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Vibroacoustic characteristics of ultrasonic cleaners
Applied Acoustics 58 (1999) 211±228
Vibroacoustic characteristics of ultrasonic cleaners Jin O. Kim a,*, Sunghoon Choi, Jung Ho Kim b a
Department of Mechanical Engineering, Soongsil University, 1-1 Sangdo 5-dong, Dongjak-gu, Seoul 156-743, South Korea b Supercomputing Lab., Samsung Advanced Institute of Technology, PO Box 111, Suwon 440-600, South Korea Received 6 November 1997; received in revised form 12 March 1998; accepted 8 July 1998
Abstract Two kinds of ultrasonic cleaners have been considered in this paper. One is operated at 28 kHz and its cleaning mechanism relies mostly on the cavitation in a cleaning liquid. The other is operated at 1 MHz and its cleaning mechanism relies on the high-frequency acceleration in the liquid. Since the cleaning performance of each type depends on the magnitude of the acoustic ®eld in the liquid of the cleaner, the wave propagation has been calculated by considering the high-frequency vibration of the exciting plate and the transmission of the ultrasound into the cleaning liquid. Based on the vibroacoustic characteristics obtained analytically and numerically, the optimal arrangement of each cleaner has been suggested in order to improve the quality of cleaning. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Ultrasonic cleaning is an ecient method removing unwanted particles from an object by exerting mechanical oscillations of high frequency. Ultrasonic cleaners used in manufacturing lines are mostly composed of an electrical oscillator and a mechanical vibrator. The mechanical vibrator, whose transducers transform an electrical oscillation signal into a mechanical vibration, is submerged in or attached to a cleaning tank which contains a cleaning liquid. The object to be cleaned is immersed in the cleaning liquid. The cleaning mechanisms are based on the high-frequency acceleration and the cavitation in a cleaning liquid. The ultrasonic cleaner operated at the frequency range of several decade kHz relies mostly on the cavitation mechanism [1]. This * Corresponding author. Tel.:+82-2-820-0662; fax:+82-2-820-0668; e-mail: [email protected] 0003-682X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S000 3-682X(98)0003 9-5
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kind of ultrasonic cleaner is suitable for removing dirty particles of several microns, and is used, for example, for the cleaning of shadow masks, which are parts of the Brown tubes. Meanwhile, the cleaner removing much smaller particles, such as 1 mm or less, and preventing cavitation damage is operated at much higher frequency, say around 1 MHz. This kind of cleaner relies on the high-frequency acceleration force [1±5] and is used for example for the cleaning of photo masks or silicon wafers in the semiconductor production. The ultrasonic cleaner operated at 28 kHz is shown in Fig. 1(a). The high-frequency vibration of the excited plate radiates ultrasonic waves into the cleaning liquid. Ultrasonic cavitation causes repetition of compression and expansion of micro-bubbles in the liquid and the explosion of the bubbles makes gap in the material to be cleaned. Finally the greasy or dirty material is separated from the object to be cleaned. The cavitation depends on the magnitude of the acoustic pressure level [6]. A two-dimensional ®nite-element analysis of the plate vibration and acoustic ®eld in the cleaning tank was reported for this kind of cleaner [7].
Fig. 1. Cross-sectional diagram of ultrasonic cleaners; (a) 28 kHz-range cleaner, (b) 1 MHz-range cleaner with an inner container.
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The ultrasonic cleaner operated at 1 MHz is sometimes called a megasonic cleaner [3,4]. As shown in Fig. 1(b), cleaning is performed in an ultrasonically-excited liquid contained in a double-structured container, whose inner container is made of a nonmetallic material such as fused quartz or Pyrex glass so as to isolate the cleaning object from metallic ions. Ultrasonic waves generated by piezoelectric transducers propagate in the outer container and are transmitted through the inner container. The cleaning performance is directly aected by the sound power in the inner container. The bottom of the inner container is inclined to make oblique incidence of the ultrasonic wave in order to raise the eciency of the wave transmission through the bottom plate [5]. This paper deals with the kHz-range and MHz-range ultrasonic cleaners, and calculates the magnitude of the acoustic ®eld in the cleaning liquid, which directly aect the cleaning quality. For the kHz-range cleaner, the acoustic pressure distribution in the liquid, resulted from the vibration of the excited plate, is calculated analytically and numerically and measured by an ultrasonic meter including a hydrophone. For the MHz-range cleaner, the wave transmission through the bottom plate in the inner container is calculated analytically by considering the interactions of the waves in the elastic plate and the liquids in contact with the plate, and calculated numerically by combining the ®nite element analysis of the vibration of the inner container and the boundary element analysis of the acoustic pressure ®eld in the cleaning liquid. Based on the calculated vibroacoustic characteristics, the optimal arrangement of each cleaner is suggested in order to improve the quality of cleaning. 2. KHz-range ultrasonic cleaner Cavitation, the cleaning mechanism of the kHz-range ultrasonic cleaner, occurs according to the magnitude of the sound pressure in the liquid. The acoustic pressure distribution in the cleaning liquid of the ultrasonic cleaner shown in Fig. 1(a) is established by the combination of the waves radiated from the vibrating plate and the waves re¯ected at the other side, which is a free surface or a rigid wall. 2.1. Theoretical prediction The acoustic pressure p r; t caused by the wave propagation in a non-viscous compressible ¯uid is governed by the following wave equation. r2 p ÿ
1 @2 p 0 c2 @t2
1
where r and t are respectively the space and time coordinates, r2 is Laplacian, and c is wave speed. If the acoustic pressure p r; t is a sinusoidal function of time, it can be expressed as p r; t P rexp i!t. The wave propagation in the cleaning liquid can be simpli®ed into two cases as shown in Fig. 2. One is the re¯ection of the
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Fig. 2. One-dimensional model of plane wave propagation; (a) free-surface re¯ection, (b) rigid-wall re¯ection.
ultrasonic waves at the free surface of the cleaning liquid as shown in Fig. 2(a), and the other is the re¯ection at the rigid wall as shown in Fig. 2(b). For the case of free-surface re¯ection, where one side at x=0 is excited by a sinusoidal pressure p 0; t P0 exp i!t and the other side at x ` is free, the solution of Eq. (1) satisfying boundary conditions P 0 P0 and P ` 0 is as follows: p x; t
P0 sin k ` ÿ x exp i!t sin k`
2
where k !=c 2=l is the wavenumber. On the other hand, for the case of rigidwall re¯ection, where the side at x ` is rigid, the solution of Eq. (1) satisfying the boundary conditions P 0 P0 and dP=dx ` 0 is as follows: p x; t
P0 cos k ` ÿ x exp i!t cos k`
3
Since exp i!t in Eqs. (2) and (3) represents the variation from -1 to +1, the magnitude of the acoustic pressure expressed by Eqs. (2) and (3) consists of the standing waves of sinusoidal (or cosinusoidal) curve shown in Fig. 2(a) and (b). The maximum (or zero) magnitude of the acoustic pressure appears repeatedly with equal distance. Even though these analytical solutions have the shortcomings of onedimensional approximation, they allow physical interpretation of the acoustic ®eld in the cleaning liquid. 2.2. Numerical analysis The vibrating plate of the cleaner is located in a cleaning tank as shown in Fig. 1(a), and the one-dimensional analysis of Section 2.1 is not sucient to evaluate the acoustic pressure distribution in the cleaning liquid. Thus the wave equation has been solved by numerical analysis. In this paper, the acoustic ®eld has been obtained
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by the boundary element method, and a commercial software SYSNOISE has been used. The single-frequency vibration of the plate, excited by the arrayed transducers, has been considered as uniform over the area. The calculated results are the acoustic pressure distribution in the space of the cleaning tank, but the distribution in a vertical symmetric plane is shown in Fig. 3(a), where the acoustic pressure is close to zero at the free surface and the extreme acoustic pressure appears repeatedly with equal distance. The period of the repetition is 28 mm, that is the half wavelength. This coincides with the trend predicted from one-dimensional analysis, shown in Fig. 2(a). In order to examine the eect of the object to be cleaned on the acoustic ®eld, a glass plate has been located vertically and the similar analysis has been performed. The result is shown in Fig. 3(b), which shows the similar pattern to Fig. 3(a). For the case that the vibrating body is installed on one side-wall and the ultrasonic wave is re¯ected at the other side-wall, the calculated acoustic pressure distribution is shown in Fig. 3(c). The extreme acoustic pressure appears repeatedly with the distance of half wavelength from the wall. This result coincides with the trend predicted from one-dimensional analysis, shown in Fig. 2(b). 2.3. Experimental comparison In order to verify the calculated results, the acoustic pressure distribution in the cleaning liquid has been measured. An experiment has been carried out for the freesurface case. An ultrasonic meter (NTK UTK-30) converts the acoustic pressure sensed by a hydrophone into voltage, and the magnitude is read at a digital voltmeter. The vibration body has been installed on the bottom of the anechoic water tank. Since the length of the hydrophone tip is about 20 mm, the measurement has been performed in the depth of more than 20 mm from the water surface. The acoustic pressure distribution measured on two vertical symmetric planes is shown in Fig. 4. The location of extreme acoustic pressure, shown as dark areas in the ®gure, appears repeatedly with 28 mm period along the depth, which corresponds to half wavelength. The measured results in Fig. 4 are compared with the calculated result in Fig. 3(a). The comparison shows good agreement, and the calculated acoustic pressure distribution is con®rmed as reasonably accurate. 2.4. Discussion Since the cavitation depends on the magnitude of the acoustic pressure, the cleaning quality is good at the location of large acoustic pressure and bad at the location of small acoustic pressure. If the object to be cleaned is ®xed or travels parallel to the vibrating plate, there may exist some portion of bad cleaning. Therefore, it is suggested to make a slope of the travel path relative to the vibrating plate and the total dierence of distance from the plate is half wavelength or larger, as shown in Fig. 5. Eqs. (2) and (3) mean that the magnitude of the acoustic pressure depends on P0 =sin 2`=l or P0 =cos 2`=l. With a cleaner of same power, the magnitude of
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Fig. 3. Calculated acoustic pressure distribution in a vertical symmetric plane in a cleaning liquid; (a) free-surface re¯ection, (b) free-surface re¯ection and a glass plate to be cleaned, (c) rigid-wall re¯ection.
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Fig. 4(a). Measured acoustic pressure distribution on two vertical symmetric planes in the cleaning liquid with free surface; (a) major-axis plane, (b) minor-axis plane.
the acoustic pressure is dierent according to the distance between the vibrating plate and the re¯ection plane. In the case of free-surface re¯ection, the distance ` which satis®es sin 2`=l 0 is even number times 1/4 wavelength, i.e. integer times half wavelength. In the rigid-wall case, the distance ` satisfying cos 2`=l 0 is odd number times 1/4 wavelength. 3. MHz-range ultrasonic cleaner The magnitude of the ultrasonic acceleration, i.e. the cleaning mechanism of the MHz-range ultrasonic cleaner, is related to the magnitude of the sound power in the liquid. The sound power in the cleaning liquid of the ultrasonic cleaner shown in Fig. 1(b) depends on the transmission of the ultrasonic waves through the inner container.
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Fig. 4(b). Measured acoustic pressure distribution on two vertical symmetric planes in the cleaning liquid with free surface; (a) major-axis plane, (b) minor-axis plane.
3.1. Theoretical prediction The transmission and re¯ection of the plane waves incident obliquely on the in®nite plate immersed in liquids as shown in Fig. 6 can be described in terms of the scalar potential and one component of the vector potential of the displacements [8,9]. The components u and w of the particle displacements in the x- and z-axis directions respectively are expressed as u
@ @ ÿ @x @z
4
w
@ @ @z @x
5
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Fig. 5. Suggestion of vibrating plate arrangements to improve the performance of the ultrasonic cleaning; (a) free-surface re¯ection, (b) rigid-wall re¯ection.
in the elastic plate. The normal stress z and shear stress xz are expressed as 2 2 @ @2 @ @2 2 z l @x2 @z2 @z2 @x@z
xz 2
@2 @2 @2 2ÿ 2 @x@z @x @z
where l and are Lame constants. The potentials and dimensional wave equations.
6
7
satisfy the following two-
@2 @2 1 @2 @x2 @z2 c2L @t2
8
@2 @2 1 @2 @x2 @z2 c2T @t2
9
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Fig. 6. Schematic diagram of the transmission and re¯ection of obliquely-incident plane waves on a plate.
where cL l 2=1=2 and cT =1=2 are the velocities of longitudinal and transverse waves, respectively, and is the mass density of the plate. For the angular frequency ! and wave velocities cL and cT , the wavenumbers kL !=cL and kT !=cT are used for later derivation. The wave in the elastic plate, which is called Lamb wave, has the solution of the following form. As cosh qz Ba sinh qz expi kx ÿ !t
10
Ca cosh sz Ds sinh sz expi kx ÿ !t
11
where As ; Ba ; Ca ; Ds are arbitrary constants and q2 k2 ÿ k2L 1=2 ; s2 k2 ÿ k2T 1=2 . The plane wave in a liquid can be expressed in terms of the scalar potential only. The incident wave potential 1 , re¯ected wave potential R , and transmitted wave potential T , which satisfy the wave equation [Eq. (8)], have the solutions of the following forms. 1 1 expik1 sin 1 x ÿ cos 1 z ÿ i!t
12
R R expik1 sin 1 x cos 1 z ÿ i!t
13
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T T expik2 sin 2 x ÿ cos 2 z ÿ i!t
221
14
where k1 !=c1 ; k2 !=c2 , and c1 and c2 are respectively the velocities of the acoustic waves in liquid 1 and liquid 2 of Fig. 6. In a liquid i i=1, 2) the acoustic pressure is p ÿi !2 ; where i is the mass density of ¯uid i, and the displacements are u @ j@x and w @ j@z. At the interfaces (z d) between the elastic plate and the non-viscous liquids, the normal component of the displacement is continuous. At the interfaces the normal component of the stress z is equivalent to the acoustic pressure and the shear stress xz is zero. Introducing Eqs. (10) and (14) into six boundary conditions, three at z ÿd and three at z d, yields the following matrix equation. 2
H11 6 H21 6 6 H31 6 6 H41 6 4 H51 H61
H12 H22 H32 H42 H52 H62
H13 H23 H33 H43 H53 H63
H14 H24 H34 H44 H54 H64
H15 H25 H35 H45 H55 H65
9 8 9 38 H16 > As > ik1 cos 1 exp ÿik1 cos 1 1 > > > > > > > > > > > Ba > > > H26 7 0 > > > > > > > 7> < = < = 7 0 H36 7 Ca 7 0 H46 7> > Ds > > > > > > > > > > > ÿ 1 =k21 exp ÿik1 cos 1 1 > H56 5> R > > > > > > > > > : ; : ; H66 T 0
15
where the elements Hij of the 66 matrix [H] are written in the Appendix. The amplitude of the transmitted wave T can be calculated relative to the amplitude of the incident wave I from Eq. (15). The transmission ratio of the elastic waves propagating from a liquid through a plate into another liquid is de®ned as jT =I j. As shown in Eq. (15), the transmission ratio depends on the plate thickness and the oblique angle of the incident wave as well as on the material properties of the media and the wave frequency. In this research the frequency of the elastic wave generated in the cleaner is 1 MHz. The material of the inner container is fused quartz, and the material properties of the plate are mass density =2,200 kg/m3, longitudinal wave speed cL =5,900 m/s, and transverse wave speed cT =3,750 m/s [10]. The liquid in the region of the incident wave, i.e. in the outer container, is pure water and the liquid in the region of the transmitted wave, i.e. in the inner container, is a solution of pure water including small amount of chemicals. The mass density and wave speed measured at 40 C as described in Section 3.3 are 1 =983 kg/m3 and c1 =1,530 m/s in the pure water and 2 =985 kg/m3 and c2 =1,530 m/s in the cleaning liquid, respectively. Transmission ratio has been calculated with Eq. (15) for various plate thickness and wave incidence angle, and the results are shown in Fig. 7, which displays the transmission ratio of an incident wave through an inclined plate as a function of the incident angle for several plate thickness. Each curve in Fig. 7 shows peaks at several values of the incident angle. This result is consistent with the experimental observation [11]. This phenomenon, the transmission characteristics of the wave through a plate of ®nite thickness, can be explained in terms of the dispersion of Lamb wave speed, which depends on the plate thickness and the frequency [9]. Since the wave frequency of 1 MHz is ®xed, only the eect of the various thickness is considered below.
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Fig. 7. Transmission ratio of an incident wave through an inclined plate as a function of the incident angle for several plate thickness.
Lamb waves, which propagate along a plate and have motion components in the directions of surface normal and wave propagation, are aected by the adjacent liquids in case the plate is immersed in liquid media as shown in Fig. 6. Such waves are called leaky Lamb waves because of the leakage of wave energy into the liquid. Leaky Lamb waves are described by Eq. (15) with I 0 and the characteristic equation is obtained when the determinant of matrix [H] is set equal to zero. The solutions of the characteristic equation represent symmetric modes s0 ; s1 ; s2 ; . . . and antisymmetric modes a0 ; a1 ; a2 ; . . . ; and the wavelength of each mode can be found. The continuity of the wave motion at the interface between the plate and the liquid implies that the displacement components of the plate and the liquid in the surface normal direction are equal to each other. Thus the wavelength l2 of the elastic wave excited by the incidence of the wave from the liquid is determined by the wavelength l1 in the liquid and the incident angle 1 as shown in Fig. 8 with the relation l2 l1 =sin1 . As the l2 value approaches the wavelength of a leaky Lamb wave mode, the incident wave generates the elastic wave in the plate eciently. As the incident angle decreases, the higher mode of the larger wave speed is excited since the l2 value increases. The ®rst peak from the right of each curve in Fig. 7 corresponds to the fundamental antisymmetric mode a0 and the second and third peaks correspond to s0 and a1 modes, respectively. Each curve has dierent locations of the peaks because the dispersion characteristic of the Lamb waves is aected by the plate thickness also.
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Fig. 8. Relation between the incident waves in the liquid and the waves generated in the plate.
3.2. Numerical analysis The analysis carried out in the previous section is valid for an in®nite plate. The geometry of the inner container of the ultrasonic cleaner is not simple enough to use a theoretical approach. As shown in Fig. 1(b) the bottom plate of the inner container is ®nite and the side walls may interact with the propagating waves. Therefore, the validity of the theoretical results in the previous section for the realistic shape of the ultrasonic cleaner shown in Fig. 1(b) must be veri®ed numerically. It is assumed that the ultrasonic waves generated at the bottom of the outer container by the transducers are plane waves and that there is no variation in the direction normal to the cross-section shown in Fig. 1(b). Thus two-dimensional analysis is good enough in this case. Since the motion of the plate is interacting with the motion of the adjacent liquids at both sides, a coupled analysis of the plate vibration and the liquid oscillation is necessary. Usually the ®nite element method (FEM) and the boundary element method (BEM) are used as convenient and powerful numerical schemes. A fully coupled analysis, which calculates the vibration of the container and the wave propagation in the liquid simultaneously, requires too many elements and too large computer capacity to be handled in the current hardware and software. Therefore, a one-way coupled analysis has been adopted for the numerical analysis as described below. First of all, the vibration of the inner container excited by the incident plane waves has been calculated by using a commercial FEM software, ANSYS. The thickness of the bottom and walls of the inner container is 4 mm. The element size of the numerical model does not exceed 0.40 mm, which is less than 1/6 of the wavelength 3.75 mm of the transverse wave in fused quartz, the material of the inner container, in order to guarantee an accurate numerical analysis. The side walls of the inner container are almost not aected by the incident wave in the liquid of the outer container, and have been modeled as line elements with the boundary conditions of zero displacements. The excitation on the bottom plate of the inner container by the incident wave has been considered as external forces of a sinusoidal function. The
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magnitude and direction of the displacements at each nodal points of the bottom elements have been calculated by frequency±response analysis. This result is used in the acoustic analysis for the sound pressure distribution in the liquid in the inner container. The acoustic ®eld in the liquid of the inner container has been calculated by using a commercial BEM software, SYSNOISE. The element size of the boundary element model has been made not exceed 0.25 mm, which is about 1/6 of the wavelength of 1 MHz waves in water, in order to assure the accuracy of the numerical analysis. The conditions of the boundaries contacting with the inner container have been given from the calculated results of the container vibration. The free surface of the top face of the liquid, which requires zero acoustic pressure, has been conditioned by a suciently large value of admittance (105 m2s/kg) because the displacement boundary condition is not compatible with the pressure boundary condition in the direct BEM option of SYSNOISE. The bottom face has been conditioned by the vibration velocities converted from the displacements component normal to the bottom face. The material properties of the liquid are those of ¯uid B mentioned in Section 3.3. The sound pressure distribution in the cleaning liquid of the inner container has been calculated by the procedure described above. The transmitted wave does not establish a standing wave ®eld but a traveling wave ®eld because of the inclination of the bottom plate of the inner container. The existence of the object in the cleaning liquid makes changes in the pattern of the sound pressure distribution but does not alter the overall level of the sound pressure. The meaning of the numerical analysis of the sound pressure distribution is explained below. By calculating the sound pressure distribution in the cleaning liquid of the inner container, the transmission ratio of the wave through the bottom plate of the inner container has been obtained in terms of sound power transmission. The sound power transmitted through the bottom plate of the inner container has been calculated by integrating the sound intensity over the area of the inclined bottom face. This calculation has been carried out by using the contribution analysis module of SYSNOISE, and the sound power P over the area S is given as follows. P
1 Repv dS 2
16
S
where p and v are the acoustic pressure and the particle velocity normal to the bottom face and (*) means complex conjugate. By taking S to be the bottom plate of the boundary element model the sound power calculated by Eq. (16) represents the wave energy transmitted through the bottom plate into the cleaning liquid during a unit time. The calculated sound power in the liquid of 40 C is displayed as a function of the inclined angle in Fig. 9. This result, obtained for the realistic ®nite region, is not identical to the theoretical curve in Fig. 7, which was obtained for the ideal in®nite region. Both results, however, show a similar trend to each other. The best angle of the bottom inclination can be found from the result of Fig. 9.
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Fig. 9. Radiated power of the wave transmitted through a 4-mm-thick bottom plate of the inner container into the cleaning liquid as a function of the inclined angle at 40 C.
3.3. Discussion The transmission of the ultrasonic wave is aected not only by the geometric and material parameters of the plate but also by the mass density and wave speed in the adjacent liquids of the incident wave region and the transmitted wave region. The mass density and wave speed in the liquid are dependent on the temperature and the chemical ratio of the solution. The liquid in the region of the incident wave region, i.e. in the outer container, is pure water and the liquid in the region of the transmitted wave region, i.e. in the inner container, is a chemical solution of water including small amount of ammonia and hydrogen peroxide to promote the cleaning process chemically. The wave speed has been measured for four kinds of liquids, such as pure water, liquids A, B, and C, at various temperatures, ranging from 20 to 60 C, approximately 10 C apart. The liquids A, B, and C are composed of water (more than 90 vol%), hydrogen peroxide (less than 10%), and a small amount of ammonia. The ratio of ammonia content in the liquids A, B, and C are 1:2.5:5. The wave speed has been obtained by measuring the time-of-¯ight of a pulse echo in each liquid. The mass density has been measured by the conventional method of measuring the mass and volume. If the inclined angle of the bottom plate is ®xed and not easy to change, the another way to raise up the wave transmission is to change the liquid temperature. The dierence in the wave speed due to the temperature change of 40 C is about 50 m/s. Meanwhile, the dierence of the wave speed for the variation of the chemical composition in the cleaning liquid is within 5 m/s, and thus its eect on the transmission ratio is relatively negligible. The transmission of the wave incident from pure water and propagating through the plate into the liquid B has been
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Fig. 10. Transmission ratio of an incident wave through the plate of 4 mm thickness at several liquid temperatures.
Fig. 11. Radiated power of the wave transmitted through a 4-mm-thick bottom plate of the inner container into the cleaning liquid as a function of the liquid temperature at 24 inclination.
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calculated for the temperatures 20, 40, 60 C of the liquid by the procedure of Section 3.1, and the results are displayed in Fig. 10 as a function of the incident angle. It appears from Fig. 10 that 50 m/s dierence in the wave speed yields 2o dierence in the incident angle yielding maximum transmission ratio. Another result shown in Fig. 11 is the variation of the sound power calculated by the procedure of Section 3.2 as a function of the liquid temperature at a ®xed inclination angle 24o. From this result it is possible to select the liquid temperature which allows the maximum transmission of the wave through the bottom plate of a ®xed inclination angle. 4. Conclusion The vibroacoustic characteristics of the kHz-range and MHz-range ultrasonic cleaners have been calculated analytically and numerically. For the kHz-range cleaner, it has been shown that the acoustic ®eld is stationary by the standing wave, and the arrangement of the vibrating plate and the traveling path of the cleaning object have been suggested to improve the quality of cleaning. For the MHz ultrasonic cleaner, it has been shown that the transmission of the sound power through the bottom plate of the inner container is aected by the plate thickness and inclination as well as the liquid temperature, and the optimal condition for the maximum cleaning performance has been found in terms of several parameters, such as the thickness and inclined angle of the bottom plate of the inner container at a constant temperature of the cleaning liquid and the temperature of the cleaning liquid at the given thickness and inclined angle of the bottom plate. Appendix The elements Hij of the 66 matrix [H] in Eq. (15) are as follows. H12=H22=q cosh(qd) H11=ÿH21=q sinh(qd) H14=ÿH24=ik sinh(sd) H13=H23=ik cosh(sd) H16=H56=0 H15=ÿik1 cos1 exp(ik1 cos1 ) H26=ÿik2 cosq2 exp(ik2 cos2 ) H25=H65=0 H31=ÿH41=-(k2 s2 ) cosh(sd) H32=H42=2ikq cosh(qd) H33=H43=ÿ(k2 s2 ) cosh(sd) H34=ÿH44=ÿ(k2 s2 ) sinh(qd) H45=H46=0 H35=H36=0 H52=ÿH62=(k2 s2 ) sinh(qd) H51=H61=(k2 s2 ) cosh(qd) H53=ÿH63=2iks sinh(sd) H54=H64=2iks cosh(sd) H66=ÿ(r2/r)k2T exp(ik2 cosy2) H55=ÿ(1 =)k2T exp(ik1 cosy1) References [1] Morita K. Ultrasonic Cleaning, Kindai Henshu Ltd, Tokyo, 1989 (in Japanese). [2] Qi Q, Brereton GJ. Mechanisms of removal of micron-sized particles by high-frequency ultrasonic waves. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 1995;42(4):619±29.
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[3] Busnaina AA, Kashkoush II, Gale GW. An experimental study of megasonic cleaning of silicon wafers. Journal of the Electrochemical Society 1995;142(8):2812±7. [4] Mayer A, Shwartzman S. Megasonic cleaning: A new cleaning and drying system for use in semiconductor processing. Journal of Electronic Materials 1979;8(6):855±64. [5] Hatano H, Kanai S. High-frequency ultrasonic cleaning tank utilizing oblique incidence. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 1996;43(4):531±5. [6] Flynn HG. Physics of acoustic cavitation in liquids. In: Physical Acoustics, vol. 1B. New York: Academic Press, 1964, (Chapter 9). [7] Ando E, Kagawa Y. Finite element simulation for the design of an ultrasonic cleaning tank. Transactions of the Japanese Institute of Electronics and Communications Engineering 1988;J71A(5):1079±90 (in Japanese). [8] Achenbach JD. Wave Propagation in Elastic Solids. Amsterdam: North-Holland Publishing, 1975, 220±6. [9] Viktorov IA. Rayleigh and Lamb Waves. New York. Plenum Press 1967;67±83:117±21. [10] Weast RC, Astle MJ, Beyer WH. CRC Handbook of Chemistry and Physics, 68th ed. Florida: CRC Press, 1988, F58. [11] Sanders FH. Transmission of sound through thin plates. Canadian Journal of Research 1939;17(9):179±93.
Vibroacoustic characteristics of ultrasonic cleaners Jin O. Kim a,*, Sunghoon Choi, Jung Ho Kim b a
Department of Mechanical Engineering, Soongsil University, 1-1 Sangdo 5-dong, Dongjak-gu, Seoul 156-743, South Korea b Supercomputing Lab., Samsung Advanced Institute of Technology, PO Box 111, Suwon 440-600, South Korea Received 6 November 1997; received in revised form 12 March 1998; accepted 8 July 1998
Abstract Two kinds of ultrasonic cleaners have been considered in this paper. One is operated at 28 kHz and its cleaning mechanism relies mostly on the cavitation in a cleaning liquid. The other is operated at 1 MHz and its cleaning mechanism relies on the high-frequency acceleration in the liquid. Since the cleaning performance of each type depends on the magnitude of the acoustic ®eld in the liquid of the cleaner, the wave propagation has been calculated by considering the high-frequency vibration of the exciting plate and the transmission of the ultrasound into the cleaning liquid. Based on the vibroacoustic characteristics obtained analytically and numerically, the optimal arrangement of each cleaner has been suggested in order to improve the quality of cleaning. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Ultrasonic cleaning is an ecient method removing unwanted particles from an object by exerting mechanical oscillations of high frequency. Ultrasonic cleaners used in manufacturing lines are mostly composed of an electrical oscillator and a mechanical vibrator. The mechanical vibrator, whose transducers transform an electrical oscillation signal into a mechanical vibration, is submerged in or attached to a cleaning tank which contains a cleaning liquid. The object to be cleaned is immersed in the cleaning liquid. The cleaning mechanisms are based on the high-frequency acceleration and the cavitation in a cleaning liquid. The ultrasonic cleaner operated at the frequency range of several decade kHz relies mostly on the cavitation mechanism [1]. This * Corresponding author. Tel.:+82-2-820-0662; fax:+82-2-820-0668; e-mail: [email protected] 0003-682X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S000 3-682X(98)0003 9-5
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kind of ultrasonic cleaner is suitable for removing dirty particles of several microns, and is used, for example, for the cleaning of shadow masks, which are parts of the Brown tubes. Meanwhile, the cleaner removing much smaller particles, such as 1 mm or less, and preventing cavitation damage is operated at much higher frequency, say around 1 MHz. This kind of cleaner relies on the high-frequency acceleration force [1±5] and is used for example for the cleaning of photo masks or silicon wafers in the semiconductor production. The ultrasonic cleaner operated at 28 kHz is shown in Fig. 1(a). The high-frequency vibration of the excited plate radiates ultrasonic waves into the cleaning liquid. Ultrasonic cavitation causes repetition of compression and expansion of micro-bubbles in the liquid and the explosion of the bubbles makes gap in the material to be cleaned. Finally the greasy or dirty material is separated from the object to be cleaned. The cavitation depends on the magnitude of the acoustic pressure level [6]. A two-dimensional ®nite-element analysis of the plate vibration and acoustic ®eld in the cleaning tank was reported for this kind of cleaner [7].
Fig. 1. Cross-sectional diagram of ultrasonic cleaners; (a) 28 kHz-range cleaner, (b) 1 MHz-range cleaner with an inner container.
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The ultrasonic cleaner operated at 1 MHz is sometimes called a megasonic cleaner [3,4]. As shown in Fig. 1(b), cleaning is performed in an ultrasonically-excited liquid contained in a double-structured container, whose inner container is made of a nonmetallic material such as fused quartz or Pyrex glass so as to isolate the cleaning object from metallic ions. Ultrasonic waves generated by piezoelectric transducers propagate in the outer container and are transmitted through the inner container. The cleaning performance is directly aected by the sound power in the inner container. The bottom of the inner container is inclined to make oblique incidence of the ultrasonic wave in order to raise the eciency of the wave transmission through the bottom plate [5]. This paper deals with the kHz-range and MHz-range ultrasonic cleaners, and calculates the magnitude of the acoustic ®eld in the cleaning liquid, which directly aect the cleaning quality. For the kHz-range cleaner, the acoustic pressure distribution in the liquid, resulted from the vibration of the excited plate, is calculated analytically and numerically and measured by an ultrasonic meter including a hydrophone. For the MHz-range cleaner, the wave transmission through the bottom plate in the inner container is calculated analytically by considering the interactions of the waves in the elastic plate and the liquids in contact with the plate, and calculated numerically by combining the ®nite element analysis of the vibration of the inner container and the boundary element analysis of the acoustic pressure ®eld in the cleaning liquid. Based on the calculated vibroacoustic characteristics, the optimal arrangement of each cleaner is suggested in order to improve the quality of cleaning. 2. KHz-range ultrasonic cleaner Cavitation, the cleaning mechanism of the kHz-range ultrasonic cleaner, occurs according to the magnitude of the sound pressure in the liquid. The acoustic pressure distribution in the cleaning liquid of the ultrasonic cleaner shown in Fig. 1(a) is established by the combination of the waves radiated from the vibrating plate and the waves re¯ected at the other side, which is a free surface or a rigid wall. 2.1. Theoretical prediction The acoustic pressure p r; t caused by the wave propagation in a non-viscous compressible ¯uid is governed by the following wave equation. r2 p ÿ
1 @2 p 0 c2 @t2
1
where r and t are respectively the space and time coordinates, r2 is Laplacian, and c is wave speed. If the acoustic pressure p r; t is a sinusoidal function of time, it can be expressed as p r; t P rexp i!t. The wave propagation in the cleaning liquid can be simpli®ed into two cases as shown in Fig. 2. One is the re¯ection of the
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Fig. 2. One-dimensional model of plane wave propagation; (a) free-surface re¯ection, (b) rigid-wall re¯ection.
ultrasonic waves at the free surface of the cleaning liquid as shown in Fig. 2(a), and the other is the re¯ection at the rigid wall as shown in Fig. 2(b). For the case of free-surface re¯ection, where one side at x=0 is excited by a sinusoidal pressure p 0; t P0 exp i!t and the other side at x ` is free, the solution of Eq. (1) satisfying boundary conditions P 0 P0 and P ` 0 is as follows: p x; t
P0 sin k ` ÿ x exp i!t sin k`
2
where k !=c 2=l is the wavenumber. On the other hand, for the case of rigidwall re¯ection, where the side at x ` is rigid, the solution of Eq. (1) satisfying the boundary conditions P 0 P0 and dP=dx ` 0 is as follows: p x; t
P0 cos k ` ÿ x exp i!t cos k`
3
Since exp i!t in Eqs. (2) and (3) represents the variation from -1 to +1, the magnitude of the acoustic pressure expressed by Eqs. (2) and (3) consists of the standing waves of sinusoidal (or cosinusoidal) curve shown in Fig. 2(a) and (b). The maximum (or zero) magnitude of the acoustic pressure appears repeatedly with equal distance. Even though these analytical solutions have the shortcomings of onedimensional approximation, they allow physical interpretation of the acoustic ®eld in the cleaning liquid. 2.2. Numerical analysis The vibrating plate of the cleaner is located in a cleaning tank as shown in Fig. 1(a), and the one-dimensional analysis of Section 2.1 is not sucient to evaluate the acoustic pressure distribution in the cleaning liquid. Thus the wave equation has been solved by numerical analysis. In this paper, the acoustic ®eld has been obtained
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by the boundary element method, and a commercial software SYSNOISE has been used. The single-frequency vibration of the plate, excited by the arrayed transducers, has been considered as uniform over the area. The calculated results are the acoustic pressure distribution in the space of the cleaning tank, but the distribution in a vertical symmetric plane is shown in Fig. 3(a), where the acoustic pressure is close to zero at the free surface and the extreme acoustic pressure appears repeatedly with equal distance. The period of the repetition is 28 mm, that is the half wavelength. This coincides with the trend predicted from one-dimensional analysis, shown in Fig. 2(a). In order to examine the eect of the object to be cleaned on the acoustic ®eld, a glass plate has been located vertically and the similar analysis has been performed. The result is shown in Fig. 3(b), which shows the similar pattern to Fig. 3(a). For the case that the vibrating body is installed on one side-wall and the ultrasonic wave is re¯ected at the other side-wall, the calculated acoustic pressure distribution is shown in Fig. 3(c). The extreme acoustic pressure appears repeatedly with the distance of half wavelength from the wall. This result coincides with the trend predicted from one-dimensional analysis, shown in Fig. 2(b). 2.3. Experimental comparison In order to verify the calculated results, the acoustic pressure distribution in the cleaning liquid has been measured. An experiment has been carried out for the freesurface case. An ultrasonic meter (NTK UTK-30) converts the acoustic pressure sensed by a hydrophone into voltage, and the magnitude is read at a digital voltmeter. The vibration body has been installed on the bottom of the anechoic water tank. Since the length of the hydrophone tip is about 20 mm, the measurement has been performed in the depth of more than 20 mm from the water surface. The acoustic pressure distribution measured on two vertical symmetric planes is shown in Fig. 4. The location of extreme acoustic pressure, shown as dark areas in the ®gure, appears repeatedly with 28 mm period along the depth, which corresponds to half wavelength. The measured results in Fig. 4 are compared with the calculated result in Fig. 3(a). The comparison shows good agreement, and the calculated acoustic pressure distribution is con®rmed as reasonably accurate. 2.4. Discussion Since the cavitation depends on the magnitude of the acoustic pressure, the cleaning quality is good at the location of large acoustic pressure and bad at the location of small acoustic pressure. If the object to be cleaned is ®xed or travels parallel to the vibrating plate, there may exist some portion of bad cleaning. Therefore, it is suggested to make a slope of the travel path relative to the vibrating plate and the total dierence of distance from the plate is half wavelength or larger, as shown in Fig. 5. Eqs. (2) and (3) mean that the magnitude of the acoustic pressure depends on P0 =sin 2`=l or P0 =cos 2`=l. With a cleaner of same power, the magnitude of
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Fig. 3. Calculated acoustic pressure distribution in a vertical symmetric plane in a cleaning liquid; (a) free-surface re¯ection, (b) free-surface re¯ection and a glass plate to be cleaned, (c) rigid-wall re¯ection.
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Fig. 4(a). Measured acoustic pressure distribution on two vertical symmetric planes in the cleaning liquid with free surface; (a) major-axis plane, (b) minor-axis plane.
the acoustic pressure is dierent according to the distance between the vibrating plate and the re¯ection plane. In the case of free-surface re¯ection, the distance ` which satis®es sin 2`=l 0 is even number times 1/4 wavelength, i.e. integer times half wavelength. In the rigid-wall case, the distance ` satisfying cos 2`=l 0 is odd number times 1/4 wavelength. 3. MHz-range ultrasonic cleaner The magnitude of the ultrasonic acceleration, i.e. the cleaning mechanism of the MHz-range ultrasonic cleaner, is related to the magnitude of the sound power in the liquid. The sound power in the cleaning liquid of the ultrasonic cleaner shown in Fig. 1(b) depends on the transmission of the ultrasonic waves through the inner container.
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Fig. 4(b). Measured acoustic pressure distribution on two vertical symmetric planes in the cleaning liquid with free surface; (a) major-axis plane, (b) minor-axis plane.
3.1. Theoretical prediction The transmission and re¯ection of the plane waves incident obliquely on the in®nite plate immersed in liquids as shown in Fig. 6 can be described in terms of the scalar potential and one component of the vector potential of the displacements [8,9]. The components u and w of the particle displacements in the x- and z-axis directions respectively are expressed as u
@ @ ÿ @x @z
4
w
@ @ @z @x
5
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Fig. 5. Suggestion of vibrating plate arrangements to improve the performance of the ultrasonic cleaning; (a) free-surface re¯ection, (b) rigid-wall re¯ection.
in the elastic plate. The normal stress z and shear stress xz are expressed as 2 2 @ @2 @ @2 2 z l @x2 @z2 @z2 @x@z
xz 2
@2 @2 @2 2ÿ 2 @x@z @x @z
where l and are Lame constants. The potentials and dimensional wave equations.
6
7
satisfy the following two-
@2 @2 1 @2 @x2 @z2 c2L @t2
8
@2 @2 1 @2 @x2 @z2 c2T @t2
9
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Fig. 6. Schematic diagram of the transmission and re¯ection of obliquely-incident plane waves on a plate.
where cL l 2=1=2 and cT =1=2 are the velocities of longitudinal and transverse waves, respectively, and is the mass density of the plate. For the angular frequency ! and wave velocities cL and cT , the wavenumbers kL !=cL and kT !=cT are used for later derivation. The wave in the elastic plate, which is called Lamb wave, has the solution of the following form. As cosh qz Ba sinh qz expi kx ÿ !t
10
Ca cosh sz Ds sinh sz expi kx ÿ !t
11
where As ; Ba ; Ca ; Ds are arbitrary constants and q2 k2 ÿ k2L 1=2 ; s2 k2 ÿ k2T 1=2 . The plane wave in a liquid can be expressed in terms of the scalar potential only. The incident wave potential 1 , re¯ected wave potential R , and transmitted wave potential T , which satisfy the wave equation [Eq. (8)], have the solutions of the following forms. 1 1 expik1 sin 1 x ÿ cos 1 z ÿ i!t
12
R R expik1 sin 1 x cos 1 z ÿ i!t
13
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T T expik2 sin 2 x ÿ cos 2 z ÿ i!t
221
14
where k1 !=c1 ; k2 !=c2 , and c1 and c2 are respectively the velocities of the acoustic waves in liquid 1 and liquid 2 of Fig. 6. In a liquid i i=1, 2) the acoustic pressure is p ÿi !2 ; where i is the mass density of ¯uid i, and the displacements are u @ j@x and w @ j@z. At the interfaces (z d) between the elastic plate and the non-viscous liquids, the normal component of the displacement is continuous. At the interfaces the normal component of the stress z is equivalent to the acoustic pressure and the shear stress xz is zero. Introducing Eqs. (10) and (14) into six boundary conditions, three at z ÿd and three at z d, yields the following matrix equation. 2
H11 6 H21 6 6 H31 6 6 H41 6 4 H51 H61
H12 H22 H32 H42 H52 H62
H13 H23 H33 H43 H53 H63
H14 H24 H34 H44 H54 H64
H15 H25 H35 H45 H55 H65
9 8 9 38 H16 > As > ik1 cos 1 exp ÿik1 cos 1 1 > > > > > > > > > > > Ba > > > H26 7 0 > > > > > > > 7> < = < = 7 0 H36 7 Ca 7 0 H46 7> > Ds > > > > > > > > > > > ÿ 1 =k21 exp ÿik1 cos 1 1 > H56 5> R > > > > > > > > > : ; : ; H66 T 0
15
where the elements Hij of the 66 matrix [H] are written in the Appendix. The amplitude of the transmitted wave T can be calculated relative to the amplitude of the incident wave I from Eq. (15). The transmission ratio of the elastic waves propagating from a liquid through a plate into another liquid is de®ned as jT =I j. As shown in Eq. (15), the transmission ratio depends on the plate thickness and the oblique angle of the incident wave as well as on the material properties of the media and the wave frequency. In this research the frequency of the elastic wave generated in the cleaner is 1 MHz. The material of the inner container is fused quartz, and the material properties of the plate are mass density =2,200 kg/m3, longitudinal wave speed cL =5,900 m/s, and transverse wave speed cT =3,750 m/s [10]. The liquid in the region of the incident wave, i.e. in the outer container, is pure water and the liquid in the region of the transmitted wave, i.e. in the inner container, is a solution of pure water including small amount of chemicals. The mass density and wave speed measured at 40 C as described in Section 3.3 are 1 =983 kg/m3 and c1 =1,530 m/s in the pure water and 2 =985 kg/m3 and c2 =1,530 m/s in the cleaning liquid, respectively. Transmission ratio has been calculated with Eq. (15) for various plate thickness and wave incidence angle, and the results are shown in Fig. 7, which displays the transmission ratio of an incident wave through an inclined plate as a function of the incident angle for several plate thickness. Each curve in Fig. 7 shows peaks at several values of the incident angle. This result is consistent with the experimental observation [11]. This phenomenon, the transmission characteristics of the wave through a plate of ®nite thickness, can be explained in terms of the dispersion of Lamb wave speed, which depends on the plate thickness and the frequency [9]. Since the wave frequency of 1 MHz is ®xed, only the eect of the various thickness is considered below.
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Fig. 7. Transmission ratio of an incident wave through an inclined plate as a function of the incident angle for several plate thickness.
Lamb waves, which propagate along a plate and have motion components in the directions of surface normal and wave propagation, are aected by the adjacent liquids in case the plate is immersed in liquid media as shown in Fig. 6. Such waves are called leaky Lamb waves because of the leakage of wave energy into the liquid. Leaky Lamb waves are described by Eq. (15) with I 0 and the characteristic equation is obtained when the determinant of matrix [H] is set equal to zero. The solutions of the characteristic equation represent symmetric modes s0 ; s1 ; s2 ; . . . and antisymmetric modes a0 ; a1 ; a2 ; . . . ; and the wavelength of each mode can be found. The continuity of the wave motion at the interface between the plate and the liquid implies that the displacement components of the plate and the liquid in the surface normal direction are equal to each other. Thus the wavelength l2 of the elastic wave excited by the incidence of the wave from the liquid is determined by the wavelength l1 in the liquid and the incident angle 1 as shown in Fig. 8 with the relation l2 l1 =sin1 . As the l2 value approaches the wavelength of a leaky Lamb wave mode, the incident wave generates the elastic wave in the plate eciently. As the incident angle decreases, the higher mode of the larger wave speed is excited since the l2 value increases. The ®rst peak from the right of each curve in Fig. 7 corresponds to the fundamental antisymmetric mode a0 and the second and third peaks correspond to s0 and a1 modes, respectively. Each curve has dierent locations of the peaks because the dispersion characteristic of the Lamb waves is aected by the plate thickness also.
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Fig. 8. Relation between the incident waves in the liquid and the waves generated in the plate.
3.2. Numerical analysis The analysis carried out in the previous section is valid for an in®nite plate. The geometry of the inner container of the ultrasonic cleaner is not simple enough to use a theoretical approach. As shown in Fig. 1(b) the bottom plate of the inner container is ®nite and the side walls may interact with the propagating waves. Therefore, the validity of the theoretical results in the previous section for the realistic shape of the ultrasonic cleaner shown in Fig. 1(b) must be veri®ed numerically. It is assumed that the ultrasonic waves generated at the bottom of the outer container by the transducers are plane waves and that there is no variation in the direction normal to the cross-section shown in Fig. 1(b). Thus two-dimensional analysis is good enough in this case. Since the motion of the plate is interacting with the motion of the adjacent liquids at both sides, a coupled analysis of the plate vibration and the liquid oscillation is necessary. Usually the ®nite element method (FEM) and the boundary element method (BEM) are used as convenient and powerful numerical schemes. A fully coupled analysis, which calculates the vibration of the container and the wave propagation in the liquid simultaneously, requires too many elements and too large computer capacity to be handled in the current hardware and software. Therefore, a one-way coupled analysis has been adopted for the numerical analysis as described below. First of all, the vibration of the inner container excited by the incident plane waves has been calculated by using a commercial FEM software, ANSYS. The thickness of the bottom and walls of the inner container is 4 mm. The element size of the numerical model does not exceed 0.40 mm, which is less than 1/6 of the wavelength 3.75 mm of the transverse wave in fused quartz, the material of the inner container, in order to guarantee an accurate numerical analysis. The side walls of the inner container are almost not aected by the incident wave in the liquid of the outer container, and have been modeled as line elements with the boundary conditions of zero displacements. The excitation on the bottom plate of the inner container by the incident wave has been considered as external forces of a sinusoidal function. The
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magnitude and direction of the displacements at each nodal points of the bottom elements have been calculated by frequency±response analysis. This result is used in the acoustic analysis for the sound pressure distribution in the liquid in the inner container. The acoustic ®eld in the liquid of the inner container has been calculated by using a commercial BEM software, SYSNOISE. The element size of the boundary element model has been made not exceed 0.25 mm, which is about 1/6 of the wavelength of 1 MHz waves in water, in order to assure the accuracy of the numerical analysis. The conditions of the boundaries contacting with the inner container have been given from the calculated results of the container vibration. The free surface of the top face of the liquid, which requires zero acoustic pressure, has been conditioned by a suciently large value of admittance (105 m2s/kg) because the displacement boundary condition is not compatible with the pressure boundary condition in the direct BEM option of SYSNOISE. The bottom face has been conditioned by the vibration velocities converted from the displacements component normal to the bottom face. The material properties of the liquid are those of ¯uid B mentioned in Section 3.3. The sound pressure distribution in the cleaning liquid of the inner container has been calculated by the procedure described above. The transmitted wave does not establish a standing wave ®eld but a traveling wave ®eld because of the inclination of the bottom plate of the inner container. The existence of the object in the cleaning liquid makes changes in the pattern of the sound pressure distribution but does not alter the overall level of the sound pressure. The meaning of the numerical analysis of the sound pressure distribution is explained below. By calculating the sound pressure distribution in the cleaning liquid of the inner container, the transmission ratio of the wave through the bottom plate of the inner container has been obtained in terms of sound power transmission. The sound power transmitted through the bottom plate of the inner container has been calculated by integrating the sound intensity over the area of the inclined bottom face. This calculation has been carried out by using the contribution analysis module of SYSNOISE, and the sound power P over the area S is given as follows. P
1 Repv dS 2
16
S
where p and v are the acoustic pressure and the particle velocity normal to the bottom face and (*) means complex conjugate. By taking S to be the bottom plate of the boundary element model the sound power calculated by Eq. (16) represents the wave energy transmitted through the bottom plate into the cleaning liquid during a unit time. The calculated sound power in the liquid of 40 C is displayed as a function of the inclined angle in Fig. 9. This result, obtained for the realistic ®nite region, is not identical to the theoretical curve in Fig. 7, which was obtained for the ideal in®nite region. Both results, however, show a similar trend to each other. The best angle of the bottom inclination can be found from the result of Fig. 9.
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Fig. 9. Radiated power of the wave transmitted through a 4-mm-thick bottom plate of the inner container into the cleaning liquid as a function of the inclined angle at 40 C.
3.3. Discussion The transmission of the ultrasonic wave is aected not only by the geometric and material parameters of the plate but also by the mass density and wave speed in the adjacent liquids of the incident wave region and the transmitted wave region. The mass density and wave speed in the liquid are dependent on the temperature and the chemical ratio of the solution. The liquid in the region of the incident wave region, i.e. in the outer container, is pure water and the liquid in the region of the transmitted wave region, i.e. in the inner container, is a chemical solution of water including small amount of ammonia and hydrogen peroxide to promote the cleaning process chemically. The wave speed has been measured for four kinds of liquids, such as pure water, liquids A, B, and C, at various temperatures, ranging from 20 to 60 C, approximately 10 C apart. The liquids A, B, and C are composed of water (more than 90 vol%), hydrogen peroxide (less than 10%), and a small amount of ammonia. The ratio of ammonia content in the liquids A, B, and C are 1:2.5:5. The wave speed has been obtained by measuring the time-of-¯ight of a pulse echo in each liquid. The mass density has been measured by the conventional method of measuring the mass and volume. If the inclined angle of the bottom plate is ®xed and not easy to change, the another way to raise up the wave transmission is to change the liquid temperature. The dierence in the wave speed due to the temperature change of 40 C is about 50 m/s. Meanwhile, the dierence of the wave speed for the variation of the chemical composition in the cleaning liquid is within 5 m/s, and thus its eect on the transmission ratio is relatively negligible. The transmission of the wave incident from pure water and propagating through the plate into the liquid B has been
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Fig. 10. Transmission ratio of an incident wave through the plate of 4 mm thickness at several liquid temperatures.
Fig. 11. Radiated power of the wave transmitted through a 4-mm-thick bottom plate of the inner container into the cleaning liquid as a function of the liquid temperature at 24 inclination.
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calculated for the temperatures 20, 40, 60 C of the liquid by the procedure of Section 3.1, and the results are displayed in Fig. 10 as a function of the incident angle. It appears from Fig. 10 that 50 m/s dierence in the wave speed yields 2o dierence in the incident angle yielding maximum transmission ratio. Another result shown in Fig. 11 is the variation of the sound power calculated by the procedure of Section 3.2 as a function of the liquid temperature at a ®xed inclination angle 24o. From this result it is possible to select the liquid temperature which allows the maximum transmission of the wave through the bottom plate of a ®xed inclination angle. 4. Conclusion The vibroacoustic characteristics of the kHz-range and MHz-range ultrasonic cleaners have been calculated analytically and numerically. For the kHz-range cleaner, it has been shown that the acoustic ®eld is stationary by the standing wave, and the arrangement of the vibrating plate and the traveling path of the cleaning object have been suggested to improve the quality of cleaning. For the MHz ultrasonic cleaner, it has been shown that the transmission of the sound power through the bottom plate of the inner container is aected by the plate thickness and inclination as well as the liquid temperature, and the optimal condition for the maximum cleaning performance has been found in terms of several parameters, such as the thickness and inclined angle of the bottom plate of the inner container at a constant temperature of the cleaning liquid and the temperature of the cleaning liquid at the given thickness and inclined angle of the bottom plate. Appendix The elements Hij of the 66 matrix [H] in Eq. (15) are as follows. H12=H22=q cosh(qd) H11=ÿH21=q sinh(qd) H14=ÿH24=ik sinh(sd) H13=H23=ik cosh(sd) H16=H56=0 H15=ÿik1 cos1 exp(ik1 cos1 ) H26=ÿik2 cosq2 exp(ik2 cos2 ) H25=H65=0 H31=ÿH41=-(k2 s2 ) cosh(sd) H32=H42=2ikq cosh(qd) H33=H43=ÿ(k2 s2 ) cosh(sd) H34=ÿH44=ÿ(k2 s2 ) sinh(qd) H45=H46=0 H35=H36=0 H52=ÿH62=(k2 s2 ) sinh(qd) H51=H61=(k2 s2 ) cosh(qd) H53=ÿH63=2iks sinh(sd) H54=H64=2iks cosh(sd) H66=ÿ(r2/r)k2T exp(ik2 cosy2) H55=ÿ(1 =)k2T exp(ik1 cosy1) References [1] Morita K. Ultrasonic Cleaning, Kindai Henshu Ltd, Tokyo, 1989 (in Japanese). [2] Qi Q, Brereton GJ. Mechanisms of removal of micron-sized particles by high-frequency ultrasonic waves. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 1995;42(4):619±29.
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[3] Busnaina AA, Kashkoush II, Gale GW. An experimental study of megasonic cleaning of silicon wafers. Journal of the Electrochemical Society 1995;142(8):2812±7. [4] Mayer A, Shwartzman S. Megasonic cleaning: A new cleaning and drying system for use in semiconductor processing. Journal of Electronic Materials 1979;8(6):855±64. [5] Hatano H, Kanai S. High-frequency ultrasonic cleaning tank utilizing oblique incidence. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 1996;43(4):531±5. [6] Flynn HG. Physics of acoustic cavitation in liquids. In: Physical Acoustics, vol. 1B. New York: Academic Press, 1964, (Chapter 9). [7] Ando E, Kagawa Y. Finite element simulation for the design of an ultrasonic cleaning tank. Transactions of the Japanese Institute of Electronics and Communications Engineering 1988;J71A(5):1079±90 (in Japanese). [8] Achenbach JD. Wave Propagation in Elastic Solids. Amsterdam: North-Holland Publishing, 1975, 220±6. [9] Viktorov IA. Rayleigh and Lamb Waves. New York. Plenum Press 1967;67±83:117±21. [10] Weast RC, Astle MJ, Beyer WH. CRC Handbook of Chemistry and Physics, 68th ed. Florida: CRC Press, 1988, F58. [11] Sanders FH. Transmission of sound through thin plates. Canadian Journal of Research 1939;17(9):179±93.