of two spheres were discussed. The force–displacement behaviors of elastic–plastic (Schubert, Thornton), elastic– dissipative (Sadd), plastic–dissipative (Walton) and viscoplastic–adhesion (Rumpf) contacts were also shown. With respect to these theories, a general approach for the time- and deformation-rate-dependent and combined viscoelastic, plastic, viscoplastic, adhesion and dissipative behaviors of a spherical particle contact was derived and explained. As the main result, the adhesion force FH is found to be a function of the force contribution FH0 without any deformation plus a pre-consolidation or loadhistory-dependent term with the normal force FN. These linear and non-linear approaches can be interpreted as general constitutive models of the adhesion force. It should be pointed out here that the adhesion force level discussed in this paper is approximately 105–106 times the particle weight of nanoparticles. This means, in other words, that one has to apply these large values as acceleration ratio a/g with respect to gravity to separate these pre-consolidated contacts or to remove mechanically such adhered particles from solid surfaces. For colliding particles a correlation between particle impact velocity and contact displacement response is obtained using energy balance. These constitutive model approaches are generally applicable for micro- and nanocontacts of particulate solids [91, 148, 149]. Hence, these contact models are intended to be applied for modern data evaluation of product quality characteristics such as powder flow properties, i.e., yield loci, consolidation and compression functions or design of characteristic processing apparatus dimensions [122, 142–151].

Mechanics of nanoparticle adhesion — A continuum approach

223

Acknowledgements The author would like to acknowledge his coworkers Dr. S. Aman, Dr. T. Gröger, Dr. W. Hintz, Dr. Th. Kollmann and Dr. B. Reichmann for providing relevant information and theoretical tips. The advices from Prof. H.-J. Butt and Prof. S. Luding with respect to the fundamentals of particle and powder mechanics were especially appreciated during the collaboration of the project “shear dynamics of cohesive, fine-disperse particle systems” of the joint research program “Behavior of Granular Media” of the German Research Association (DFG). Symbol a A aF=0

Unit nm nm2 nm

Ca CH

– J

CH,sls

J

d E F FH FH0 FN FT G h hK k kN kT m p pf pVdW r rK t v

µm kN/mm2 N nN nN nN nN kN/mm2 mm nm – N/mm N/mm kg kPa MPa MPa µm Nm h m/s

Description contact separation particle contact area minimum center separation for molecular force equilibrium capillary number Hamaker constant [69] based on interacting molecule pair additivity Hamaker constant according to Lifshitz theory [70] for solid–liquid–solid interaction particle diameter or particle size (in powder technology) modulus of elasticity force adhesion force adhesion force of a rigid contact without any deformation normal force tangential force shear modulus zone height height of overlap, indentation or center approach coordination number contact stiffness in normal direction contact stiffness in tangential direction mass contact pressure plastic micro-yield strength of particle contact attractive van der Waals pressure particle radius contact radius time particle velocity

J. Tomas

224

vH vR W Wm δ ε ηK κ

m/s m/s J J/g nm – Pa⋅s –

κp κp,t κvis

– – –

µi ν ϕi ρ σ σM σR σsls σt σ0 σ1 σ2 τ ΦT ψ

– – deg kg/m3 kPa kPa kPa mJ/m² kPa kPa kPa kPa kPa – –

Indices A at b br c crit diss e el

critical sticking velocity bounce velocity deformation work mass related energy absorption by inelastic deformation tangential contact displacement porosity particle contact viscosity elastic–plastic contact consolidation coefficient, see Eq. (71) plastic repulsion coefficient, see Eq. (43) viscoplastic repulsion coefficient, see Eq. (61) total viscoplastic contact consolidation coefficient, see Eq. (74) coefficient of internal friction, i.e., Coulomb friction Poisson ratio angle of internal friction between particles density normal stress center stress of Mohr circle [1, 149] radius stress of Mohr circle [1, 149] surface tension of solid–liquid–solid interaction tensile stress isostatic tensile strength of the unconsolidated powder major principal stress minor principal stress shear stress dimensionless bond strength according to Tabor [74] loading parameter according to Thornton [53]

detachment- or contact-area-related attraction bulk brittle compressive critical dissipation effective elastic

Mechanics of nanoparticle adhesion — A continuum approach

f F=0 H i iso K l m M min N p pl r R rep s S sls ss st Sz t T th tot U V VdW vis 0 (0) 1,2 3 50

225

flow or yield potential force equilibrium (potential minimum) adhesion internal isostatic particle contact liquid mass related center minimum normal pressure related plastic micro-roughness radius repulsion solid surface, shear solid-liquid-solid interaction between particles solid-vacuum-solid interaction between particles stationary shear zone loading time dependent tangential theoretical total unloading volume related van der Waals total viscoplastic initial, zero point beginning of iterations particle 1, particle 2 mass basis of cumulative distribution of particle diameter (d3) median particle diameter, i.e., 50% of cumulative distribution

REFERENCES 1. F. Ziegler, Techn. Mechanik der festen und flüssigen Körper, Springer Verlag, Wien (1985). 2. H. Göldener, Lehrbuch höhere Festigkeitslehre, Vols. 1 and 2, Fachbuchverlag, Leipzig (1992).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 231–244 Ed. K.L. Mittal © VSP 2003

A new thermodynamic theory of adhesion of particles on surfaces M.A. MELEHY∗ Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT 06269-1157, USA

Abstract—In his theory of the Brownian motion, Einstein introduced a basic concept into thermodynamics: the rate of change of momentum, associated with the thermal motion of particles suspended, or dissolved in a liquid. Einstein’s theory was not concerned with the transport through the liquid surface, or any other interface. This paper applies some basic theoretical results of this author’s generalization to interfacial systems of Einstein’s theory. A fundamental consequence will then be shown: if certain thermodynamic parameters vary across a surface, or any other interface, the first and second laws require the existence of electric charges at such sites. This result, which explains numerous interfacial phenomena of interdisciplinary interest, confirms Newton’s conception in the 18th century of the electric nature of the forces of capillarity, cohesion and attraction between particles. Further corroboration of the interfacial electrification theory has recently been reported by numerous direct observations, some of which are described in this article. The experimental observations reveal the existence of significant electric surface charges, which are many orders of magnitude higher than those caused by van der Waals forces. In the particular case of particles on surfaces, significant electric dipole charges are formed that exert mutually attractive Coulomb forces. Such forces can, in principle, be calculated in terms of the thermodynamic, physical and geometric parameters. But much theoretical research work remains to be done for evaluating the thermodynamic parameters of all materials of interest. These parameters must reflect the rate of change of the molecular thermal momentum, as in Einstein’s theory described above. Keywords: Particle adhesion; surface charges; interfacial electrification; interfacial thermodynamics.

1. INTRODUCTION

The phenomenon of adhesion between a particle and a surface has been attributed to the existence of electric charges between the surfaces. Among the explanations for these electric charges are van der Waals forces and some localized surface electric charges [1]. There is no attempt in this article to review the extensive literature on this topic [2, 3]. Rather, the primary objective here is to present a new thermodynamic theory that predicts the electric forces of adhesion. Specifically, it is shown that when two surfaces are brought in contact, provided that certain ∗

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thermodynamic parameters are different across their interface, the first and second laws require that an electric dipole charge be formed. Consequently, the two surfaces will be attracted to each other under the action of Coulomb forces. The theory of particle adhesion, presented in this paper, is based on this author’s generalization to interfacial systems [4–7] of Einstein’s 1905 thermodynamic theory of the Brownian motion [8–10]. In treating this problem, Einstein introduced into thermodynamics a highly significant concept: the time rate of change of the molecular thermal momentum per unit area. He then derived the widely-used diffusion–mobility/viscosity relations. Unfortunately, Einstein’s monumental theoretical contribution to thermodynamics passed unnoticed for over half a century, despite the general use of Einstein’s final results in a number of disciplines. In the 1960s and 1970s, an attempt was made by this author to explore the possibility of unifying the theory of conduction in semiconductor diodes and solar cells [4–6]. Since such devices had profoundly large concentration gradients across their junctions, it was thought then that a generalization of Einstein’s thermodynamic theory of the Brownian motion to interfacial systems might provide the answer. As the thermodynamic theory was developed, its application led to a unified theory of semiconductor diodes and solar cells, which accurately predicted extensive experimental observations, reported by about 27 authors over a period exceeding a quarter of a century [4–6]. These results have been reviewed in a recent article [7]. This paper will briefly discuss the basic thermodynamic principles underlying interfacial electrification [11] and particle adhesion. The direct experimental observations of the phenomena of interfacial electrification have been reported by many authors. Historically, its first conception goes back to the 18th century. In this connection, Heilbron [12] has described this interesting, important historic fact. Specifically, Heilbron writes: “... One draft (of Newton’s Principia that survived) asserts that ‘attraction’ between particles, the force of cohesion and capillarity, is ‘of the electric kind.’ ... .” More recently, many authors in different disciplines have reported direct observations of surface charges. For example, Chalmers [13] and Williams [14] have detected electric charges on cloud rain drops. Wentzel and Bickel [1] and others [2, 3] have indicated that adhesion between a particle and a wall is caused by van der Waals forces and by electric charges. Williams [15] reported that charge separation occurred as frost grew. Further experimental confirmation of the theory, and its relevance to the adhesion of particles on surfaces, is described below.

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2. THERMODYNAMIC GENERALIZATION OF THE MAXWELL–EINSTEIN DIFFUSION FORCE

For simplicity, consider a one-component system which is isothermal. Let, at any point in the system, n and P be, respectively, the concentration and internal pressure of the system molecules. The internal pressure is defined here as the pressure that accounts for the rate of change of the molecular thermal momentum per unit area. This pressure is not the external one measured with a manometer. The internal and external pressures are equal only for ideal, classical, monatomic gases. For other systems, the internal and external pressures can be drastically different from one another. For example, for conduction electrons in Cu, the internal pressure is well known to be about 3.77 ´ 1010 N/m2, whereas the vapor pressure of emitted electrons from the Cu surface, which is the electron external pressure, is almost zero at room temperature. It can be shown [7] that, by accounting for the rate of change of the molecular thermal momentum per unit area, the first and second laws of thermodynamics lead to an expression for the diffusion force per molecule, which under isothermal conditions is given by æ ö fd = − 1 ∇P = − 1 ç 1 x ∂P + 1 y ∂P + 1z ∂P ÷ ∂y ∂z ø n n è ∂x

(1)

Here 1x, 1y and 1z are unit vectors, respectively, along the Cartesian coordinates x, y and z. Hereafter, we shall call the force per molecule a force field. Equation (1) reduces to the diffusion forces derived by Maxwell [16–18] and Einstein [8–10] for the respective special cases treated by each author. As Maxwell and Einstein described it, fd is a mechanical force in the Newtonian sense. This force represents, on average, the force exerted on each transported molecule crossing an interface by the non-transported molecules of the host system. Within the bulk, ÑP vanishes, but at an interface, it can be significantly large in magnitude, and so will fd. As explained in the next section, fd, will contribute, at least in part, to the latent heat of phase change. A detailed discussion of the fundamental properties and interactions with electric fields, at and near equilibrium, may be found in a recent article [7]. 3. INTERFACIAL ELECTRIFICATION: A NEW CONSEQUENCE OF THE FIRST AND SECOND THERMODYNAMIC LAWS [11]

For simplicity, consider an interface in a one-component system, which may be a liquid, or a solid. Let the system be surrounded by its vapor. Now consider that the system is closed and is approaching a state of thermodynamic equilibrium, so that the transport through the interface is tending to vanish, and the entire system is tending to be isothermal. In the limit, all dissipative

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forces vanish. Suppose then that some molecules are transported quasi-statically through the interface, i.e., a finite number of molecules are evaporating during a period of time that approaches infinity. As the molecules cross the interface, each one of these microscopic particles, on average, will be subjected to the resultant of all motive (active) forces, fta. The subscript a designates the property of being motive (active). For a detailed definition and description of the properties of motive (active) and dissipative (passive) forces and processes, the reader may wish to refer to a recent article [7]. Briefly, at interfaces, motive forces are the most predominating forces. Now the motive force, which resides at the interface, is exerted on the transported molecules by the non-transported ones. Thus, the first law requires the internal energy of the non-transported molecules to decrease. Quantitatively, if the molecules are displaced by a differential length, dl, through the interface, on average, an amount of work dW will be done on each molecule by the non-transported ones. This work will be given by dW = fta·dl

(2)

The first law, therefore, requires the internal energy of the non-transported molecules to decrease by dW. This decrease will be in the thermal energy of the interface. To restore the internal energy of the non-transported molecules to its original state, an amount of reversible heat dQ = T ds, per molecule, has to be added to the interface. Here T is the absolute temperature and s is the entropy per molecule. Thus, T ds – fta·dl = 0

(3)

If the differential change in entropy ds, per molecule, occurs over the differential length dl, which equals (1x dx + 1y dx + 1z dx), then

( )

( ) (

)

é ù æ ö ds = ê 1 x ∂s + 1 y ç ∂s ÷ + 1z ∂s ú ⋅ 1 x dx + 1 y dy + 1z dz = ∇s ⋅ dl ∂x ∂z û è ∂y ø ë

(4)

where all symbols are as defined earlier. Therefore, from Eqs. (3) and (4), it follows that (fta – T Ñs)·dl = 0

(5)

Since Eq. (5) is valid for any arbitrary choice of magnitude and direction of dl, then fta = T Ñs

(6)

It can be shown [7, 11], however, that, at equilibrium, Ñs = (1/T ) [fda + Ñ(u + P/n)]

(7)

where fda is the motive (active) diffusion force field and u is the internal energy per molecule.

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The force field fda is due to the collisions between molecules crossing the interface and the non-transported ones. Therefore, the total force field fta must have fda, as a component. Then we may write fta = fda + fia

(8)

where fia is some force field, whose value and nature are to be determined. The force field fia cannot be associated with the gradient of the internal pressure and collisions, because any such force field is entirely accounted for by fda. Thus, fia has to be associated with none other than fields involving action-at-a distance, i.e., electric, magnetic, or gravitational fields. As we shall see, fia depends on ÑP. In an interface between two metals, for example, fia will start abruptly at one surface, and will terminate abruptly on the other surface. Can fia, therefore, be gravitational in nature? This is not possible for at least two reasons: The gravitational attraction between microscopic particles is minutely small. The second reason: a gravitational force cannot start abruptly and then end abruptly, because there are no isolated negative masses found in nature that will terminate the lines of force. Can fia be magnetic? Again, there are no isolated magnetic charges found in nature that will have lines of force emanating and terminating at boundaries. It can then be concluded that the force field fia has to be electric in nature, and from hereon it will be designated by fea, and called an electric force field. The subscript e signifies pertinence to electricity. Now from Eqs. (6), (7) and (8), it follows that fea = Ñ(u + P/n)

(9)

For a multicomponent system, for which the thermodynamic parameters can be calculated separately for each constituent, j, it is believed that for reasons beyond the scope of this paper, the resultant motive electric force per molecule will be v

f tea = å ∇ é u j + ( Pj / n j ) ù ë û

(10)

j =1

where v is the number of constituents in the multicomponent system. It should be remembered that P, appearing in the last two equations, is the pressure that reflects the rate of change of the molecular thermal momentum per unit area, and not the pressure measurable with a manometer. The implication of Eqs. (9) and (10) is that fea will exist wherever the parameters (u + P/n) vary in space, such at surfaces and other interfaces. In turn, the existence of fea requires the existence of electric charges.

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4. EXPERIMENTAL CORROBORATION OF SURFACE ELECTRIFICATION

The experiments described in this section appear to confirm unambiguously the existence of significant electric charges on surfaces, as predicted thermodynamically. The effects caused by the electrostatic surface charges appear to extend to millimeters and centimeters, which are many orders of magnitude higher than what can be accounted for by van der Waals forces. It is this universal property of surface electrification, which underlies the adhesion of small particles on surfaces, among numerous other interfacial phenomena [11]. The first two experiments [11] were conducted on clean, polished, flat, solid plates, that were impervious. The plates were accurately placed horizontally, so as to eliminate the gravitational effects parallel to the plate surfaces. Some coloring substance was dissolved in water, which was used to draw some specific figures on the plates. As shown in Fig. 1, three semicircular films, with diameters of about 15 cm each, were painted on a Corian (plastic made by DuPont) plate. The gap between the two adjacent semicircles facing each other was about 4 mm. The third semicircle was sufficiently far from the two semicircles, so it can be considered nearly

Figure 1. The different accumulations of color seen in the shown semicircles resulted after painting colored water films on a smooth, horizontal Corian plate, which is impervious. The film was left to dry. Initially the color was homogeneous. In the isolated semicircular film (diameter 15 cm), before drying occurred, the Coulomb repulsion between the charged surface molecules propelled the water film with its color away from the interior of the semicircle towards its outer peripheries, where the highest color accumulation can be seen. By contrast, the surface charge on each of the adjacent semicircles repelled the charge on the other one, across an air gap of about 4 mm. The outcome was that the color accumulation on the two, close, straight edges is considerably less than that on the straight edge of the isolated semicircle. This experiment showed that the effects of the Coulomb forces extended over the entire water film of 15-cm diameter and across the 4-mm air gap, as predicted thermodynamically.

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isolated electrostatically. The patterns were painted with a paint brush, using the prepared colored water, and were left to dry. Figure 1 shows the result of the experiment, after complete drying had occurred. Initially, all water films were homogeneous in color. In the separate semicircle, gradually the water film with its color migrated from the inner parts outwardly, towards the peripheries. The intensity of color accumulation became about equal on the curved and straight edges of the semicircle. But in the case of the two close semicircles, the migration of the colored film occurred appreciably more towards the curved peripheries than towards the straight ones. The pattern of color accumulation in the three semicircles has significant implications: in the case of the isolated pattern, each charged surface molecule was repelled by all others on the film. Thus, as seen in Fig. 1, the resultant forces were repulsive and pushed various parts of the water film towards the peripheries. In the case of the two adjacent semicircles, the same phenomenon occurred on either side of the gap. But, unlike in the nearly isolated pattern, the charges on either semicircular film repelled the charges on the other semicircular film. That ac-

Figure 2. The different accumulations of color seen here resulted after the drying of a semicircular film (diameter 15 cm) of homogeneously-colored water painted on a smooth, horizontal, Corian plate. Before any drying and migration of colored water occurred, a square Corian tile (dimensions: 15 ´ 15 ´ 1.2 cm) was placed with one edge 3 mm away from the straight periphery of the colored water film. A comparison of the pattern of color accumulation on the straight edge with that of the isolated semicircle in Fig. 1, shows that there exist repulsive Coulomb forces between the Corian tile surface and the water film. This experiment confirms that the Corian plate has an electric surface charge, as predicted thermodynamically. It is this significant surface charge that predominantly causes the adhesion of particles on surfaces.

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Figure 3. Dew accumulation on the top edge of a grass leaf, rather on the lowest point as Newtonian mechanics would predict. The phenomenon reveals repulsive forces between the negatively charged ground [13] and the drop charge. The Coulomb forces that lift the drop are the same as those that make the fog particles to be suspended, as they are repelled from the negatively charged Earth’s surface [13].

tion occurred across the 4-mm air gap. Thus, the accumulation on the straight peripheries was much less than that on the outer curved peripheries. Such an outcome is characteristic of significant repulsive Coulomb forces, which, unlike mechanical forces, involve action-at-a-distance. It is this behavior near the air gap, which reveals the repulsive Coulomb forces, that unambiguously confirms electrification of the water surface. The variation of color accumulation within the dimension of the each semicircle (15 cm) and across the air gap of about 4 mm, confirms the fact that the intensity of surface charges on water surface is many orders of magnitude higher than that can be caused by van der Waals forces. Clearly, at the water–Corian interface there will be a dipole charge. The resulting attractive Coulomb forces constitute adhesion forces. Such forces explain why a drop can, despite its weight, stick to even an impervious ceiling, such as that of glass, Corian, or Teflon, as shown in the last two experiments. The objective of the experiment of Fig. 2 was to examine whether a solid surface, such as that of a Corian plate, was electrostatically charged, as predicted thermodynamically. Towards that goal, a 15-cm semicircular thin film of colored water was painted on a Corian plate. A second, square Corian plate (dimensions: 15×15×1.2 cm) was placed on the first plate with one edge parallel to the semicircular straight edge of the water film. The gap between the two edges was about 3 mm. Figure 2 shows the outcome after complete drying had occurred.

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Figure 4. Under the action of the attractive Coulomb forces between the dipole charges on the water and glass surfaces, the water stream bends, then approaches and touches the glass surface, and continues to adhere to it, despite its weight [19]. This experiment demonstrates that glass has a surface charge, and attractive Coulomb forces exist between the glass and the water surfaces. These forces are the same as those between particles and surfaces, as required thermodynamically. The experiment is further evidence of the universality of electric surface charges.

A comparison of the color accumulation on the straight edge of the isolated semicircle in Fig. 1 and that in Fig. 2, leads to an important conclusion: the significantly lighter color of the straight edge in Fig. 2 compared to that of the isolated semicircle of Fig. 1 reveals the existence of repulsive Coulomb forces between the water-surface charge and the Corian-surface charge. Because the Coulomb forces are repulsive, the Corian-surface charge has to be similar in kind to that on the water film, which means it is a negative charge, a result that will be explained in Section 6. The important conclusion from this experiment is that it shows the existence of the surface electric charge on a solid material such as Corian, which by the laws of electrostatics will attract small particles and make them stick to the surface. Furthermore, the experiment demonstrates visually the strength of the Coulomb forces to be many orders of magnitude higher than those than can be caused by van der Waals forces.

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Figure 5. A water stream spirals downwardly around an inclined rod [19]. This experiment again confirms all the conclusions of Fig. 4.

Figure 3 shows the dew formation of a drop residing on the top of a grass leaf rather than residing on its bottom, whose potential energy, according to Newtonian mechanics, has the lowest possible value. Reason: it is well known that the ground is negatively charged [13]. Likewise, the water drop is negatively charged. The repulsive Coulomb force between the negatively-charged water drop and the ground balances the weight. If the drop were to be electrically neutral, it would have fallen to the ground. Again the experiment illustrates the intensity of the Coulomb forces, which are the same as those that cause the fog drops to be suspended, despite their weight. Walker [19] conducted two interesting experiments, which demonstrate how water surface can attach itself to other surfaces with significant intensity. Figure 4 shows a water stream adhering to the glass. This phenomenon is caused by the existence of a dipole charge that resides at the water–glass interface, as predicted thermodynamically. It is interesting to see how the water stream, as it exits the upper tube, bends towards the glass, and then sticks to the surface as it flows downward. The stream bending reveals the existence of significant attractive Coulomb forces between the water and the glass surface, orders of magnitude greater than van der Waals forces. Figure 5 shows, again, that as the water stream touches an inclined slender, cylindrical rod, it continues to spiral downwardly. The two preceding experiments require the water stream not to exceed a critical speed, otherwise the inertial forces would overcome the Coulomb forces.

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The above two experiments demonstrate the intensity of the dipole surface charges between the water and solid surfaces, a property universal to almost all surfaces, as predicted thermodynamically. 5. EQUILIBRIUM ELECTRIC CHARGE ON AN ISOLATED SPHERICAL BODY

It is well known that a surface charge on an isolated spherical object will be distributed uniformly. The resulting electric field will be radial and either emanating, or terminating on the surface of the object, depending on whether the charge is positive, or negative, respectively. The assumption made here is that the system is in equilibrium with its vapor. Although the vapor internal pressure, P, for most solids is practically zero, say, at and below room temperature, the ratio of P to the molecular concentration n of the vapor will not necessarily vanish. Now to calculate the charge Q on the sphere, we must first calculate the absolute voltage, V, of the surface, i.e., the voltage with respect to a point at infinity. To do so, imagine that some finite number of molecules evaporate quasistatically, i.e., the process occurs in a period of time that approaches infinity. On average, the work done by the electric field on a molecule as the molecule is transported from the surface to infinity can be obtained by integrating fea over a fictitious radial line, C, that begins at a point just below the surface and extends to infinity. If all parameters are expressed in the meter–kilogram–second (MKS) system, the answer will be expressed in joules, which when divided by the magnitude of the electronic charge e will be expressed in (electron)volts. Therefore, the magnitude of V will be ∞ ìé P ù é P ùü V = 1 ò fea ⋅ dl = 1 í ê uo + o ú – ê uv + v ú ý (volt) (11) e R e îë no û ë nv û þ Here R is the radius of the sphere, dl is a differential length on the radial path, C, and the subscripts o and v, respectively, signify pertinence to the molecules inside the spherical object and those of its vapor. The spherical object can, of course, be a solid, or a liquid drop. For a charged sphere, the relation between its absolute voltage and charge is well known. In our case, the magnitude of the equilibrium charge, Q, on the sphere will be ìé P ù é P ùü (12) Q = 4π κ RV = 4π κ R í ê uo + o ú – ê uv + v ú ý e îë no û ë nv û þ Here κ is the dielectric constant of the surroundings, expressed in the rationalized MKS system. In vacuum and air, κ = κo
8.854×10–12 F/m. In distilled water κ
80 κo.

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6. ANATOMY OF PARTICLE ADHESION

As explained above, when two surfaces, of different materials, are brought in contact, then, as required thermodynamically, a dipole charge has to form. Consequently, the oppositely-charged surfaces will be attracted to each other by Coulomb forces. These forces appear to be the most significant adhesion forces that make light particles stick to surfaces. The intensity of such Coulomb forces, predicted thermodynamically, are many orders of magnitude stronger than van der Waals forces. This fact has been confirmed experimentally. The creation of the charges on both surfaces takes place as some electrons depart from some molecules of one surface and reside on the other surface. The side that lost the electrons will become positively charged. There are two possibilities that are thermodynamically allowable, but there is only one way that will actually occur and that way is the one that will take less energy to accomplish than the other. As an example, what polarity will the water surface charge be when the water is exposed to air, such as in a cup? It is well known that it takes less energy to capture an electron from an air molecule by a water molecule than the reverse. Thus, in air, under ordinary circumstances [11], this scenario will occur and the water-surface charge will be negative. The charge on the air molecule is not thermodynamically constrained. Thus, the positive charge leaks to the ground. Such a result is confirmed by the experiment shown in Fig. 3. In this figure, because the drop has a negative charge, it is repelled upwards from the Earth’s surface, which is well known to be negatively charged [13]. This phenomenon is most clearly demonstrated by the suspension of fog droplets, despite the weight of each droplet. As seen in Eq. (12), the equilibrium electric charge on an isolated spherical particle is proportional to the particle radius, R, but the weight of such a particle is proportional to R3. Thus, for the particle to adhere to a ceiling, for example, it must be sufficiently small. In a zero-gravity environment, the size of the weightless particles might cease to be a factor. 7. CONCLUSIONS

It has been shown that, if certain thermodynamic parameters vary across an interface, the first and second laws of thermodynamics require the existence of electric charges at such sites. In the case of surfaces, the condition is usually satisfied for electrification. Such theoretical results have been verified by various experiments, discussed above. These experiments demonstrate that the intensity of surface charges exert Coulomb forces that extend over millimeters and centimeters. Such distances exceed, by many orders of magnitude, the field of influence of van der Waals forces.

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As explained above, surfaces exposed to air are usually negatively charged. Thus, the charges on the surfaces shown, for example, are negative. Likewise, small particles are negatively charged. Because of the difference in the electric voltage between the two charged objects, if they are in sufficiently close proximity, the laws of electrostatics predict [20] that the particles would be attracted and adhere to the surfaces. As a speculation, it might be possible to find materials that if sprayed on the surface of interest will result in matching the thermodynamic parameters of the surface with those of the air. Such materials, if found, may prevent surface electrification, and reduction of the Coulomb forces between small particles and the surface of interest. If this speculation is realized, a challenging question remains: can the same method be used to remove charges from small particles, which are stray and in all probability differ in thermodynamic parameters from one another? Acknowledgements This author is indebted to Dr. A. K. T. Assis, Institute of Physics, State University of Campinas, Brazil, who pointed out that Heilbron indicates in his book [12] that Newton believed in the involvement of electric forces in some interfacial phenomena. REFERENCES 1. T. M. Wentzel and W. S. Bickel, in: Particles on Surfaces 2: Detection, Adhesion and Removal, K. L. Mittal (Ed.), pp. 35-48, Plenum Press, New York, NY (1989). 2. K. L. Mittal (Ed.), Particles on Surfaces 5&6: Detection, Adhesion and Removal, VSP, Utrecht (1999). 3. K. L. Mittal (Ed.), Particles on Surfaces 7: Detection, Adhesion and Removal, VSP, Utrecht (2002). 4. M. A. Melehy, in: Proceedings of the 1969 Pittsburgh International Symposium on A Critical Review of Thermodynamics, E. B. Stuart, B. Gal-Or and A. J. Brainard (Eds.), pp. 345-405, Mono Book, Baltimore, MD (1970). 5. M. A. Melehy, Foundations of the Thermodynamic Theory of Generalized Fields, Mono Book, Baltimore, MD (1973). 6. P. T. van Heerden, Am. J. Phys. 44, 895-896 (1976). 7. M. A. Melehy, Phys. Essays 10, 287-303 (1997). 8. A. Einstein, Ann. Phys. 17, 549-560 (1905). 9. A. Einstein, in: Investigations on the Theory of the Brownian Movement, pp. 1-18. Dover Publications, New York, NY (1956). 10. A. Einstein, in: Investigations on the Theory of the Brownian Movement, pp. 68-85. Dover Publications, New York, NY (1956). 11. M. A. Melehy, Phys. Essays 11 (3), 430-443 (1998). 12. J. L. Heilbron, Electricity in the 17th and 18th Centuries: A Study in Early Modern Physics, p. 239, Dover Publications, New York (1999). 13. J. A. Chalmers, Atmospheric Electr., p. 190, Pergamon Press, London (1957). 14. E. R. Williams, Sci. Am. 259, 88-99 (1988).

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15. E. R. Williams, J. Geophys. Res. 117, 409-420 (1991). 16. J. C. Maxwell, Phil. Mag. 20, 21 (1860). 17. W. D. Niven (Ed.), in: The Scientific Papers of James C. Maxwell, Vol. I, pp. 377-391. Dover Publications, New York, NY (1952). 18. W. D. Niven (Ed.), in: The Scientific Papers of James C. Maxwell, Vol. I, pp. 394-396. Dover Publications, New York, NY (1952). 19. J. Walker, Sci. Am. 251, 144-154 (1984). 20. J. C. Maxwell, Elementary treatise on electricity, pp. 81-88, Oxford at the Clarendon Press (1881).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 245–253 Ed. K.L. Mittal © VSP 2003

Particle adhesion on nanoscale rough surfaces BRIJ M. MOUDGIL,∗,1,2 YAKOV I. RABINOVICH,2 MADHAVAN S. ESAYANUR1,2 and RAJIV K. SINGH1,2 1

Department of Materials Science and Engineering, University of Florida, Gainesville, FL, USA Engineering Research Center for Particle Science and Technology, University of Florida, Gainesville, FL, USA

2

Abstract—Nanoscale roughness on surfaces strongly affects the adhesion force. All existing models of adhesion have been shown to underestimate the force of adhesion. The lack of a reliable model to predict the adhesion between nanoscale rough surfaces has limited the understanding of the flow characteristics of fine powders both in the dry and wet states. In this investigation, a new model based on the height and breadth of the asperities has been proposed and experimental results are presented to validate the theoretical formulae developed. It has been determined that the onset of capillary forces occurs at higher values of relative humidity with increasing surface roughness. The adhesion force results are in good agreement with theoretical predictions as compared to previous models. Keywords: Adhesion; atomic force microscopy; nanoscale roughness; particles.

1. INTRODUCTION

Nanoscale roughness has been known to reduce adhesion between adhering materials [1-8]. One of the earliest studies to evaluate the effect of roughness was by Fuller and Tabor [8] between rubber and a poly(methyl methacrylate) (PMMA) surface. Iida et al. [9] made a quantitative study of adhesion between particles and glass surfaces, estimating the adhesion force to be the average force needed to retain half of the particles on the glass surface after using a liquid or air jet. However, in all the earlier models, the interaction has been considered due to the contact between the surface of the particle and the asperities, and the non-contact force arising from the influence of the underlying substrate is neglected. At very low values (nanoscale) of substrate roughness, this interaction could lead to significant underestimation of the total adhesion force.

∗

To whom all correspondence should be addressed: Dr. Brij M. Moudgil, 205 Particle Science and Technology Bldg., University of Florida, P.O. Box 116135, Gainesville, FL 32611-6135, USA. Phone: (352) 846-1194, Fax: (352) 846-1196, E-mail: [email protected]

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One of the first models of adhesion has been the Rumpf model [10], based on contact of a single hemispherical asperity, centered at the surface, interacting with a large spherical particle along a line normal to the surface connecting their centers as shown in Fig. 1. The limitation for the center of the asperity to be at the surface is not representative of real surfaces. Modifications to the Rumpf model were developed by Greenwood and Williamson [11] and Xie [12]. In the Greenwood and Williamson model, the surface was considered as consisting of hemispherical asperities of equal radii, with the origin offset from the average surface plane according to a Gaussian probability function. Xie made a theoretical study determining the effect of substrate surface roughness on particle adhesion. In this study, a modified van der Waals force depending only on the radius of asperities was proposed utilizing two geometrical models. The first model was similar to Rumpf’s but ignored the interaction of the particle with the asperities on the substrate surface. The second model assumed the asperities to be small particles positioned between two larger surfaces (sandwich model). It was concluded that if the radii of surface asperities were small (less than 10 nm), the surface could be treated as smooth. Both these studies [11, 12] could not predict the adhesion with any more significant accuracy than the Rumpf model. In addition to the effect of roughness, the presence of humidity induces spontaneous formation of a meniscus between the surfaces leading to a large increase in the adhesion force. Fundamen-

Figure 1. Schematic of roughness based on Rumpf model. The roughness on the surface is shown as a hemispherical asperity of radius r, with the center lying at the surface plane, interacting with a large spherical particle.

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tal understanding of the onset of capillary force on nano-rough surfaces is an issue of major concern in many industrial applications, such as the transport and handling of fine powders and removal of abrasive particles after a polishing operation in the semiconductor industry. All the above-mentioned studies have been on the dry adhesion of particles to surfaces with roughness on the microscale. There are several studies on the effect of relative humidity on the onset of capillary forces [13-15]. However, the change in the critical humidity for the onset of capillary adhesion due to surface roughness was not considered. The objective of the present investigation was to develop a model that predicted adhesion force between nanorough surfaces both in the dry and wet ambient conditions. 2. THEORY

2.1. Dry adhesion of surfaces with nanoscale roughness In this study a roughness model based on the asperity height and the peak-to-peak distance is used [16, 17]. This model describes the surfaces of real materials more realistically without any limitations on the position of the center of the asperities. Based on this model, the force of adhesion between a flat substrate and a sphere of radius R in dry state is given by Eq. (1), 1 1 é 2 ê 58 R ⋅ RMS + 2 æ 58 R ⋅ RMS1 ö æ 1.82RMS2 ö ê1 + AR ê ÷ ç1 + ÷ ç1 + λ22 λ12 H0 Fad = è øè ø 2 6H 0 ê 2 H0 ê ê (1 + 1.82(RMS + RMS ))2 1 2 ë

ù +ú ú ú ú ú ú û

(1)

where A is the Hamaker constant, Ho is the separation distance and RMS and λ are the root mean square roughness and the peak-to-peak distance between the asperities, respectively. The subscripts 1 and 2 for RMS correspond to the asperities with the longer distance (approximately 1 µm) of fluctuation, λ1, and the other to the smaller distance (approximately 0.25 µm), λ2. 2.2. Onset of capillary forces on surfaces with nanoscale roughness The effect of relative humidity on the onset of capillary forces for nanoscale rough surfaces was developed using the Laplace equation and the Kelvin equation [18, 19]. The roughness model used in the dry adhesion case was incorporated to develop a theoretical formula for the total adhesion force as a function of relative humidity and surface roughness, given by Eq. (2).

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é 1.82RMS ù F = 4πγ L R cosθ ê1 − 2r cosθ úû ë

(2)

where γL is the surface tension of the liquid, θ is the contact angle, r is the radius of the meniscus and RMS is the root mean square roughness of the surface. The RMS is measured using an Atomic Force Microscope (AFM) and the radius of the meniscus, r, is calculated using the Kelvin Equation for any given value of relative humidity and particle radius, R. 3. MATERIALS AND EXPERIMENTAL METHODS

The adhesion force was measured using an AFM (Nanoscope III, Digital Instruments, Inc.) All measurements were done with a colloidal particle attached to an AFM cantilever as described by Ducker and Senden [20]. The spring constant ‘k’ of each cantilever was determined by the frequency method [21]. The roughness of the flat substrates was measured by topographical imaging of the samples using a contact-mode AFM cantilever. The dry adhesion measurements were carried out using flat plates with controlled roughness, fabricated by deposition of titanium films (100 nm thick) on a silicon wafer substrate. Auger Spectroscopy was used to verify the homogeneity of the deposited film. The silicon wafer used had an RMS roughness of 0.17 nm. Glass spheres obtained from Duke Scientific Inc. were mounted on AFM cantilevers using an epoxy glue (melting point 90-100°C), Epon R 1004 from Shell Chemical Company. Capillary adhesion measurements were done under controlled atmospheric conditions. An environmental chamber was constructed that enclosed the entire AFM (without microscope). The chamber had a recirculating fan and the AFM was placed on an anti-vibration pad inside the chamber. Relative humidity was monitored using two Fisher Scientific High Accuracy Thermo-Hygrometers placed at the top and the bottom of the chamber. During each experiment, the atmosphere within the chamber was saturated with water in petri dishes and then allowed to dry with time. To achieve lower values of relative humidity, a desiccant was exposed to absorb the moisture or the chamber was purged with pure nitrogen gas. The silica substrates used included an oxidized, silicon wafer (180 nm thick oxide) of 0.2 nm RMS roughness provided by Dr. Arwin (Linköping University, Sweden); a plasma-enhanced chemical vapor deposited (PE-CVD) silica (2 µm thick) of 0.3 nm RMS roughness on silicon (Motorola Corporation), and a sample of the PE-CVD silica treated in a 1:1 mixture of hydrogen peroxide and ammonium hydroxide for 6 h to obtain an RMS roughness of 0.7 nm. The robustness of the model was tested also using other substrates: sapphire (MTI Corp., Richmond, CA) of 0.3 nm RMS roughness, a sputtered titanium surface deposited on silicon of 1.4 nm RMS roughness and a sputtered silver surface of 3.0 nm RMS roughness (both from Motorola Corporation).

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4. RESULTS

The model developed for adhesion between nanoscale rough surfaces has been used to predict the adhesion between the four different samples of titanium coated silica substrates and the results are summarized in Table 1. Each adhesion force result is the average of at least 20 measurements taken at different locations on the surface. The roughness of the samples was measured using topography imaging mode of the AFM, and the values of roughness shown in Table 1 correspond to the short-scale values (RMS2) for the first two samples and to the large-scale roughness (RMS1) for the third and fourth samples. The values of adhesion based on the Rumpf model largely underestimate the force in comparison to the new model. The experimental results are in good agreement with the predicted values, hence validating the applicability of the new model to nanoscale rough surfaces. Table 1. Comparison of model predictions of adhesion between a smooth spherical particle and a flat substrate with experimental results for different values of substrate roughness Normalized force of adhesion (mN/m) RMS roughness (nm)

Rumpf model prediction

Current model prediction Measured value

0.17 1.64 4.60 10.6

72 3.0 0.6 0.5

100 23 22 25

101 27 23 19

The onset of capillary forces was identified to be at a critical relative humidity value marked by a large increase in the force of adhesion. For surfaces with nanoscale roughness, the adhesion force remained constant with increasing relative humidity. At a certain value of humidity, the spontaneous formation of a capillary led to a large increase in the force of adhesion. The value of critical humidity increased with increasing surface roughness of the substrates, as shown in Figs 2 and 3. This is a direct consequence of the fact that with increasing surface roughness a larger liquid volume is required to form a bridge between the asperities on the surface and the spherical particle. Furthermore, the formation of a larger bridge can occur only at a higher relative humidity value. Table 2 shows the values of roughness for the three different silica substrates used and the experimentally measured values of critical humidity. Based on the theory, Eq. (2), the fitting value of roughness corresponding to this value of critical humidity is also reported. The experimental values of roughness are in good agreement with the values predicted by the theory, validating the applicability of the model. The robustness of the model was tested using other substrates: sapphire, titanium and silver. Table 3 shows the values of critical humidity observed for these substrates with the corresponding experimental and fitting values (from theory). The values for sap-

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Figure 2. Force of adhesion as a function of relative humidity for silica surfaces of increasing roughness. Circles represent the oxidized silicon wafer (0.2 nm measured RMS roughness), squares represent the PE-CVD substrate (0.3 nm measured RMS roughness), and triangles represent the etched PE-CVD surface (0.7 nm measured RMS roughness). Solid lines are theoretical predictions for both the dry adhesion (horizontal lines from Eq. 1) and capillary adhesion regimes (Eq. 2) based on the information in Table 2. Reprinted with permission from Ref. [19]. Copyright 2002 Elsevier Science B.V.

Table 2. Comparison of the measured values of critical humidity at the onset of capillary forces for silica substrates with varying roughness and theoretical value of roughness corresponding to the same critical humidity based on the model Critical humidity (%)

Measured roughness (nm)

Theoretical value of roughness (nm)

22

0.2 ± 0.02

0.22

38

0.3 ± 0.03

0.34

62

0.7 ± 0.03

1.20

phire and titanium are observed to be similar to the theoretically predicted values. And in the case of silver, the measured value of roughness is larger than that expected from the theory. However, the reason for this discrepancy is suspected to be due to the plastic deformation of the soft silver substrate upon application of load using the AFM probe. The low yield strength of silver could lead to deformation of the asperities bringing the surfaces into intimate contact and hence increasing the adhesion force.

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Figure 3. Force of adhesion as a function of relative humidity for substrates of sapphire (circles: measured RMS roughness of 0.3 nm), titanium (squares: measured RMS roughness of 1.4 nm), and silver (triangles: measured RMS roughness of 3.0 nm). Solid lines are theoretical predictions for both dry adhesion (horizontal lines from Eq. 1) and capillary adhesion (Eq. 2) regimes based on the information in Table 3. Reprinted with permission from Ref. [19]. Copyright 2002 Elsevier Science B.V.

Table 3. Comparison of the measured values of critical humidity at the onset of capillary forces for different substrates with nanoscale roughness, and theoretical value of roughness corresponding to the same critical humidity based on the model Sample

Critical humidity (%)

Measured roughness (nm)

Theoretical value of roughness (nm)

Sapphire

40

0.3 ± 0.05

0.38

Titanium

65

1.4 ± 0.03

1.2

Silver

47

3.0 ± 0.02

0.58

The adhesion forces presented in this study show large deviation from ideally smooth surfaces. This is important considering that the surface roughness was varied only by a few nanometers. These results illustrate the critical nature of nanoscale surface roughness in controlling the adhesion of surfaces. Many industrial powders and substrate surfaces have asperities that are much larger than used here, but these results suggest that it may be the nano-scale roughness that con-

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trols the interaction of surfaces both in the dry and humid environments. The theoretical expressions presented in this study are greatly simplified, yet these basic approaches can elucidate the role of nanoscale roughness for known geometries of surfaces. 5. SUMMARY

In this study, the force of adhesion between surfaces of controlled nanoscale roughness was measured in dry and humid environments. A theoretical framework for the prediction of the magnitude and onset of capillary and dry adhesion forces was developed. The theoretical results were validated with experimental measurements using the AFM. The Rumpf model underestimated the values for dry adhesion of nanoscale rough surfaces and the validity of the current model is proven by the agreement with the measured values of the adhesion force. The model for prediction of the onset of capillary forces was validated for various different substrates showing the robustness of the model. The critical relative humidity, where capillary forces are first observed, increases as roughness on the nanoscale increases. This suggests that it is the smallest scale of roughness that primarily controls the adhesion of surfaces. Acknowledgements The authors acknowledge the financial support of the Engineering Research Center (ERC) for Particle Science and Technology at the University of Florida, The National Science Foundation (NSF) grant #EEC-94-02989, and the Industrial Partners of the ERC. REFERENCES 1. 2. 3. 4. 5.

D. Tabor, J. Colloid Interf. Sci. 58, 2 (1977). B.J. Briscoe and S.S. Panesar, J. Phys. D: Appl. Phys. 25, A20 (1992). H. Krupp, Adv. Colloid Interf. Sci. 1, 111 (1967). K.L. Johnson, K. Kendall and A.D. Roberts, Proc. R. Soc. London A: 324, 301 (1971). H.A. Mizes, in: Advances in Particle Adhesion, D.S. Rimai and L.H. Sharpe (Eds.), pp. 155. Gordon and Breach Publishers, London (1996). 6. D. Maugis, J. Adhesion Sci. Technol. 10, 161 (1996). 7. D.M. Schaefer, M. Carpenter, B. Gady, R. Reifenberger, L.P. DeMejo and D.S. Rimai, J. Adhesion Sci. Technol. 9, 1049 (1995). 8. K.N.G. Fuller and D. Tabor, Proc. R. Soc. London A: 345, 327 (1975). 9. K. Iida, A. Otsuka, K. Danjo and H. Sunada, Chem. Pharm. Bull. 41, 1621 (1993). 10. H. Rumpf, Particle Technology. Chapman and Hall, London (1990). 11. J.A. Greenwood and J.B.P. Williamson, Proc. R. Soc. London A: 295, 300 (1966). 12. H.Y. Xie, Powder Technol. 94, 99 (1997). 13. M.C. Coelho and N. Harnby, Powder Technol. 20, 197 (1978). 14. M.C. Coelho and N. Harnby, Powder Technol. 20, 201 (1978). 15. L.R. Fisher and J.N. Israelachvili, Colloids Surf. A 3, 303 (1981).

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16. Y.I. Rabinovich, J.J. Adler, A. Ata, B.M. Moudgil and R.K. Singh, J. Colloid Interf. Sci. 232, 10 (2000). 17. Y.I. Rabinovich, J.J. Adler, A. Ata, B.M. Moudgil and R.K. Singh, J. Colloid Interf. Sci. 232, 17 (2000). 18. A.W. Adamson, Physical Chemistry of Surfaces, 2nd ed., Wiley-Interscience, New York, NY (1967). 19. Y.I. Rabinovich, J.J. Adler, M.S. Esayanur, A. Ata, R.K. Singh and B.M. Moudgil, Adv. Colloid Interf. Sci. 96, 213 (2002). 20. W.A. Ducker and T.J. Senden, Langmuir 8, 1831 (1992). 21. J.P. Cleveland, S. Manne, D. Bocek and P.K. Hansma, Rev. Sci. Instrum. 64, 403 (1993).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 255–270 Ed. K.L. Mittal © VSP 2003

Advanced wet cleaning of sub-micrometer sized particles R. VOS,1,∗ K. XU,1 G. VEREECKE,1 F. HOLSTEYNS,1 W. FYEN,1 L. WANG,2 J. LAUERHAAS,3 M. HOFFMAN,4 T. HACKETT,4 P. MERTENS1 and M. HEYNS1 1

IMEC, Kapeldreef 75, B-3001 Leuven, Belgium Shanghai Huahong, Technology Centre, 4/F, 191 Chang Le Road, Shanghai, 200020 P.R. China 3 Verteq, 1241 E. Dyer Road, Suite 100, Santa Ana, CA 92706, USA 4 Ashland Chemical, 5200 Blazer Parkway, Dublin, OH 43017, USA 2

Abstract—Sub-micrometer particles on a wafer surface can have a detrimental effect on the yield in semiconductor device manufacturing and with shrinking dimensions of IC structures, this effect becomes more and more important. The critical particle sizes as set by the ITRS roadmap indicate that for sub-100-nm technologies, particles on the order of a few tens of nanometers will have to be removed. Therefore, there is a growing need to optimise the surface cleaning in order to control the density of these particles. In this paper, an overview is given of the current state-of-the-art in wafer cleaning technology and various approaches to achieve a good removal of all kinds of particles on various substrates are presented. Keywords: Particle removal efficiency; dilute HF; SC1; megasonic cleaning; etching.

1. INTRODUCTION

Since decades, wet chemical cleaning has been the preferred method to keep/make wafer surfaces clean during the fabrication of integrated circuits. This is because the removal of metallic, particulate and organic contamination is facilitated by many chemical and physical properties of liquid solutions. The RCA clean as published in 1970 by Kern and Poutinen [1] has been the basis for the development of most front-end wet cleaning recipes. The original RCA clean consists of two cleaning solutions that are used sequentially. The first cleaning solution, also commonly known as SC1 (or APM or ammonium hydroxide/hydrogen peroxide/water (NH4OH/H2O2/H2O) mixture) is used to remove organic contaminants and particles while the second cleaning solution, also known as SC2 (or HPM or hydrochloric acid/hydrogen peroxide/water (HCl/H2O2/H2O) mixture) removes metallic con∗

To whom all correspondence should be addressed: Phone: (32-16) 281-534, Fax: (32-16) 281-315, E-mail: [email protected]

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tamination. Often an SPM cleaning step (sulfuric acid/hydrogen peroxide (H2O2/H2SO4) mixture at 90°C) is added to remove heavy organic contamination followed by a dilute HF step to remove the native oxide and contaminants entrapped in this layer. This adapted RCA cleaning cycle is time- and chemical consuming. In the 30 years since, many modifications and improvements have been introduced [2, 3] and many researchers have developed more environmentallyfriendly and cost-effective cleanings. A possible roadmap [4] summarizing the trend to develop more efficient wafer cleanings is given in Fig. 1. More dilute cleaning solutions that are as effective have replaced the commonly used mixtures [5, 6] and the number of cleaning steps has been reduced [7–9], resulting in a much lower cost-of-ownership. In the standard RCA cleaning cycle particles are removed using the SC1 cleaning step. In many reduced cleaning sequences, particle removal is done using dilute-HF-based cleaning recipes. However, these cleanings have to be carefully optimized in order to obtain a good particle removal efficiency and avoid particle re-contamination [10, 11]. Recently, single wafer cleaning has gained interest and it is expected that this will be more widely implemented due to process integration and cycle time concerns [12]. Preferably, a single chemistry should be used to remove all kinds of contaminations in one cleaning step. Promising candidates for use as a single chemistry cleaning solution are APM (NH4OH/H2O2/H2O)-based cleaning mixtures to which metal complexing agents are added [13, 14]. The surface preparation requirements are given by the ‘International Technology Roadmap for Semiconductors’ [15] with respect to particulate, metallic and organic contamination. As the critical dimensions of the devices for future genera-

Figure 1. Suggested roadmap for cleaning recipes with lower chemical and DI-water consumption.

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tions of technology continue to scale down, more stringent targets for wafer cleaning need to be set. The ITRS roadmap indicates that for the upcoming technology nodes, particles with sizes of only a few tens of nanometers will have to be removed. By using the current state-of-the-art light-scattering metrology such as the KLA Tencor SP1-TBI or SP1-DLS tools there is a limitation to measure particles with a size smaller than 50 nm as individually resolved light point defects (LPDs). It has been demonstrated that this lower size-detection limit can be decreased if haze measurements are used [16]. This can be done if a high density of particles is present on the wafer surface. Using the haze method it is possible to optimise cleaning recipes for these nano-sized particles that will become critical for the device yield within a few years. In this paper, an overview is given of the current approaches to achieve a good removal for all kinds of particles from various substrates. The focus will be on the two cleaning mixtures that are mostly used to remove particles from silicon substrates, namely APM or SC1 mixtures on the one hand, and HF-based cleanings on the other hand. 2. PARTICLE REMOVAL MECHANISMS

In order to remove a particle attached to a wafer surface, the forces that are holding the particles have to be broken (see Fig. 2). This can be done by underetching using either HF or SC1 based cleanings. A minimum etch depth of 3 nm is found to be necessary to break the van der Waals forces and allowing the liquid to pene-

Figure 2. Schematic description of particle removal from and particle deposition on a wafer surface.

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trate underneath the particle [17]. If a physical removal force such as megasonic agitation or brush cleaning is used more dilute and lower temperature cleanings can be used allowing less etching and surface loss [18]. After breaking the binding forces, the particle has to be removed from the surface by some kind of repulsive force in order to prevent re-deposition. The particle-substrate interaction forces can be described in terms of the classical DLVO theory [19, 20]. According to this theory, the main forces that operate on a particle in the vicinity of a surface are the van der Waals interaction forces and electrostatic attraction/repulsion forces. Van der Waals interactions originate from the interactions of atomic and/or molecular dipoles whose orientations are correlated [21]. These forces operate only on a short distance (approx. 3 nm) and are mostly attractive. Electrostatic interactions exist because of the interactions of charges that are always present on surfaces in polar liquids, and can be either attractive or repulsive depending upon the surface charges of both the particle and the substrate. The action radius of this interaction is dependent upon the properties of the liquid, such as the ionic strength. The Debye–Hückel double-layer thickness κ –1 is a measure of the action radius of the electrostatic interaction forces and some values of κ –1 for typical cleaning chemistries are summarized in Table 1. The surface potentials of particles and substrates can be approximated by their zeta-potentials (i.e., the potential at the shear plane) as determined by electrophoretic light scattering (see Fig. 3). A more detailed description of these interaction forces can be found elsewhere [10, 11]. However, at very short distances of approach (typically less than a few nanometers), the DLVO theory often fails [21]. It has been observed that solvated surfaces experience an additional short-range repulsion that dominates the DLVO interactions. In an aqueous solution, these forces have been called ‘hydration forces’. Alternatively, between hydrophobic surfaces immersed in water, a strong long-range attraction has been measured which has been called the hydrophobic force. Also,

Table 1. pH, ionic strength (I) and Debye–Hückel double-layer thickness (κ –1) for different cleaning mixtures at room temperature Mixture

pH

I (M)

κ –1 (nm)

1/1/5 NH4OH/H2O2/H2O 1/1/50 NH4OH/H2O2/H2O 1/1/500 NH4OH/H2O2/H2O 1/1/5000 NH4OH/H2O2/H2O 0.5% HF 0.5% HF/0.5 M HCl DI-H2O H2O/HCl H2O/HCl

10.5 10.5 10.6 10.6 1.9 0.3 6 4 2

0.3 0.03 0.004 0.0006 0.01 0.5 10-6 10-4 10-2

0.5 1.7 5.1 12.4 2.7 0.42 300 30 3.0

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Figure 3. Measured zeta-potentials of different particles as function of pH. The ionic strength was adjusted to 10-3 M using KCl.

this force is significantly stronger compared to the van der Waals attraction and is measurable at surface separations as large as 10 nm. In addition, in presence of surfactants, steric repulsion forces have been measured between surfaces. 3. EXPERIMENTAL DETAILS

The particle removal efficiency of different cleaning recipes was determined using 6- or 8-inch CZ, p-type monitor wafers purchased from Wacker. Before each experiment, the wafers received an IMEC-cleanTM [17] as a preclean to render the wafer surface perfectly clean. Since the last step of this cleaning sequence consisted of an O3/DIW rinse, the bare silicon wafers were covered with a thin chemical oxide. Also wafers with 500-nm-thick thermal oxide were used. Wafers were contaminated with different particles using an immersion-based contamination, i.e., by immersing the wafers in a particle-contaminated solution followed by an overflow rinse and drying. Poly(ether ether ketone) (PEEK) and Teflon particles were deposited using a spin-based contamination procedure. A summary of the different particles used as contaminations is given in Table 2. The zetapotentials of the particles used were measured using electrophoretic light scattering on a Nicomp Model 370 apparatus purchased from Particle Sizing Systems. All other chemicals used for the cleaning experiments were purchased from Ashland Chemical and were of a GigaBitTM grade.

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Table 2. Summary of the different particles used for the controlled contamination experiments Particle

Vendor/source

SiO2 140 nm SiO2 80 nm SiO2 30 nm SiO2 Si3N4 Al2O3 TiO2 Teflon (Poly(tetrafluoroethylene)) PEEK (Poly(ether ether ketone)) PSL ((Polystyrene latex)) Si Ti W

Rodel ILD1300 Bangs Laboratories Bayer Clariant Elexsol Johnson Matthey Rodel QCTT1010 MSP Aldrich Victrex 150XF Duke Scientific MSP MSP MSP

Cleaning was done in a static bath or in a recirculation tank followed by a 10min rinse in an overflow tank and Marangoni drying. The different APM cleanings were done in a recirculation bath with a megasonic transducer at the bottom (0.8 MHz operated at 600 W) using a cleaning time of 5 min at room temperature. Cleaning times for the different HF cleanings were adjusted for 3 nm oxide removal (i.e., 2 min for the 0.5% HF/0.5 M HCl (dHF/HCl) or 90 s for the 0.5% HF (dHF)). The overflow rinse bath was equipped with a Verteq Turbo Sunburst megasonic transducer operated at 300 W. The pH of the final rinse was adjusted using HCl. Wafers were dried using a Marangoni drying (MgDry) step that was always at the same pH as the overflow rinse (OFR). Single wafer cleaning was done on a Verteq GoldfingerTM cleaning system using 1 min cleaning time followed by spin rinse and RotagoniTM drying. Particle contamination was measured using either light point defects (LPDs) or haze measurements on a KLA Tencor SP1-TBI or SP1-DLS apparatus. The particle removal efficiencies (PREs) were calculated using the appropriate signals before contamination, after contamination and after the cleaning procedure under investigation using æ

PRE = ç1 − ç è

Signal After Clean − Signal Before CC ö÷ × 100 Signal After CC − Signal Before CC ÷ ø

where SignalBeforeCC is the initial LPD counts or haze signal, i.e., before the controlled contamination, SignalAfterCC is the LPD counts or haze signal after the controlled contamination (i.e. before the cleaning under investigation) and

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SignalAfterClean is the LPD counts or haze signal after the cleaning under investigation. All measurements were done using an oblique illumination angle and detection over a wide collection angle (Dark Field Wide Oblique or DFWO). The sizes of the measured LPDs are reported as the sizes of PSL spheres with equal scattering intensity (and are expressed as Latex Sphere Equivalent diameters or Φ LSE). 4. OPTIMISATION OF CLEANING MIXTURES

As mentioned in the Introduction, historically SC1 or APM cleaning mixtures have been designed to remove particles from wafer surfaces. Especially in combination with megasonic agitation, these cleaning mixtures show an outstanding particle removal efficiency [18]. The key mechanisms of megasonic cleaning include different types of acoustic streaming such as microstreaming caused by bubbles generated in the megasonic field that undergo a pulsating motion and cavitation [22, 23]. It has been calculated that microstreaming generates local liquid flows with velocities as large as several hundred m/s, causing an additional drag force that can dislodge the particles attached to a wafer surface [23]. However, once the particles are released from the surface, re-deposition has to be prevented. This can only be achieved if the pH of the cleaning mixture is such

Figure 4. Removal of different particles from HF-last (hydrophobic) and O3-last (hydrophilic) silicon substrates using 5 min DI-water or 1/1/50 APM cleaning solution with megasonic irradiation at room temperature followed by 10 min overflow rinse and Marangoni drying (ΦLSE = 0.08–0.3 µm).

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that there are no attraction forces operational. Figure 4 shows that if megasonic cleaning with only DIW is used, particles such as SiO2 can be easily removed from O3-last silicon surfaces. On the other hand, Si3N4 particles are more difficult to remove from O3-last silicon surface. This can be explained by a strong electrostatic attraction in DIW between these positively charged particles and the negatively charged substrate. Also the removal of Teflon particles from hydrophobic HF-last silicon substrates is difficult probably because of hydrophobic attractions. However, when a 1/1/50 APM cleaning mixture at room temperature with megasonics is used, all these particles can be removed with an efficiency near 100%. These excellent particle removal properties can be attributed to the fact that at the pH of the APM mixture, all particles and the wafer surface bear a negative surface charge. In addition, because of the oxidizing nature of the peroxide, the silicon wafer becomes covered with a chemical oxide rendering a hydrophilic surface and eliminating any hydrophobic attractions. In Fig. 5, again it is shown that a DIW cleaning in combination with megasonic agitation results in a low removal efficiency. In this case, for particle sizes measured in the range 0.06–0.12 µm, negative removal efficiencies were determined, suggesting that many of the bigger-sized particles were fragmented and redeposited on the surface during the cleaning. The most important conclusion from Fig. 5 is that more diluted APM cleaning mixtures result in a similar cleaning performance as the 1/1/5 or 1/1/50 dilution. Many researchers have attributed the excellent removal efficiency of APM cleaning mixtures to the favourable electro-

Figure 5. Si3N4 particle removal efficiency from O3-last silicon substrates using 5 min APM cleaning with megasonic irradiation at room temperature followed by 10 min overflow rinse and Marangoni drying (ΦLSE = 0.06–0.12 µm and 0.12–0.3 µm).

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static interactions at the high pH of these cleaning mixtures [24]. However, due to the relative high ionic strength of these cleaning mixtures, electrostatic repulsion forces must be limited. As summarized in Table 1, the Debye–Hückel doublelayer thickness (κ –1) which is a measure of the action radius of the electrostatic interaction forces is very small especially for the 1/1/5 and 1/1/50 APM mixtures. Consequently, the main benefit of an APM cleaning mixture is not the existence of electrostatic repulsion at the high pH but rather the elimination of any electrostratic attraction that might occur at neutral pH. When this electrostatic attraction, which is rather long ranged, is eliminated, other repulsion forces such as hydration forces [11] must be responsible to prevent particles from re-deposition onto the wafer surface. Figure 5 also shows that at a 1/1/50 APM cleaning at room temperature without megasonic agitation has negligible particle removal efficiency because at this low temperature virtually no etching occurs, hence the particle adhesion forces that are holding the particle to the surface cannot be broken. Figure 6 shows the effect of particle size on the removal efficiency. The 80and 140-nm SiO2 particles were measured as LPDs while for the 30-nm SiO2 the haze method was used. For LPD measurements, low particle densities on the wafer were deposited (105 particles/wafer) while for the haze method much larger densities were needed (1010 particles/wafer). Figure 6 compares the cleaning performance of a batch megasonic system with a single wafer cleaner. For the batch megasonic cleaning system, the particle removal efficiency using a 1/1/50 APM cleaning at room temperature decreases if the particle size becomes smaller. From the haze map after cleaning of 30-nm SiO2 particles (see Fig. 7) it is observed that the cleaning is not uniform over the wafer surface. These small-sized particles are

Figure 6. SiO2 particle removal efficiency as a function of particle size using 1/1/50 APM cleaning at room temperature using two different megasonic systems (ΦLSE = 0.08–0.3 µm or haze measurements).

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Figure 7. Haze intensity distribution plot (top) and wafer map (bottom) showing the measured haze intensity signal on the wafer surface after cleaning of 30 nm SiO2 particles from O3-last silicon substrate using 1/1/50 APM cleaning solution with megasonic irradiation at room temperature.

better cleaned at the wafer area close to the transducer at the bottom of the cleaning tank (lower haze values measured after cleaning). However, at the top of the wafer, the cleaning efficiency is less. This non-uniform cleaning is related to a non-uniform distribution of the megasonic energy in the cleaning bath [25, 26]. Figure 6 shows that the smaller particles are more sensitive to these lower intensity regions in the cleaning bath. In Fig. 6 it is also shown that when a single-wafer cleaning system with an optimised uniform acoustic wave distribution on the overall wafer surface is used, an excellent removal of all particle sizes is obtained. Fig-

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ure 6 also proves that the lower size limit of 0.1 µm for particle removal using megasonic cleaning as proposed in reference [27] is an overestimation. In Fig. 8, the particle removal from silicon substrates using HF-based cleanings is presented. No significant difference is observed for the dHF and the dHF/HCl cleanings. Only when surfactant is added to the dHF, particle removal efficiency is affected. For this experiment, all the particles were deposited on an O3-last silicon substrate covered with a thin chemical oxide about 1 nm thick [28] that is etched away during the HF cleaning. Since this distance between the wafer surface and the particles is so small, van der Waals attraction forces are still important at the moment the chemical oxide is etched away. In addition, because of the high ionic strength of the dHF cleaning mixtures (see Table 1), electrostatic interaction forces are greatly shielded. Consequently, the driving force for the removal of particles cannot be found in the classical DLVO-theory but must be looked for elsewhere. It is interesting to note that for all particles with a high water-contact

Figure 8. Particle removal from O3-last silicon substrates using 0.5% HF (dHF), 0.5% HF/0.5 M HCl (dHF/HCl) or 0.5% HF/1% anionic surfactant (dHF/surfactant) cleaning followed by 10 min overflow rinse and Marangoni drying (ΦLSE = 0.1–0.3 µm for all particles except for Teflon and PEEK ΦLSE = 0.2–2.0 µm).

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angle such as Si, PEEK, etc., a low removal efficiency using dHF or dHF/HCl was found, whereas the hydrophilic particles such as Si3N4, SiO2, etc., could be removed easily from the silicon substrate. Therefore, it is postulated that the observed removal efficiencies for the dHF and dHF/HCl cleaning mixtures must be related to the existence of attractive hydrophobic or repulsive hydration forces between the particle and the silicon [11]. For the polymeric particles that are rather easily deformable, the increased contact area between the particles and the surface causing an increase in the van der Waals attraction [29] might also contribute to their low removal efficiency. Figure 9 shows the removal of different-sized PSL particles from O3-last silicon substrates using dHF cleanings. It is shown that the removal efficiency decreases both for the dHF and the dHF/HCl cleanings if the particle size becomes smaller. This can be explained by the fact that the adhesion forces, such as the van der Waals attraction force, that cause the particles to adhere to the surface show a squared dependence on the particle size while many mechanical removal forces such as drag forces depend on the volume of the particles, i.e., they scale with R3, R being the radius of the particle, if the particle becomes smaller [30]. Consequently, smaller particles are more difficult to remove. When a surfactant is added to the dHF cleaning mixture, it is observed that the removal efficiency of all the hydrophobic particles such as Si, PEEK, Teflon and PSL is improved (see Fig. 8) and also the small-sized PSL particles can be removed with an efficiency near 100% (see Fig. 9). Surfactants adsorb selectively at the surfaces of both the particle and the wafer surface, and this has a major effect

Figure 9. Polystyrene latex particle removal efficiency as function of particle size from O3-last silicon substrates using 0.5% HF (dHF), 0.5% HF/0.5 M HCl (dHF/HCl) or 0.5% HF/1% anionic surfactant (dHF/surfactant) cleaning followed by 10 min overflow rinse and Marangoni drying.

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upon the forces that are acting between them. It is proposed that for the hydrophobic particles and Si substrate, the surfactant will adsorb with its hydrophilic head group exposed towards the liquid and the hydrophobic tail oriented towards the hydrophobic surface (see Fig. 10). This would remove any hydrophobic attraction force and add a steric repulsion force between the particle and the surface. In addition, it has also been reported that van der Waals attractions can be decreased when a surfactant is present [31]. In any case, our data show that the use of surfactants in cleaning mixtures provides an efficient means to increase the removal efficiency. A cleaning cycle is never complete without a rinse and a drying step. We have demonstrated that the final rinse conditions can significantly influence the particle-removal performance of a cleaning recipe. As discussed in detail in Ref. [10], this is especially important for hydrophilic wafers where particles are transported via the carry-over layer into the overflow rinse bath where they can redeposit, at least if the rinse conditions are not optimized. This is illustrated in Fig. 11 where it is shown that the rinse conditions after the dHF cleaning step can significantly alter the particle removal efficiency. Figure 11 shows that the removal of positively-charged Si3N4 particles from thermal oxide substrates is rather low after a dHF or dHF/HCl cleaning followed by a neutral rinse. By using a low-pH rinse, the removal efficiency is significantly enhanced. This has been explained because the electrostatic attraction between the positively-charged Si3N4 particles and the negatively-charged SiO2 substrate during a rinse at neutral pH is eliminated by rinsing at a pH below the isoelectric point of oxide substrate. Since at a pH of 2 and the corresponding relatively high ionic

Figure 10. Schematic model for the adsorption of an anionic surfactant on silicon wafer and particle surfaces.

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Figure 11. Si3N4 and SiO2 particle removal efficiency from a thermal oxide substrate using a 2 min 0.5% HF/0.5 M HCl (dHF/HCl) or a 0.5% HF (dHF) cleaning followed by 10 min overflow rinse (OFR) and Marangoni drying (MgDry) as a function of pH and megasonic agitation (meg.) during rinse and Marangoni drying.

strength, the surface charge is greatly shielded, van der Waals attractions become important, resulting in removal of not all the particles from the surface. This carry-over effect also explains the difference in removal efficiency for the dHF and the dHF/HCl cleanings. Since for the dHF/HCl cleaning the initial pH is almost two pH units lower compared to the dHF cleaning, it takes longer for the pH to reach values above the isoelectric point of silica where the electrostatic attraction forces will dominate. Consequently, the particle removal efficiency for dHF/HCl cleaning is higher compared to dHF cleaning. For the removal of SiO2 particles that always have a similar surface charge as the thermal oxide substrate, the electrostatic interactions with the substrate are repulsive at all pH values. In this case, by lowering the pH of the overflow rinse, a lower removal efficiency is obtained. This has been explained by compression of the electrostatic double layers resulting in less electrostatic repulsion and a van der Waals interaction that becomes dominant. In order to eliminate the van der Waals attractions at the low pH, an additional removal force must be added. For instance, this can be done by using megasonic irradiation in the bath. As illustrated in Fig. 11, the use of megasonics in combination with a low pH during the final rinse results in an optimal removal efficiency for both the Si3N4 and the SiO2 particles. 5. CONCLUSIONS

An overview of some important current insights in particle cleaning technology has been presented in this paper. These insights are important for the development of single wafer and single chemistry cleaning solutions. Two distinct cleaning

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mixtures have been discussed in detail, namely APM and dilute HF-based cleaning mixtures. It has been demonstrated that for both cleaning mixtures, smallersized particles are more difficult to remove. The addition of surfactants and/or the use of megasonic agitation can significantly improve the removal efficiency for these small sized particles. Zeta-potential control remains important to eliminate electrostatic attraction forces that otherwise would control the removal of particles not only during the actual cleaning step but also during the subsequent rinsing and drying steps. REFERENCES 1. W. Kern and D. Poutinen, RCA Rev. 31, 187 (1970). 2. W. Kern, in: Handbook of Semiconductor Wafer Cleaning Technology, W. Kern (Ed.), p. 44, Noyes Publications, Park Ridge, New Jersey (1993). 3. T. Hattori, in: Ultraclean Surface Processing of Silicon Wafers – Secrets of VLSI Manufacturing, T. Hattori (Ed.), p. 441, Springer-Verlag, Berlin (1995). 4. M. Heyns, T. Bearda, I. Cornelissen, S. De Gendt, L. Loewenstein, P. Mertens, S. Mertens, M. Meuris, M. Schaekers, I. Teerlinck, R. Vos and K. Wolke, in: Cleaning Technology in Semiconductor Device Manufacturing, J. Ruzyllo and R. Novak (Eds.), PV99-36, p. 3, The Electrochemical Society, Pennington, NJ (2000). 5. T. Hurd, P. Mertens, L. Hall and M. Heyns, in: Proceedings of the 2nd International Symposium on Ultra-Clean Processing of Silicon Surfaces, M. Heyns, M. Meuris and P. Mertens (Eds.), p. 42, Acco Leuven, Belgium (1994). 6. T. Dhayagude, W. Chen, M. Shenasa, D. Helms and M. Olesen, in: Science and Technology of Semiconductor Surface Preparation, G.S. Higashi, M. Hirose, S. Raghavan and S. Verhaverbeke (Eds.), Symp. Proc. Vol. 477, p. 217, Materials Research Society, Pittsburgh, PA (1997). 7. M. Meuris, P.W. Mertens, A. Opdebeeck, H.F. Schmidt, M. Depas, G. Vereecke, M.M. Heyns and A. Philipossion, Solid State Technol., 109 (July 1995). 8. F. Tardif, T. Lardin, P. Boelen, R. Novak and I. Kashkoush, in: Proceedings of the 3rd International Symposium Ultra-Clean Processing of Silicon Surfaces, M. Heyns, M. Meuris and P. Mertens (Eds.), p. 175, Acco, Leuven, Belgium (1996). 9. T. Ohmi, J. Electrochem. Soc., 143, 2957 (1996). 10. R. Vos, I. Cornelissen, K. Xu, M. Lux, W. Fyen, M. Meuris, P. Mertens and M. Heyns, in: Particles on Surfaces 7: Detection, Adhesion and Removal, K.L. Mittal (Ed.), p. 427, VSP, Utrecht (2002). 11. R. Vos, M. Lux, K. Xu, W. Fyen, C. Kenens, T. Conard, P. Mertens, M. Heyns, Z. Hatcher and M. Hoffman, J. Electrochem. Soc. 148, G683 (2001). 12. D. Levy, P. Garnier, P. Boelen and S. Verhaverbeke, presented at Sematech Cleaning Workshop (2002). 13. H. Morinaga, M. Aoki, T. Maeda, M. Fujisue, H. Tanaka and M. Toyoda, in: Science and Technology of Semiconductor Surface Preparation, G.S. Higashi, M. Hirose, S. Raghavan and S. Verhaverbeke (Eds.), Symp. Proc. Vol. 477, p. 35, Materials Research Society, Pittsburgh, PA (1997). 14. R. Vos, M. Lux, S. Arnauts, K. Kenis, M. Maes, B. Onsia, J. Snow, F. Holsteyns, G. Vereecke, P.W. Mertens, M.M. Heyns, O. Doll, A. Fester, B.O. Kolbesen, T. Hackett and M. Hoffman, Solid State Phenomena, 92, M. Heyns, M. Meuris and P. Mertens (Eds.), Scitec, ZürichUetikon, Switzerland (2003). 15. International Technology Roadmap for Semiconductors – Front End Processes version 2001 (http://public.itrs.net).

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16. K. Xu, R. Vos, G. Vereecke, M. Lux, W. Fyen, F. Holsteyns, K. Kenis, P. Mertens, M.M. Heyns and C. Vinckier, in: Particles on Surfaces 8: Detection, Adhesion and Removal, K.L. Mittal (Ed.), p. 47, VSP, Utrecht (2003). 17. M. Meuris, S. Arnauts, I. Cornelissen, K. Kenis, M. Lux, S. De Gendt, P. Mertens, I. Teerlinck, R. Vos, L. Loewenstein and M.M. Heyns, Semiconductor Fabtech, 11th Edition, p. 292, ICG Publishing, London (2000). 18. S.L. Cohen, D. Rath, G. Lee, B. Furman, K.R. Pope, R. Tsai, W. Syverson, C. Gow and M. Liehr, in: Ultraclean Semiconductor Processing Technology and Surface Chemical Cleaning and Passivation, M. Liehr, M. Heyns, M. Hirose and H. Parks (Eds.), Symp. Proc. Vol. 386, p. 36, Materials Research Society, Pittsburgh, PA (1995). 19. B.V. Derjaguin and L.D. Landau, Acta Physicochim. URSS 14, 633 (1941). 20. E.J.W. Verwey and J.Th.G. Overbeek, Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam (1948). 21. J.N. Israelachvili, Intermolecular and Surface Forces. Academic Press, London (1992). 22. A.A. Busnaina and F. Dai, Semiconductor Int., 85 (August 1997). 23. J. Lauerhaas, Y. Wu, K. Xu, G. Vereecke, R. Vos, K. Kenis, P.W. Mertens, T. Nicolosi and M. Heyns, in: Cleaning Technology in Semiconductor Device Manufacturing, J. Ruzyllo and R. Novak (Eds.), PV01-26, p. 147, The Electrochemical Society, Pennington, NJ (2002). 24. F. Tardif, P. Patruno, T. Lardin, A.S. Royet, O. Demoliens, J. Palleau and J. Torres, in: Proceedings of the 3rd International Symposium on Ultra-Clean Processing of Silicon Surfaces, M. Heyns, M. Meuris and P. Mertens (Eds.), p. 335, Acco, Leuven, Belgium (1996). 25. F. Holsteyns, G. Vereecke, V. Coenen, R. Vos and P.W. Mertens, to be published in: Forum Acusticum 2002, Sevilla, Spain. 26. G. Vereecke, R. Vos, F. Holsteyns, M.O. Schmidt, M. Baeyens, S. Gomme, J. Snow, V. Coenen, P.W. Mertens, T. Bauer and M.M. Heyns, Solid State Phenomena, 92, M. Heyns, M. Meuris and P. Mertens (Eds.), Scitec, Zürich-Uetikon, Switzerland (2003). 27. M. Olim, J. Electrochem. Soc. 144, 3657 (1997). 28. F. De Smedt, C. Vinckier, I. Cornelissen, S. De Gendt and M. Heyns, J. Electrochem. Soc. 147, 1124 (2000). 29. S. Krishnan, A.A. Busnaina, D.S. Rimai and L.P. De Mejo, J. Adhesion Sci. Technol. 8, 1357 (1994). 30. M.B. Ranade, Aerosol Sci. Technol. 7, 161 (1987). 31. M.L. Free, as in Ref. 16.

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 271–277 Ed. K.L. Mittal © VSP 2003

Modified SC-1 solutions for silicon wafer cleaning CHRISTOPHER BEAUDRY,∗ JENNIFER BAKER, ROMAN GOUK and STEVEN VERHAVERBEKE Applied Materials, 974 E. Arques Ave, M/S 81307, Sunnyvale, CA 94086, USA

Abstract—The RCA clean is widely used in the semiconductor industry for many wet-chemical cleaning processes. The traditional RCA clean consists of a particle removal step, the Standard Clean 1 or SC-1, and metallic impurity removal step, the Standard Clean 2 or SC-2 step. In this work we have demonstrated the cleaning performance of a single-step “all-in-one” cleaning solution based on dilute SC-1 chemistry enhanced with chelating agents and surfactants. In particular, we will discuss the effect of surfactants in such solutions on sub-micrometer particle removal for three particle types: SiO2, Si3N4 and Si. The use of a single step cleaning strategy in a single wafer mode dramatically reduces the cycle time of cleaning. Keywords: RCA clean; silicon wafer cleaning; chelating agent; surfactant; modified SC-1; particle removal.

1. INTRODUCTION

SC-1 cleaning is widely used in the semiconductor industry during various wetchemical cleaning processes due to its outstanding particle removal efficiency. Although SC-1 solution, a mixture of NH4OH/H2O2/H2O, is an efficient particle removal solution, it inherently allows some metallic impurities from solution to deposit on the wafer surface [1]. For this reason a conventional SC-1 solution is typically followed by SC-2 solution, a mixture of HCl/H2O2/H2O, which exhibits excellent metallic impurity removal efficiency [2]. This sequence of SC-1 followed by SC-2 cleaning is known as the RCA clean and has been in use for over 30 years. Adding an appropriate chelating agent to SC-1 can remove, as well as prevent deposition of metallic impurities during the particle removal step and eliminate the need for a follow-up metallic impurity removal step [3, 4]. Not only does this reduce the number of chemical cleaning steps required, saving money and time, it also avoids the adverse effect of particle re-deposition during typical metallic impurity removal steps, such as SC-2 or an HF dip. Furthermore, an appropriately ∗

To whom all correspondence should be addressed. Phone: (1-408) 584-0957, Fax: (1-408) 584-1132, E-mail: [email protected]

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chelate-enhanced SC-1 solution can potentially remove metallic contamination even more efficiently than SC-2 solution, and its ability to bind free metal ions in solution will potentially prevent process excursions from affecting process yield. In addition to enhancing the metallic cleaning ability of SC-1 solutions, we have also investigated the use of surfactants in our modified SC-1 solution. In liquids, the attraction or repulsion between particles and the wafer surface is dependent on the van der Waals interactions (always attractive) and the electrostatic double layer forces (usually repulsive, except at low pH). The combination of these interactions will determine the potential energy of interaction and, thus, the barrier to adhesion [5-7]. The barrier to adhesion is related to the particle material type and size, solution pH and ionic strength, and the respective charges on the wafer surface and particle. Cleaning down to submicrometer and smaller sizes becomes increasingly difficult as the barrier to adhesion decreases with decreasing particle size. Thus, the tendency to re-deposit on the wafer surface increases as the particle size decreases. Surfactants may prevent particle deposition in two ways: (i) electrostatically by increasing surface potentials and, thus, increasing the repulsion force between materials of like signs (particles and wafer surface) and (ii) physically by providing steric hindrance which does not allow particles to get close enough to the surface for van der Waals interactions to dominate. With this in mind, the surfactants added to SC-1 can be a critical component to prevent submicrometer particles removed from the wafer surface from re-deposition, thus increasing the particle removal efficiency for small particles. This is increasingly important as the dimensional size of semiconductor devices continues to decrease. The focus of this work was to study the performance of several surfactants in SC-1 solutions and develop “all-in-one” cleaning solution based on a dilute SC-1 solution enhanced with chelating agents and surfactants. In addition, we studied the potential for residual organic contamination from both the chelating agent and surfactant (for the optimized “all-in-one” solution). 2. EXPERIMENTAL

All cleaning experiments were performed with a 300-mm OasisTM Single Wafer Cleaning System (Applied Materials). We carried out experiments using a modified SC-1 solution with a composition of 1:2:80 by volume (NH4OH:H2O2:H2O). The concentration of chelating agent (carboxylic acid based) was less than 0.1 wt% of the solution. The concentration of the surfactant was also less than 0.1 wt% of the solution, with the exception of the conventional SC-1 solution, which did not contain any surfactant. Three different surfactants were evaluated. Megasonic energy was applied during the particle removal step unless noted (power density was varied and is noted in the figures). The cleaning process time was 30 s at a temperature of 50°C or 80°C followed by a rinse at the same temperature and a spin dry. The rinse time was also varied during the initial surfactant

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Figure 1. An example of the deposition pattern used for particle removal experiments (particles ≥0.09 µm, measured on KLA-Tencor SP1TBI).

evaluation experiments from 10 s to 30 s. Additionally, early data on the effect of megasonic power density on particle removal are reported. Prime silicon wafers for particle removal studies were prepared with an automated aerosol particle deposition tool made by MSP (Model 2300D). Two categories of particle deposition pattern were used. For the particle removal aspect of surfactant evaluation experiments we deposited 3 spots (1 each of the following: SiO2, Si3N4 and Si) on a single wafer. Otherwise the deposition pattern was a combination of full random coverage and a spot (Fig. 1). The particle measurements were performed on a KLA-Tencor SP1TBI instrument. Surface metal measurements were carried out with the vapor phase decomposition–ion coupled plasma mass spectrometry (VPD–ICPMS) technique. Time-of-flight secondary ion mass spectrometry (TOF-SIMS) was used to assess if any residual chelating agent or surfactant remained on the wafer surface (after the rinsing and drying). 3. RESULTS

The initial surfactant evaluation consisted of evaluating particle addition and particle removal performance of each solution composition. The particle addition results were calculated by the difference of particle count after cleaning (all wafers had initial particle counts of less than 25 ≥ 0.09 µm). Fig. 2 shows the results for particle addition ≥0.09 µm as a function of rinse time for conventional SC-1 and three SC-1 solution compositions containing a surfactant. The SC-1 solutions containing a surfactant were named SC1 + surfactant 1, 2, or 3. From Fig. 2 we see how addition of the surfactants under evaluation can reduce particle addition compared to conventional SC-1. We can also assess how easy the solutions are to

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Figure 2. Particle addition for the four SC-1-based solutions tested as a function of rinse time. The initial particle counts were less than 25 and each data point represents a single wafer (particles ≥0.09 µm, measured on KLA-Tencor SP1TBI).

Figure 3. Average particle removal for the four SC-1-based solutions tested. The initial particle count for each particle type (Si3N4, SiO2 and Si) was ~ 800, the megasonic power density was 1.13 W/cm2 and each data point represents an average of 4 wafers (particles ≥0.09 µm, measured on KLA-Tencor SP1TBI).

rinse off by the amount of rinse time required to be particle neutral. SC1 + surfactant 1 was particle neutral as long as the rinse time was ~ 20 s or more. Figure 3 shows the results for particle removal for all four solution compositions evaluated. It is important to note that for this run of experiments the target

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Figure 4. Average particle removal efficiency for the optimized SC-1 solution with varied power densities. The starting particle count for each particle type (Si3N4 and Si) was ~ 1000 and each data point represents a single wafer (particles ≥0.09 µm, measured on KLA-Tencor SP1TBI).

particle size for the deposition was 0.1 µm for all particle types. SC-1 solution containing surfactant 1 outperformed all other solutions for all of the particle types studied. It is also apparent that the SiO2 particles were the easiest to remove and that Si were the most challenging. The particle removal and addition performances of surfactant 1 clearly suggested it as the best choice of surfactant. All further results reported in this paper were obtained with an optimized solution containing a chelating agent and surfactant 1. In order to qualify the optimized solution with respect to particle addition we evaluated more than 250 wafers with our baseline process. The average particle addition was actually negative with an average starting count of approximately 15 particles (≥0.09 µm). In addition we investigated the effect of power density on particle removal. Figure 1 illustrates the deposition pattern used for contaminating these particle removal challenge wafers: full coverage across the wafer surface combined with a localized spot. Figure 4 demonstrates the effect of power density on removal efficiency for 0.2 µm Si3N4 and 0.1 µm Si particles. Without the use of megasonic energy (power density equal to 0) the removal of very small Si particles is dramatically reduced. This is not seen for larger Si3N4 particles as only a slight reduction in removal efficiency was observed (this may be due to the particle type and/or size difference). Increasing the megasonic power increases the particle removal efficiency for all the particle types tested, but more so for the more challenging Si particles.

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Figure 5. Average surface trace metals levels after modified SC-1 clean as determined by VPD– ICPMS for 5 wafers.

In order to complete this study we investigated potential concerns regarding final surface metal level and organic residue with the use of an SC-1 last cleaning (containing chelating agents and/or surfactants). The first was to confirm that the optimized solution did not deposit any metallic ions onto the wafer surface. The VPD–ICPMS results shown in Fig. 5 illustrate the excellent performance, in particular for the chelating agent, of the optimized solution. The average surface metals levels after the modified SC-1 clean was equal to or below today’s VPD– ICPMS detection limits. Note that the 1 σ error bars are generally within the symbol for the average for 5 wafers (Fig. 5). Finally, with TOF-SIMS we confirmed that no traces of organic residues specific to the chelating agent and surfactant were left on the wafer after rinsing. 4. SUMMARY

In this paper we have shown that the addition of an appropriately selected surfactant to SC-1 solutions can enhance particle removal efficiencies for very small particle sizes (~ 0.10 µm). The addition of a chelating agent can eliminate the need for an additional metal removal step, potentially saving time and money. This modified SC-1 solution, containing both additives, was shown to have excellent particle removal efficiency and to reduce metal deposition on the wafer surface to current VPD–ICPMS detection limits. Furthermore, rinsing can be optimized to eliminate all traces of the chelating agent and surfactant residues. The developed “all-in-one” cleaning solution is a viable single step replacement for the traditional RCA cleaning sequence (SC-1 solution followed by SC-2 solution).

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REFERENCES 1. H. Hiratsuka, M. Tanaka, T. Tada, R. Yohsimura and Y. Matsushita, Ultra Clean Technol., 3, 18-27 (1991). 2. W. Kern, in Cleaning Technology in Semiconductor Device Manufacturing, J. Ruzyllo and R.E. Novak (Eds.), PV 90-9, pp. 3-19, Electrochemical Society, Pennington, NJ (1990). 3. C. Beaudry, H. Morinaga and S. Verhaverbeke, in Cleaning Technology in Semiconductor Device Manufacturing VII, J. Ruzyllo, R. Novak, T. Hattori and R. Opila (Eds.), PV 2001-26, pp. 118-125, Electrochemical Society, Pennington, NJ (2001). 4. C. Beaudry, J. Baker and S. Verhaverbeke, in Proceedings of the 21st Annual Semiconductor Pure Water and Chemicals Conference, M. Balazs (Ed.), pp. 110-118, Balazs Laboratories, San Jose, CA (2002). 5. R. Donovan and V. Menon, in Handbook of Semiconductor Wafer Cleaning Technology, W. Kern (Ed.), pp. 152-197, Noyes Publications, Westwood, NJ (1993). 6. D. Riley, in Contamination-Free Manufacturing for Semiconductors and Other Precision Products, R. Donovan (Ed.), pp. 221-264, Marcel Dekker, New York, NY (2001). 7. M. Itano and T. Kezuka, in Utraclean Surface Processing of Silicon Wafers: Secrets of VLSI Manufacturing, T. Hattori (Ed.), pp. 115-136, Springer-Verlag, Berlin (1995).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 279–292 Ed. K.L. Mittal © VSP 2003

Investigation of ozonated DI water in semiconductor wafer cleaning JERRY DEBELLO1 and LEWIS LIU∗, 2 1 2

Mattson Technology, Inc., 325 Technology Drive, Malvern, PA 19355, USA Akrion, LLC., 6330 Hedgewood Drive, #150, Allentown, PA 18106, USA

Abstract—Ozonated DI water (DIO3) was generated efficiently by dissolving ozone gas into DI water in a newly designed module, which supplied DIO3 to Mattson’s OMNITM system (a single chamber design) for semiconductor wafer wet cleaning. In this study, DIO3 has been investigated for particle removal, silicon dioxide (SiO2) growth, photoresist stripping and polymer residue cleaning. The results show that DIO3 processes are particle-neutral, have high particle removal efficiencies on particle-challenged wafers, and grow quickly thin SiO2 films on wafer surfaces. DIO3 processes also remove various photoresists (although removal rates are low) and clean polymer residues efficiently, when dilute HF is added. Overall, the results indicate that DIO3 is an alternative to the traditional RCA chemicals and it will play an important role in future wafer cleaning. Keywords: Ozonated DI; 0.085 µm particles; particle cleaning by DIO3; (HF + DIO3) mixture.

1. INTRODUCTION

RCA clean has been a traditional solution for semiconductor wafer aqueous cleaning for decades. It consists generally of SC1 (a mixture of DI water, NH4OH and H2O2) for particle cleaning, SC2 (a mixture of DI water, HCl and H2O2) for metal cleaning, HF for silicon dioxide (SiO2) etching, and SPM (sulfuric acid and hydrogen peroxide mixture) or SOM (sulfuric acid and ozone mixture) for photoresist stripping. DIO3 has been studied and reported in wafer cleaning for years. DIO3 is a lowcost chemical and has low environmental impact in wafer cleaning [1, 2]. Ozone (O3) in DIO3 is an oxidant with a very high oxidation potential, making it effective in polymer organic removal, such as in photoresist stripping and post-ash residue cleaning [3–7]. DIO3 contains both O3 molecules and hydroxyl radicals (OH*). OH* is also an oxidant and is even more reactive than ozone itself. OH* in DIO3 initiates chain reactions with O3 to form more OH* radicals [7]. The organic ∗

To whom all correspondence should be addressed. Phone: (1-610) 530-3425, E-mail: [email protected] The paper was prepared while he was working for Mattson Technology, Inc.

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removal is explained by a mechanism [3] in which the photoresist is directly decomposed by molecular O3 or reacts with OH* radicals. Some investigators used DIO3 and HF together and found that the combination could efficiently clean organic, metallic and particulate contaminations [8, 9]. DIO3 is also effective at wafer-surface treatment. DIO3 enables the Si surface to promptly grow a thin native oxide layer, which effectively functions as a protective film for silicon wafers [10]. Additionally, DIO3 causes neither SiO2 loss nor Si surface damage (roughness) during cleaning, whereas SC1 processes do both [11]. In this study, we have obtained information on DIO3 generation and decay in the DIO3 module. We have demonstrated that DIO3 is a particle-free chemical on wafers. It is able to grow quickly a thin film of silicon dioxide and is also able to strip photoresists. We have also demonstrated that the mixture of DIO3 and HF is able to clean polymer residues after dry ash. Remarkably, we have found that DIO3 alone is capable of cleaning particles, even though the particle cleaning mechanism is not clear. One possible explanation is addressed by the theory [12] in which oxidation occurs on both the particle surface and the wafer surface, rendering them hydrophilic with negative zeta potentials and resulting in a strong electrostatic repulsion between them. 2. EXPERIMENTAL

An OMNITM system, made by Mattson Technology, was used as a cleaning tool in this study. The OMNITM system is a wet cleaning tool with a single chamber. Wafers are vertically stationed inside the chamber during cleaning. The chamber opens only while loading or unloading wafers. DI water or chemicals come in from the bottom of the chamber and come out from its top. SC1, SC2, HF, SOM and DIO3 chemicals are available on the tool. A cleaning recipe can be written at will by selecting any of the chemicals in a chemical step. A de-ionized (DI) water rinse is always introduced between two chemical steps if a recipe has multiple chemical steps and is always introduced before IPA (isopropyl alcohol) vapor drying. The wafer drying is always used as the last step of wafer cleaning. DirectDisplacementTM IPA drying technique provides IPA vapor into the chamber from the top. The vapor is condensed into a 2.54-cm-thick IPA layer on top of the liquid (DI water), and continuously and slowly pushes the liquid down to the bottom drain. The IPA layer is designed intentionally to dry wafers by sweeping across the wafers during the slow draining, so that IPA replaces any water spots on the wafers by its lower surface tension. The wafers come out watermark-free after the drying process. The chemical ratio is controlled by injecting the required amount of the chemical into a controlled DI stream, which flows into the chamber from its bottom. The chemical and DI water are mixed very well due to high turbulent flow of the DI water. The required amount of chemical is adjusted by a needle valve. Both

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the DI water temperature and flow rate are controlled by an APC (adaptive process control) algorithm that regulates the valves. The chemical is used only once (not circulated). A module was used to generate DIO3 for the OMNITM. The DIO3 module is made of an 18-gallon cylinder with a pump and a static mixer. A DIO3 pipe connects the three together as a circulation loop. In the loop, DIO3 flows out from the bottom of the cylinder through the pump, the static mixer, and back into the top of the cylinder. After DI water fills up the cylinder and starts to circulate in the loop, O3 gas sparges into the circulating DI water between the pump and the mixer in the loop, forming DIO3. The amount of O3 gas absorbed by the DI water, or “dissolved ozone level” is measured in parts per million or ppm (henceforth, it will be represented as x ppm DIO3). The sparging is continued until injection step. During injection, both the circulation and the sparging are stopped and N2 gas enters the cylinder from the top, pressurizes the cylinder, and displaces the DIO3 out of the cylinder from the bottom into DI water stream. The concentration and temperature of the mixture are adjustable by controlling the relative flow rates of the DI water and the DIO3. After blending with the DI stream, the DIO3 enters the chamber for wafer cleaning. The metrology tools used were Tencor SP1 for LPD (light point defect), Rudolph Ellipsometer or O.P (Opti-Probe, Thermawave) for SiO2 film thickness measurement, Prometrix UV-1080 (KLA-Tencor) for photoresist thickness measurement, and SEM (scanning electron microscope) to obtain images of IC (integrated circuit) device structures. 3. RESULTS AND DISCUSSION

3.1. DIO3 generation and its decay Figure 1 shows O3 concentration profiles in the DIO3. In this case, DI water filled the cylinder for 70% (12.6 gallons or 47.6 liters DI water) of its 18-gallon volume, before the O3 sparging was started. The experimental temperature was 23oC (room temperature). The profiles from the four tests in Fig. 1 show that O3 concentration reached 80 ppm in 28 min and remained at this concentration level with further O3 sparging. The gas-phase pressure in the cylinder was controlled at 775.7 torr (15 psig), which is a differential pressure from the atmosphere. In order to obtain a high O3 concentration in the cylinder, we found that the gas-phase pressure and the use of static mixer for DI water and O3 mixing were the two most important factors. The gas phase pressure is the combined pressure of O3 vapor and DI water vapor in the cylinder. Increasing the gas phase pressure will increase the O3 concentration according to Henry’s law [6]. However, the gas-phase pressure is limited by the O3 gas supply, which is also used for continuous sparging. The liquid pressure at the O3 sparging inlet must be below the maximum available O3 sparging pressure. If the gas-phase pressure is set too high,

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Figure 1. O3 concentration profiles during DIO3 generation by dissolving ozone gas into DI water in Mattson’s DIO3 module at room temperature.

Figure 2. O3 concentration decay in DIO3 cylinder at atmospheric pressure and 23°C.

it can cease the dissolution of O3 in DI water. 775.7 torr was found to be the highest pressure after trial and error and was used in this study. The purpose of the static mixer is to enhance the efficiency of dissolution of O3 gas in DI water by increasing the contact area between O3 gas and DI water. Without the mixer in the circulation loop, it took 53 min to reach 80 ppm O3 concentration, which is almost double the time with the static mixer. Because the DIO3 module injects 80 ppm DIO3 into DI water steam and the mixture comes into the wafer-cleaning chamber, the O3 concentration and temperature in the cleaning chamber are controlled by the mixing flows and temperatures of both DIO3 and DI water, which are determined by the cleaning recipe.

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The achievable ranges in the chamber are 0 to 80 ppm for O3 concentration and 23 to 65°C for temperature. Researchers have published on applications of DIO3 in wafer cleaning. Most of them used less than 60 ppm DIO3 [1–6]. After we investigated the DIO3, we found there was no significant difference of O3 concentration from 20 to 80 ppm in silicon dioxide growth. There was a slight difference in particle removal and the higher the O3 concentration, the higher the removal percentage. There was a difference in bulk photoresist stripping and the higher the O3 concentration, the faster the stripping. Figure 2 shows the O3 concentration decay in the DIO3 cylinder. The experiment was conducted with 12.6 gallons (47 liters) of 51 ppm DIO3 in the cylinder. The DIO3 remained stagnant in the cylinder during the entire decay. The temperature was 23°C, the gas-phase pressure was atmospheric and the pH of the DIO3 was 3.5. Figure 2 shows that the O3 concentration decreased from 51 to 42 ppm in 46 min. Similar O3 decay behavior was observed in the work by researchers from IMEC [6]. 3.2. Particle addition and particle removal by DIO3 Figure 3 shows particle addition by DIO3 cleaning followed by DI rinsing and IPA drying (DIO3–IPA drying). The monitor wafers used were 200 mm bare Si wafers, which had pre-cleaning particle counts below 30 from 0.085 to 1.00 µm size. Five of the monitor wafers and 95 dummies were used per run for a total of four runs. The results show that the average number of adders per wafer was 3 and the maximum was 14. These results are very promising, and well within typical particle addition specifications for semiconductor device manufacturing. The process sequence carried out for the data obtained in Fig. 3 was as follows: (1) wafers were loaded in the chamber and the chamber closed; (2) DI water rinsed the wafers for 30 s; (3) 15 l/min of 80 ppm DIO3 at 23°C was injected into 15 l/min of DI water stream at 37°C to make 40 ppm O3 concentration at 30°C in the chamber; (4) the wafers were immersed in the 40 ppm DIO3 at 30°C for 6.5 min with megsonics; (5) high-flow DI water rinsed the wafers until the resistivity in the chamber reached 18 mΩ; and (6) Direct-DisplacementTM IPA drying (described above) was carried out for 9 min. The particle addition testing is designed to evaluate the cleanliness of the entire DIO3 system by measuring the particle adders per wafer after the cleaning. The lower the number of adders, the cleaner the system. The particles, indicated by LPDs (light point defects), were measured from 0.085 to 1.00 µm size with 5 mm edge exclusion by Tencor SP1. The smallest size in the detection range is called threshold. Thresholds above 0.1 µm are very popular in current wet cleaning. Since the IC design is moving toward 0.13 or 0.10 µm (130 or 100 nm) technology nodes, wet cleaning approach needs to develop new ways to remove sub-0.1µm particles. Because of this, we have been developing the cleaning process for 0.085-µm particles.

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Figure 3. Particle adders per wafer by DIO3 (40 ppm DIO3, megasonics, 30°C, 6.5 min)–IPA drying.

Figures 4–7 show particle removals by DIO3 and their comparison with SC1 or DI water. Particles were determined in terms of LPD by Tencor SP1. Figures 4–6 show data for particle-challenged wafers with Si3N4 particles at 0.16 µm or larger. Figure 7 shows data for particle-challenged wafers with PSL (polystyrene latex) particles at 0.085 µm or larger. Both types of particle-challenged wafers are commonly used in evaluating particle removal capability. Figure 4 illustrates the capability for Si3N4 particle removal by DIO3 in the OMNITM tool. The wafers were cleaned by 63 ppm DIO3 at 33°C with megasonics for 20 min followed by DI water rinsing and IPA drying. The removal efficiency on every wafer was above 95%. Figure 5 shows a comparison of DIO3 (Process #1 and Process #2) vs. DI water (Process #3) and a comparison of IPA drying (Process #2) vs. N2 drying (Process #4) for Si3N4 particle removal by DIO3. In the first comparison, the DI water process was run at the same conditions as the DIO3, except for 0 ppm O3 concentration. Both processes were followed by DI rinsing and IPA drying. In this comparison, 91.7% of the particles were removed by 53 ppm DIO3, 96.2% by 63 ppm DIO3 and only 2.1% by DI water alone, which shows that the DIO3 has a significantly higher capability to remove particles than pure DI water. In the second comparison, both processes were run at the same conditions except for the last step of drying. 96.2% particles were removed by DIO3–IPA drying (DIO3 followed by DI rinsing and IPA drying) and 95.7% particles were removed by DIO3– N2 drying (DIO3 followed by DI rinsing and N2 drying). Thus, there was no significant difference between IPA drying and N2 drying in particle removal.

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Figure 4. Si3N4 particle removal from particle-challenged wafers by DIO3 (63 ppm, 33oC, 20 min, megasonics)–IPA drying.

Figure 5. Si3N4 particle removal% comparison for DIO3 vs. DI water, and for IPA drying vs. N2 drying. Process 1: DIO3 (53 ppm, 33oC, 20 min, meg.) - IPA drying. Process 2: DIO3 (63 ppm, 33oC, 20 min, meg.) - IPA drying. Process 3: DI Water Rinse (33oC, 20 min, meg.) - IPA drying. Process 4: DIO3 (63 ppm, 33oC, 20 min, meg.) - N2 drying.

Figure 6 shows a comparison of SC1 vs. DIO3. The SC1 was a dilute chemical mixture in the volumetric ratio DI water/NH4OH/H2O2 = 80:1.3:2.2 at 40oC, which is a suggested SC1 process for particle cleaning in OMNITM system. The DIO3 contained 63 ppm of dissolved ozone at 40°C. Both processes were run for 5 min with megasonics. The results show that the particle removal was 92% by the SC1 and 89.8% by the DIO3. The removal efficiency by the SC1 was only 2.2% higher than that by the DIO3.

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Figure 6. Si3N4 particle removal% comparison for DIO3 vs. SC1. Process 1: SC1 (DI water:NH4OH:H2O2=150:1.3:2.2, 40oC, 5 min, meg.)–IPA drying. Process 2: DIO3 (63 ppm, 40oC, 5 min, meg.)–IPA drying.

Figure 7. PSL particle removal% by DIO3, SC1 and DI water, followed by DI rinse and IPA drying. Test#1: SC1 (DI water/NH4OH/H2O2=80:2.2:3.1), 45oC, 6 min, meg. Test#2: DIO3 (30 ppm), 30oC, 20 min, meg. Test#3: DI water, 30oC, 20 min, meg.

Figure 7 shows PSL particle removal results by SC1, DIO3 and pure DI water. Three wafers were used per test. The SC1 had a volumetric ratio DI water/NH4OH/H2O2 = 80:2.2:3.1 and was run at 45°C with megasonics for 6 min (Test#1). 30 ppm DIO3 was run at 30°C with megasonics for 20 min (Test#2).

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The DI water process was run under the same conditions as the DIO3 process with 0 ppm O3 concentration in the DIO3 step (Test#3). All three processes were followed by DI water rinsing and IPA drying. The results show 79%, 50%, 4% average particle removal by the SC1, DIO3, DI water processes, respectively. The SC1 had 29% higher particle removal than the DIO3 and the DI water had 46% lower than the DIO3. It was confirmed again that DIO3 is promising in particle removal, even though its removal capability is lower than SC1. As can be seen in Fig. 7, there are variations in particle removal percentages from wafer to wafer within a single test. These variations are likely to be caused by variations in the wafers themselves or by non-uniform distribution of megasonic energy in the chamber. Nevertheless, even with these variations considered, the data of Fig. 7 show the particle removal% are distributed clearly in three clusters, distinguished by each test, with significant differences between their averages. Based on this, the above conclusions were made. The mechanism of removing particles by DIO3 is not fully understood. A possible explanation is in terms of electrostatic double-layer theory [12]. Because both the particle surface and the wafer surface are oxidized by ozone molecules in DIO3 and both oxidized surfaces have negative zeta potentials, there is a mutual electrostatic repulsion which overcomes the attractive van der Waals force. The net repulsive force separates the particle from the wafer surface. Once the particle is separated, the repulsive force forms a potential energy barrier to prevent the particle from re-depositing. Mechanical agitation by megasonics or DI water flow in the system also helps particle separation. This high particle removal capability of DIO3 could open a new way in particle cleaning without surface damage. 3.3. Silicon dioxide growth by DIO3 Figure 8 shows data for silicon dioxide (SiO2) growth by DIO3. The wafers were bare silicon and were pre-treated with a strong HF to remove the native SiO2 layer completely, followed by DI water rinsing and IPA drying. Figure 8 shows that silicon dioxide growth is very fast in the first minute by DIO3, and then slows down. It reaches 6.1 Å in the first minute and grows only 1.5 Å in the following 35 min. Three different O3 concentrations were used (3.3, 7 and 20 ppm), yet the data show that all of the measurement points lie on a single curve. This indicates that the growth rate is independent of the O3 concentration in DIO3 in the 3.3 to 20 ppm range. In a different test, the growth reached 13 Å in the first minute and almost stopped (saturated) after that. We believe that the wafers and the metrology tools caused the thickness difference. The thin SiO2 film demonstrated good quality in Qbd (stress charge breakdown) tests, which will not be discussed any further in this paper.

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Figure 8. SiO2 growth by 3.3, 7.0 or 20 ppm DIO3 at 40°C.

3.4. Photoresist stripping and polymer residue cleaning by DIO3 Figure 9 shows results from photoresist stripping tests by DIO3. The photoresist was I-line (PFI-56, Sumitomo) and was baked (annealed) at 90°C for 90 s before stripping. The DIO3 process involved a DIO3 cleaning followed by a DI water rinsing and N2 drying (without IPA). IPA was not used in the last drying step, because IPA itself may slightly remove the photoresist. Figure 9 shows that stripping rates are 239.3, 459 or 526.4 Å/min (i.e., 23.9, 45.9, 52.6 nm/min) in 63 ppm DIO3 at 23, 33 or 35°C, respectively. These rates are much lower than those by SOM (H2SO4+O3) or by SPM (H2SO4+H2O2) for a bulk photoresist stripping (some thousands of Å/min). Both SOM and SPM are aggressive chemicals and are commonly used in stripping organic photoresists in the wet cleaning industry. The drawbacks of these chemicals are their high operational cost and environmental issues [3]. For this reason, the cleaning industry seeks an alternative (e.g., DIO3) to strip photoresists. DIO3 stripping of a photoresist film on the wafer starts from the film surface and removes the film uniformly down to the wafer surface. SOM or SPM undercuts the film at the interface between the photoresist and the wafer and peels the film off. Both DIO3 and sulfuric acid-based stripping mechanisms are thoroughly discussed in Ref. [1]. Figure 10 shows the stripping results by DIO3 from other tests. The stripping rates were measured for JSR, TOK and UVII photoresists with various O3 concentrations in DIO3 with and without megasonics. The maximum stripping rate was 205.1 Å/min (20.5 nm/min) from a JSR photoresist stripping by 58 ppm DIO3 at 28°C with megasonics. The stripping data from Fig. 10 again show that

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Figure 9. Baked I-line photoresist stripping by 63 ppm DIO3 for 5 min at 23°C (Process 1), at 33oC (Process 2) and at 35°C (Process 3), followed by DI water rinsing and N2 drying.

Figure 10. Photoresist (PR) striping rate by DIO3 at 28oC with or without megasonics followed by DI water rinsing and N2 drying.

DIO3 has a much lower stripping rate than SOM or SPM. Therefore, it is confirmed again that DIO3 is not able to directly replace SOM or SPM in wet photoresist stripping. The results also show that the photoresist stripping rates are sensitive to O3 concentration in DIO3 as well as to the use of megasonics. Figure 11 shows SEM pictures in a 4 ´ 4 µm2 area of a device wafer before (Fig. 11a) and after cleaning (Fig. 11b). The device was made of polysilicon Ushape trenches on top of a thin silicon dioxide film. The pictures show that the

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Figure 11. (a) SEM picture of a post-ashed wafer before cleaning. (b) SEM picture after the coinject (DIO3+HF) cleaning.

trenches were laid on the wafer. The cleaning process used a mixture of DIO3 with dilute HF, followed by DI rinsing and IPA drying. Figure 11a shows white strips on the U-edges, which reflects the presence of polymer residues on the trench walls. Figure 11b shows clear U-edges, which indicates that the polymer residues were completely removed by the cleaning. The cleaning process used in Fig. 11b was coinjected DIO3 + HF in the OMNITM system. The mixture was formed by injecting 300:1 HF (volumetric ratio DI water/HF=300:1) into 63 ppm DIO3, and then injecting the mixture into the OMNITM chamber. The wafer was immersed in the mixture at 33°C with megasonics for 5 min. After the immersion, it was rinsed by 70 l/min DI water for 5 min (18 mΩ was reached at the end of the rinsing) and IPA drying. The wafers containing polymer residues were also cleaned by DIO3 or by HF separately. None of these chemicals could clean out the residues completely. An alternative method to clean the residues is HF followed by SPM on wet bench tools, which is often used for polymer residue cleaning in semiconductor device manufacturing. The idea of using the mixture of DIO3 and HF in wafer cleaning has been previously published by many researchers [8, 9]. The mechanism by which DIO3 + HF removes polymer residues is through the oxidation property of DIO3 along with light etching of the SiO2 underneath the polymer residues by the HF. The mixture of DIO3 and HF is an efficient alternative for polymer residue cleaning.

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4. CONCLUSIONS

This study has demonstrated that the DIO3 module is able to generate 12.6 gallons of 80 ppm DIO3 in 28 min and has also shown that the OMNITM8100 system is able to run DIO3 processes continuously without any problems. From the investigation of DIO3 in wafer cleaning, the following conclusions can be drawn: 1. Particle addition tests at 0.085 µm LPD threshold show that the average particle adders per 200 mm wafer was 3 and the maximum was 14. DIO3 demonstrated that it is essentially particle-neutral on wafers at 0.085 µm particles. 2. DIO3 showed a high capability in cleaning Si3N4 and PSL particle-challenged wafers. This is a new application for DIO3. It can be concluded that DIO3 is an alternative to the traditional SC1. Although the cleaning mechanism is not quite fully understood and needs to be further studied, the electrostatic double layer theory probably offers a suitable explanation for its cleaning behavior. 3. It demonstrated that DIO3 grows a thin, high-quality SiO2 film on Si surface with thickness from 6 to 13 Å. Most of the growth occurs in the first minute of exposure, and the growth rate appears to be independent of the O3 concentration in the 3.3 to 20 ppm range. 4. With stripping rates of only some hundreds of angstroms (tens of nanometers) per minute for various types of photoresists, it can be concluded that the DIO3 is much slower than SOM or SPM in photoresist stripping. DIO3 cannot fully replace SOM or SPM at least for the time being. With the combination of DIO3 and HF, however, the mixture cleans organic residues after plasma dry ashing very well, which is a new area for further investigation.

REFERENCES 1. 2. 3. 4. 5.

J. Song, R. Novak, I. Kashkoush and P. Boelen, Micro, 51-57 (January 2001). E. Olson, C. Reaus, W. Ma and J. Butterbaugh, Semiconductor Intl., 70-76 (August 2000). S. De Gendt, J. Wauters and M. Heyns, Solid State Technol., 57-60 (December 1998). C. Muti and R. Matthews, Precision Cleaning, 11-15 (October 1997). H. Vankerckhoven, F. De Smedt, B. Van Herp, M. Claes, S. De Gendt, M. Heyns and C. Vinckier, in Proceedings of the Fifth International Symposium on Ultra Clean Processing of Silicon Surfaces, M. Heyns, P. Mertens and M. Meuris (Eds.), pp. 207-210, Scitec Publications, Uetikon-Zürich, Switzerland (2001). 6. F. De Smedt, S. De Gendt, M. Heyns and C. Vinckier, in Proceedings of the Fifth International Symposium on Ultra Clean Processing of Silicon Surfaces, M. Heyns, P. Mertens and M. Meuris (Eds.), pp. 211-214, Scitec Publications, Uetikon-Zürich, Switzerland (2001). 7. S. Lim and C. Chidsey, in Proceedings of the Fifth International Symposium on Ultra Clean Processing of Silicon Surfaces, M. Heyns, P. Mertens and M. Meuris (Eds.), pp. 215-218, Scitec Publications, Uetikon-Zürich, Switzerland (2001). 8. E. Bergman, S. Lagrange, M. Claes, S. De Gendt and E. Rohr, in Proceedings of the Fifth International Symposium on Ultra Clean Processing of Silicon Surfaces, M. Heyns, P. Mertens and M. Meuris (Eds.), pp. 85-88, Scitec Publications, Uetikon-Zürich, Switzerland (2001).

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9. T. Hattori, T. Osaka, A. Okamoto, K. Saga and H. Kuniyasu, J. Electrochem Soc., 145, 32783283 (1998). 10. T. Ohmi, T. Isagawa, W. Kogure and T. Imaoka, J. Electrochem. Soc., 140, 804-810 (1993). 11. G. Gale, D. Rath, E. Cooper, S. Estes, H. Okorn-Schmidt, J. Brigante, R. Jagannathan, C. Settembre and E. Adams, J. Electrochem. Soc., 148, G513-G516 (2001). 12. D. Riley, in Contamination-Free Manufacturing for Semiconductors and Other Precision Products, R. Donovan (Ed.), Chap. 7, Marcel Dekker, New York, NY (2001).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 293–302 Ed. K.L. Mittal © VSP 2003

Possible post-CMP cleaning processes for STI ceria slurries ROBERT SMALL∗ and BRANDON SCOTT DuPont/EKC Technology, Inc., 2520 Barrington Ct., Hayward, CA 94545, USA

Abstract—Chemical-mechanical planarization (CMP) is an established semiconductor process step for the integrated production of logic and memory devices on silicon wafers. The STI (Shallow Trench Insulation) polishing process involves planarizing CVD silicon oxide films as part of the gate oxide structure. Both silica- and ceria-type slurries have been used for this process. There has been some concern that cerium ions (besides other metal ions) will be adsorbed onto the very sensitive STI structure and affect the device performance. This paper discusses initial results for the performance of hydrogen peroxide and buffered chelating solutions (BCS) used with single-wafer postCMP cleaning equipment with either megasonic or brush or a combination of both in reducing metal and ceria particle contamination. The effectiveness of these post-CMP buffered chelating solutions (pH 4.2 and 7.5) for reducing cation ion contamination from 9E10 to 2E8 atoms/cm2 has been demonstrated. These solutions can also remove other trace metal ions and ceria particle residues. The data also show that ceria particles can be removed from wafer surfaces (98+%) with various BCS/hydrogen peroxide solutions, but there are a number of factors that must be understood when developing a post-CMP chemistry for ceria. The chemistry to be used, the mechanical process (brush or megasonic methods) and the mass transport (contact time) with the particles are some of the important considerations. Other chemistries, including sulfuric acid/hydrogen peroxide and BCS (pH 8.5) with hydrogen peroxide, are also discussed. Initial results also suggest that time (and rinse water) consuming processes can be modified with these dilute chelating/hydrogen peroxide chemicals in single-wafer cleaning equipment. Keywords: STI; ceria polishing; post-CMP cleaning; buffered chelating solutions; hydrogen peroxide.

1. INTRODUCTION

CMP is an established semiconductor process step for the integrated production of logic and memory devices on silicon wafers. A typical fab consumes >240 million gallons of water [1] (approx. 1100 gallons/300 mm wafer) for both BEOL and FEOL processes, yet the 2001 ITRS Road Map calls for consumption of only approx. 600 gallons/300 mm wafer in 2005 [2, 3]. Currently the CMP process accounts for about 5–7% of the total water consumed in a fab. Yet, there is still a ∗

To whom all correspondence should be addressed. Phone: (1-510) 784-5846, Fax: (1-510) 784-9181, E-mail: [email protected]

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critical need to eliminate particle and metal ion contamination while attempting to reach these reduced water usage levels. In recent years, ceria slurries have become important for polishing CVD silicon oxide films, which are part of the shallow trench insulation (STI) structures [4]. These structures are at the very heart of the IC device gate structure and require close critical dimension tolerances. Silica slurries have been used, but often require aggressive polishing procedures, which can result in over-polishing of the STI features. Newer ceria slurries are designed to polish the STI structures without the use of reverse mask processes [5, 6] and to stop on the SiN layers. There is some concern that the cerium ions and ceria particles will become bound to the device structure and affect the device performance. Typical ceria slurries have pH values between 6 and 10. In this pH range, the silicon oxide interlayer dielectric films may adsorb metal species (S.F. Cheah, personal communication) [7]. Following the polishing step, post-CMP wafer cleaning is then required for removing particles and trace metal contamination. Though it has not been proven that residual cerium contamination will interfere with the gate performance, the semiconductor industry is looking for effective post-CMP cleaning processes. Particle removal is of utmost importance after the CMP process and any postCMP chemistry used will have to overcome or modify the surface charge of the wafer as well as surface charge (adhesion) of the slurry particles after polishing. CMP slurry particles have several mechanisms for adhering to a wafer surface. Van der Waals and electrostatic forces are usually the most dominant for particle adhesion. The adhesion mechanism can also include chemical bonding (which would require either etching or redox chemistries to remove bonded particles). This bonding mechanism is especially important for ceria slurries since cerium atoms appear to “bond” to silicon surfaces during the polishing process. These various forces and the possible chemical bonding complicate the post-CMP cleaning problem for STI. When designing chemistries to remove ion and particle contaminations, the counterion for Ce3+/Ce4+ cations must be chosen carefully. In the appropriate pH ranges, many of the resulting salts are insoluble, e.g., phosphates, carbonates, oxalates and fluorides. Cerium sulfate is only partially soluble while the nitrate and acetate compounds have much higher solubility. It is suspected that the cerium salts formed with the BCS chemistries will be soluble. Therefore, the rinse solution pH, solution oxidation potential and/or chelator concentration will have significant effect on the success for wafer cleaning. Previous STI post-CMP cleaning has been successful with sulfuric acid/hydrogen peroxide chemistries using wet benches, but these low pH (<1) solutions can be corrosive for standard metal cleaning equipment, have limited bath life and usually require extended process times (>5 min) at elevated temperatures [6]. Other proposed processes involved a four-step procedure with a heated ammonium hydroxide/hydrogen peroxide cleaning chemistry followed by ammonium

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hydroxide pre-soak and then an HF dip. The final step was a hydrochloric acid/hydrogen peroxide cleaning with a total process time approaching 20 min [8]. Li et al. [9] have recently reported results using dilute SC-1 chemistry (pH ~ 10) with double-sided scrubbing equipment but were not able to reduce the residual cerium ions below 5E11 atoms/cm2. Previous work in our laboratory [10] has shown that buffered chelating solutions (BCS) at either pH 4.2 or 7.5 were effective in reducing a variety of anions, cations including transition metal ions as well as silica and alumina particles on wafer surfaces. This current study examines the effect of BCS chemistries (pH 4.2 and 7.5) with and without hydrogen peroxide for post-CMP cleaning of cerium residues. Other formulations with pH values between <1 and 10 are also briefly reviewed. There are also other issues including reducing DI water and chemical consumption and attempting to meet the DI water recycle/reclaim objectives (70% by 2005) [2] and to simplify the type of chemistries that need to be addressed. The results from this current research should help in designing cleaning processes that effectively utilize the chemistry and rinse water. 2. EXPERIMENTAL

2.1. Metal ion contamination Prime TEOS wafers (200 mm) were cleaned in an aqueous HF solution (49% HF/H2O, 1:100) for 1 min, rinsed and air-dried. The wafers were then dipped in a 100 ppb metal ion solution (K, Ca, Ce, Cu and Fe) for 30 min, which was adjusted to pH 5.3. The wafers were air-dried. The control wafer #1 (Table 1 and Fig. 1) shows the residual contamination levels after an HF cleaning and wafer #2 was a control wafer that was also cleaned with a combination of BCS and hydrogen peroxide in a simple dip process and rinsed with DI water. Wafer #3 was a wafer that had been cleaned and dipped in the metal ion solution and dried. Wafer #4 was a wafer that had been cleaned, dipped in the metal ion solution and then dipped into the ceria slurry sample and quickly rinsed with DI water (approx. 5 s). Wafer #5 was a wafer #4 rinsed twice with DI water. Wafers #4 and #5 establish the range for metal ion and cerium oxide contaminations after simple DI water rinsing. The remaining wafers were processed through 1% BCS chemistries (DuPont/EKC Technology’s PCMPTM5000, pH 4.2; or LPX-100, pH 7.5) and/or 1% hydrogen peroxide at room temperature. A Solid State Equipment Co. (SSEC) 3301 TrilenniumTM double-sided single wafer cleaning unit was used for the cleaning experiments. The SSEC 3301 postCMP cleaning equipment has two chemical dispense tanks, a brush cleaner and a megasonic unit. The megasonic unit (12.6 cm2) operated at 1.25 MHz frequency. The PVA poly(vinyl alcohol) brushes were the primary method for removing particles while the megasonic unit was designed to prevent particle reattachment during the final rinse. Total contact time for the chemical solutions was 60 s for each

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Figure 1. Cerium contamination after cleaning.

Table 1. VPD-ICP/MS results for metal ion contamination in atoms/cm2 Wafer

Method

Ca

K

Na

Fe

Cr

Ni

Zn

Mg

Cu

1 2 3 4 5

Control 1 26.0 Control 1 (H2O2/BCS) 1.5 Control 2 (Metal) 12.0 Control 3 (Met/Slur) 10.0 2.1 Control 3 and DI

0.4 * 480.0 260.0 220.0

* * 1.1 0.3 *

* 0.1 0.7 0.6 0.2

3.5 1.9 3.9 15.0 8.8

2.6 1.2 49.0 30.0 7.1

2.5 1.7 8.7 2.8 3.3

6 7

H2O2//Brush&Meg BCS//Brush&Meg

1.4 0.7

2.0 1.2

2.1 0.8

110.0 68.0

* *

1.1 0.3

3.6 3.3

5.3 3.5

4.1 2.4

8 9

H2O2/B//BCS/M BCS/B//H2O2/M

1.7 5.4

160 6.1

2.9 3.5

97.0 140.0

0.1 0.3

0.3 0.6

3.8 6.0

7.4 11.0

2.9 4.2

10 11

BCS/H2O2//Brush BCS/H2O2//Meg

0.9 1.0

2.1 2.6

1.3 1.8

88.0 79.0

* 0.6

0.1 0.5

2.6 2.8

4.0 12.0

2.5 2.8

12

BCS/H2O2//B-M *Detection Limit

0.9 0.5

2.4 0.5

0.9 0.5

55.0 0.1

* 0.05

* 0.1

1.7 0.2

3.6 0.2

1.6 0.1

1.0 4.7 * 0.9 10.0 18.0 4.0 7.2 1.5 1.4

B=brush, M=1.25 MHz megasonics. BCS/B//H2O2/M means BSC solution through the brush followed by hydrogen peroxide through the megasonic unit.

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cleaning step (60 s of roller contact and/or 60 s of megasonic contact). The wafers were then rinsed with DI water for 120 s while spinning the wafer from 100 to 1000 rpm and finally dried at 1000 rpm. The contaminated samples (Table 1 and Fig. 1) were analyzed by the Vapor Phase Decomposition-Inductively Coupled Plasma/Mass Spectroscopy (VPD-ICP/MS) at Balazs Laboratories. 2.2. Particle contamination The particle data in Table 2 were obtained with an Ebara EPO 220 D polisher after a 30-s buffing step with various slurries. The blanket wafers were cleaned in the Ebara single-wafer cleaner with a standard brush and 1 inch2 “pencil” cleaner. Each wafer was cleaned with the brush and DI water for 30 s, 60 s with DI water and the “pencil” cleaner, 40 s with 1% hydrogen peroxide and finally 30 s with brush/DI water. The dried wafer was scanned with a SurfScan 6420 particle analyzer. The wafers used in Table 3 (#13 to 20, except #16) were scanned with a KLATencor SP1TBI before and after the experiments. The wafers were dipped into a ceria slurry (DuPont/EKC Technology’s MicroPlanarTM STI2100TM) and rinsed with 18 MΩ DI water for approx. 30 s and processed through the SSEC 3301 TrilenniumTM double-sided single wafer cleaning unit. The chemistries included 1% BCS chemistries (PCMPTM5000, pH 4.2; LPX-100, pH 7.5; EKCTM5200, pH 7.5 and EKCTM5100, pH 8.5) and/or 1% hydrogen peroxide and a 1% sulfuric acid/hydrogen peroxide solution at room temperature. Total contact time for the chemical solutions was 60 s for each cleaning step (60 s of brush contact and/or 60 s of megasonic contact). The wafers were then rinsed with DI for 120 s while spinning the wafer from 100 to 1000 rpm and finally dried at 1000 rpm. After cleaning, the wafers were scanned with the SP1TBI. Wafer #16 was buffed on the Ebara EPO 220 D polisher, cleaned with DI water, dried and LPDs determined with the SP1TBI. The wafer was then cleaned in the Caro’s acid bath for 10 min at 95oC, then rinsed with DI water, dried and scanned again with the SP1TBI. Table 2. SP1TBI cerium oxide and silicon oxide Light Point Defect (LPD) results Slurry

Rinse

LPDs

Colloidal SiO2 Fumed SiO2 CeO2 CeO2

DI H2O DI H2O DI H2O H2O2/H2O

117 199 185 58

SP1TB1 at 0.17 µm.

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Table 3. SP1TBI cerium oxide LPD results with selected chemistries Wafer

Method

Time (min)

Temp.

pH

LPDs

13

Control 3 (Met/Slur)

14

Control 3 and DI

1

25

~6

2

25

~6

>70000 7002

15

H2SO4/H2O2

16

H2SO4/H2O2

5

25

<1

28571

10

95

<1 4.2 7.5 7.5 8.5

110∗ 2528 87 1874 105

17 18 19 20

PCMP5000/H2O2 LPX-100/H2O2 PCMP5200/H2O2 PCMP5100/H2O2

5 5 5 5

25 25 25 25

SP1TB1 at 0.17 µm. ∗ 6420 at 0.2 µm.

3. RESULTS

3.1. Ionic contamination Metal ions can contaminate wafer surfaces either by ionic or covalent bonds to the silicon oxides. A silicon-wafer surface has a negative charge across most of the pH range (>3). Positively-charged cations can be adsorbed by electrostatic attraction on negatively-charged surfaces, therefore, cleaning solutions should have either high pH (relying on ion exchange) or low pH relying on the tendency for cations to desorb. Ammonium hydroxide can exchange NH4+ for the adsorbed metal ions, removing them from the surface (although the formation of metal oxide species can restrict this process). Alternatively, a low pH solution may tend to cause desorption of metal ions by simply modifying the surface charge of the substrate surface groups. Chelating compounds in solution can promote the desorption process and keep the dissolved metals from readsorbing or precipitating on the wafer surface. Such solutions are called buffered chelating solutions (BCS). The Pourbaix diagram (Fig. 2) shows that cerium can assume two oxidation states, Ce+3 and Ce+4 (as Ce(OH)2+2) (S. Raghavan et al., personal communication; software is STABCAL from Montana Technology College, Butte, MT, USA) [11, 12]. Above pH 7 the cerium is primarily in the +4 state (as the solid CeO2) and to a lesser degree in the +3 state (as the solid Ce(OH)3). Both of these compounds have low solubility at pH >5. Cerium oxide can be dissolved slowly at low pH (<3) but usually a reducing agent (hydrogen peroxide, Sn2+, etc.) will be needed to accelerate the process which produces Ce+3 species. This information indicates that a BCS chemistry with a pH 4.2 might be ineffective at removing cerium contamination unless the reducing agent has a reduction potential greater than 0.5 V (Fig. 2, when the cerium concentration is between 1E–1 and 1E–6 mol). The situation is more difficult to predict with a pH

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Figure 2. Cerium–Water Pourbaix diagram (Ce-H2O at 25oC).

7.5 BCS. Depending on the cerium concentration on the wafer surface, there are several possible thermodynamically stable species, Ce(OH)3, CeO2 and Ce+3. If the cerium concentration is between 1E–6 and 1E–4 mol, then any chemistry with a reduction potential above 0.0 V should form the Ce+3 species. If the concentration is greater, then there is no reduction potential chemistry capable of forming the Ce+3 species. Therefore the rinse solution’s pH, oxidation potential and/or chelating agent will have a significant effect on the success of the wafer cleaning process. The metal ion cleaning performance of the BCS/hydrogen peroxide chemistries is demonstrated with the data in Table 1 using the VPD-ICP/MS analysis method. The test wafers had a low level of contamination (control, wafer #1) after the dilute HF cleaning step, and a combination of BCS and hydrogen peroxide (wafer #2) in a simple dip process (with a DI water rinse) reduced residual metal contamination, in some cases to the analysis detection limits. A simple rinse with DI water (pH approx. 6) with wafer #4 (Met/Slur) did partially reduce contamination levels, though the cerium level was still at the 5E9 atoms/cm2. Comparison of hydrogen peroxide versus BCS (wafers #6 and #7) shows that the BCS solution is more effective for lowering metal ion contamination. When changing the order of addition through the brushes (#8 and #9), the hydrogen peroxide followed by BCS appears to be a better (except for the potassium value) sequence. Wafers #10 and #11 compare the physical method for cleaning the wafers with a pre-mixed BSC/H2O2 chemistry. The results indicate that the megasonic method

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is not quite as effective as the brushes. Since the brushes can make direct contact with the surface through the boundary layer, there is more effective cleaning. The low powered megasonic unit was not as effective for transporting chemistries across the surface boundary layer. The best procedure for reducing the metal ion from contaminated wafers was a combined BCS/hydrogen peroxide mixture (wafer #12) using both the brushes and the megasonic apparatus. One reason that the hydrogen peroxide solution (#6) was effective at all was possibly due to its natural pH (approx. 3–4), which could promote a simple ion exchange with the Si–OH groups on the TEOS surface. 3.1.1. Cerium results Figure 1 summarizes the post-CMP cleaning procedures for cerium. The DI rinse only (wafer #5) reduced the cerium by 95% (5E9 atoms/cm2), while the BCS (pH 4.2) solutions removed 99.8% of the contamination to 2E8 atoms/cm2. The best overall procedures were either the BCS or the BCS/H2O2 (wafer #12) using both the brushes and megasonic units. The BCS (pH 7.5) chemistries were also able to reduce the cerium contamination to the analysis detection limit (1E8 atoms/cm2). 3.2. Particle contamination In Table 2 TEOS wafers were buffed with various slurries and then cleaned in an Ebara post-CMP cleaner with DI water with a 190-s total process time at 25oC. In one cerium oxide experiment, 1% hydrogen peroxide was included in the cleaning process. The results show that hydrogen peroxide solutions could be effective in reducing ceria particle contamination compared to the simple DI water process. Other cerium oxide post-CMP cleaning data (Table 3, wafer #16) showed that Caro’s acid mixture (1:1 30% H2O2/30% H2SO4) at approx. 95oC could reduce cerium oxide LPD (dipped wafers) from about 1050 to about 100 after 10 min immersion (LPDs measured at 0.2 µm with the SurfScan 6420) [6]. Though these solutions are effective, they are very corrosive, have a limited bath life and the process times can be long compared to the desired total single-wafer processing time of 2–3 min. Table 3 shows the results for cleaning the TEOS wafers after dipping the wafers in a ceria slurry without any buffing. These results only show relative effectiveness of the various chemistries. Wafer #13 shows that the cerium oxide slurry can easily contaminate the wafers even after the short DI rinse. When the wafer (#14) was rinsed a second time the LPDs (light point defects) were only reduced to 7000 particles. This value was assumed to be the contamination “base line”. The results show that the LPX-100 with hydrogen peroxide solutions (wafer #18) with brushes and megasonics gave the best performance (LPDs = 87) under these non-optimized conditions. The LPX-100 chemistry is a BCS that contains a “weak surfactant” component. In contrast, the BCS chemistry (pH 7.5) for wafer #19 does not include this “surfactant” component. The second best method was found to be BCS (EKC5100, pH 8.5 and hydrogen peroxide) with brushes and

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megasonics (wafer #20). The EKC5100 also contains the “weak surfactant” component. The dilute sulfuric acid/hydrogen peroxide mixture (wafer #15) at room temperature had very high LPD counts with these conditions. The data show that cerium species (ions or particles) can be removed from wafer surfaces, but there are at least four factors that must be understood when developing a post-CMP chemistry for cerium oxide. The chemistry to be used, the mechanical process, the redox potential of the chemicals, and finally, the mass transport time (contact time) of the chemistries with the particles are all important aspects. The mass transport process needs to include time-dependent diffusion of the chemical to the particle for converting the cerium species to the proper soluble species. It is important to maintain the proper pH/concentrations to transport the converted species from the surface into the bulk solution. The following equations: 2CeO2 + H2O2 + 10H+ à 2Ce+3 + 6H2O

(1)

2Ce+3 + O2 + 4 H+ à 2CeO2·2H2O

(2) 2+

indicate that the concentration of the reducing agents (H2O2, Sn , etc.) need to be high enough to maintain the cerium in the +3 oxidation state, since it can easily be converted back to the insoluble cerium oxides on exposure to atmospheric oxygen. The post-CMP cleaning process for cerium oxide particles is not simple. 4. CONCLUSIONS

The effectiveness of the EKC’s post-CMP buffered chelating solutions (pH 4.2 and 7.5) for reducing cation ion contamination during the cerium oxide slurry cleaning process has been demonstrated with VPD-ICP/MS data. The cerium contamination can be reduced from 9E10 to 2E8 atoms/cm2. These solutions can also remove other trace metal ions residues. The data also show that ceria particle removal can be >98% from wafer surfaces, but certain factors need to be understood when developing an effective post-CMP chemistry for ceria. The chemistry to be used and the mechanical process (brush or megasonic methods) are important considerations. Though the brushes in this study were effective, the current megasonics unit was not. The other important factors include the redox potential and the mass transport (contact time) and pH (<8.5) of the chemistries in contact with the particles. The anions for the cerium species are also important and should not include phosphates, fluorides or high concentrations of hydroxide which form insoluble cerium compounds. The effect of surfactants needs to be examined further. Preliminary data also indicate that both DI water and chemical consumption can be reduced (though the exact percentages are not known) when comparing the traditional Caro’s acid or Piranha acid processes (approx. 10 min) with the BCS chemistries (approx. 5 min).

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Acknowledgements We would like to thank Ken Sheldon of Solid State Equipment Co. for assistance with the SSEC 3301 TrilenniumTM equipment and Haruki Nojo and Pascal Berar for the Ebara cleaning results. REFERENCES 1. M. Lester, Semiconductor Int., 145 (March 2002). 2. ITRS: “The International Technology Road Map for Semiconductors”, International Sematech (2001). 3. D. Deal, Precision Cleaning, 24 (June 1994). 4. E. Zhao and C. S. Xu, Semiconductor Int., 145 (June 2001). 5. T. Sakurada, paper presented at the 2001 International CMP Symposium, Lake Placid, NY (2001). 6. P. Leduc, P. Berar, J.-F. Lugand, H. Nojo and M. Rivoire, Proc. Fifth Int. Chemical-Mechanical Planarization for ULSI Multilevel Interconnection Conference, p. 239, Santa Clara, CA (2002). 7. K. B. Agashe and J. Regalbuto, J. Colloid Interface Sci. 185, 174 (1997). 8. Y. Wang, T. Wang. J. Wu, W. Tseng and C. Lin, Thin Solids Films, 332, 385 (1998). 9. H. Li, J. Li and D. Hymes, Proc. Fifth Int. Chemical-Mechanical Planarization for ULSI Multilevel Interconnection Conference, p. 359, Santa Clara, CA (2002). 10. R. Small, M. Carter, M. Peterson, L. Pagan and L. Pigott, A2C2, 4(1), 19 (2001). 11. B. Kilbourn, Cerium: A Guide to its Role in Chemical Technology, Molycorp, Inc., White Plains, NY (1992). 12. R. Horrigan, in: Industrial Applications of Rare Earth Elements, K. A. Gschneidner (Ed.), ACS Symp. Ser. 164, p. 95, American Chemical Society, Washington, D.C. (1998).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 303–314 Ed. K.L. Mittal © VSP 2003

The ideal ultrasonic parameters for delicate parts cleaning TIMOTHY PIAZZA1 and WILLIAM L. PUSKAS2,∗ 1

Jamestown Community College, P.O. Box 20, 525 Falconer Street, Jamestown, NY 14702-0200, USA 2 Blackstone–Ney Ultrasonics, Inc., P.O. Box 220, 9 North Main Street, Jamestown, NY 14701, USA

Abstract—Of utmost importance to the process engineer, employing ultrasonics, are the achievable levels of cleanliness and damage minimization. This paper highlights the most dramatic variables involved in an ultrasonic system’s performance. These variables are sweep, power control and center frequency control. The effects these variables have upon cavitation and cleaning in general are discussed.

1. INTRODUCTION

The various ultrasonic parameters, or degrees of freedom, available to the process engineer define what the ultimate limits are for the cleaning process. The traditional degrees of freedom available in an ultrasonic cleaning system have included modulation of a single center frequency (sweep), variable duty cycle and amplitude control at a single frequency. All of these variables allow control of gross, or macroscopic, variables such as raw power into the liquid. The latest class of aqueous cleaning technology allows variation of the afore-mentioned parameters, but at multiple center frequencies in a single process tank. Multiple center frequencies allow precise microscopic tuning of the energy in the individual cavitation event. Understanding and optimizing the parameters yields maximal cleaning efficiency with minimal substrate damage. The primary physical phenomenon behind the technology of ultrasound is an event known as cavitation. Indeed, any proper treatment of ultrasonic cleaning must begin with a discussion of cavitation. Cavitation is the creation and subsequent collapse of microscopic bubbles within a liquid. These bubbles are formed when a large pressure gradient is introduced into a fluid. During the low-pressure part of a sound wave the fluid is subjected to tension. When the amplitude of this sound wave exceeds the local tensile strength of the fluid a void, or cavity, is cre∗

To whom all correspondence should be addressed: Phone: (1-800) 766-6606, E-mail: [email protected]

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ated in the medium. This cavity grows for the rest of the half cycle of sound. As this bubble grows, both dissolved gasses and liquid vapor diffuse through the walls of the cavity and into the bubble via a process known as rectified diffusion. As the instantaneous pressure associated with the sound wave begins to go positive, one of two things can happen. The bubble, which grows to a certain size R0 during the half cycle, can collapse partially. In this case the entrained gasses act as a shock absorber and the bubble may undergo further stable oscillations. The second possibility is that the bubble can suffer complete implosion, an event labeled transient cavitation. Both of these processes re-radiate absorbed energy from the incident acoustic field. It is this re-radiated energy that impinges upon a substrate and does the bulk of the cleaning. Cavitation is one of nature’s most efficient and dramatic amplifiers of energy density currently known; indeed, there are recent reports that suggest nuclear fusion accompanies cavitation in certain exotic fluids [1]. Each bubble collapse is accompanied by the local generation of temperatures on the order of thousands of degrees centigrade and pressures exceeding hundreds of atmospheres. Though recognized for almost a century [2], physicists have yet to construct a complete description of this final collapse. Although much of the final implosion event is shrouded in mystery, the bubble dynamics prior to this is quite well understood [3–5]. Armed with this phenomenological explanation of cavitation, we can begin to examine the effects of the various ultrasonic parameters. The relevant questions to be asked are: how does the generator impart energy to the transducers, how do the transducers impart that energy to the cavitating cleaning solution and then how does the sonic energy excite the part being cleaned? The cleaning system is composed of both the cleaning solution and the part or parts being cleaned. 2. IDEAL ULTRASONIC PARAMETERS

2.1. Sweep Sweeping frequency, the most primitive type of frequency modulation (FM), has had a major impact on the ultrasonic cleaning industry over the last twelve years. When done correctly, it improves the performance of an ultrasonic cleaner and generally reduces the damage to delicate parts caused by constant frequency ultrasonics. By way of example, Fig. 1 shows a graph of frequency versus time for a typical sweeping frequency 104-kHz ultrasonic generator with a 4-kHz bandwidth and a 500-Hz sweep rate. Introducing a change in the frequency, as a function of time, of an ultrasonic array can affect what happens in a tank in a number of ways. This includes how energy is transferred to the fluid, how efficiently that sound energy is converted into cavitational energy, and how that energy is transferred to the part. All parts absorb energy to a greater or lesser degree, and unless extreme precaution is taken in the generation of the frequency modulation (FM) of the driving signal, this energy can be a significant source of damage. In spite of this fact, it is an effect often neglected.

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Sound energy is transferred to a tank via an electromechanical device called a transducer, vibrating at resonance or one of its overtones. Resonance is defined as that frequency at which a mass, in this case a transducer, oscillates with maximum speed amplitude [6]. A transducer’s resonant frequency is determined solely by its geometry and composition. An electrical signal, supplied by an ultrasonic generator to the transducers, is converted into an acoustic signal, which is then transmitted into the bath. Natural variations, δf, exist in the resonant frequency, f, of one transducer compared to another. These random variations occur as a result of variables as mundane as dimensional tolerance build up and transducer-to-tank bond variations. These resonant frequency variations occur with equal probability on either side of the average frequency of the array, f0=104 kHz in our example, and can be on the order of hundreds of hertz. Thus, the resonant frequency distribution of the composite transducer array has an average frequency of f0 with a width of δf (Fig. 2). With this in mind, any generator supplying a constant frequency, f0, to a transducer array will be exciting only a fraction of the transducers at their actual resonant frequency. The rest of the transducers will radiate less efficiently, by virtue of being driven at a frequency significantly off of resonance, and portions of a tank will appear acoustically dim. In contrast, if the frequency is swept, say plus or minus 2 kHz, the transducers will all spend an equal amount of time at their resonant frequency. If the transducers are swept quickly (with respect to the typical

Figure 1. Constant sweeping frequency.

Figure 2. Distribution of center frequencies of a transducer array.

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lifetime of a sound wave propagating through the liquid), the entire array will be excited equally and the sound field in the tank will be very uniform in time. This is a way in which the act of sweeping the frequency of the signal to the transducers results in a more uniform and effective energy transfer into the tank. Once a certain amount of ultrasonic energy has been transferred to the fluid medium one must examine how much of that energy is expressed in the form of cavitation. An effective way of representing this is with a mathematical tool known as the acoustic interaction cross-section. Simply, this is the amount of energy subtracted from an acoustic wave by a bubble driven into oscillation. This energy is subsequently re-radiated by the bubble via pulsation or implosion and affects much of the cleaning accomplished by ultrasonics. More precisely the acoustic interaction cross section is the ratio of the power subtracted from an acoustic wave due to a bubble’s presence, to the intensity of the incident beam [1]. As its name suggests, it has the unit of area, i.e., square meters. The cross-section is strongly a function of a bubble’s radius, see Fig. 3. This means that a single frequency picks out its favorite size bubble and pumps energy into it preferentially. The resonant bubble radius R0, at that frequency, is approximately determined by the following equation: R0

1 . 3 κp 0 ω0 ρ

(1)

where κ=polytropic index, p0=hydrostatic liquid pressure outside the bubble, ρ=medium density and ω=2πf. For most aqueous solutions we use κ = 1.3, p0 = 106 dynes/cm2 and ρ = 1 g/cm3. This gives a bubble radius of 0.008 cm. If we sweep the frequency, then we are exciting a range of bubble sizes. For a sweep of plus or minus 2 kHz all of

Figure 3. Normalized acoustic interaction cross-section as a function of bubble radius (mm) for 40 kHz ultrasonics. Ω40 is the cross section at 40 kHz, Ω38 is the cross-section at 38 kHz, and Ω42 at 42 kHz. This demonstrates how sweeping the ultrasonic frequency creates a band over which a bubble population is excited.

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the bubbles whose sizes range from 0.0075 cm and 0.0083 cm are maximally excited. Bubbles whose sizes differ from the resonant size interact less strongly with the incident acoustic field and subsequently absorb less energy for cavitation. This line of thinking would indicate that the larger the sweep bandwidth the better the activity. This is true only to a point. As a transducer is driven off of its primary resonance, the efficiency with which it converts electrical energy to mechanical energy decreases. It becomes a game of diminishing returns. A larger sweep bandwidth allows the excitation of a larger bubble population but with little delivered energy at the ends of the bandwidth of the transducer. The optimum transducer is designed with a wide bandwidth resonance allowing a significant transfer of ultrasonic energy into the tank over the entire sweep range. Thus far, we have told two-thirds of the story. First, we examined the way in which sweep affects the amount and uniformity of energy transferred to a fluid medium. Second, we treated the way in which this acoustic energy couples with a bubble distribution in a fluid. Lastly, we must discuss those ways in which energy is transferred to a part. All too often the designers of ultrasonic systems fail to address the question of how a part can be excited in an ultrasonic system. In many cases, the knowledge that an ultrasonic system is composed of the sonicated fluid as well as the immersed part is critical. Methods by which energy is transferred to a part must be understood in order to prevent damage modes. The potential damage modes associated with a fixed frequency sweep rate are eliminated by use of a non-constant sweep rate. This type of frequency modulation (FM) can be accomplished by making the sweep rate random or by changing the sweep rate as a function of time. This type of modulation, known as a “Designer waveform” is often referred to as sweeping the sweep rate, or dual sweep. An example of a non-constant sweep rate is shown in Fig. 4. The main reason for a non-constant sweep rate is to eliminate any single frequency sweep rate from the system because a part being cleaned can be excited into resonance by two times the frequency of the single frequency sweep rate. Many delicate parts will fracture when excited into resonance. When a typical Langevin-type transducer is swept through a bandwidth of frequencies, the output power is not constant for each frequency. Generally, the out-

Figure 4. Non-constant, or dual, sweeping frequency.

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put power of the generator peaks near the center of the bandwidth. When sweeping up in frequency, a peak pulse of power is put into the tank at the center of the sweep range. When sweeping down in frequency, another peak pulse of power is put into the tank at the center of this sweep range. This process continues to produce equally-spaced power pulses at a rate equal to two-times the sweep rate. This is exactly the prescription required for the high-amplitude oscillations associated with a resonant condition. Whenever periodic (equally spaced in time) bursts of energy are injected into a system at or near its resonant frequency, or that of any of its overtones, that system can undergo large amplitude oscillations that can lead to part damage. Introduction of a non-constant sweep rate will vary the spacing between the power pulses. There is no fixed frequency at which the power pulses are supplied to the liquid and, therefore, no repetitive single frequency to excite the part being cleaned into resonance. Designer waveforms strive to eliminate all possible damage modes that can be introduced into the system. 2.2. Power control Power control typically comes in two flavors, the first being amplitude control, the second is duty cycle control. The first changes the integrated power into the liquid by scaling the amplitude of the pressure transmitted into the tank. The second changes the power into the tank primarily by changing the duty cycle, or period, over which the ultrasonics are operated. Amplitude control is important in applications where part damage due to peak cavitation intensity is a possibility. The magnitude of a pressure wave is directly affected by amplitude control. Though sound pressure cannot constitute a quantitative measurement of cavitation present in a tank, it is a parameter critical to the strength of cavitation. A certain minimum amount of ultrasonic energy must be present in a tank before a liquid will cavitate. That minimum amount of energy is known as the threshold of cavitation. The threshold of cavitation is a strongly rising function of the frequency of the ultrasonics (Fig. 5), especially in the high (>100 kHz) frequency range [7, 8]. At moderate powers, in a well established cavitation field, the implosion energy is roughly proportional to the square of the difference between the pressure amplitude and the ambient pressure. The reduction of the incident pressure wave’s amplitude tends to reduce the mean value of the overall energy distribution of cavitation events, but it changes it slowly and only over a very narrow range. Because of this, amplitude control alone is an exceptionally rough and unreliable tool by which to eliminate part damage and cavitation erosion. Duty cycle is a measure of the fraction of the time that a generator’s ultrasonic output is turned on over a given period. At a duty cycle of 50%, the ultrasonic output of a generator spends half of the time “on” and half of the time “off”. The primary effects of duty cycle are twofold. The first comes from an understanding that the mechanisms of contaminant removal, as well as part damage, are probabilistic in nature. Duty cycle serves to change the total number of cavitation

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Figure 5. Log of the pressure required to initiate cavitation in filtered tap water, normalized to 1 atm. Note the dramatic rise above 100 kHz [6–8].

events that a part is exposed to over a given period. With fewer implosions, and less opportunity to damage, a low-duty cycle is kind to soft substrates. As with most variables care must be taken as there is a trade between damage and cleanliness level, less cavitation offers fewer opportunities to remove particles. The second positive effect of duty cycle power control is to reduce what is often referred to as the degas time of a liquid. Time-averaged radii of oscillating bubbles tend to increase during sonication through rectified diffusion [9]. This means that large bubbles (compared to R0) continue to grow to a size where buoyancy forces drive them to the surface of the liquid. The “off” times introduced by a duty cycle help to give these bubbles an opportunity to travel to the surface. This is an active mechanism by which a bubble population purges itself of large bubbles as well as a pumping action that tends to degas a solution. Via the same mechanism bubble nuclei and small bubbles grow until such time as they are of resonant size and undergo transient collapse. The shattered bubble fragments from this collapse are then new nuclei that further seed the bubble population in a self-sustaining cycle. Members of a bubble population that fall just above the resonant size are allowed to dissolve to a smaller radius during the “off” times introduced by a duty cycle. These bubbles then have a large interaction cross section and contribute to the cleaning process. These are two ways in which duty cycle, sometimes called pulse mode ultrasonics, can improve overall cleaning performance through degassing. 2.3. Center frequency control For the purposes of cleaning, the important parameters are the amount of energy released in a cavitation event, and the density of cavitation events. These parameters have a simple relation based upon bubble size. As the bubble radius increases, the energy released at implosion also increases (Table 1). With a constant power input into a liquid, this means that the larger the typical bubble, the fewer total

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Table 1. Functional dependency of the cavitation energy with some standard variables Variable

Symbol

Dependence of cavitation energy

Frequency

ω P

ω−2 P5/3

σ ρ R

σ1/3 ρ−1/2 R2

Pressure amplitude Surface tension Density Bubble radius

Figure 6. Variation in cavitation bubble radius as a function of driving frequency.

number of bubbles will develop per unit of time. An equivalent way of saying this is to say that, at constant input power, the implosion energy is proportional to the square of the bubble radius and inversely proportional to bubble density. Armed with this knowledge we can customize cleaning by modifying the bubble radius, and thus the energy in each event, as well as the number density of events. The most effective way of doing this is by changing the frequency of insonation. Low frequencies allow bubbles plenty of time to grow large, while high frequencies give cavitation bubbles only little time to evolve. This is most clearly illustrated in Fig. 6 where the resonant bubble radius from equation (1) is plotted as a function of frequency. Controlling the energy in each cavitation implosion is important to prevent pitting or craters on the surface of the substrate being cleaned. From a cleaning perspective, there is much research on particle removal efficiencies (PRE) at different frequencies. It is observed that low-frequency ultrasound has superior PRE for large particles and that high-frequency ultrasound is best suited for sub-micrometer particle removal [10, 11]. Thus, in an optimized single process, one would employ low-frequency ultrasonics (few high-energy events) to remove large particles and/or gross contamination, and high-frequency

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ultrasonics (many small low-energy events) to remove sub-micrometer particles. This constitutes the ideal cleaning process, in which a part can be exposed to relatively low-frequency ultrasound, i.e., 40 kHz or 72 kHz, for short lengths of time and then to high-frequency ultrasound, i.e., 104 kHz or 170 kHz for long times. Such a process would avoid the damage often associated with low-frequency ultrasonics but run the gamut in excellent particle removal efficiency, from large to sub-micrometer-sized particles. The most recent technological advances in ultrasonic systems allow such a processing scheme to be realized. There is a new class of liquid-cleaning and processing equipment in which there is one transducer array and one generator that produces ultrasound at the primary resonance, or one of a number of overtones, of that transducer array for some given period of time. After this programmed time, the frequency then discontinuously jumps, as specified by the process engineer, to a different overtone of the transducer array for some other specified time before discontinuously jumping to a third overtone, and so on. The improved part cleanliness is best demonstrated by graphs of percent particle removal versus inverse particle size. It has been well established that higher frequencies remove a higher percentage of small particles than do low frequencies [10]. There is some minimum size that a frequency removes efficiently; by the same token, there is a maximum size particle that any frequency can remove efficiently. If this curve is assumed to be Gaussian in nature, then the graph shown in Fig. 7 results for a selected center frequency. This graph is plotted as a function of the inverse of particle size, this is done to prevent small particles from “piling up” near the origin and distorting the shape of the graph. The dotted line in Fig. 7 represents 100% and the reciprocal of particle size was used on the x-axis. Consider using the same selected center frequency as was used to generate Fig. 7, but increase the exposure time to the ultrasonics, and the result is Fig. 8. Figure 8 shows that higher percentages of all particles are removed with longer exposure time with 100% removal at particle sizes within the optimum range for the selected frequency. However, the efficiency of particle removal for particle sizes distant from the optimum size is poor. Consider the effect on the curve in Fig. 8 if a higher center frequency is selected. The curve in Fig. 9 results. The optimum particle size removal is a set of smaller size particles at this higher ultrasonic frequency.

Figure 7. Particle removal for a selected center frequency.

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Figure 8. Percent particle removal with increased exposure time to the selected center frequency. The dotted line represents 100% particle removal.

Figure 9. Particle removal at a higher center frequency. The dotted line represents 100% particle removal.

Figure 10 shows the percent particle removal versus the reciprocal of particle size for five different center frequencies. The exposure time at each frequency is chosen to give 100% removal for a range of particle sizes around the optimum value for that frequency. The sixth graph (from top) in Fig. 10 is the sum of the 40-kHz, 72-kHz, 104-kHz and 170-kHz graphs. It shows that a wide range of particle sizes can be efficiently removed by scanning through multiple frequencies. 3. CONCLUSIONS

The various ultrasonic parameters available to the user define what the achievable levels of cleanliness and damage minimization are. In this paper we have attempted to highlight and discuss the most dramatic variables involved in an ultrasonic system’s performance. Specifically these variables are sweep, power control and center frequency control. Modulation of the frequency through sweep affects ultrasonic performance via three main mechanisms. First, sweeping ensures that all of the transducers emit ultrasound evenly and uniformly. Second, by introducing more frequencies into a tank sweep excites, at resonance, a larger bubble population. This pumps more energy into bubble pulsation and implosion. The third important aspect of sweep is the minimization of damage mechanisms. Smoothly or otherwise varying the sweep frequency, such as dual sweep, eliminates potentially damaging equally spaced power impulses. The equal spacing of these impulsive excitations, especially in transducers characterized by a sharp resonance, threaten to excite delicate parts into damaging sympathetic vibration. With an understanding of the effects

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Figure 10. The first five graphs show particle removal for various ultrasonic frequencies. The sixth graph (from the top) shows the wide range of particle size removal that results from the use of multiple frequencies.

of a sweeping frequency the ideal sweep is a fast sweep with a constantly varying rate, over as large a bandwidth as the transducers allow.

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Modulation of power into a tank through duty cycle and amplitude control affects ultrasonic activity in different ways. Changing the peak pressures in a tank through amplitude control changes the average implosion energy about which a bubble population is centered, but smoothly and slowly. Duty cycle serves to quickly modify a bubble population through degassing. Duty cycle also changes the number of cavitation implosions a part is exposed to thus reducing the opportunity for damage. The ideal power control is strongly a function of the part being cleaned as well as the type of contaminant, and must be addressed on an individual application basis. The ability to discretely change the ultrasonic frequency in a tank from a transducer’s primary frequency to any of its overtones, i.e., center frequency control, is perhaps the most versatile and important of the various modifiable ultrasonic parameters available to the engineer. Cavitation implosion energy changes as the inverse of the square of the frequency. As such the only method by which to affect large scale changes in implosion energy is through large discontinuous jumps in frequency, say 72 kHz to 104 kHz. Again the efficacy of cleaning is strongly a function of implosion energy and is different for each application. The ideal ultrasonic device allows center frequency control in a single process for maximal particle removal efficiency across a wide spectrum of particle sizes. REFERENCES 1. R.P. Taleyarkhan, C.D. West, J.S. Cho, R.T. Lahey, Jr., R.I. Nigmatulin and R.C. Block, Science 295, 1868-1873 (2002). 2. Lord Rayleigh, Phil. Mag. 34, 94-98 (1917). 3. T.G. Leighton, The Acoustic Bubble, Academic Press, San Diego, CA (1994). 4. G.L. Gooberman, Ultrasonics Theory and Application, Hart Publishing Company, New York, NY (1969). 5. J.R. Blake et al., Phil. Trans. R. Soc. 357, No. 1751, 251 (1999). 6. L.E. Kinsler, A.R. Frey, A.B. Coppens and J.V. Sanders, Fundamentals of Acoustics, John Wiley, New York, NY (1982). 7. J.R. Frederick, Ultrasonic Engineering, John Wiley, New York, NY (1965). 8. S.A. Neduzhii, Sov. Phys.-Acoust. 7, 221 (1961). 9. L.A. Crum, Ultrasonics 22, 215-223 (1984). 10. C. Genet, A2C2 1, No. 5, 7-10 (1998). 11. A.A. Busnaina, J. Acoustical Soc. Am. 100, No. 4, Pt. 2, 2775 (1996).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 315–322 Ed. K.L. Mittal © VSP 2003

Effects of megasonics coupled with SC-1 process parameters on particle removal on 300-mm silicon wafers STEPHANIE L. WICKS, MATHEW S. LUCEY∗ and JOHN J. ROSATO SCP Global Technologies, 400 Benjamin Lane, Boise, IA 83704, USA

Abstract—The effects of megasonic use, bath temperature and NH4OH:H2O2:H2O ratio were studied to determine an effective means of particle removal from a bare 300-mm silicon wafer. This is one of the first studies in 300-mm-process development on particle removal in which two types of megasonics were used: a divergent lens megasonic and a focused beam megasonic. Experimental results show overall removal efficiencies greater than 98% of predeposited nitride particles for both megasonics when coupled with optimized temperature and chemistry. The particle removal efficiencies per bin size were analyzed for the deposited particles and were found to be greater than 90%. Keywords: Particle removal; megasonics; SC-1; silicon wafer.

1. INTRODUCTION

The use of megasonic energy has been shown to enhance the cleaning performance when combined with SC-1 chemistry. The mechanisms of cleaning in a megasonic field have been studied extensively in the semiconductor industry but their discussions are beyond the scope of this paper. Rather, this paper focuses on the optimization of SC-1 process and overall particle removal efficiency with the use of megasonics. An effective use of megasonic cleaning is to couple its design with optimized process parameters to provide the maximum megasonic energy to the wafer surface [1, 2]. When the operating parameters are optimized, the activity distance between the surface of the wafer and the megasonic energy is reduced, therefore, allowing the removal of particles previously unable to be removed. As the activity distance is reduced, the acoustic energy can assist in overcoming the adhesion forces acting on the particles by transferring mechanical force/action to particles [3]. ∗

To whom all correspondence should be addressed: Phone: (1-208) 6854371, Fax: (1-208) 6854124, E-mail: [email protected]

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The results of these tests show that adjusting certain variables within the process contributes significantly to the effectiveness of megasonic cleaning. For example, increasing the fluid temperature decreases the fluid viscosity and provides less resistance to the sound waves of the megasonic field. Also, decreasing the circulation flow rate within the process reduces flow disturbances. Decreasing the chemical concentrations decreases the amount of gases evolved in the process, which provides less resistance to the sound waves and reduces flow disturbances within the tank. In addition, increasing the power to the megasonic crystals increases the acoustic energy in the fluid. The variables that affect megasonic cleaning are summarized in Table 1. Table 1. Variables that affect megasonic cleaning Power to crystals SC-1 liquid temperature SC-1 circulation flow rate Chemical concentration in SC-1 bath

The need for optimized process parameters combined with SC-1 cleaning is more pronounced with 300-mm wafers, due to the large wafer size and the high volume of the tank. This paper illustrates the effectiveness of optimized process parameters combined with megasonics and provides a comparison of overall removal between focused beam and divergent megasonics. 2. EXPERIMENTAL PROCEDURES

Test wafers (<1000 initial particles) with silicon nitride particles deposited onto their surfaces were selected. The mean size distribution of these particles was 0.16 µm. The initial particle count of each wafer, before deposition of silicon nitride particles, was recorded as Cbackground. The 300-mm wafers were scanned with a Tencor© SP1 instrument to 0.16 µm particle size with a 3-mm-edge exclusion. A standardized silicon nitride deposition process developed at SCP was used. This process included preparing a standard stock solution with silicon nitride powder; and a predetermined amount of this solution was added to the deposition chamber with DI water at 40°C. For the test, 13 wafers were introduced into the deposition chamber for 5 min. After the silicon nitride particles were deposited on the wafers, the wafers were dried in a vapor jet dryer (VJD). The number of particles were recorded as CPRE. Five runs for each test condition were performed with a SCP Global Technologies 300 mm Surface Preparation System enclosed in a class-1 mini-environment. Three wafers (with deposited silicon nitride particles) were used in each run in

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slots 2, 26 and 50 with the remaining slots occupied with cleaned ‘dummy wafers.’ It should be noted that slot 2 was used instead of slot 1 because it was initially thought that the divergent megasonic transducer might have been damaged in the area of slot 1. However, upon inspection the divergent transducers appeared normal and functioned as expected. Also, when the SC-1 performances of slot 1 and slot 2 were compared there was no noticeable difference. To provide consistency, the remainder of the tests were performed in slot 2. Dummy wafers were run through an RCA cleaning process before each test to minimize carry-over contamination and parameter variation. The wafers were loaded into a SCP Global Technologies 300 mm tool and processed automatically via the robotic wafer load/unload station and the SCP wafer transfer system (WTS). After the SC-1 process was complete, the cassette was transferred to the VJD for drying. From the VJD, the cassette was transferred back to the wafer load/unload station. The wafers were scanned again and the values were recorded as CPOST. The overall cleaning efficiencies of each of the runs and tests were calculated using Equation (1). The cleaning efficiencies per bin size were graphed using Equation (2). (CPOST – Cbackground)/(CPRE – Cbackground)

(1)

(CPOST – CPRE )/CPRE

(2)

Two SC-1 processing tanks were used. One was equipped with a megasonic system that consisted of an array of individual transducer elements, which fire in an alternating sequence to provide a focused beam of megasonic energy over the surface (Fig. 1). Four of the transducers were pulsed at one time, to clean different portions of the wafer surface. This type of megasonic offers the advantage of con-

Figure 1. Focused beam megasonic energy field generated by transducer lens.

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centrating high power levels into short bursts of megasonic energy. The duration of the energy pulse can vary, but is typically set for optimal conditions where the bursts occur for approx. 1 s [4]. It should be noted that due to the focused orientation of the megasonic energy generated from the transducer elements, this is susceptible to shadowing effects. A shadowing effect occurs from elements such as tank furniture, which lie directly in the path of the beam of megasonic energy, resulting in a streak of contaminants that are not removed from the wafer surface. This, however, with proper design of the cassette and tank furniture, is not an issue. The second 300-mm SC-1 tank was equipped with transducer elements fitted together in two curved lenses to produce a divergent beam of megasonic energy (Fig. 2). In this system, the megasonic energy patterns produced a distinct cleaning pattern. By examining the wafer map, there are different cleaning nodes that diverge from the transducer lens. If the operating conditions are not optimized with divergent transducer design, there may be areas of reduced cleaning of the wafer. Additionally, shadowing effects may occur in this system due to tank furniture. However, again, this is not a concern in the SCP tanks due to the proper tank and furniture design. The critical process parameters such as temperature, circulation flow rate, time, megasonic power level and solution chemistry are important variables for effective megasonic cleaning. To examine these elements in more detail, a designed experiment was conducted to investigate the significance of these parameters on cleaning efficiency for both megasonic designs. Table 2 shows the parameters that were varied as part of the SC-1 megasonic process optimization tests. The focused beam megasonic equipment does not have an adjustable tuning algorithm, they fire in a predetermined sequence.

Figure 2. Acoustic energy field generated by a divergent transducer lens.

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Table 2. Megasonic SC-1 process variables

Divergent megasonic process variables Flow rate (chemical circulation rate) Tuning algorithm Power to megasonics Temperature SC-1 composition Focused beam megasonic process variables Power Tuning algorithm

Range I

Range II

8 gallons/min Megasonics Off 10 s of 30-s cycle 250 W per crystal Ambient 1:1:5

4 gallons/min Megasonics Off 3 s of 30-s cycle 300 W per crystal 50ºC 1:1:50

300 W per crystal (not adjustable) Not adjustable

300 W per crystal (not adjustable) Not adjustable

3. RESULTS AND DISCUSSION

The test results showed that divergent megasonics, when used on 300 mm wafers, left signature marks when the process variables were not optimized, similar to Figure 3a. As the process variables are optimized, the signature is moved ‘up’ the wafer and eventually off the wafer, as illustrated in Fig. 3b and 3c. The data show that with further optimization of each of the megasonic process variables and the combination of the effects, the particle removal performance of the SC-1 cleaning with divergent megasonic was significantly improved. Increasing the process temperature from ambient to 50°C led to a large increase in the particle removal, as did reducing the chemical concentrations of the NH4OH and H2O2 from 1:1:5 to 1:1:50. Reducing the circulation flow rate led to an increase in particle removal. Increasing the power input to the megasonic along with improving megasonic tuning algorithm increased the particle removal effectiveness. As expected and shown in Fig. 4a, b and c, the optimized process parameters reduced the interference patterns due to the divergent transducer design.

Figure 3. (a). Meg pattern from divergent lens at non-optimized operating conditions. (b) Meg pattern from divergent lens at semi-optimized operating conditions. (c) Meg pattern from divergent lens at optimized operating conditions.

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Figure 4. (a) Divergent megasonic signature, un-optimized process parameters. (b) Divergent megasonic signature, semi-optimized process parameters. (c) Divergent megasonic signature, optimized process parameters.

The optimized 300-mm SCP SC-1 process parameters using the divergent megasonics are summarized in Table 3. Figure 5 shows the removal efficiency by bin size of an optimized SC-1 bath coupled with divergent megasonic energy. The SC-1 composition was a dilute 1:1:50 and the bath temperature was 50°C. The addition of megasonic energy has a significant effect on the particle removal efficiency for all bin sizes. The bin sizes analyzed correspond to those of the particles that were deposited. The test results showed that focused beam megasonics, when used on 300-mm wafers, did not leave signature marks on the wafers. The proper design of the focused beam megasonic arrangement in the SCP SC-1 tank along with cassette design are believed to be the reason that there are no patterns. Because of the lack of patterns when using the focused beam megasonics at different process conditions,

Table 3. Optimized SC-1 parameters using 300-mm wafers Increase temperature to 50°C Decrease SC-1 composition (H2O2, NH4OH, H2O) to 1:1:50 Improve tuning algorithm Increase power to 1200 W, or 300 W per crystal Decrease flow rate to 4 gpm

Table 4. Optimized SC-1 process parameters using 300-mm wafers Ambient temperature Decrease SC-1 compostion (H2O2, NH4OH, H2O) to 1:1:50 Set firing sequence Set power of 300 W per crystal Decrease flow rate to 4 gpm

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Figure 5. Particle removal efficiency for optimized divergent megasonic by bin size.

Figure 6. Focused beam megasonic operating conditions comparison.

the results are not as clearly defined as the results of the divergent megasonic. When optimizing the focused beam megasonic the same variables were tested in order to optimize the particle removal efficiency. The optimized parameters for the focused beam megasonic are summarized in Table 4.

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Figure 7. Particle removal efficiencies of optimized focused and divergent beam megasonics.

The results of a dilute chemistry, ambient temperature SC-1 process performed with the focused beam megasonic SC-1 tank are shown in Fig. 6. When looking at the overall removal efficiencies for the two systems, when optimized, their performance was statistically equivalent as shown in Fig. 7. 4. CONCLUSIONS

The design of the megasonics coupled with a SCP 300-mm SC-1 tank designs required process variables to be adjusted to optimize the cleaning process. The overall results from both systems reveal that lower chemical concentrations improve and/or provide the same cleaning efficiencies as the more concentrated chemistries. This can result in a significant reduction in cost of ownership due to reduced chemical usage, extended bath life and likely reduced surface roughening. Both megasonic systems tested performed adequately in removing deposited particles along with overall particle removal. Testing also showed that the optimization of megasonics when processing 300-mm wafers required proper tank design along with megasonic arrangement within the tank to be considered. REFERENCES 1. 2. 3. 4.

R.M. Hall and L. Li, Future Fab Int. 5, 267 (1998). R.M. Hall, T.D. Jarvis, T. Perry, L. Li and R.C. Hawthorne, MICRO, 63, (July/August 1996). A.A. Busnaina and I. Kashkoush, Chem. Eng. Commun. 125, 47-61 (1993). R.M. Hall, T. Jarvis and T. Parry, Mater. Res. Soc. Symp. Proc. 477, 15-20 (1997).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 323–334 Ed. K.L. Mittal © VSP 2003

Influences of various parameters on microparticles removal during laser surface cleaning Y.F. LU,∗,1 Y.W. ZHENG,2 L. ZHANG,2 B. LUK’YANCHUYK,2 W.D. SONG2 and W.J. WANG2 1

Department of Electrical Engineering, University of Nebraska, Lincoln, NE 68588-0511, USA Laser Microprocessing Laboratory, Department of Electrical and Computer Engineering and Data Storage Institute, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 2

Abstract—The efficiency of dry laser cleaning to remove spherical particles (SiO2, 5.0, 2.5, 1.0 and 0.5 µm) from different substrates (Si, Ge, NiP and quartz) was investigated. The influence of different parameters (particle size, laser wavelength, incident angle, substrate material, surface roughness and irradiation direction) on the cleaning efficiency is presented. The laser cleaning efficiency is closely related to these parameters. The relationship between the laser cleaning efficiency and the experimental parameters can be explained both within the frame of the Mie theory of scattering and by considering optical resonance in particles attached onto solid surfaces. Spherical silica particles with a size of 0.5 µm were placed on silicon (100) substrates. After irradiation with a KrF excimer laser (248 nm wavelength), hillocks with a size of about 100 nm were obtained at the original positions of the particles. Mechanisms of the formation of the sub-wavelength structures were investigated and were found to be the near-field optical resonance effects induced by particles on the surface. Theoretical prediction of the near-field light intensity distribution was carried out, which was in agreement with the experimental result. Keywords: Laser cleaning; particle removal; spherical particles; surface roughness.

1. INTRODUCTION

Recently, laser-particle-surface interaction has attracted considerable interest in both experimental and theoretical studies. There are three main impetuses for this: first, as the dimensions of active elements shrink drastically in IC and highdensity hard disk manufacturing, even a sub-micrometer particle may induce fatal damages to the whole system. In the process to remove a particle, both the inertial force m &x& containing mass m ∝ R 3 (R is radius of the particle) and the adhesion force Fadh ∝ R are involved. Therefore, the necessary acceleration to remove the particle is given by &x& ∝ R − 2 [1]. Typically, it is about 107 times higher than the ∗

To whom all correspondence should be addressed. Phone: (1-402) 472-8323, Fax: (1-402) 472-4732, E-mail: [email protected]

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gravity force for a 1-µm particle [2]. Traditional cleaning methods, such as hydrodynamic jet and ultrasonic vibration, cannot remove small particles efficiently. Fortunately, pulsed laser heating of absorptive particles or substrates can produce such high acceleration [3-26]. Second, due to the simplicity of the laser-particlesurface system, it can be applied to the study of the particle adhesion and deformation on a solid substrate [27-31]. Third, fascinating physics arise in laser cleaning associated with near-field focusing of laser by particles with sizes comparable to laser wavelengths [17-21]. In recent studies of dry-cleaning mechanisms, spherical particles of standard sizes are used in experiments. These particles, with almost uniform size and fine sphericity, can greatly minimize the uncertainties that are mostly induced by surface asphericity. From the viewpoint of practical applications, as the sphericity of the particles tends to increase with reduced particle size [32], it is necessary to explore the mechanism of laser cleaning for spherical particles from solid substrates. Furthermore, since most of the theoretical models are based on the simplification that particles are spherical, it is convenient to compare theoretical calculation and experimental results based on spherical particles. However, most experimental investigations have concentrated only on the influence of laser fluence and particle size on the cleaning efficiency. Other cleaning parameters, such as laser wavelength, incident angle, irradiation direction and substrate properties, are not fully covered. In this paper, the influence of these parameters on the cleaning efficiency is reported. The study of the influence of surface roughness, although preliminary due to the complexity of this topic, is also presented. Another important topic is the interaction of laser light with the particle on a surface, which is also ignored in previous studies. An exact solution of this problem shows that the near-field light intensity, produced by the optical resonance and substrate reflection, is completely different from the intensity profile of the incident laser light. These calculation results can explain many experimental phenomena in laser cleaning, as presented in the following sections. The “true” light intensity profile should be employed for solving the heat equations in the cleaning model (for calculating substrate thermal expansion and tensions). 2. EXPERIMENTAL

A KrF excimer laser (Lambda Physik) with a wavelength of 248 nm, pulse width of 23 ns, a maximum pulse repetition rate of 30 Hz was used as the light source for laser cleaning. The fluctuation of fluence in the 2.5 cm × 4.0 cm spot area is less than 7%. A Nd:YAG laser was also used to produce different wavelengths of 355 nm, 532 nm and 1064 nm. The Nd:YAG laser consists of a Q-switched oscillator and an amplifier. Three detachable harmonic generators extend the wavelength range to the second, third and fourth harmonics. The output laser beam has a Gaussian distribution with a diameter about 0.8 cm. The pulse duration is 7 ns.

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2.1. Laser cleaning of spherical particles from Si substrates As described in our previous paper [21], particles of verified sizes (Duke Scientific) were used in the experiment. The particles were spherical and uniform in size. Figure 1 shows the cleaning efficiency as a function of laser fluence. It is found that the laser cleaning efficiency increases sharply with the laser fluence. For particles with sizes of 0.5 and 1.0 µm, threshold laser fluences are about 225 and 100 mJ/cm2, respectively. For 2.5 and 5.0 µm particles, the threshold laser fluences are found to be lower than 5 mJ/cm2. This experiment shows that there is a size effect for small particles. However, it should be emphasized that the threshold fluences are not proportional to R–2, this is because the rough estimation does not include the laser-particle interaction. 2.2. Influence of substrate properties on cleaning efficiency In this experiment, the cleaning efficiencies of 1.0 µm silica particles from Si, Ge and NiP surfaces were examined (see Fig. 2). It is found that the laser cleaning efficiency increases sharply with the laser fluence. For 1.0 µm particles, threshold laser fluences are about 100 mJ/cm2 for Si, about 30 mJ/cm2 for Ge and about 8 mJ/cm2 for NiP substrate. It is also concluded that particle removal from NiP is the easiest among the three substrates, while removal from Si is the most difficult. To analyze the differences in cleaning results, it is important to examine the physical parameters of the materials. The van der Waals force for particles on Ge is the greatest among the three substrates, while the adhesion force on NiP is only

Figure 1. Cleaning efficiency as a function of laser fluence for particles of different sizes. Size effect is obvious for small particles.

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Figure 2. Laser cleaning efficiency for removal of silica particles from NiP, Ge and Si substrates. Total pulse number is 200.

about two-third of Ge. However, particle removal is related not only to the adhesion force, but also to the optical and thermal properties of the substrate. For Si, the absorption and thermal expansion coefficients are much less than those for Ge and NiP. Therefore, a higher laser fluence is required to remove particles from Si substrate. Removal from NiP is the easiest, not only because the adhesion force is the least among the three substrates, but also because its absorption and thermal expansion coefficients are much greater than the other substrates. The small thermal conductivity of NiP also contributes to its low threshold, since the real heating process is more analogous to “point heating” due to the near-field effect. This work indicates that substrate thermal expansion, enhanced by near-field optical focusing effects, is the dominant mechanism for dry laser cleaning. 2.3. Influence of incident angle on cleaning efficiency To investigate the influence of incident angle, the Si pieces with particle contamination on their surfaces were placed on triangular planes that had tilt angles of 5º, 10º, 15º, 20º, 30º, 45º and 60º. Since the incident light was kept normal to the stage, the incident angles with respect to the substrate surface were determined by the triangular planes. The surfaces before and after laser irradiation were observed with a high-resolution optical microscope. The laser fluence is proportional to A(θ)cosθ, where θ is the incident angle and A is the absorptivity. The variation of incident angle from 0º to 15º caused the effective laser fluence to drop only by less than 3.5%. Since 43 mJ/cm2 was far above the threshold laser fluence (below 5 mJ/cm2 for 2.5 µm particles), the particles should be completely removed with such a small drop of fluence (see Fig. 1). However, the experiment shows that the cleaning efficiency drops to 0 when the

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Figure 3. A steep decline of cleaning efficiency appears with increasing incident angle. The uniform light intensity is multiplied by 100, the Mie solution is multiplied by 0.81. This figure shows that the near-field light intensity is sensitive to the incident angle.

incident angle is greater than 15º (Fig. 3). A similar result was found in the literature [19]. From the calculation based on Mie theory, we found that the near-field light intensity declined from 100% to 0 when the tilt angle increased from 0º to 15º. This calculation is in agreement with the experimental results. 2.4. Influence of surface roughness on cleaning efficiency In the IC process, although the Si wafer starts with a perfect surface structure, the morphology will change drastically after a few steps of oxidation, etching, doping, diffusion and mechanical polishing [33]. In this section, the influence of surface roughness on the cleaning efficiency is investigated. The Si surfaces were modified with anisotropic etching in KOH solution for different times, and subsequently observed by an atomic force microscope (AFM), as shown in Fig. 4. It is found that both peak-valley roughness (Rp-v) and root mean square roughness (rms) increase with increasing etching time. The cleaning efficiencies for different samples are shown in Fig. 5. The particle size is 1.0 µm. Although theoretical prediction shows that particle adhesion force drops even with the presence of a very small roughness [34-36], the increasing roughness produced less efficiency in this experiment. In our early explanation, it was assumed that the surface elasticity was reduced by the roughness. New examination shows that the near-field light intensity drops sharply with increasing particle-surface distance. Since the cleaning efficiency is sensitive to laser fluence, the reduction in the near-field light intensity due to the surface asperities causes drop in cleaning efficiency.

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(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 4. Surface morphology of Si substrates with different etching times: (a) 0; (b) 1; (c) 5; (d) 10; (e) 15; (f) 20; (g) 25 and (h) 30 min. The roughness increases with etching time.

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(a)

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Figure 5. Cleaning efficiencies for samples with different surface roughnesses. The surface roughness increases in alphabatical order. It is shown that a higher roughness produces a lower cleaning efficiency. R is the radius of the silica particles.

2.5. Influence of laser wavelength on cleaning efficiency A Q-switched Nd:YAG laser with wavelengths of 1064, 532 and 355 nm was employed as the light source to remove 0.5 µm spherical silica particles from Ge substrates. The cleaning efficiencies are shown in Fig. 6. It is found that the cleaning effect for 1064 nm light is very poor. The threshold laser fluence for a longer wavelength is higher than that for short wavelengths. The influence of wavelength on the cleaning efficiency can be ascribed to two aspects: First, the substrate absorption coefficient of laser light is wavelength dependent. For Ge substrates, the absorption coefficients for 355, 532 and 1064 nm light are 0.5, 0.48 and 0.61, respectively (at 300 K). Second, the interaction of laser light with particles results in localized light intensity near the particlesubstrate contacting area. This interaction strongly depends on both the wavelength and particle size. 2.6. Influence of laser irradiation direction on cleaning efficiency In order to investigate the influence of laser irradiation direction on laser cleaning efficiency, quartz substrates with Si particles (micrometer size) were used in the experiments. The KrF excimer laser was used to irradiate each sample either from the front side (with Si particles) or the reverse side (without Si particles). Ten laser pulses were used for each sample. Figure 7 shows the cleaning efficiency as a function of laser fluence for laser irradiation from the front and reverse sides of quartz substrates. It is observed that the cleaning efficiency increases with in-

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creasing laser fluence both for the front and reverse side irradiations. However, it was noted that the laser cleaning efficiency for reverse-side irradiation had a much higher value than that for front-side irradiation.

Figure 6. Cleaning efficiency with respect to different wavelengths. The laser spot size is about 0.3 cm2.

Figure 7. Cleaning efficiency as a function of laser fluence for KrF excimer laser irradiation from the front and reverse sides of a quartz substrate with silicon particles.

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The reason why the laser cleaning efficiency is higher for reverse-side irradiation is that the laser irradiation in this direction creates a higher temperature rise at the particle/substrate interface. The higher temperature rise causes a larger thermal expansion in the particles at the particle/substrate interface that results in a stronger cleaning force. Therefore, it is more efficient to carry out laser cleaning by reverse-side irradiation if the substrate material is transparent to the laser wavelength. 3. INTERACTION OF PARTICLES AND LASER LIGHT: OPTICAL RESONANCE AND NEAR-FIELD EFFECTS

The near-field light intensity is based on the solution of the boundary problem: i.e., a spherical particle on a flat semi-infinite substrate. The solution of this problem is rigorous, and it is beyond the scope of this paper. The details can be found in reference [23]. For a non-absorptive spherical particle, incident light could excite some resonance modes inside the particle and produce enhanced light intensities near the contacting area. In this case the particle acts like a lens, as was shown in Refs. [22-26]. Some laser cleaning phenomena observed in experiments can be explained by the near-field light profile. When incident light irradiates from a small tilt angle, the focusing point will shift away from the contacting point, therefore the cleaning efficiency drops rapidly. The cleaning efficiency is sensitive to the wavelength, because different wavelengths produce different intensity profiles. The near-field light intensity is also sensitive to the distance between the particle and the rough surface, as we assume that the particle is “lifted up” by some surface asperities. Figure 8 shows that the surface light intensity drops sharply with increasing distance. The light intensity beneath the particle center reduces to almost half of the value for the case of a particle on a flat surface, as the distance reaches 50 nm. This distance is comparable to the surface roughness of the samples used in the experiments. Spherical silica particles with a size of 0.5 µm were placed on a Si (100) substrate. After irradiation with the KrF excimer laser (wavelength: 248 nm), hillocks with a size of about 100 nm were obtained at the original positions of the particles. The mechanism of the formation of the sub-wavelength structures was investigated and found to be the near-field optical resonance effect induced by particles on the surface. Atomic force microscopy (AFM) was used to locate the spots corresponding to the original particle positions. The hillocks have a diameter of 150 nm and a height of 30 nm (Fig. 9). The same laser fluence (340 mJ/cm2) was also irradiated on clean Si (100) surfaces (without particles), and no damage spots were observed. It is obvious that a higher intensity was achieved due to the spherical particles in our experiment and this resulted in the formation of the hillocks.

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Figure 8. Scattered light intensity on the substrate as a function of the distance between the particle and the substrate. Light intensity drops drastically with increasing distance.

Figure 9. An AFM image (top) and height profile (bottom) of a hillock created on Si (100) surface.

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4. CONCLUSIONS

It is shown that laser cleaning efficiency to remove small particles from solid surfaces strongly depends on a number of physical parameters: particle size, substrate material, incident angle, surface roughness, laser wavelength and irradiation direction. The threshold fluence for laser cleaning strongly depends on the particle size (smaller particles need higher fluence). The strong angular dependence in the cleaning efficiency for small incident angles shows that the intensity distribution (originated from near-field focusing effects) plays a major role in dry laser cleaning. The optical and thermal properties of materials play more important role in laser cleaning than the adhesion force by itself. Experiments show large variation in threshold laser fluences for the materials whereas the Hamaker constants are practically the same. These results suggest that thermal expansion, enhanced by near-field optical focusing effects, is the dominant mechanism in dry laser cleaning. A nontrivial influence of the surface roughness was found in dry laser cleaning. It is well known that the surface roughness leads to a decrease in adhesion force. At the same time, calculation of the near-field effects shows that the laser intensity on a surface decreases rapidly with distance between the particle and the surface. Thus, with increase of the surface roughness, the efficiency of dry laser cleaning decreases rapidly. In addition, the optical resonance in microparticles under laser irradiation can cause nanoscale damage to the substrate surface. REFERENCES 1. W. Zapka, W. Ziemlich and A.C. Tam, Appl. Phys. Lett. 58, 2217 (1991). 2. K.L. Mittal (Ed.), Particles on Surfaces 1: Detection, Adhesion, and Removal, Plenum Press, New York, NY (1988). 3. S.J. Lee, K. Imen and S.D. Allen, J. Appl. Phys. 74, 7044 (1993). 4. J.D. Kelly and F.E. Hovis, Microelectron. Eng. 20, 159 (1993). 5. A.N. Jette and R.C. Benson, J. Appl. Phys. 75, 3130 (1994). 6. R. Larciprette and E. Borsella, J. Electr. Spectrosc. Relat Phenom. 76, 607 (1995). 7. Y.F. Lu, W.D. Song, M.H. Hong, T.C. Chong and T.S. Low, Appl. Phys. A 64, 573 (1997). 8. A.A. Kolomenskii, H.A. Schuessler, V.G. Mikhalevich and A.A. Maznev, J. Appl. Phys. 84, 2404 (1998). 9. P. Liederer, J. Boneberg, M. Mosbacher, A. Schilling and O. Yavas, Proc. SPIE 3274, 68 (1998). 10. Y.F. Lu, Y.W. Zheng and W.D. Song, Appl. Phys. A 68, 569 (1999). 11. V. Dobler, R. Oltra, J.P. Boquillon, M. Mosbacher, J. Boneberg and P. Leiderer, Appl. Phys. A 69, S335 (1999). 12. G. Vereecke, E. Röhr and M.M. Heyns, J. Appl. Phys. 85, 3837 (1999). 13. X. Wu, E. Sacher and M. Meunier, J. Appl. Phys. 86, 1744 (1999). 14. M. She, D. Kim and C.P. Grigoropoulos, J. Appl. Phys. 86, 6519 (1999). 15. D.R. Halfpenny and D.M. Kane, J. Appl. Phys. 86, 6641 (1999). 16. R. Oltra, E. Arenholz, P. Leiderer, W. Kautek, C. Fotakis, M. Autric, C. Afonso and P. Wazen, Proc. SPIE 3885, 499 (2000). 17. Y.F. Lu, Y.W. Zheng and W.D. Song, J. Appl. Phys. 87, 2404 (2000).

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18. X. Wu, E. Sacher and M. Meunier, J. Appl. Phys. 87, 3618 (2000). 19. G. Vereecke, E. Röhr and M.M. Heyns, Appl. Surf. Sci. 157, 67 (2000). 20. D.R. Halfpenny, D.M. Kane and R.N. Lamb, Appl. Phys. A 71, 147 (2000). 21. Y.W. Zheng, Y.F. Lu, Z.H. Mai and W.D. Song, Jpn. J. Appl. Phys., 39, 5894 (2000). 22. P. Leiderer, J. Boneberg, V. Dobler, M. Mosbacher, H.-J. Münzer, N. Chaoui, J. Siegel, J. Solis, C.N. Afonso, T. Fourrier, G. Schrems and D. Bäuerle, Proc. SPIE 4065, 249 (2000). 23. B.S. Luk’yanchuk, Y.W. Zheng and Y.F. Lu, Proc. SPIE 4065, 576 (2000). 24. M. Mosbacher, H.J. Münzer, J. Zimmermann, J. Solis, J. Boneberg and P. Leiderer, Appl. Phys. A72, 41 (2001). 25. Y.F. Lu, L. Zhang, W.D. Song, Y.W. Zheng and B.S. Luk’yanchuk, JETP Lett. 72, 658 (2000). 26. H.J. Münzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer and J. Boneberg, J. Microsc., 202, 129 (2001). 27. D.S. Rimai, L.P. DeMejo and R.C. Bowen, J. Appl. Phys. 68, 6235 (1990). 28. A. Stalder and U. Durig, J. Vac. Sci. Technol. B 14, 1259 (1996). 29. L.J. Douglas and F.V. Swol, J. Chem. Phys. 106, 3782 (1997). 30. A.B. Mann and J.B. Pethica, Appl. Phys. Lett. 69, 907 (1996). 31. M.T. Bengisu and A. Akay, J. Acoust. Soc. Am. 105, 194 (1999). 32. K.L. Dishman, P.K. Doolin and J.F. Joffman, Ind. Eng. Chem. Res. 32, 1457 (1993). 33. G.Y. Chang and S. M. Sze, ULSI Technology, McGraw-Hill International, Singapore (1996).

Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 335–343 Ed. K.L. Mittal © VSP 2003

Particle removal with pulsed-laser induced plasma over an extended area of a silicon wafer THOMAS HOOPER, JR. and CETIN CETINKAYA∗ Dept. of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA

Abstract—The removal of micro- and nanoparticles during manufacturing processes is of great importance in many industries. Specifically, the cleaning of silicon wafers is of extreme importance in the semiconductor, microelectronics and optics industries. The development of dry, rapid, noncontact, and non-damaging particle removal techniques is a critical challenge. The Laser-Induced Plasma (LIP) removal technique under evaluation is a novel method for removing particles from substrates. The LIP technique is a dry, non-contact method that takes advantage of the strong shock wavefront from expanding plasma created by focusing a laser pulse in air. This pressure field acts on the target particles to produce a rolling mode of detachment from the substrate. In the current work, the LIP removal technique is employed repeatedly to remove particles over an area of a silicon wafer, and a systematic efficiency study for the removal effectiveness is conducted. A Qswitched Nd:YAG pulsed laser operating at 1064 nm with a 370 mJ pulse energy and 5 ns pulse length is utilized. 0.99 µm diameter silica spheres and 3.063 µm diameter polystyrene spheres were successfully removed with no substrate damage. The removal efficiency at various gap distances between plasma core and substrate is reported. The reported work is the first demonstration of the LIP removal technique over an extended area. The results substantiate the LIP removal technique as a viable option for particle removal from large flat surfaces. Keywords: Particle removal; nanoparticles; laser-induced plasma.

1. INTRODUCTION

Virtually every industrial process creates particles. The removal of particles during manufacturing processes is of great importance in many industries, including semiconductors, optics, photonics and micro-electromechanical systems (MEMS). Currently the critical particle size in semiconductor manufacturing is given as 58 nm, and it is predicted to reach as low as 30 nm by 2007 [1]. With the need for removal of smaller particles comes the need for improved cleaning techniques. These techniques must remove particles quickly and efficiently while avoiding substrate damage. Additionally, reducing chemical usage is of serious concern for ∗

To whom all correspondence should be addressed. Phone: (1-315) 268-6514, Fax: (1-315) 268-6695, E-mail: [email protected]

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workplace safety and environmental conservation. The development of dry, rapid, non-contact and non-damaging particle removal methods is a critical need for many manufacturing processes. 2. PARTICLE ADHESION

Three modes of particle detachment have been identified [2]. Particles may be removed by rolling, sliding, or lifting detachment modes. Lifting detachment is known to be the dominant removal mechanism in the direct laser method [3]. The lift-off force must be greater than the combined forces of adhesion and gravity in order to lift the particle from the surface. It is known that rolling detachment is the dominant mode for spherical particles on flat substrates under an applied pressure field [2], and so this will be referenced as the principal mechanism in the current technique. In practice, detachment will be some combination of these three effects. In the Laser-Induced Plasma (LIP) removal technique, the dominant removal mode is rolling under a transient pressure field generated by a shock wavefront. Figure 1 depicts a spherical particle on a flat surface under an applied pressure field. The pressure, p, acts on the area, As, producing force, Fp. α is the change in diameter due to adhesion force. The Johnson, Kendall and Roberts (JKR) model of particle adhesion gives the force of adhesion, FA, between a spherical particle and a flat substrate as

3 FA = π WA D 4

(1)

where WA is the work of adhesion between the particle and the substrate and D is the diameter of the spherical particle [4]. The radius, a, of the contact circle between the substrate and the particle at the onset of detachment is determined as

Figure 1. Geometric features of a spherical particle attached to a smooth surface.

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1/ 3

æ 3π WA D 2 ö a=ç ÷ è 8K ø where

(

) (

(2)

)

1 −ν 22 ù 4 é 1 −ν 12 + K= ê ú 3 ë E1 E2 û where ν1 and E1 are, respectively, the Poisson’s ratio and the Young’s modulus of the particle material, and ν2 and E2 are, respectively, the Poisson’s ratio and the Young’s modulus of the substrate material. Due to the small size of the particle, the pressure is reasonably approximated to be uniform over the entire particle surface. In order to analyze the rolling mode of removal, a moment equilibrium about point O is required. It is determined that the critical pressure needed for rolling detachment can be expressed as

prolling =

2a ( FA + mg ) As ( D cosθ − 2a sinθ )

(3)

where m is the mass of the particle, As is the effective cross-sectional area perpendicular to the pressure field, g is the gravitational acceleration, and θ is the angle between the force vector and a plane parallel to the substrate surface. Since FA is many orders of magnitude larger than mg when dealing with micrometer and submicrometer particles, mg can neglected in equation (3). Adhesion forces and required pressures for removal can be calculated from these relations. In the case of a 1 µm silica particle on a silicon wafer, the force of adhesion is 51 nN and the required pressure for removal is approximately 690 Pa when θ approaches 0 or π. For a 3 µm polystyrene particle, the force of adhesion is 146 nN and the required pressure for removal is approximately 521 Pa when θ approaches 0 or π. These calculations can be made for a multitude of particle– substrate combinations. These calculations, coupled with the use of varying particle sizes, could be used to characterize unknown pressure fields based on observed removal. The smallest particles removed would be used to pinpoint the maximum pressure present. 3. LASER-INDUCED PLASMA

In the current method, laser induced plasma is generated by focusing a laser beam to a point in air. Near the focal point the energy density is large enough to cause the breakdown of air into plasma. This phenomenon has been studied since the early 1960s [5]. Very high temperatures are present in the plasma burst core. Strong shock waves are generated as the plasma rapidly expands outward. It is

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Figure 2. Schematic of the Laser-Induced Plasma (LIP) removal technique.

known that in the near field, the pressure, p, is related to the radial distance from the blast center, r, by p~1/r3 [6–8]. In the far field, p~1/r. The laser induced plasma technique is a novel method for particle removal using the pressure field created by LIP [9–11] (see Fig. 2). In the experiments, an incident laser beam is focused through a convex lens. Near the focal point of the lens, the energy density is high enough to cause the breakdown of air into plasma. The pressure field created acts over the surface of the particle as in Fig. 1, creating an equivalent moment about the adhesion area. If the moment due to the pressure field is strong enough, a crack is initiated in the adhesion bond between the particle and the substrate. The crack will propagate as the particle rolls. The removal of the particle will be initiated when it loses contact with the surface. It is observed that the removal effectiveness relies heavily on the distance, d, between the center of the plasma and the substrate since this dictates the applied pressure field on the surface of the particle [9]. The closer the particle is to the blast center, the higher the pressure that will act over the surface of the particle. Moving the substrate closer to the blast center increases the magnitude of the moments experienced by the particles, which increases the effectiveness of the removal phenomenon. However, damage concerns increase as the substrate is moved closer to the plasma core. These two issues must be successfully mitigated for damage-free particle removal.

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4. EXPERIMENTAL METHODS AND SETUP

The substrates used were reclaimed 125 mm silicon wafers with a 1 µm thermal oxide layer supplied by Silica-Source Technology Corp. (Tempe, AZ, USA). Prior to particle deposition, the wafers were cleaned using an ultrasonic bath to minimize initial contamination. A 132 kHz ultrasonic generator was used in conjunction with a Crest Ultrasonics tank. The bath was a 2% solution of Chem-Crest 14 in de-ionized water. It was held at 50oC with full power from the generator for 25 min. Following the ultrasonic bath cleaning, the wafers were rinsed with deionized water. The wafers were individually dried with a spinning cycle of 1800 rpm for 25 s in an Evergreen Solid State Equipment brush scrubber. Particles were deposited onto the silicon wafers using a drop-agitation technique. The objective of deposition was to achieve a uniform distribution of particles with minimal aggregation and proper density to facilitate analysis in the target areas of the wafer. The particles were silica spheres with a diameter of 0.99±0.05 µm and polystyrene spheres with a diameter of 3.063±0.027 µm. The particles were placed in a suspension of methanol. Methanol was used as the suspending medium due to its quick evaporation time and lack of residual contaminants left on the substrate. The wafers were attached to a rigid post sitting in a Blitz Ultra Jewelry Cleaning Machine in order to vibrate the surface. The surface vibration was used in order to reduce particle aggregation while the suspension was drying on the surface. The suspension was applied to the center area of the wafer. The wafer was allowed to completely dry through evaporation of the methanol following deposition. It was observed that it was sufficient to repeat this process twice per wafer in order to obtain the appropriate particle density. Both initial cleaning and deposition were conducted in a class-10 cleanroom. The wafers were then taken to the laser setup outside of the cleanroom for application of the LIP removal technique. The laser used is a Q-switched Nd:YAG operating at a fundamental wavelength of 1064 nm with a pulse energy of 370 mJ. It has a pulse length of 5 ns, a repetition rate of 10 Hz, and a beam diameter of 5 mm. A 25 mm diameter, 100 mm focal length lens with a 1064 nm specific antireflective coating was used to converge the beam. A shorter focal length lens would be more ideal due to the superior quality of the plasma burst produced [10, 11], but wafer positioning requirements demanded a larger focal length lens. The wafer was placed onto a stage and held in place with a light adhesive tape. Horizontal translation was achieved in two dimensions using sliding posts with millimeter markings. More exact translation was required in the vertical dimension to control the critical parameter d. A linear translational stage with a 20±10 µm resolution was used for this purpose. A He-Ne laser was used for positioning of the lens and vertical alignment of the sample with the Nd:YAG beam. A diode laser was used to mark the horizontal position of the plasma and to align the sample. Previous experimental results showed that a single pulse affected a circular area with a diameter of about 2-3 mm [11]. In order to completely remove particles from a larger area, these circular areas needed to be overlapped. An 8×8

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square grid was used with a spacing, s, of 1 mm. The wafer was positioned so that the lower left grid corner was the first to be cleaned. The firing then proceeded sequentially along the grid. After each alignment, one pulse was delivered to each point on the grid. Particle counting was achieved using a Particle Measuring Systems, Inc., Surface Analysis System and an optical microscope. The surface analysis system is capable of taking surface analysis scans (SASs) confined to any circle centered on the wafer. These radially-specific measurements are accomplished through varying the edge size parameter. The edge size is the radial distance from the edge of the wafer that is not counted in the Surface Analysis System. This allows for localized measurements to be taken in and between any concentric circles. An SAS with edge size of 59 mm was used for analysis with the 8×8 grid, giving data on the 7 mm diameter circular region inscribed in the grid. This was sufficient to analyze the ability of the laser technique to clean an extended area. Optical microscopy was used to support the SAS data collection. 5. RESULTS AND DISCUSSION

A series of trials using 3.063 µm polystyrene spheres were conducted with the gap distance between the plasma core and substrate, d, set to 3.0, 2.5, 2.0 and 1.5 mm. Due to the range in actual particle size and the precision error of the particle counting system, the Surface Analysis System recorded the 3.063 µm particles ranging from 2-4 µm. This range was used to calculate the removal efficiency of the process. No removal was seen with d=3.0 mm. At d=2.5 mm and d=2.0 mm, the removal efficiency rose to 27% and 73%, respectively. At d=1.5 mm, the removal efficiency was 96%. The SAS scan taken after the d=1.5 mm trial can be seen in Fig. 3. Cleaning efficiency results are summarized in Fig. 4. The Surface Analysis System reports particle counts in both a color-coded graph and a spatial representation of the wafer. Green regions denote 5-10 µm particles, blue denotes 2-4 µm particles, red denotes 0.7-1.5 µm particles, purple denotes 0.4-0.6 µm particles, and light blue denotes 0.1-0.3 µm particles. In the second part of the experimental work, smaller particles were used. A series of trials was performed with 0.99 µm silica spheres with d set to 2.5, 2.0 and 1.5 mm. Optical microscope analysis verified that deposition was uniform with minimal clumping. At d=2.5 mm, a significant reduction in the number of particles present was observed. There remained mainly aggregations of two and three at these distances. It is expected that these clusters of particles will require a much greater applied pressure to induce rolling removal due to increased contact area and changed geometry. At d=1.5 mm, no particles were found to remain in the intended removal zone at the center of the silicon wafer. The SAS recorded varying particle sizes with the 0.99 µm silica particles for an unknown reason. A potential cause of this error is the particle material type. The particle measuring system

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Figure 3. The surface analysis scan of 3.063 µm polystyrene particles after LIP removal at d=1.5 mm. The drawn oval indicates the boundary of the area of deposition. The drawn square surrounds the removal zone.

Figure 4. Removal efficiency of 3.063 µm polystyrene particles for LIP removal trials at varying gap distances, d.

uses the optical properties of silicon in its process. Therefore using particles with the same optical properties may make proper detection difficult, if not impossible. Although the SASs were insufficient in determining particle sizes and exact removal numbers for these trials, they provided a qualitative picture of the lessening density in the removal zone. Figure 5 presents these SAS images. The color change in the center of the wafer from image to image indicates the effect of the LIP removal technique.

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(a)

(b)

(c)

(d)

Figure 5. Surface Analysis Scans of silicon wafer substrates (a) after deposition of 0.99 µm silica spheres, (b) after LIP removal at d=2.5 mm, (c) after LIP removal technique at d=2.0 mm and (d) after LIP removal at d=1.5 mm. Starting with (b), the area of the removal grid becomes visible. Further removal is observed in this region in (c) and (d).

6. CONCLUSIONS

The effectiveness of particle removal for large areas using laser-induced plasma has been demonstrated. It is reported that the LIP technique has been proven to be effective in removing particles over an extended area on a full-size silicon wafer through practical application. Both 3.063 µm diameter polystyrene spheres and 0.99 µm silica spheres were removed at a gap distance of 1.5 mm. The removal was accomplished with no substrate damage. In a separate study, damage was documented to first occur at a gap distance of 0.75 mm. Particle removal for particles with diameters less than 0.99 µm is expected to be possible by using gap distances between 1.5 mm and the damage threshold of 0.75 mm. Further study is

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necessary to conclude on the minimum particle size removable with the laser induced plasma technique. In earlier work, 460 nm silica particles were successfully removed without substrate damage [10, 11]. Additional research is also needed in order to incorporate potential optimizations into the removal process. Further research is underway. Acknowledgements The authors would like to thank Richard Vanderwood, currently with Bechtel Plant Machinery, for his help with the original LIP set-up. Thanks to Tom Norment of Brumley-South for providing a calibration standard wafer. Thanks must be given to the Clarkson University Honors Program and the Ronald E. McNair Program for their support. The authors also acknowledge the New York State Science and Technology Foundation and the Center for Advanced Materials Processing for their financial support. REFERENCES 1. International Technology Roadmap for Semiconductors (2001 Update, http://public.itrs.net/Files /2001ITRS/Home.htm). 2. M. Soltani and G. Ahmadi, J. Adhesion 44, 161-175 (1994). 3. C. Cetinkaya, C. Li and J. Wu, J. Sound Vibration 231, 195-217 (2000). 4. K.L. Johnson, K. Kendall and A.D. Roberts, Proc. R. Soc. Lond. A. 324, 301-313 (1971). 5. P.D. Maker, R.W. Terhune and C.M. Savage, in: Quantum Electronics, P. Grivet and N. Bloembergen (Eds.), Vol. 2, pp.1559, Columbia University Press, New York, NY (1963). 6. A.H. Taub (Ed.), The Collected Works of John von Neuman, Vol. VI, pp. 219-237, Pergamon, New York, NY (1963). 7. G.I. Taylor, Proc. R. Soc. A 201, 159-174 (1950). 8. L.I. Sedov, Similarity and Dimensional Methods in Mechanics, Academic Press, New York, NY (1961). 9. J.M. Lee and K.G. Watkins, J. Appl. Phys. 89, 6496-6500 (2001). 10. R. Vanderwood, M.S. Thesis, Clarkson University, Potsdam, NY (2002). 11. C. Cetinkaya, R. Vanderwood and M. Rowell, J. Adhesion Sci. Technol. 16, 1201-1214 (2002).

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Particles on Surfaces 8: Detection, Adhesion and Removal, pp. 345–352 Ed. K.L. Mittal © VSP 2003

Particle removal by collisions with energetic clusters JULIUS PEREL,∗,1 JOHN MAHONEY,1 PETER KOPALIDIS2 and ROB BECKER2 1

Phrasor Scientific Inc., 1536 Highland Ave., Duarte, CA 91010, USA Axcelis Technologies, 108 Cherry Hill Drive, Beverly, MA 01915, USA

2

Abstract—A novel method for dry cleaning is described that uses an energetic microcluster beam, capable of in situ cleaning within process chambers. This method employs charged liquid clusters generated directly from an aqueous solution and electrically accelerated to impinge upon a surface and remove submicrometer debris by momentum transfer. With anticipated low operating costs and non-hazardous chemical usage, environmental impact issues are virtually non-existent. The accelerated clusters reach supersonic velocities and impart impulsive forces sufficient to physically remove surface films as well as particles. The match between the impacting clusters, well below one micrometer, with that of the submicrometer particles to be removed assures efficient momentum transfer. In addition, low energy electrons can be injected into the beam when required to compensate for charge build-up on insulating surfaces. This process can be integrated into a cluster tool, enabling smooth operation between process steps, or used as a stand-alone supplement for removing residue following wet cleaning. Cleaning tests were performed in situ in a Scanning Electron Microscope (SEM), operating in the 10–5 Torr pressure range. Wafer pieces contaminated with particle debris were first examined and photographed. The samples were cleaned by the microcluster beam, and then re-staged to the examination position, without breaking vacuum. SEM photos taken of the same location before and after cleaning clearly show the ability of energetic microclusters to completely remove particles ranging from about 5 µm down to 0.05 µm. There is no known theoretical lower limit of the particle size that can be removed by the method. Keywords: Surface cleaning; submicrometer particles; environmentally friendly; energetic clusters; SEM analysis.

1. INTRODUCTION

Cleaning of semiconductor surfaces for the fabrication of microelectronic devices is of increasing importance in the deep submicrometer integration regime. Even minute amounts of foreign material can have a strong negative effect on the fabrication process and the operation of devices. Therefore, a strict control of surface cleanliness is of high importance. The most common types of contaminants are molecular films, discrete particles, particle clusters, and atomic and ionic species. ∗

To whom all correspondence should be addressed. Phone: (1-626) 357-3201, Fax: (1-626) 357-3203, E-mail: [email protected]

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Common sources of contamination are from the process equipment, wafer handling mechanisms and procedures, human operators, device manufacturing processes and materials used. A variety of surface cleaning processes have been developed to provide the required cleanliness prior to critical fabrication steps [1, 2]. These can be largely classified as wet processes, gas phase and other dry cleaning processes. The last two have gained in popularity in recent years because they require lower chemical consumption and because of their compatibility with integrated cluster tool processing. Recently, the advantages of single wafer cleaning methods have received much interest and are expected to play a more important role in the future [3]. The tests reported here were performed to demonstrate the ability of charged microcluster impingement cleaning, named NanoClean, to remove submicrometer particles from the surface of silicon wafers. To determine the effectiveness of the basic process for cleaning silicon substrates, a technique allowing pre- and postclean measurements was critical. Since the range of particle sizes being examined would require the use of a scanning electron microscope (SEM), it was determined that the best place to perform the experiments would be directly in the specimen chamber of the microscope. Being able to run the entire test without breaking vacuum allowed the sample to be examined, cleaned and re-examined without the introduction of external contaminants [4-6]. The SEM is a powerful diagnostic tool for imaging surface particles with very high spatial resolution. Use of SEM for in situ comparative analysis of surface cleaning methods in the semiconductor industry is restricted by the inability to integrate existing cleaning techniques with the low pressure (vacuum) operating environment of SEM instruments. For example, wet or spray chemistries, carbon dioxide snow, argon aerosol and dry plasma cleaning all require removal of wafers from the cleaning platform and transportation of cleaned wafers, under cleanroom conditions, to an SEM instrument. 2. MICROCLUSTER BEAM CLEANING

Particle removal by an energetic cluster impact primarily involves a single cluster impacting a single debris particle, and so efficiency is best achieved when the masses of the cluster and the debris particle are reasonably matched. This provides optimum momentum transfer at impact. Debris particles, much larger (greater mass) than the impacting clusters, remain virtually unaffected by beam impact. Microcluster beams are generated using electrified capillary nozzles to produce energetic charged microclusters, directly from the liquid state that are then accelerated by the electric field. The liquid (typically an aqueous solution) is fed under pressure to a compact, vacuum-mounted cleaning head enclosing an array of closely spaced emitters. Atomization occurs when voltage is applied to the emitters forming a hypervelocity beam of submicrometer clusters [7, 8]. Charged microcluster beam cleaning has several potential advantages compared to other

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cleaning methods. The process is compatible with in situ vacuum wafer processing. The cleaning head contains no moving parts and consumes ultra-low quantities of cleaning solution (estimated at a few microliters/wafer). The impacting clusters have an average size well below 1 µm, which corresponds to that of the submicrometer debris, and so assures efficient momentum transfer. The clusters, electrically accelerated to reach supersonic velocities, impart impulsive forces sufficient to physically remove surface films as well as particles. To increase area coverage, linear nozzle arrays have been developed which are operated with scanning mechanisms. Thus, broad surfaces as well as selective small areas can be cleaned. The cleaning action can be regulated to be ultragentle, by lowering impact velocities to levels below those capable of producing micro-damage. At the other extreme, coatings and layers, such as oxide films, can readily be removed [7]. Because the NanoClean head is compact and vacuum compatible, it can be integrated into a cluster tool with minimal or no interference, or can perform as a stand-alone cleaning unit, which is projected to have a small footprint, 1.3 m × 1.3 m. Compared to the existing cleaning methods, NanoClean is economical, consumes low power and does not require expensive liquids or hazardous chemicals. Surface cleaning applications, considered for the semiconductor industry, include cleaning of wafer backsides, flat panel displays, photolithography masks and post-CMP cleaning and drying. Additional areas of application include disk drives, MEMS devices, optical gyroscopes and space optics in the aerospace arena. The NanoClean action lowers the contact resistance of probe tips by removing oxides of aluminum. Typically, an array of over 125 tips having resistances ranging from a few to nearly 25 Ω was cleaned to levels well below one ohm [7-9]. 3. EXPERIMENTAL ARRANGEMENT

Tests reported here were performed in situ in an SEM, at pressures in the 10–5 Torr range. Small wafer samples containing particle debris produced by intentional scratch marks were placed on the stage in the SEM, and then photographed. The wafer piece was transported to the position to be bombarded by the microcluster beam, and then re-staged to the examination position after cleaning. SEM photos were taken of the same location before and after cleaning which clearly show the ability of energetic microclusters to completely remove particles ranging from about 5 µm down to 0.05 µm (limited by the resolution of the microscope). This sequential SEM analysis gave direct, visual confirmation of the type and size of particles removed without introducing wafer transport and handling steps. Unfortunately, the dynamic cleaning process could not be observed due to the distortion of the SEM electron beam in the presence of the charged cluster beam. Before cleaning, particles ranging from submicrometer to tens of micrometers and

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more were observed on the surface, as well as in the scribed “vias”. Debris, shielded from cleaning by very large features, was left undisturbed because the cleaning is a line-of-sight process. Since NanoClean can operate in situ, the entire test was performed in the available Cambridge Steroscan 200 SEM without exposing the samples to the atmosphere between photographs of the contaminated and cleaned wafer pieces. Samples were affixed to a five-axes manipulator arm, which could be moved into various positions for viewing and cleaning. The only modification required was the design of a special adaptor to mate the cleaning head to the SEM flange. Fig. 1 shows a schematic diagram of the SEM chamber, illustrating the sample stage position for cleaning and the target position for microphotography. Pieces of wafers were scribed with a diamond tip to provide a field with abundant particles, and then mounted on the target stage. Microphotographs were made of selected areas of interest, showing the debris before cleaning. Careful procedures were developed to assure that original locations could be located and photographed after

Figure 1. Schematic diagram of the experimental layout.

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cleaning (many of the photos reveal features that were unaffected by the cleaning process, and so were used to confirm local identity). Some samples were removed from the SEM and remounted on a special cleaning stage to achieve near-normal angle of incidence. No critical effects were observed resulting from exposure of the samples to the laboratory atmosphere for a very short time. 4. RESULTS

Many samples were cleaned and SEM micrographs taken to demonstrate the capabilities of NanoClean. Several are shown which illustrate some of the most interesting features of this line-of-sight momentum process for removing debris. These initial tests were valuable in directly demonstrating the process as a viable technique for nanometer cleaning. Systematic tests involving varying operational parameters are planned for subsequent investigations. Fig. 2 shows a 0.2 mm2 area on the wafer surface, containing debris with a wide range of particle sizes. Scratch marks that produced the particles are visible, and so is a large “boulder” about 80 µm in length, in the middle of the photo. Note the “haze” due to small particles throughout the field of view. The same area

Figure 2. SEM micrograph of debris field with large “boulder” before cleaning.

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Figure 3. SEM micrograph of the same area as in Fig. 2, after cleaning.

Figure 4. SEM micrograph (magnified) of the area enclosed by the rectangle seen in Fig. 3.

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Figure 5. SEM micrographs of the scratch mark before cleaning (top) and after cleaning (bottom).

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is shown in Fig. 3, after a 5-min clean, while operating the cleaning head at 15 kV and 0.5 µΑ of microcluster current. Particles over 5 µm remained intact while the smaller ones were removed. The area including the “boulder”, enclosed by a small rectangle in Fig. 3, is enlarged and shown in Fig. 4. Note the small particle debris on and near the “boulder”, which shows that cleaning occurs in a line-of-sight fashion. The beam impinged on the surface at a grazing angle coming in from above, while the “boulder” shielded part of the surface, resulting in small debris remaining in the shadowed areas. Fig. 5 shows two SEM micrographs, of the same area, with a nearly horizontal scratch mark. The top figure, before cleaning, shows the resulting debris composed of particles below 5 µm. After cleaning, the bottom figure shows all particles are removed, except for very few shielded in the crevices of the scratch mark [10]. 5. CONCLUSIONS

The capability of NanoClean for removing submicrometer debris was clearly demonstrated with this series of tests. In addition, these tests provided verification of the following performance features of NanoClean: in situ operation, particle removal down to 0.05 µm, line-of-sight cleaning, and impingement angular effects. REFERENCES 1. K.L. Mittal (Ed.), Particles on Surfaces 5 & 6: Detection, Adhesion and Removal, VSP, Utrecht (1999). 2. K.L. Mittal (Ed.), Particles on Surfaces 7: Detection, Adhesion and Removal, VSP, Utrecht (2002). 3. A. Hand, Semiconductor Int., 24, 62 (Aug. 2001). 4. M. Lester, Semiconductor Int., 22, 52 (Sept. 1999). 5. J.F. Mahoney, C. Sujo, J. Perel, P. Kopalidis and R. Becker, in: Cleaning Technology in Semiconductor Device Manufacturing, R.E. Novak, J. Ruzyllo and T. Hattori (Eds.), PV 99-36, pp. 429-436, Electrochem. Soc., Pennington, NJ (2000). 6. J. Perel, CleanTech 2000 Proc., 415 (2000). 7. J.F. Mahoney, J. Perel, C. Sujo and J.C. Andersen, in Particles on Surfaces 5 & 6: Detection, Adhesion and Removal, K.L. Mittal (Ed.), pp. 311-325, VSP, Utrecht (1999). 8. J.F. Mahoney, Int. J. Mass Spectrom. Ion Proc., 174, 253 (1998). 9. J.F. Mahoney, J. Perel, C. Sujo and J.C. Andersen, Solid State Technol., 149 (July 1998). 10. J. Perel, C. Sujo and J.F. Mahoney, Precision Cleaning VII, 18 (Sept. 1999).