Ultrasonic Waves

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

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Mechanisms of Removal of Micron-Sized Particles by High-Frequency Ultrasonic Waves Quan Qi and Giles J. Brereton

forces generated by high-frequency ultrasonificationprocesses and to identify the likely mechanisms whereby small particles are removed from surfaces. Small particles in an ultrasonic field near a solid surface experience two kinds of forces of particular interest to this study: adhesion forces; and cleaning forces that arise through interactions of ultrasound with particles. Adhesion forces, in general, comprise capillary forces, van der Waals forces, electrostatic image forces, and electrical double-layer forces [ 131, [ 2 ] .During cleaning operations, components are usually immersed in a liquid to ensure good acoustic coupling, in which case both capillary and electrostatic image forces become insignificant. Consequently, the adhesion forces of most importance are van der Waals forces and electrical double layer forces. In ultrasonic fields, the cleaning forces on particles are hydrodynamic ones which arise from linear as well as nonlinear interactions between the ultrasonic field and particles in fluid. I. INTRODUCTION Linear interaction forces include added mass, drag, lift, and NE of the most important applications of particle- Basset forces while nonlinear ones include radiation pressure removal technology is the cleaning of small particles forces and drag forces due to acoustic streaming. An important from silicon wafer surfaces. The presence of particles on the difference between these two kinds is that linear forces are surfaces of semiconductors has long been recognized as a time-dependent and have zero means while nonlinear ones cause of reduced yields in the production of semiconductor have a time-independent component and, on average, take devices through contamination of processes such as etching, nonzero values; linear interaction forces are usually much photoresist stripping and prediffusion cleaning [ 171. As the larger than nonlinear counterparts in conventional applications characteristic linewidths, and so the size of the particles which at moderate frequencies (up to, say, megahertz). must be cleaned, continue to decrease, conventional cleaning There have been relatively few studies of mechanisms techniques become less effective. of particle removal. Olson [ 191 conducted a finite-element Conventional ultrasonic cleaning techniques depend on the computational study of the forces imparted by small-amplitude mechanisms of (1) chemical solvation, and ( 2 ) acoustic cavi- plane waves to a sphere on a surface, at frequencies as high tation, both of which can have undesirable effects. Solvents are as one gigahertz, and concluded that acoustic excitation at often environmentally hazardous and cavitation thresholds are wavelengths of the order of one radius led to the greatest hard to predict, cavitation forces are difficult to control, and amplitude of the surface-normal oscillatory force on a spherimay cause damage to the component being cleaned. Recently, cal particle. Geers and Hasheminejad [7] considered a model the removal of particles by high-frequency focused ultrasound in which a spring and a damper were used to represent the in water [4] has shown great promise as a technique which adhesion force and proposed that a possible mechanism of requires no solvents and may be applied below thresholds at particle removal from the surface was through excitation of which cavitation occurs. The goal of this paper is to analyze the the particle at the resonance frequency of the particle-springManuscript received November 5 , 1993; revised November 16, 1994; damper system. These removal mechanisms are both linear and so have no provision for mean displacement of particles. In accepted November 16, 1994. This work was supported by the Materials Research Center of the University of Illinois (MRC MCM CTR). Q. Qi was the following sections, the principal adhesion forces and linear supported by the Acoustical Society of America and the Hunt Fellowship. G. and nonlinear hydrodynamic interaction forces are reviewed. Brereton was supported by IBM, T. J. Watson Research Center. Order of magnitude analyses are presented from which it Q. Qi is with the Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61 801 USA. is shown that the combined effect of the interaction forces G. Brereton is with the Department of Mechanical Engineering and Applied and mechanisms of advection of the loosened particles must Mechanics, University of Michigan, Ann Arbor, MI 48109 USA. IEEE Log Number 9409984. be considered if removal mechanisms are to be explained.

Abstract-In this paper, theories of particle removal by highfrequency ultrasonic waves are discussed and tested against recent experimental data. First, the principal adhesion forces such as van der Waals forces are briefly reviewed and the typical uncertainties in their size in particle-surface systems are assessed. The different ultrasound-induced forces-linear forces such as added mass, drag, lift, and Basset forces and nonlinear ones due to radiation pressure, and drag exerted by acoustic streaming-are discussed and their magnitudes are evaluated for typical cleaning operations. It is shown that highfrequency ultrasound can clean particles most effectivelyin media with properties like water because: (1) the wavelength can be made comparable to the particle radius to promote effective sound-particleinteraction; (2) the viscous boundary layer is thin, minimizing particle “hide-out;” and (3) both the added mass and radiation pressure forces exceed typical adhesion forces at high frequencies. Based on these analyses, possible mechanisms of particle removal are discussed and interpreted in terms of experimental observations of particle cleaning.

0

0885-3010/95$04.00 0 1995 IEEE

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

Based on these analyses, mechanisms of particle removal are proposed and used to interpret recent experimental results. 11. BRIEFREVIEWOF ADHESIONFORCES For particles fully immersed in a liquid, the dominant adhesion forces are van der Waals and double layer forces. Van der Waals forces can be classified in the categories of [23]: (1) dipole-dipole forces; (2) dipole-induced dipole forces; and (3) dispersion forces. Of these, the nonpolar dispersion force (also called the London-van der Waals force) is believed to be the most important [2], [3]. Under the assumptions of “nonretardation” and “additivity,” the resulting interaction force between a particle and a plane surface can be characterized by the conventional Hamaker constant. A more satisfactory approach was developed later by Lifshitz [3] in which the principal parameter was the Lifshitz-van der Waals constant, defined as an integral function of the imaginary parts of the dielectric constants of the adhering materials. Israelachvili [lo] has shown that in some cases Hamaker constants can be calculated on the basis of the Lifshitz theory. Hence a one-to-one correspondence between the Hamaker constant and the Lifshitz-van der Waals constant can be established. Electrical double layer forces are associated with particles whose effective diameters are smaller than 5 microns [3]. A surface contact potential is created between two different materials based on each material’s respective local energy state. The resulting surface charge build-up needed to preserve charge neutrality sets up a double-layer charge region, thus creating the electrostatic attraction. However, for particle adhesion, [ 131 concluded that the electrostatic double layer force can at best be of the same order of magnitude as the van der Waals force and can generally be neglected in favor of the van der Waals force. Consequently, for order-of-magnitude analyses of adhesion forces it is usually sufficient to consider only the van der Waals force.

As the adhesional distance z increases, (1) loses its validity and the adhesion force becomes retarded. Strictly speaking, the Hamaker constant is never a constant [lo] but decreases progressively as z increases. The effect of retardation has been accounted for [23] by introducing a second relation

2rBR for relatively large z 323 where B is called the Hamaker constant for the retarded force; a typical value is B 20-28 Jm. When elastic deformation of the sphere and the surface takes place, there is an additional contribution to the van der Waals force, given by [3] as FvdW =

~

N

(3) The first term describes the nondeforming van der Waals force while the second accounts for deformation of the particle and/or surface. The parameter h is the Lifshitz-van der Waals constant and p is the radius of the adhesive surface area. Comparison between (1) and the first part of (3) gives the relation between the Hamaker constant and Lifshitz-van der Waals constant as h A=-. (4) 8T

A number of complications arise when using these models. First, in (1)-(4) the adhesional distance z cannot be calculated from theoretical considerations and so is usually approximated as a constant. For example, a value of z = 0.4 nm is suggested in [13] while [ 101 uses z = 0.2 nm in numerical computations. Moreover, particle asperity also complicates the choice of an appropriate value for z and the range of validity of (1) and (2) is not well known. Second, real particles are seldom spherical in shape and use of effective radii can involve considerable approximation. Third, the value of the Hamaker constant, as obtained from the Lifshitz theory, does not always agree with those evaluated from experimental data on colloid stability [3]. Hence it is, in essence, an adjustable parameter describing adhesion phenomena. Finally, the deformation of the particle A. van der Waals Force or surface can induce an additional adhesion force which There exist two different theories describing van der Waals may exceed the nondeforming van der Waals force [3]. The forces: the microscopic theory of de Boer and Hamaker estimation of these forces is uncertain owing to the difficulties and the macroscopic theory proposed by Lifshitz. These two in evaluating the contact area. These difficulties constitute theories can be related, though many experimental results are sources of uncertainty in the prediction of adhesion forces. The extreme importance of the van der Waals force to in better agreement with the macroscopic one. Comprehensive treatments of both theories can be found in [13], [23], [lo]. micron particle removal can be appreciated by comparing its For the purpose of this paper, we restrict attention to these size with the gravitational force on a spherical particle, which interaction forces for the case of a spherical particle near a flat is given by surface. The van der Waals attraction force is then modeled as 4 F,,, = -rR3pg. 3 F,,~W = for relatively small z For particles on the order of a micron, FvdW 106Fg,,!

$

N

where A is the Hamaker constant for the nonretarded force; R is the radius of the sphere, and z is the distance of maximum force of adhesion (adhesional distance). A typical value for A in a gaseous medium is A J, although immersion in a liquid usually reduces A by an order of magnitude. Appropriate values of the Hamaker constant for _ .different combinations of materials can be found in [IO]. N

111. CLEANING FORCESINDUCED BY ULTRASOUND The transmission of ultrasound through a liquid has a number of consequences. First, any particles suspended in the liquid oscillate at the driving frequency and experience significant acceleration at high frequencies. Second, a timeinvariant mean flow known as acoustic streaming is generated.

QI AND BRERETON: MECHANISMS OF REMOVAL OF MICRON-SIZED PARTICLES BY HIGH-FREQUENCY ULTRASONIC WAVES

62 1

Although its magnitude is usually of secondary importance to that of the primary ultrasonic field, its role in mean particle transport may be very important. Third, particles in the path of the ultrasound scatter acoustic waves and reduce the acoustic energy density through reradiation, leading to a reaction force called radiation pressure force. Viscous boundary layers also develop near the liquid-solid interface, the thickness of which depends on the driving frequency and the kinematic viscosity of the liquid. Each of these phenomena involves different interaction forces between the particle and the liquid. The acceleration Fig. 1. Schematic representation of a particle removal. Liquid density and of liquid leads to the so-called added mass force, which viscosity of the liquid: p and p . Acoustic wave frequency: f and the intensity: I . The radius of the particle: R and the thickness of the boundary layer: 6. will be shown to play a key role in high-frequency particlefluid interaction. Both the time-dependent and time-invariant flows of surrounding liquid relative to the particle generate propagates towards a surface, on which a particle rests, the drag forces which have different scalings depending on the added-mass force is diminished, but still accelerates fluid Reynolds number regime. Thus primary acoustic fields induce above and below the midplane through the particle. Hence instantaneous drag forces and secondary acoustic streaming this force should be oscillatory in sign, alternatively promoting leads to a steady drag force on particles. The radiation pressure removal and attachment. Lift Force: Circulation of fluid around a particle generates also applies a net force on particles. This force increases a lift force of inviscid character, with a surface-normal comwith frequency and hence plays an important role in particle ponent acting to remove the particle. The pressure difference removal with high-frequency ultrasound. Finally, a so-called Basset force is also present as a result of flow-particle inter- between the bottom and top of the particle may be estimated action with a typical magnitude between that of added mass from the Bernoulli’s equation to yield an estimate of lift force as and Stokes drag forces. Our principal interest in these forces is to make assessments (7) of the conditions under which one or more can reach the same order of magnitude as the adhesion forces and hence can be For smaller particles at surfaces, viscous effects may become utilized to remove particles adhering to a surface. For these important and estimates of lift from Navier-Stokes equation purposes, we consider a spherical particle adhering to a plane solutions have been made by [16], [6]. It was concluded [6] surface (Fig. 1). The radius of the particle is denoted by R , that the lift force is decreased by the presence of a wall for the density of the particle by pp, the viscosity of the fluid particles sufficiently close to the wall. Equation (7) may be by p, and the density of fluid by p. The ultrasound field is regarded as an upper limit for lift force. Drag Forces: Drag forces take different forms, depending characterized by a frequency f and an intensity I . When a on the regime of the flow Reynolds number, defined as viscous boundary layer is present, its thickness is denoted by PRu 6. Derivation of exact expressions for the forces on a particle Re = submerged in a sonofied liquid is rarely possible as analytic P solutions are only known in idealized cases [8], [9]. More When Re << O( 1) the well-known Stokes drag is of the order generally, solutions have to be obtained numerically. For the Fs ~ R u . (9) purpose of this study, order-of-magnitude estimates of these forces are of primary interest and are analyzed in the following On the other hand, when Re >> O(l), the drag force is of sections. Similar analyses and discussions can be found in the the order review on suspension mechanics by Kim and Lawrence [ 111. Fo ~ ( u R ) ~ . (10) N

N

A. Linear Interaction Forces Added-Mass Force: The added-mass force Fa, on a contaminant particle is an effect of the acceleration of the fluid. For a spherical particle, this force is parallel to the direction of acceleration, and its magnitude may be estimated as if it were an isolated sphere. The exact value is expected to differ by a factor of order unity when the presence of the plane surfaces is accounted for. The added-mass force is then

[1/(pc)]’l2is the instantaneous fluid particle where U velocity associated with the acoustic wave and I is the intensity of the incident acoustic waves. When a plane wave N

The relative importance of viscous and inertial effects at different Reynolds numbers is reflected by the proportionality of Fs to the viscosity of the liquid, radius of the particle and the velocity, while Fo scales linearly on the density of the liquid, and quadratically on velocity and particle diameter. Basset Force: When the particle radius R is comparable / ~ ,added to the boundary layer thickness S ( p / 2 ~ f p ) l the mass force will be modified by a force of “Basset”-type from the shear in the boundary layer and the resultant modification of the pressure field. This force can be estimated, for particle exposure to monochromatic acoustic waves, as N

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

from which FB is the geometric average of the added-mass and the Stokes drag forces. In ultrasonic fields, the time-averaged values of these forces are zero. Furthermore, as the size of the particles decreases, the Stokes drag becomes increasingly important-unlike other interaction forces, it depends on particle radius only linearly.

FORCES (IN N) VERSUS

TABLE I R (RADIUSIN pm) FOR f = lo6/ 2T HZ

PARTICLE SIZE

R

0.1

1 .o

10.0

F,,,

2x104

2 x 10-8

2 x 10-7

Fam

2~ 10-13

2 x 10-10

2 x 10-7

FL9FD

4 x 10-13

4 x 10-11

4 x 10-9

2 x 10-10

2 x 10-9

B. Nonlinear Interaction Forces

Radiation Pressure: The radiation pressure force on an isolated solid particle in an ideal fluid induced by a plane wave was deduced by King (1934) as

~~

R

for 2 r f - << O(1) (12) c where c is the sound speed in the liquid medium. This solution requires the particle to be small or acoustically “compact.” King also derived the related expression for larger particles FRT

-

p

(

~

) 1~ 95- - 48(P/PP)

89

5 + 6(P/P,)

C

2 x lo-’*

2 x 10-10

2 x 10-8

F,,

2 x 10-16

2 x 10-13

2 x 10-10

i.e. V u 2 / c . Therefore the drag force which results from boundary layer-generated acoustic streaming FST is given by N

U2

FST p R ;

N

N

0(1)

(13)

The above equations are for traveling waves. For stationary waves, King showed that 8p

FB

+ 36(P/Pp)2 R

N

2x

+ 2(P/PP) for 2 r f -

FRS

lo-”

F,

(F)

- P/PP> R3u2sin 2kl 1 + 2 +P/Pp R for 2 r f << 0 ( 1 ) (14)

where 1 is the distance between the center of the particle and a nodal plane of the stationary wave. For 2 r f R / c << O(l ) , it can be verified that FRS >> FRT. For 2 n f R / c O(1); no analytic expression is available for FRS,We shall nevertheless use (14) for approximate estimations. Yosioka and Kawasima [25] extended King’s results by including the effect of compressibility of the particle, though the correction is small for solid particles and did not affect the outcome of order-of-magnitude analyses. When particles are positioned on surfaces, the radiation pressure imparted by plane acoustic waves directed normal to the surface is into the surface. Thus this nonlinear force would act to retain particles at the surfaces. When the incident wave is not normal or the particle is at the edge of an ultrasonic beam, a force component due to radiation pressure in the direction parallel to the surface will also be present, which acts to remove the particle from the contaminated area. A more detailed discussion of such a removal is given later. Drag Force Due to Acoustic Streaming: The acoustic streaming motion generated by an ultrasonic field near a solid surface leads to a drag force, caused by interaction between the mean flow and particles. It is described by (9) when the streaming velocity is substituted in place of the instantaneous velocity. It can be shown [18] that, for streaming near a solid surface, the magnitude of the streaming velocity v is of the order of the product of Mach number and U , N

(15)

where the Stokes drag is assumed to be the relevant one at typically low Mach numbers in particle removal. The principal difference between the nonlinear and linear forces is that nonlinear forces have nonzero time averages and so provide a mean component to the removal force. Streaming is ordinarily parallel to surfaces and so can potentially advect particles along the surfaces. OF FORCES I v . ESTIMATION

A. Forces in Plane Wave Fields Based on the development of the previous sections, the orders of magnitude of the forces in (1) and (6)-(15) will be considered for particles with radii in the range 0.1-10 pm. For illustrative purposes, a mica particle is assumed to adhere to a mica surface in water, in which case we N sm-2, c = have A = 2.0 x J [lo], p = 1500 ms-l and p = 1000 kgm-3. Material properties of mica are similar to those of silicon and other materials used in semi-conductor processing. The intensity of the ultrasonic 0.6 x lo5 WmF2, which is a value field is given by I representative of those used in commercial ultrasonic cleaning operations. Consequently U N ( I / p ~ ) l z / ~0.2 ms-l and Re 0.02, 0.2, 2 for R = 0.1, 1, 10 pm, respectively. At for an acoustic frequency of 106/2r Hz, 2 r f R l c N R = 1 pm. The corresponding orders of magnitude of forces are given in Table I, assuming an adhesional distance z = 0.4 nm without particle or surface deformation. For this relatively small adhesional distance, these estimates for van der Waals forces are upper bounds on their approximate values. These results illustrate the increasing difficulty experienced in removing particles of decreasing size, for acoustic excitation at megahertz frequencies. The reduction in van der Waals force with increasing adhesional distance emphasizes that, once the particle is dislodged and suspended in the medium, N

N

~

QI AND BRERETON: MECHANISMS OF REMOVAL OF MICRON-SIZED PARTICLES BY HIGH-FREQUENCY ULTRASONIC WAVES

TABLE I1 FORCES(IN N) VERSUS PARTICLE SIZER (RADIUS IN pm) FOR^= 106/2a Hz

R

0.1

1.0

10.0

Fam

2 x 10-IO

2 x 10-7

2 x 10-4

FRs

2~ 10-13

2x 10-10

2 x 10-7

623

\ e2nfir

Acoutic streaming components

displacement

the adhesion force decreases drastically. An important issue in cleaning is therefore the prevention of dislodged particles from readhering to the surface. It is interesting to evaluate when the van der Waals force will be comparable to the gravitational force. For a given particle radius, this determines the separation distance at which the adhesion force becomes insignificant. This distance can be estimated from (l), (2), and (5). The following results are given for a micron-sized mica particle

AR

4

622 = -7rpgR3 3 27rBR 4 3z3 = 57rpgR3

+

+

z = 0.3 pm z = 0.47 pm

(16)

(17)

where we have taken B = Jm [23, p. 221. They indicate that adhesive forces are no longer dominant when micron particles are displaced from the surface by roughly one third of a particle radius, at which point other hydrodynamics forces determined subsequent particle motion. At f = 106/27r Hz, the van der Waals force Fvdw in Table I is at least an order of magnitude larger than all the other forces for micron and submicron particles. As particle size increases, the added-mass force first becomes comparable to the van der Waals force. This is because the adhesion forces are linearly proportional to the radius of the particles while acoustically induced hydrodynamic forces (with the exception of the Stokes drag force) are proportional to particle diameter squared or cubed. Furthermore, the particle velocity is limited by the ultrasound intensity level. Consequently, the smaller the particle size, the more dominant the adhesion forces. However, in ultrasonic cleaning applications, the choice of acoustic frequency may be used to advantage-higher frequencies generate higher acceleration of the liquid and so larger added-mass forces as illustrated in the order-ofmagnitude estimates in Table 11. Except for radiation pressure and added-mass forces, other forces are not affected by the increase of frequency and hence are not reproduced in this table. For the case of acoustic excitation at gigahertz frequencies, the force due to the radiation pressure field is still much smaller than the van der Waals force for micron and submicron particles. A comparison of Table I and Table I1 shows that the added-mass force at f = 109/2.rr Hz dominates adhesion forces for particles of micron size or larger. However, the van der Waals force remains dominant for particles of the order of 0.1 pm. The boundary layer thickness can be estimated using 6 (,~/27rfp)’/~:S 1 pm for f = 106/27r Hz and S 0.032 pm for f = 109/27r Hz. Consequently, small N

N

-

Fig. 2. Acoustic streaming flows and their interaction with particles. The horizontal streaming flow helps push the particle off the contaminated area, and the vertical streaming flow helps prevent readhesion of the particle to the surface (left). Particle removal (right): added mass force overcomes the adhesion force and mean forces generate a net displacement. The accumulation of displacement leads to removal.

particles are submerged (“hide-out”) in the boundary layer at relatively low frequencies. In contrast, most particles are outside the boundary layer at gigahertz frequencies and are subject to the effective action of hydrodynamic forces. The drag forces presented in Table I are for the instantaneous local velocity near the particle. The drag due to streaming flows, on the other hand, exerts a constant force on particles. The order of magnitude of the drag force associated with the acoustic streaming is estimated as follows. The Reynolds number based on the streaming velocity is given by Re” = ( p R u 2 ) / ( c p ) .For I = 0.6 x lo5 W/m2, we find Re”

-

3x

lop6, 3 x

3 x lop4

for R = 0.1, 1, 10 pm.

(18)

Applying the Stokes drag relation of (9), the drag forces based on the streaming velocity are

F,

-

3x

3x

3x for R = 0.1, 1, 10 pm

(19)

which are larger than the gravitational force for submicron particles. Since the streaming velocity induced beyond a viscous boundary layer is independent of acoustic frequency, these results hold for both megahertz and gigahertz frequencies. Recently, an improved description of acoustic streaming near a plane boundary was obtained for plane waves [20]. It was shown that in addition to the streaming flows in the travelling wave direction, a streaming flow perpendicular to the plane surface is also generated because of compressibility of the medium; its magnitude is of the order of u2d w / c 2 . Although this component is usually small, it may play a role in preventing particle readhesion once the particles are loosened from the surface and suspended in liquid, especially for neutrally buoyant particles. This effect is shown on the left-hand side of Fig. 2. Just as the drag force due to streaming motion is constant with time, so is the radiation pressure force. However, unlike acoustic streaming near a plane boundary, the radiation pressure force does increase with frequency. In this regard,

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

TABLE Ill FORCES IN (N) VERSUS

PARTICLE SIZE (RADIUS IN

pm) FOR f = 10' 2T Hz

R

0.1

1.o

10.0

Fa"

4x 10-8

4 x 10-5

4 x 10-2

FL'FD

4 X lo-'

4 x 10-7

4 x 10-5

FRS

2 x 10-8

2~ 10-5

2 x 10-2

FS,

3x10-1'

3 x 10-10

3 x 10-9

radiation pressure forces are expected to be smaller than those presented in Table 111. Nevertheless, the values of radiation pressure forces give approximate estimates for submicron particles. The increase of several orders of magnitude in the drag force due to streaming emphasizes its dominance over the gravitational force. Consequently, if the added-mass and/or radiation pressure forces can move the particles out of the region of influence of adhesion forces, the subsequent particle motion will then be determined by steady drag alone. This issue is discussed further when experimental results are described.

v. radiation pressure has been used successfully in particle fractionation [24], in which particles suspended in a liquid are separated with the aid of radiation pressure force. At megahertz frequencies, the drag forces due to acoustic streaming and radiation pressure force are of the same order of magnitude for micron-sized particles. For smaller (larger) particles the drag force due to acoustic streaming is greater (smaller) than radiation pressure force. At gigahertz frequencies, however, radiation pressure force dominates the drag force due to acoustic streaming.

B. Forces in Focused Wave Fields

MECHANISMS OF REMOVAL

The analyses in Sections 11-IV can be summarized as the following. The prediction of adhesion forces involves a number of uncertainties, including the proper choice of the adhesional distance and the estimation of particle asperities. It is therefore more appropriate to describe a range of plausible adhesion forces for a given situation. Particle removal is expected if the largest possible adhesion force can be overcome by cleaning forces. High-frequency ultrasound in liquids like water can be generated with wavelengths that are comparable to the size of particles being cleaned, which permits effective interactions between particles and the sound field. Furthermore, increasing frequency also has the added benefits of larger added-mass and radiation pressure forces, and thinner viscous boundary layers, thus exposing particles to the effective action of cleaning forces. The drag force due to acoustic streaming generated near the viscous boundary layer is independent of frequency. The mean radiation pressure force increases with frequency. Both forces have nonzero time averages and promote displacements of particles. Water may be used effectively as a cleaning medium, thereby avoiding the use of environmentally hazardous solvents. High frequency ultrasound can be used so that the cavitation threshold is not exceeded and a focused acoustic wave can be used to compensate attenuation loss.

The high values of forces such as added-mass forces attained during high-frequency excitation are one reason for the success of ultrasonic cleaning. However, one undesirable feature is the quadratic increase in attenuation with the driving frequency. It is therefore conceivable that a large part of the energy in the plane wave would be attenuated when the driving frequency was high, thus compromising the effective delivery of ultrasound energy for particle removal. One option for improved cleaning effectiveness is to use focused ultrasound. When ultrasound is focused, energy can be purposely directed to the focal region and generate highly localized velocity and acceleration fields. Brereton and Bruno [4] have devised a focused ultrasound apparatus in which individual particles can be manipulated selectively in this way. In this apparatus the energy density at the focal point reaches a value of ( E )M 390 x lo3 Jm-3. Consequently, if the sound speed is A. Proposed Removal Mechanisms taken as c = 1500 ms-', then I = ( E ) cx 58.5 x lo7 WmP2 From previous discussions, the following particle removal and U M 20 ms-'. Clearly, the local fluid particle velocity mechanisms are proposed. at the focal region is much higher than in the case of a plane For micron-sized particles in close contact with the surwave. Based on these estimates, we have Re = 2, 20, 200 and face, increasing frequency (to the gigahertz range) promotes ReS = 0.027, 0.27, 2.7 for R = 0.1, 1, 10 pm, respectively. particle removal at commonly used intensity levels. Removal is accomplished by combined effects of the time-dependent The corresponding forces are given in Table 111. A comparison between Table I and Table I11 reveals that added-mass force and the time-invariant forces due to radiation with the high-intensity focused beam even submicron par- pressure and acoustic streaming. During exposure to acoustic ticle removal becomes possible. The significant increase of excitation, when the added mass force overcomes the adhesion radiation pressure force implies that particles in the focal force and causes momentary removal, the particle is also region may be forced out of the path of the ultrasonic beam subject to streaming and radiation pressure force which can instantaneously, especially in the case of relatively large cause a net displacement in the direction of streaminghadiation particles where cleaning forces overwhelm the adhesion force. pressure forces, before reversal of the direction of the addedThese conclusions are based on application of (14), which is mass force restores the particle to the surface. The cumulative f R/c limit; the actual displacement might amount to large-scale displacement over not strictly applicable in the large 27~

QI AND BRERETON: MECHANISMS OF REMOVAL OF MICRON-SIZED PARTICLES BY HIGH-FREQUENCY ULTRASONIC WAVES

many acoustic cycles, as shown on the right of Fig. 2. Additionally, the streaming motion may also remove particles by advection. If the contact between the particle and the surface is imperfect, adhesion forces may be much smaller. In this case, the radiation pressure force alone may be sufficient to remove particles, though particle displacement is not necessarily tangent to the surface. The applied ultrasonic field and the asperities and elastic properties of the surface and particle all play a role in determining the trajectories of particles departing from the surface. For particles larger than 10 pm, the mean forces of streaming and radiation pressure may be sufficient to remove particles at gigahertz frequencies. At megahertz frequencies, the addedmass force may again be needed to overcome the adhesion force. In general, large particles are much easier to remove. For particles of 0.1 pm or smaller, cleaning requires greater forces. If the particles are truly spherical, they still may be removed by the roll-off mechanism proposed by Bhattacharya and Mittal [l]. However, if the particles are irregular in shape, rolling may not take place and a focused ultrasonic beam of high local intensity might provide sufficient force for removal. Forces due to added mass and radiation pressure can reach the same order of magnitude as the adhesion forces, as shown by the comparison of Table I and Table 111. Successful cleaning also depends upon preventing readhesion of particles, either through convection patterns of surrounding fluid or by other means.

B. Comparison with Experiments Experiments have been carried out using both focused and unfocused ultrasound to remove particles from surfaces. Because of the complexity involved, very few such experiments have been performed. In general, the local contact conditions of particles at surfaces cannot be measured and so one can only use order-of-magnitude analysis to assess whether there is rough agreement between experimental results and theory. Imprecise knowledge of particle adhesional distance, and the quadraticlcubic dependence of adhesion force on this distance, make comparison of the adhesive and removal forces still more difficult. Given these difficulties, general agreement to an order of magnitude is the best one might hope for based on existing experimental knowledge. The studies of Kashkoush and Busnaina [14] addressed the performance of standard unfocused ultrasonic cleaning equipment which comprised steel tanks with surface-mounted acoustic transducers. In these studies, particle counting equipment was used to measure the efficiency with which contaminant polystyrene latex (PSL) particles could be removed from wafer surfaces. Efficiencies were measured as functions of particle size, excitation frequency, acoustic power density, and exposure time. Experiments conducted with point-focused ultrasound have been carried out by Brereton and Bruno [5] who constructed a gigahertz system which allowed observation of particle removal events (Fig. 3). They energized a commercially available acoustic microscope objective, to which they delivered as much as 1 W of power in pulses as long as 20

625

sapphire Cylinder

\;---“4

Water Drop

I

-\ 20 microns

Fig. 3. Acoustic transducer for spherical focusing of gigahertz-frequency waves.

ps. The objective could focus an acoustic beam to an Airy diameter of 1.2 pm. They observed different particle responses to acoustic excitation at the beam focus and adjacent to it, and studied particle behavior as functions of acoustic power and proximity to the beam. For each of these series of experiments, estimates of the acoustic forces were made and compared with forces of attraction and experimental results on particle removal. These data are compiled in Table IV. In the studies of Kashkoush and Busnaina [ 141, clean wafers were contaminated with PSL particles of 0.3, 0.5, 0.7, and 1.0 pm. Sonification was applied for time periods as long as 30 minutes, at power levels of 50 to 400 W, and at frequencies of 40, 65, 80, and 100 kHz. Removal efficiencies typically increased with exposure time and varied between 40% and 80% of the particle population. They also decreased with decreasing particle size, with little dependence on frequency over the range studied. These results were reported as the net percentage of particles removed, so those remaining may also have been removed but subsequently reattached. Since all removal efficiencies were of the same order, these data are summarized in a single column in Table IV. From knowledge of the acoustic power delivered, the results of the previous sections were used to estimate the relevant acoustic forces. Of these, the Stokes drag force appeared to be the largest N) and was within several orders of magnitude of the upper estimate of the van der Waals adhesion force. Thus a case can only be made for the reasonableness of the theory if the van der Waals adhesion force of PSL particles is a gross overestimation of the true particle-adhesion force. Although the drag force is linearly proportional to the acoustic power, Kashkoush and Busnaina [14] reported only a slight increase in removal efficiency (10%) at 400 W, compared to 50 W. This result might be a consequence of a distribution in particle size about its mean value, which could require an increase in power by an order of magnitude to increase removal efficiency by 10%.

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

TABLE IV COMPARISONS OF ACOUSTIC

FORCEESTIMATES WITH EXPERIMENTAL OBSERVATIONS

Iiamond Diamond ,Diamond PSL Diamond 5-15 .

........

f (Hz)

1

2-4

1

I

.. ."I-...

i

2-4i

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

2-4

2-6

.

I

4 x lo4 -105

1 ..

-

.I

. . .

__ .....

.......

...

,

.-

FRS

.

..

particle: Observations removei

* Experiments of Kashkoush & Busnaina (1993); these experiments demonstrated particle removal efficiencies of 60% to 90% over a range of frequencies, exposure times and power levels, using unfocused ultrasonic excitation. PSL refers to polystyrene latex particles.

* Experiments of Brereton and Bruno (1994); this series of focused-beam experiments explored single-particle response to streaming, away from the beam focus. Isurfoce is the local power density estimated from the observed streaming, away from the beam. #Experiments of Brereton and Bruno (1994);these focused-beam experiments concern single-partick removal at the beam focus and could not accurately measure the likelihood of distant particle re-attachment.

In the focused-beam experiments of Brereton and Bruno [4], observations were made of manipulation and removal of micron-sized particles on flat surfaces, for varying power levels and duty cycles. The acoustic lens achieved beam waists of approximately 1.2 pm so that individual particles could be interrogated by exposure to ultrasonic waves propagating normal to the surface. Particle response was recorded using video microscopy at 30 frames per second, allowing resolution of streaming effects, particle presencehonpresence, and sometimes particle position during displacement. The effect of the focused beam on the surrounding liquid was to set up circulatory streaming motions, as shown on the left of Fig. 4. Thus both the direct effect of the acoustic beam and the indirect effects of streaming on particle removal could be studied by positioning the focus of the beam at different distances from particles. When small (1 pm) tracer particles were introduced into the flow, their frame-to-frame displacement could be used to estimate velocities of streaming motions. When the power of the focused acoustic wave was adjusted to induce near-surface streaming at around 0.1 d s , it was

found that diamond particles of 5-15 pm in diameter could be dislodged and occasionally rolled away. Typical removal events are shown in the companion videotape to Brereton and Bruno [ 5 ] . The relative insensitivity of this effect to distance from the beam focus suggested that streaming might drive this effect. Streaming patterns have been computed by Brereton and Bruno [5] using a decomposition by the method of successive approximations and a spherical model for the acoustic beam, leading to the patterns shown on the right of Fig. 4. This streaming pattern illustrates that, for the conditions of this study, streaming motions along the surface were of comparable velocity as far from the beam focus as 25 pm. Similar patterns were computed for all power densities used in these experiments. By using the streaming velocity to estimate the local power density, estimates of the acoustic forces beyond the acoustic beam could be made. Beyond the beam, the intensity of scattered acoustic radiation would be small and so the radiation pressure and added mass forces were neglected. An upper N. It estimate of the van der Waals adhesion force was 2 x

QI AND BRERETON: MECHANISMS OF REMOVAL OF MICRON-SIZED PARTICLES BY HIGH-FREQUENCY ULTRASONIC WAVES

621

(rm) Fig. 4. Streaming velocity field driven by a focused ultrasonic beam in an axisymmetric cavity model of a water drop. The beam focus is at the 0, 0 coordinate. The accompanying sketch on the left shows the motions observed experimentally.

is conceivable that the actual value is smaller and comparable to a mean Stokes drag force of lo-' N (Table IV). This point is partly verified by the experimental observation that streaming rolls away many particles of this scale. Since diamond particles are clearly not spherical, considerable variability in the ease of removal was observed, and this was thought to be due to the local contact conditions of individual particles. When 1 pm particles were studied under the same experimental conditions, it was not possible to dislodge or roll away any. From the models developed earlier, the upper limit of the adhesive force would be reduced by about five, while the Stokes drag would be lowered by about 10 (third column, Table IV). Thus the Stokes drag may not be sufficient to overcome the adhesion force for particles 1 micron in size under these conditions. In these focused-beam experiments, the acoustic intensity at the surface was believed to be approximately 100 times greater within the beam than beyond it. The acoustic intensity within the beam, at the surface, was deduced from the attenuation of the acoustic signal when it had reached the surface, and the Airy diameter of the beam. The attenuation was found by measuring the power to the transducer, and by observing on an oscilloscope the strength of the acoustic signal reflected back from the surface, through the transducer. By using attenuation properties of water, we assume a 3 dB loss at the surface and reciprocity in attenuation losses in the forward and return directions, the signal strength at the surface could be deduced [4]. The acoustic intensity beyond the beam was estimated from the observed magnitude of the stream velocity. When the power supplied to the transducer was reduced from its removal level by a factor of 10 and the point of focus was repositioned over a particle, an effective increase in local power density experienced by the particle of about 10 was achieved. These power densities relate to the fourth and fifth

columns in Table IV. Under these conditions, particles at the focus could be either manipulated or occasionally dislodged a short distance from the focus. It was possible to manipulate individual particles about their point of contact with the surface through remote translation of the acoustic transducer. This capability is also demonstrated in the companion videotape to Brereton and Bruno [4]. Single particles such as diamond and polystyrene latex particles 2-4 pm in diameter positioned at the beam focus appeared to rotate to align themselves to present the most streamlined shape towards the axis of the acoustic beam. At slightly higher power levels they were swept away from the acoustic axis, beyond the field of observation. Within the beam, the unsteady added-mass force appears to exceed the upper limit on the force of adhesion by several orders of magnitude. However, this force has no component which causes mean displacement. Of the nonlinear forces which would cause mean motion, the radiation pressure force appears to be the greatest and exceeds the estimated adhesion force by a couple of orders of magnitude. Since this force is localized within the beam and would taper off sharply at the beam edges, the observed alignment of particles might be with this radiation pressure field. From the estimates of the magnitudes of acoustic forces, one might expect the radiation pressure force to account for complete removal of particles. However, this force is so localized in the focused beam experiments that additional farfield forces may be necessary to effect complete removal. At the highest power levels possible in the focused beam studies, all visible particles (1-4 pm diamond, 2-4 pm aluminum, 2-6 pm micron polystyrene latex) in the 1 pm-wide path traced by the transducer could be removed, following trajectories almost normal to the acoustic axis. Fig. 5 shows a possible trajectory in this direction. Photographs of the

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IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 42, NO. 4, JULY 1995

Focused Acoustic Wave ( g H z )

Streaming Motions

~~~~~~~~~~~~~~~~~~~~~

Fig. 5. Suggested trajectory for removal by the combined action of the added-mass, radiation pressure, and streaming induced drag forces.

systematic depletion of particle population by this cleaning technique are shown in [5] with video evidence in [4]. In these experiments (the last three columns in Table IV), the dominant forces again appear to be the added-mass and radiation-pressure ones. Since the direction of the primary acoustic waves is towards the surface, the nonlinear Stokes drag and radiation pressure forces are also in this direction. The impenetrability of the surface obviously modifies estimates of these forces, which are for a plane wave acting on a particle in an infinite medium. Nonetheless, they are adequate first approximations and, for the acoustic intensity levels at the beam focus, the corresponding radiation pressure force is large at gigahertz frequencies, and is estimated from (14) as 2x N. It is interesting to note that the amplitude of the oscillatory added mass force, which produces no mean removal effect, is only slightly larger. Thus what are ordinarily thought of as secondary forces appear to play a very significant role in particle removal under gigahertz-frequency excitation. It appears likely that the combination of oscillatory addedmass forces and the mean radiation-pressure forces produces the mechanism of momentary detachment and outward displacement which removes particles by sweeping them away. Off-axis components of radiation-pressureforce arise wherever there is wavefront curvature (i.e., everywhere but at the focus of an acoustic lends without astigmatism). With any typical intensity distribution within the beam (i.e. Gaussian), radiationpressure forces decrease with distance from the acoustic axis, leading to gradients in radiation-pressure force normal to the acoustic axis. When particles interfere with the beam, they are subjected to radiation pressure forces parallel to the acoustic axis, and to axis-normal components, both of which vary around the particle, especially in the vicinity of the beam focus. Solution of around complex particle-acoustic beam interaction is beyond present capabilities. However, unless the acoustic axis coincides with the particle’s axis of symmetry or some other chance symmetries occur, there should exist radiation pressure forces away from the acoustic axis, as well as towards the surface adhesivehepulsive force while forces away from the acoustic axis are opposed by the shear component of the adhesive force. When this can be overcome, there exists a mechanism for mean displacement of particles away from the acoustic axis. When the trajectory given to particles by

these forces has both a surface-normal component and one normal to the acoustic axis, they would follow an outward path, relaxing from their oscillatory motion towards the motion of the streaming field as shown in Fig. 5. When the intensity at the beam focus reached 10’ W/m2, streaming motions were noticeably more vigorous beyond the beam; this may be the reason why complete removal is observed in the near field, rather than particle rotation or manipulation, since the principal forces are otherwise comparable to those discussed in the previous paragraph. While complete removal was seen in near-field observations, when the microscope objective was changed to allow a broader view, it was found that many particles (as many as 50%) reattached after displacement of some 30-50 pm from their original position. It has been shown [4] that this distance is comparable to the scale of the recirculating streaming motions, with reattachment probably taking place at the outermost parts of streaming orbits. This point emphasizes again that particle removal must be viewed as the combined processes of overcoming adhesion forces, lifting particles from surfaces and convecting them away.

VI. CONCLUDING REMARKS By considering orders of magnitude of various forces involved in an ultrasonic cleaning operation, particle removal mechanisms are proposed and compared with experimental results. It appears that removal of particles attached to a plane surface at high-frequency is achieved by the combined effects of added-mass forces and time-independent forces due to radiation pressure and acoustic streaming: the added mass force overcomes the adhesion force instantaneously and mean forces cause particle displacement. In the event that the particle can be forced away from the plane surface momentarily, the effective entrainment of the particle in the streaming flow then determines the path of the particle, because the adhesion force is reduced significantly by the increase of the separation distance. These deductions would be strengthened substantially with corroboration from further experiments, designed to access the sizes of both adhesive and removal forces. The goal of the analysis presented here is to identify the particle removal mechanism during an ultrasonic cleaning operation and provide guidance for more detailed investigation of the problem. As can be seen from the work by Goldman et al. [8] and Goren and O’Neill [9], even for Stokes flows and spherical particles, rigorous analysis of the forces on particles becomes complicated if the presence of the plane surface is to be accounted for. However, these analyses strongly suggest that (6)-( 11) evaluate the relevant force to the correct order of magnitude, which is as much as one should expect without more detailed description of individual particle-surface contact conditions. Thus these analyses and experiments lend considerable insight into the mechanisms of particle removal by ultrasonic waves. They provide means for estimating the effectiveness of existing systems for cleaning prescribed highfrequency systems for specific particle-removal tasks.

QI AND BRERETON: MECHANISMS OF REMOVAL OF MICRON-SIZED PARTICLES BY HIGH-FREQUENCY ULTRASONIC WAVES

ACKNOWLEDGMENT John G. Harris, Robert E. Johnson, and William D. O’Brien are thanked for fruitful discussions. REFERENCES

S. Bhattacharya, and K. L. Mittal, “Mechanics of removing glass particulates from a solid surface,” Sur$ Technol., vol. 7, pp. 413-425, 1978. R. A. Bowling, “An analysis of particle adhesion on semiconductor surfaces,” J. Electrochem. Assoc., vol. 132, pp. 2208-2214, 1985. R. A. Bowling, “A theoretical review of particle adhesion,” in Particles on Surjiace-Detection, Adhesion, and Removal, K. L. Mittal, Ed. New York Plenum Press, 1988. G. J. Brereton and B. A. Bruno, “Manipulation and removal of micron particles by focused acoustic waves,” Int. video J. Eng. Res., vol. 2, no. 3, 1992. G. J. Brereton and B. A. Bruno, “Particles removal by focused ultrasound,” J. Sound and vibration, vol. 173, no. 5, p. 683, 1994. D. A. Drew, “The lift force on a small sphere in the presence of a wall,’’ Chem. Eng. Sci., vol. 43, no. 4, pp. 769-773, 1988. T. L. Geers, and M. Hasheminejad, “Linear analysis of an ultrasonic cleaning problem,” J. Acoust. Soc. Amer., vol. 29, no. 4, p. 669, 1991. A. J. Goldman, R. G. Cox, and H. Brenner, “Slow viscous motion of sphere parallel to a plane wall-I1 Couette flow,” Chem. Eng. Sei., vol. 22, pp. 653-660, 1967. S. Goren and M. E. O’Neill, “On the hydrodynamic resistance to a particle of a dilute suspension when in the neighborhood of a large obstacle,” Chem. Eng. Sei., vol. 26, pp. 325-338, 1971. J. Israelachvili, Intermolecular and Surface Forces. London: Academic Press, 1992. S. Kim and C. J. Lawrence, “Suspension mechanics for particle contamination control,” Chem. Eng. Sei., vol. 43, pp. 991-1016, 1988. L. V. King, “On the acoustic radiation pressure on spheres,” in Proc. R. Soc. London, Ser. A, vol. 147, p. 212, 1934. H. Krupp, “Particle adhesion theory and experiment,” Advances in Colloid and Inte&ce Sei., vol. 2, pp. 111-239, May 1967. I. I. Kashkoush and A. A. Busnaina, “Recent developments in submicrometer particle removal,” in Particles on Surfaces 4 , K. Mittal, Ed. New York: Plenum, 1993. L. D. Laudau and E. M. Lifshitz, Fluid Mechanics. Oxford: Pergamon, 1987. D. Leighton and A. Acrivos, “The lift on a small sphere touching a plane in the presence of a simple shear flow,” J. Applied Math and Phys., vol. 36, pp. 174178, 1985. K. L. Mittal, Ed., Particles on Surface-Detection, Adhesion, and Removnl. New York: Plenum Press, 1988.

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[I81 W. L. M. Nyborg, “Acoustic streaming,” in Physical Acoustics, W. P. Mason, Ed. New York: Academic Press, 1965, vol. 11-Part B, pp. 265-33 1. [19] L. G. Olson, “Finite element model for ultrasonic cleaning,” J. Sound and vibration, vol. 126, p. 387, 1988. [20] Q. Qi, “The effect of compressibility on acoustic streaming for a plane travelling waves near a rigid boundary,” J. Acoust. Soc. Amer., vol. 94, no. 2, pp. 109G1098, 1993. [21] M. B. Ranade, “Adhesion and removal of fine particles on surfaces,” Aerosol Sei. and Technol., vol. 7, pp. 161-176, 1987. [22] S. Shwartzman and A. Mayer, “Megasonic particle removal from solidstate wafers,” RCA Rev., vol. 46, pp. 81-105, 1985. [23] D. Tabor, Gases, Liquids, and Solids and Other States of Matter. New York: Cambridge. [24] T. L. Tolt and D. L. Feke, “Separation of dispersed phases from liquids in acoustically driven chambers,” Chem. Eng. Sei., vol. 48, pp. 527-540, 1993. [25] K. Yosioka and Y. Kawasima, “Acoustic radiation pressure on a compressible sphere,” Acustica, vol. 5, pp. 167-173, 1995.

Quan Qi, for photograph and biography, see p. 36 of the January issue of this TRANSACTIONS.

Giles J. Brereton was awarded the BSc. in Mechanical Engineenng at Imperial College, University of London, in 1980. He subsequently earned the M.S. in Mechanical Engineering at Stanford University, in 1983, and completed the Ph.D. degree in expenmental turbulence research at Stanford in 1987. He joined the faculty of the University of Michigan in 1987, where he is an Assistant Professor. His interests in unsteady fluid mechanics have grown to include research into internal combustion engine emissions, nonlinear acoustics, optical diagnostics techniques, and measurement and modeling of unsteady turbulent flows. Dr. Brereton is a Member of the American Physical Society and the Amencan Society of Mechanical Engineers, and is faculty advisor to the ASME student section at the University of Michigan. He received the Silver Medal of the Royal Society of A r t s in 1980 and was a Fulbright scholar in 1981.