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,...

Author: K. L. Mittal

390 downloads 959 Views 10MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Particles on Surfaces 8: Detection, Adhesion and Removal

K.L. Mittal, Editor

VSP

Particles on Surfaces 8: Detection, Adhesion and Removal

This page intentionally left blank

PARTICLES ON SURFACES 8: DETECTION, ADHESION AND REMOVAL

Editor: K.L. Mittal

UTRECHT 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

77

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

141

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

153

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

167

vi

Contents

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

245

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

271

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

279

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

293

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

323

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

335

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

345

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;

viii

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


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]

4

R. Kohli

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 (70%, while differential mobility size spectrometry can provide size distribution of particles in the 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]):


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 =


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)


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)


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).


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

)

)


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].

212

J. Tomas

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].


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-

J. Tomas

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,


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 > 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):

J. Tomas

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:


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)

J. Tomas

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.


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)

220

J. Tomas

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.


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].


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


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).

226

J. Tomas

3. A.W. Jenike, Gravity Flow of Solids, Eng. Exp. Station, Bull. No. 108, University of Utah (1961). 4. A.W. Jenike, Storage and Flow of Solids, Eng. Exp. Station, Bull. No. 123, University of Utah (1964). 5. J. Schwedes and H. Wilms, in P. Martens (Ed.), Silo - Handbuch, Ernst & Sohn, Berlin (1988). 6. M.D. Ashton, D.C.D. Cheng, R. Farley and F.H.H. Valentin, Rheol. Acta 4, 206-218 (1965). 7. D.C.H. Cheng, Chem. Eng. Sci. 23, 1405-1420 (1968). 8. P.T. Stainforth and R.C. Ashley, Powder Technol. 7, 215-243 (1973). 9. P.T. Stainforth and R.E.R. Berry, Powder Technol. 8, 243-251 (1973). 10. P.T. Stainforth, R.C. Ashley and J.N.B. Morley, Powder Technol. 4, 250-256 (1971). 11. B.J. Briscoe and M.J. Adams (Eds.), Tribology in Particulate Technology, Adam Hilger, Bristol (1987). 12. U. Tüzün, in: Tribology in Particulate Technology, B.J. Briscoe and M.J. Adams (Eds.), pp. 3862. Adam Hilger, Bristol (1987). 13. O. Molerus, Powder Technol. 12, 259-275 (1975). 14. O. Molerus, Powder Technol. 20, 161-175 (1978). 15. O. Molerus, Schüttgutmechanik - Grundlagen und Anwendungen in der Verfahrenstechnik, Springer Verlag, Berlin (1985). 16. O. Molerus, Principles of Flow in Disperse Systems, Chapman & Hall, London (1993). 17. R.M. Nedderman, U. Tüzün, S.B. Savage and S.T. Houlsby, Chem. Eng. Sci. 37, 1597-1609 (1982); Chem. Eng. Sci. 37, 1691-1709 (1982); Chem. Eng. Sci. 38, 189-195 (1983). 18. R.M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press (1992). 19. M. Satake and J.T. Jenkins, Micromechanics of Granular Materials, Elsevier, Amsterdam (1988). 20. G.I. Tardos, Powder Technol. 92, 61-74 (1997). 21. P.A. Cundall and O.D.L. Strack, Geotechnique 29, 47-65 (1979). 22. C.S. Campbell, Annu. Rev. Fluid Mech. 22, 57-92 (1990). 23. O.R. Walton, Mech. Mater. 16, 239-247 (1993). 24. O.R. Walton, in: Particulate Two-Phase-Flow, M.C. Roco (Ed.), pp. 913-950. ButterworthHeinemann, Boston, MA (1993). 25. H.J. Herrmann and S. Luding, Continuum Mechanics and Thermodynamics 10, 189-231 (1998). 26. C. Thornton, KONA – Powder and Particle 15, 81-90 (1997). 27. H. Rumpf, Chemie Ingenieur Technik 6, 317-327 (1953). 28. F. Löffler, Staub - Reinhaltung Luft 28, 456-461 (1968). 29. F. Löffler, Staubabscheiden, G. Thieme Verlag, Stuttgart (1988). 30. D. Tabor, in [11] pp. 207-219. 31. J. Bridgwater, in [11] pp. 364-374. 32. H. Rumpf, Chemie Ingenieur Technik 30, 144-158 (1958). 33. H. Rumpf, Chemie Ingenieur Technik 46, 1-11 (1974). 34. H. Schubert, Chemie Ingenieur Technik 51, 266-277 (1979). 35. K. Borho, R. Polke, K. Wintermantel, H. Schubert and K. Sommer, Chem. Ing. Tech. 63, 792808 (1991). 36. T. Hattori (Ed.), Ultraclean Surface Processing of Silicon Wafers, Springer, Berlin (1998). 37. M. Adachi and K. Okuyama, in: Ultraclean Surface Processing of Silicon Wafers, T. Hattori (Ed.), pp. 67–81. Springer, Berlin (1998). 38. A. Saito and K. Ota, in [36] pp. 105-114. 39. M. Itano and T. Kezuka, in [36] pp. 115-136. 40. H. Inaba, in [36] pp. 137-152. 41. H. Hertz, J. Reine Angew. Math. 92, 156-171 (1882). 42. M.T. Huber, Annal. Physik 14, 153-163 (1904). 43. B.V. Derjaguin, Kolloid Zschr. 69, 155-164 (1934). 44. R.S. Bradley, Phil. Magn. 13, 853-862 (1932).


227

45. R.S. Bradley, Trans. Faraday Soc. 32, 1088-1098 (1936). 46. C. Cattaneo, Academia Nationale dei Lincei, Rendiconti, Serie 6, 27, 342-348, 434-436, 474478 (1938). 47. R.D. Mindlin, Trans. ASME J. Appl. Mech. 16, 259-267 (1949). 48. G. Sperling, Eine Theorie der Haftung von Feststoffteilchen an Festkörpern, Dissertation TH Karlsruhe (1964). 49. H. Krupp, Adv. Colloid Interface Sci. 1, 111-239 (1967). 50. J.A. Greenwood and J.B.P. Williamson, Proc. Roy. Soc. Lond. A 295, 300-319 (1966). 51. K.L. Johnson, K. Kendall and A.D. Roberts, Proc. Roy. Soc. Lond. A 324, 301-313 (1971), in [67]. 52. B. Dahneke, J. Colloid Interface Sci. 40, 1-13 (1972). 53. C. Thornton and K.K. Yin, Powder Technol. 65, 153-166 (1991). 54. C. Thornton, J. Phys. D: Appl. Phys. 24, 1942-1946 (1991). 55. M.H. Sadd, Q. Tai and A. Shukla, Int. J. Non-Linear Mech. 28, 251-265 (1993). 56. H. Krupp and G. Sperling, Z. Angew. Phys. 19, 259-265 (1965). 57. H. Schubert, K. Sommer and H. Rumpf, Chem. Ing. Tech. 48, 716 (1976). 58. D. Maugis and H.M. Pollock, Acta Metall. 32, 1323-1334 (1984). 59. O.R. Walton and R.L. Braun, J. Rheol. 30, 949-980 (1986). 60. C. Thornton and Z. Ning, Powder Technol. 99, 154-162 (1998). 61. W.H. Yang, Trans. ASME J. Appl. Mech., 33, 395-401 (1966). 62. H. Rumpf, K. Sommer and K. Steier, Chem. Ing. Tech. 48, 300-307 (1976). 63. R.D. Mindlin and H. Deresiewicz, Trans. ASME J. Appl. Mech. 20, 327-344 (1953). 64. A.R. Savkoor and G.A.D. Briggs, Proc. Roy. Soc. Lond. A 356, 103-114 (1977), in [88]. 65. B.V. Derjaguin, V.M. Muller, Yu.P. Toporov, J. Colloid Interface Sci. 53, 314-326 (1975). 66. V.M. Muller, V.S. Yuschenko and B.V. Derjaguin, J. Colloid Interface Sci. 77, 91-101 (1980). 67. K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge (1985). 68. K. Kendall, in: Tribology in Particulate Technology, B.J. Briscoe and M.J. Adams (Eds.), pp. 110-122. Adam Hilger, Bristol (1987). 69. H.C. Hamaker, Physica 4, 1058-1072 (1937). 70. E.M. Lifshitz, Sov. Phys. JETP 2, 73-83 (1956). 71. M.J. Adams and B. Edmondson, in [11] pp. 154-172. 72. B.J. Ennis, J. Li, G.I. Tardos and R. Pfeffer, Chem. Eng. Sci. 45, 3071-3088 (1990). 73. S.J.R. Simons and J.P.K. Seville, Chem. Eng. Sci. 49, 2331-1339 (1994). 74. D. Tabor, J. Colloid Interface Sci. 58, 2-13 (1977). 75. J.N. Israelachvili, Intermolecular and Surface Forces, Academic Press, London (1992). 76. D. Maugis, J. Colloid Interface Sci. 150, 243-272 (1992). 77. P.G. Howe, D.P. Benton and I.E. Puddington, J. Can. Chem. 33, 1375-1381 (1955). 78. H.-J. Butt, M. Jaschke and W. Ducker, Bioelectrochemistry and Bioenergetics 38, 191-201 (1995). 79. R. Raitieri, H.-J. Butt, D. Beyer and S. Jonas, Phys. Chem. Chem. Phys. 1, 4881-4887 (1999). 80. J.A. Greenwood and J.H. Tripp, Trans. ASME J. Appl. Mech. 34, 153-159 (1967). 81. J.A. Greenwood, Trans. ASME J. Lubrication Technol. 89, 81-91 (1967). 82. U.D. Schwarz, O. Zwörner, P. Köster and R. Wiesendanger, Phys. Rev. B 56, 6987-6996 (1997). 83. R.W. Carpick, N. Agrait, D.F. Ogletree and M. Salmeron, Langmuir 12, 3334-3340 (1996). 84. S. Ecke and H.J. Butt, J. Colloid Interface Sci. 244, 432-435 (2001). 85. D. Maugis, J. Adhesion Sci. Technol. 1, 105-110 (1987). 86. D. Maugis and B. Gauthier-Manuel, J. Adhesion Sci. Technol. 8, 1311-1321 (1994). 87. I.U. Vakarelski, A. Toritani, M. Nakayama and K. Higashitani, Langmuir 17, 4739-4745 (2001). 88. A.R. Savkoor, in: Friction, Arching, Contact Dynamics Workshop, D.E. Wolf and P. Grassberger (Eds.), pp. 25-45. World Sci. Publ., Singapore (1996). 89. D.E. Wolf and P. Grassberger (Eds.), Friction, Arching, Contact Dynamics Workshop, World Sci. Publ., Singapore (1996). 90. H.M. Pollock, D. Maugis and M. Barquins, Appl. Phys. Lett. 33, 798-799 (1978).

228

J. Tomas

91. J. Tomas, Characterisation of the Rheo-Mechanical Properties of Wet-Mass Powders, IFPRI Review, Magdeburg (2001). 92. G. Böhme, W. Kling, H. Krupp, H. Lange and G. Sandstede, Z. Angew. Phys. 16, 486-490 (1964). 93. G. Böhme, W. Kling, H. Krupp, H. Lange, G. Sandstede and G. Walter, Z. Angew. Phys. 19, 265-270 (1965). 94. W. Schütz and H. Schubert, Chem. Ing. Tech. 48, 567 (1976). 95. W. Schütz and H. Schubert, Chem. Ing. Tech. 52, 451-453 (1980). 96. K.K. Lam and J.M. Newton, Powder Technol. 65, 167-175 (1991). 97. R.K. Singh, A. Ata, J. Fitz-Gerald, Y.I. Rabinovich and W. Hendrickson, KONA – Powder Particle 15, 121-130 (1997). 98. B. Hoffmann, G. Hüttl, K. Heger, B. Kubier, G. Marx and K. Husemann, KONA – Powder Particle 19, 131-143 (2001). 99. K. Spindler, U. Schünemann, B. Kubier, D. Höhne and K. Husemann, Schüttgut 4, 203-209 (1998). 100. S. Moser and K. Sommer, Powder Technol. 17, 191-195 (1977). 101. H. Schubert, Kapillarität in porösen Feststoffsystemen, Springer, Berlin (1982). 102. H. Schubert, Powder Technol. 37, 105-116 (1984). 103. M.H. Pahl and R. Wicke, Aufbereitungs-Technik 29, 371-380 (1988). 104. J. Visser, Powder Technol. 58, 1-10 (1989). 105. M.J. Lehmann and B. Schmidt, Chem. Ing. Tech. 70, 1319-1321 (1998). 106. J.P. Sonnenberg and B. Schmidt, Chem. Ing. Tech. 74, 1591-1595 (2002). 107. J. Dück, E. Zvetanov and Th. Neeße, Chem. Ing. Tech. 71, 692-696 (1999). 108. J.Y. Walz, L. Suresh and M. Piech, J. Nanoparticle Res. 1, 99-113 (1999). 109. S. Niedballa and K. Husemann, Chem. Eng. Technol. 23, 795-801 (2000). 110. J. Visser, Particulate Sci. Technol. 13, 169-196 (1995). 111. D.S. Rimai and A.A. Busnaina, Particulate Sci. Technol. 13, 249-270 (1995). 112. D.S. Rimai, L.P. DeMejo and R.C. Bowen, in Mittal Festschrift on Adhesion Science and Technology, W.J. van Ooij and H.R. Anderson, Jr. (Eds.), pp. 161-178. VSP, Utrecht (1998). 113. Y.I. Rabinovich, J.J. Adler, A. Ata, B.M. Moudgil and R.K. Singh, J. Colloid Interface Sci. 232, 10-16 (2000). 114. Y.I. Rabinovich, J.J. Adler, A. Ata, B.M. Moudgil and R.K. Singh, J. Colloid Interface Sci. 232, 17-24 (2000). 115. Y.I. Rabinovich, J.J. Adler, M.S. Esayanur, A. Ata, B.M. Moudgil and R.K. Singh, Adv. Colloid Interface Sci. 96, 213-230 (2002). 116. N. Gane and F.P. Bowden, J. Appl. Phys. 39, 1432-1435 (1968). 117. M. Ghadiri, in Powder Technology Handbook, K. Gotoh, H. Masuda and K. Higashitani (Eds.), pp. 61-72, Marcel Dekker, New York, NY (1997). 118. J. Tomas and H. Schubert, Proc. Intern. Symp. on Powder Technology '81, pp. 118-124, Kyoto (1981). 119. J. Tomas and H. Schubert, Aufbereitungs-Technik 23, 507-515 (1982). 120. J. Tomas and H. Schubert, Aufbereitungs-Technik 26, 399-404 (1985). 121. J. Tomas, K. Graichen and H. Schubert, Aufbereitungs-Technik 31, 475-481 (1990). 122. J. Tomas, Modellierung des Fließverhaltens von Schüttgütern auf der Grundlage der Wechselwirkungskräfte zwischen den Partikeln und Anwendung bei der Auslegung von Bunkeranlagen (Modelling of the flow behavior of bulk materials on basis of the particle interaction forces and application at bunker plant design, Sc.D. Theses), Habilitation, Bergakademie Freiberg (1991). 123. J. Tomas, Proc. Intern. Symp. on Reliable Flow of Particulate Solids II, pp. 335-372, Oslo (1993). 124. J. Tomas, Schüttgut 2, 31-51 (1996). 125. J. Tomas, Chem. Ing. Tech. 69, 455-467 (1997).


229

126. R. Hiller, Der Einfluß von Partikelstoß und Partikelhaftung auf die Abscheidung in Faserfiltern, Dissertation Universität Karlsruhe (1980). 127. M. Corn and L. Silverman, Amer. Ind. Hygiene Ass. J. 22, 337-346 (1961). 128. M. Corn, J. Air Pollution Control Ass. 11, 566-574 (1961). 129. M. Corn and F. Stein, Amer. Ind. Hyg Ass. J. 26, 325-336 (1965) 130. B. Dahneke, J. Colloid Interface Sci. 51, 58-65 (1975). 131. R.M. Davies, Proc. Roy. Soc. Lond. A 197, 417-432 (1949). 132. J. Reed, in: Tribology in Particulate Technology, B.J. Briscoe and M.J. Adams (Eds.), pp. 123134. Adam Hilger, Bristol (1987). 133. W. John, Aerosol Sci. Technol. 23, 2-24 (1995). 134. S.R. Salmagne, Untersuchung zur Reinigung von GaAs(001)-Oberflächen u. Charakterisierung von AIN/GaAs(001)-Grenzflächen, Dissertation Universität Duisburg (1996). 135. J. Haberland, Reinigung und Entschichtung mit Trockeneisstrahlen - Grundlegende Untersuchung des CO2-Strahlwerkzeuges und der Verfahrensweise, Fortschr.-Ber. VDI, Reihe 2 502, Düsseldorf (1999). 136. S. Eichenlaub, K. Cooper, A. Gupta and S. Beaudoin, in Ultra Clean Processing of Silicon Surfaces 2000, M. Heyns, P. Mertens and M. Meuris (Eds.), pp. 283-290, Scitec Publications, Zuerich-Uetikon (2001). 137. F. Zhang, A.A. Busnaina and G. Ahmadi, J. Electrochem. Soc. 146, 2665-2669 (1999). 138. F. Zhang and A.A. Busnaina, Electrochem. Solid State Lett. 1, 184-187 (1998). 139. F. Zhang and A.A. Busnaina, Appl. Phys. A 69, 437-440 (1999). 140. F. Zhang, A.A. Busnaina, M.A. Fury and S. Wang, J. Electronic Mater. 29, 199-204 (2000). 141. G. Ahmadi and X. Xia, J. Electrochem. Soc. 148, G99-G109 (2001). 142. Th. Kollmann and J. Tomas, 3rd Israeli Conference for Conveying and Handling of Particulate Solids, Proceedings Vol. 1, pp. 3.66-3.72, The Dead Sea (2000). 143. Th. Kollmann and J. Tomas, Particulate Sci. Technol. 20, 15-31 (2002). 144. B. Reichmann and J. Tomas, Proc. Int. Symp. on Reliable Flow of Particulate Solids III, Proceedings, pp. 393-402, Porsgrunn (1999). 145. B. Reichmann and J. Tomas, Powder Technol. 121, 182-189 (2001). 146. J. Tomas, Proc. Int. Symp. on Reliable Flow of Particulate Solids III, pp. 641-656, Porsgrunn (1999). 147. J. Tomas, KONA – Powder Particle 18, 157-169 (2000). 148. J. Tomas, Particulate Sci. Technol. 19, 95-110 (2001). 149. J. Tomas, Particulate Sci, Technol. 19, 111-129 (2001). 150. J. Tomas and B. Reichmann, Chem. Eng. Technol. 25, 1053-1060 (2002). 151. J. Tomas, Schüttgut 6, 522-537 (2002).



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 ∗

Fax: (1-860) 456-4600, E-mail: [email protected]

232

M.A. Melehy

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.

A new thermodynamic theory of adhesion of particles on surfaces

233

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

M.A. Melehy

234

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.


235

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.

236

M.A. Melehy

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.


237

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.

238

M.A. Melehy

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.


239

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.

240

M.A. Melehy

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.


241

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.

242

M.A. Melehy

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.


243

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).

244

M.A. Melehy

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).


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]

246

B.M. Moudgil et al.

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.

Particle adhesion on nanoscale rough surfaces

247

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).

248

B.M. Moudgil et al.

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).


249

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-

B.M. Moudgil et al.

250

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.


251

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-

252

B.M. Moudgil et al.

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).


253

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).



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]

256

R. Vos et al.

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.

Advanced wet cleaning of sub-micrometer sized particles

257

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.

R. Vos et al.

258

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


259

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.

R. Vos et al.

260

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


261

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).

262

R. Vos et al.

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).


263

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).

264

R. Vos et al.

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-


265

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).

266

R. Vos et al.

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.


267

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.

268

R. Vos et al.

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


269

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).

270

R. Vos et al.

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.


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]

272

C. Beaudry et al.

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

Modified SC-1 solutions for silicon wafer cleaning

273

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

274

C. Beaudry et al.

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


275

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.

276

C. Beaudry et al.

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).


277

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).



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.

280

J. DeBello and L. Liu

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

Investigation of ozonated DI water in semiconductor wafer cleaning

281

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,

282


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.


283

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.

284


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.


285

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.

286


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).


287

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.

288


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


289

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

290


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.


291

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).

292


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).


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]

294

R. Small and B. Scott

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 (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

Possible post-CMP cleaning processes for STI ceria slurries

295

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 70000 7002

15

H2SO4/H2O2

16

H2SO4/H2O2

5

25

5. Cerium oxide can be dissolved slowly at low pH (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 (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

The ideal ultrasonic parameters for delicate parts cleaning

309

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

T. Piazza and W.L. Puskas

310

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


311

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.

312


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


313

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.

314


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).


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]

316

S.L. Wicks et al.

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 (

Particles on Surfaces 8: Detection, Adhension and Removal

Focus On Curves and Surfaces

Lectures on Riemann surfaces

Lectures on Surfaces

Graphs on surfaces

Geometries on surfaces

Adsorption on Silica Surfaces

Chapters on algebraic surfaces

Lectures on Riemann Surfaces

Adsorbed Layers on surfaces

Burrs - Analysis, Control and Removal

Statistical thermodynamics on surfaces and interfaces

Topics on Riemann surfaces and Fuchsian groups

Conformal mapping on Riemann surfaces

Conformal mapping on Riemann surfaces

Hardy classes on Riemann surfaces

Theta Functions On Riemann Surfaces

Conformal mapping on Riemann surfaces

Lectures on vector bundles on Riemann surfaces

Particles, sources, and fields

Particles, sources, and fields

Particles, sources, and fields

Particles, sources, and fields

Theta functions on Riemann surfaces

Theta Functions on Riemann Surfaces

Surfaces

Surfaces

Surfaces

Surfaces

Surfaces

Particles, Sources, and Fields

Particles on Surfaces 8: Detection, Adhension and Removal

Focus On Curves and Surfaces

Lectures on Riemann surfaces

Lectures on Surfaces

Graphs on surfaces

Geometries on surfaces

Adsorption on Silica Surfaces

Chapters on algebraic surfaces

Lectures on Riemann Surfaces

Adsorbed Layers on surfaces

Burrs - Analysis, Control and Removal

Statistical thermodynamics on surfaces and interfaces

Topics on Riemann surfaces and Fuchsian groups

Conformal mapping on Riemann surfaces

Conformal mapping on Riemann surfaces

Hardy classes on Riemann surfaces

Theta Functions On Riemann Surfaces

Conformal mapping on Riemann surfaces

Lectures on vector bundles on Riemann surfaces

Particles, sources, and fields

Particles, sources, and fields

Particles, sources, and fields

Particles, sources, and fields

Theta functions on Riemann surfaces

Theta Functions on Riemann Surfaces

Surfaces

Surfaces

Surfaces

Surfaces

Surfaces

Particles, Sources, and Fields

Recommend Documents