Ultrasonics 56 (2015) 530–538
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Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Contribution of ultrasonic traveling wave to chemical–mechanical polishing Li Liang a,⇑, He Qing b, Zheng Mian a, Liu Zheng b a b
College of Science, Liaoning University of Technology, Liaoning 121001, China Institute of Vibration Engineering, Liaoning University of Technology, Liaoning 121001, China
a r t i c l e
i n f o
Article history: Received 10 February 2014 Received in revised form 8 June 2014 Accepted 3 October 2014 Available online 13 October 2014 Keywords: Ultrasonic Vibrator Chemical–mechanical polishing Silicon wafer Morphology
a b s t r a c t The ultrasonic vibrators are introduced into the chemical–mechanical polishing devices, and in this polishing system, the ultrasonic vibrators generate ultrasonic traveling wave and keep coaxial with the polished silicon wafer rotating at given speed so as to compare the texture of the polished silicon wafers. And the experiments on the chemical–mechanical polishing with assisted ultrasonic vibration are accomplished in order to investigate the effect of the ultrasonic vibration on the chemical–mechanical polishing. Via comparing the roughness average of the two silicon wafers polished with assisted ultrasonic vibration and without assisted vibration, it is found that the morphology of the silicon wafer polished with assisted vibration is superior to that without assisted vibration, that is, this series of experiments indicate that the ultrasonic vibration is beneficial to the chemical–mechanical polishing. Aiming at understanding the contribution of the ultrasonic vibration to chemical–mechanical polishing in detail, the model of the chemical–mechanical polishing with the assisted ultrasonic vibration is built up, which establishes the relationship of the removal rate and the polishing variables such as the rotary speed of silicon wafers, the amplitude and the frequency of vibrators, the particle density of polishing slurry and the characteristics of polishing pad etc. This model not only could be used to explain the experimental results but also to illuminate the roles played by the polishing variables. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The chemical–mechanical polishing is a physicochemical process used to make wafer surfaces locally and globally flat [1]. It can be regarded as a hybrid of chemical etching and free abrasive polishing. With the development of semiconductor technology, it has been accepted wildly [2], and as the rising of ultra large scale integration chips in recent years, it gains ever increasing attentions [3] and appears to be the only available method for global planarization [4,5]. In order to widen the application area and lower the manufacturing cost of chemical–mechanical polishing, many scholars have made efforts to research this polishing technology experimentally and theoretically [6–11], to date, it is also the point at issue [4,12]. Generally, in process of chemical–mechanical polishing, the slurry with abrasive particles suspending makes the surface of the polished object produce chemical change and the relative ⇑ Corresponding author at: Liaoning University of Technology, 169 Shiying Street, Guta District, Jinzhou, Liaoning 121001, China. Tel.: +86 416 4199830. E-mail addresses: [email protected] (L. Li), [email protected] (Q. He), [email protected] (M. Zheng), [email protected] (Z. Liu). http://dx.doi.org/10.1016/j.ultras.2014.10.006 0041-624X/Ó 2014 Elsevier B.V. All rights reserved.
movement between the polishing pad and the surface of the polished object also makes the abrasive particles grind the surface of the object [13]. These two processes are the main mechanism of the chemical–mechanical polishing. Thus, the variables describing this system roughly consist of the following four categories, namely, tool process parameters, wafer variables, slurry variables and pad variables. The tool process parameters include pressure applied to the wafer and pad, relative speed between wafer and pad, polishing time, etc; the wafer variables refer to film type and pattern density; the slurry variables involve chemistry, particle size, and other properties; and the pad variables are hardness, roughness, and other properties of the pad [14]. The further development of the chemical–mechanical polishing requires an insight into the roles played by these parameters in the polishing process, which is still ongoing work at this moment [4,12] and also the aim of this paper. The engineering application of ultrasonic technology arose in 1920s [15], it is the synthesis technology consisting of the electric technique, measurement technique, mechanical vibration and material science etc [15]. It has been attempted for many years to introduce the ultrasonic technology into the process of the hard and brittle material’s planarization [16–19]. The early ultrasonic machining mostly relies on the ultrasonic vibration of the
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instrument which makes the suspending abrasive particles gain sufficient energy to impact the polishing object aiming at removing the rougher part of the surface. But the efficiency of this type of technology is very low. In recent years, a type of advanced instrument combining the vibration of ultrasonic frequency and the rotation at high speed of 1000–5000 r s1 came into being, which have been wildly applied in the areas of aviation and atomic energy [16,17]. Then more and more technologies of the ultrasonic combined machining emerge in response to the need of times, which are regarded as the most effective method to machine the hard and brittle material and rapidly become a research hotspot [20,21]. The chemical–mechanical polishing with ultrasonic vibration assisted discussed in this paper just belongs to this type of technology. As a promising polishing technology, the chemical–mechanical polishing with ultrasonic vibration assisted has become an important subject of many researchers and be applied to the polishing of silicon wafer, copper and sapphire and so on [22–25]. However, at present the effects of the ultrasonic vibration on the polishing process are still being discussing on basis of the experimental researches, and there is not an exhaustive theory to analyze the roles played by the ultrasonic vibration in the chemical–mechanical polishing so far. In this paper, the experiments of chemical– mechanical polishing with assisted ultrasonic vibration is analyzed, and the roughness average of the silicon wafers polished with assisted ultrasonic vibration was compared with that without assisted vibration so as to investigate the role played by the ultrasonic vibration. In addition, the contribution of the ultrasonic vibration to the chemical–mechanical polishing is also theoretically analyzed in detail, and it is found that the theoretical results qualitatively agree with the experimental results.
2. Experiments 2.1. Experimental devices
to
Aim at investigating the contribution of the ultrasonic vibration the chemical–mechanical polishing, the author’s team
Precise grinding and polishing machine
conducted a series of polishing experiments. In these experiments, the ultrasonic vibrators are introduced into the chemical–mechanical polishing system. The polishing effect with assisted ultrasonic vibration was compared with that without assisted vibration, so as to analyze the role of the ultrasonic vibration in the chemical– mechanical polishing. The polishing experiments were accomplished on the precise grinding and polishing machine UNIPOL-802, as shown in Fig. 1. During polishing, the silicon wafer fixed on the platen rotates synchronously with the platen, and the polishing pad adheres to the working face of vibrator which generates ultrasonic traveling wave without macroscopic rotation and swing. The polishing slurry is injected into the area between the silicon wafer and the polishing pad in advance, and further injected into the polishing pad in the process of the polishing experiment. The gravity of the vibrator and the weights serves as the polishing normal force, which can be precisely measured. Considering that the polishing pad and the vibrator must not rotate freely due to high-frequency voltage loaded on the vibrator, three clamps are used to ensure that vibrator don’t rotate and swing. The axis of the vibrator approximately coincides with the axis of the silicon wafer in order to compare the polishing texture of the corresponding area. The other conditions of these experiments are listed in Table 1. 2.2. Experimental results The first experiment is conducted to investigate the polishing effect varying with the measured sites. In this experiment, the vibrator is shown as Vibrator I in Fig. 1, which has a diameter of 0.02 m and could generate a traveling wave composed by a series of second-order bending vibrations and a series of first-order longitudinal vibrations. During experiment, the input voltage is 100 V, the frequency is 27.99 kHz, the polishing normal force is 8.212 N, the rotary speed is 60 r min1 and the polishing time is 4 min. The morphology of the silicon wafers polished with assisted ultrasonic vibration and without vibration is both measured by NV5000 5022S 3-D surface profiler, and the schematic diagram of the measured sites is shown in Fig. 2. The effective measurement
Vibrator II
Vibrator I Normal Force
Vibrator Polishing pad Polishing Pad
Vibrator
Silicon wafer
Fig. 1. The photos and schematic diagrams of the experimental devices.
Slurry
Platen
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Table 1 The conditions of experiments. Parameters
Polishing pad
Polyurethane polishing pad with application of gum, 0.5 mm in thickness CMP slurry for UPP/SS010 silicon material, PH = 10–12, SiO2 particles with the diameter 60–80 nm 70 mL/min 24 °C
Polishing slurry Slurry supply Temperature
0.7
without assisted ultrasonic vibration with assisted ultrasonic vibration
0.6 0.5
Ra (µm)
Item
0.4 0.3 0.2 0.1 0.0
1
2 3 4 5 The ordinal of the measured sites
6
7
Fig. 4. The experimental values of Ra varying with the measured sites. The results were directly measured by NV5000 5022S 3-D surface profiler of which the step height accuracy is not more than 0.75% and the vertical resolution is up to 0.1 nm.
Fig. 2. The schematic diagram of measured sites on the polished silicon wafer.
area of every measured site is the rectangle with 1.79 mm in length and 1.34 mm in width, the central measured site is exhibited by 3D morphological picture in Fig. 3. From Fig. 3, it is easy to see that the polishing effect of the silicon wafer polished with assisted ultrasonic vibration is superior to that without assisted vibration. Furthermore, the roughness average Ra of the measured sites is represented by the curves in Fig. 4. It is clear that the roughness average of the silicon wafer polished with assisted ultrasonic vibration is lower than that without vibration; and the former is more uniform than the latter, which indicates that the flatness of the silicon wafer polished with assisted ultrasonic vibration is better than that without assisted vibration. Another experiment was also accomplished to study the contribution of the ultrasonic vibration to the polishing effect when the rotary speed of the silicon wafers changes. The ultrasonic vibrator of this experiment has an outer diameter of 30 mm, and the width of its teeth is 5.1 mm, as is shown by Vibrator II in Fig. 1. This vibrator could generate a rotary traveling wave. During polishing, the input voltage is 15 V, the frequency is 50 kHz, the polishing time is 5 min and the polishing normal force is 5.223 N. And the experimental results measured by JB-4C surface roughometer are represented by the curves in Fig. 5. From Fig. 5 it is found that the
positive effect of the ultrasonic vibration keeps obvious all the time with the rotary speeds varying. To sum up, the conclusion could be drawn that the ultrasonic vibration has a positive effect on the chemical–mechanical polishing. In addition, it must be pointed out that these experiments just qualitatively indicate that the ultrasonic vibration is helpful for the chemical–mechanical polishing, and it is difficult to obtain the accurate quantitative results due to the randomness of the morphology of the silicon wafer and the uncontrollability of the experimental conditions. 3. Methods and theories The experimental results indicate that the ultrasonic traveling wave has positive effect on the chemical–mechanical polishing when the silicon wafer rotates relative to the polishing pad. But the current experiments cannot quantitatively explain the mechanism of improvement of the polishing effect. In order to understand the contribution of the ultrasonic traveling wave, a theoretical model is proposed in this section. 3.1. Effective polishing particles The polishing pads are usually made of some soft material with a large number of open or closed cells and its surface consists of lots of open cells and the relative flat area, shown as Fig. 6. Under the action of the external normal pressure, the relative flat area sufficiently makes contact with surface of the silicon wafer and
Fig. 3. The 3-D morphology of the central sites of the polished silicon wafers; (a) the silicon wafer polished without assisted vibration; (b) the silicon wafer polished with assisted ultrasonic vibration.
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0.38 0.36 0.34 0.32
Ra (µm)
0.30 0.28 0.26 0.24 0.22 0.20
with assisted ultrasonic vibration without assisted ultrasonic vibration
0.18 0.16 60
70
80 90 100 Rotary speed (r min-1)
110
120
Fig. 5. The measured values of Ra changing with rotary speed of the silicon wafer. The measured site is 12 mm away from the center of the silicon wafer. The results were directly measured by JB-4C surface roughometer of which the indication error is ±5% and the resolution is 1 nm.
polishing particle is defined as the effective polishing particle from the time instant when it come into the contact area between the pad’s flat area and the silicon wafer until it leaves this contact area. Since a large number of cells are randomly distributed on the surface of the polishing pad, the polishing particles always come into the contact area from a certain cells and then leave this area and come into another cell. Thus, an effective polishing particle must come into being at the edge of some cell and annihilate at the edge of the other cell. Because the effective polishing particles are sandwiched between the polishing pad and the silicon wafer during contact polishing, the thickness of the thin film of the slurry should approach the diameter of the polishing particles. Hence, if the speed of some cell is v relative to the silicon wafer, the number of effective polishing particles generated at its moving leading edge in unit time could be estimated as fellows,
dNðv Þ ¼ 2Rkn
Z
1
jv jdt;
ð1Þ
0
where R the radius of the polishing particles, n the particle number density of the polishing slurry and the integral term is the distance traveled by the considered cell in unit time. If the number of the cells with speed v is M(v), the number of the effective polishing particles generated due to the movement of all the cells with speed v in unit time is given by
Nðv Þ ¼ Mðv Þ2Rkn
Z
1
jv jdt:
ð2Þ
0
Consider that the polished silicon wafer rotates relative to the polishing pad, and the sites with speed v = x0r are distributed in the annulus with radius from r to r + dr. So the number of the cells with speed v could be estimated as
M½v ðrÞ ¼ 2prdr r; Fig. 6. The surface of the polishing pad mentioned in Table 1, (a) the photo, (b) the microscopic photo.
could be regarded as flat area; in addition, those open cells on surface would deform due to the normal pressure. In order to facilitate modeling, the surface of polishing pad under the action of normal pressure is considered as the collection of the open cells scattering on the flat surface, that is to say, the surface of the polishing pad consists of a large number of open cells and the flat area. Generally speaking, the shape of the cells is irregular and the size is also nonuniform [26], which present difficulties in modeling. In this work, the cells on the surface of the pad are further idealized as the columnar cells with the average diameter k and average depth l. During polishing, the thin film of the polishing slurry between the flat area of the pad and the silicon wafer is effective for polishing. Whereas, the open cells and the surface of the polished silicon wafer form many closed cells which is filled up with the polishing slurry and will burst with the increasing internal pressure of the slurry. The slurry in such cells is the good store and necessary complement for the effective slurry of the thin film between the flat area of the pad and the surface of the silicon wafer. Considering that the external polishing pressure is large enough, the flat area of the polishing pad sufficiently touches the surface of silicon wafer and drives the abrasive particles to carry out contact polishing. Whereas if the ultrasonic vibration is not too strong, the impact force upon the silicon wafer of the polishing particles in the slurry of the cells is very small in comparison to the external pressure, so its effects on the polishing could be ignored. That is, only polishing particles, between the flat area of the pad and the silicon wafer, contribute to the polishing. Hereafter, a
ð3Þ
where r is the distance between the measured site and the axis of rotation and r is the areal density of the cells. Hence, Eq. (2) has the following form,
NðrÞ ¼ 2Rkn
Z
1
jv jdt r 2prdr:
ð4Þ
0
Under consideration of the contribution of the ultrasonic vibration v has the following form,
v ¼ x0 r þ Ah x sinðxtÞ;
ð5Þ
where Ah is the amplitude of the displacement in transverse direction, x is angular frequency, x0 is angular speed of the polishing pad, and r is the distance between the measured site and the axis of rotation. Because the velocity in Eq. (5) has a very small period, Eq. (4) could be replaced by
NðrÞ ¼
x 2p
Z
2p
x
jx0 r þ Ah x sinðxtÞjdt 4pRrknrdr:
ð6Þ
0
Obviously, if x0r > Ah x,
NðrÞ ¼ x0 r 4pRrknrdr;
ð7Þ
And if x0r < Ah x,
2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 5
x4 x0 r x0 r x0 r NðrÞ ¼ 4 arcsin þ 4Ah 1 Ah x x Ah x 2p 4pRrknrdr:
ð8Þ
It is easy to understand that N(r) has the same form as Eq. (7) if no assisted vibration.
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then the following equation is obtained, which represents the time evolution of the mass density of the polishing slurry,
3.2. Increment of number of effective polishing particles due to ultrasonic vibration See Fig. 7, the cylindrical coordinate systems is established, of which the origin is on the center of the vibrator. During working, the traveling waves along the transverse direction vibrate in both axial direction and transverse direction in the polishing pad. In that the cells is very small, the velocity of the slurry in such cells could be approximated as
~ v ðr; h; z; tÞ ¼ ~eh Ah x sinðxt kr rh þ /Þ ~ez Az x sinðxt kr rh þ wÞ;
ð9Þ
where r, h, z are coordinates, ~ eh and ~ ez are the unit vectors in transverse direction and axial direction, Ah and Az are the amplitudes of the displacements in transverse direction and axial direction, x is angular frequency, kr is the angular wavenumber changing with radial coordinate r, / and w the initial phases of vibrations in transverse direction and axial direction, t is time. The polishing slurry is considered as the perfect fluid which obeys the equation of continuity as fellows,
@q þ r ðq~ v Þ ¼ 0; @t
ð10Þ
where q is the mass density of polishing slurry. Now only slurry in the small cells is considered and the gradient of mass density of the slurry in such cells could be ignored, hence
dq þ qr ~ v ¼ 0: dt
ð11Þ
So
dq
q
¼ ðr ~ v Þdt:
ð12Þ
qðtÞ
q0
dq
q
Z
t
kr rh
r v dt;
x
ð13Þ
ð14Þ
From Eq. (14), it is clear that the mass density of the slurry in a specific small cell varies with time periodically if divergence r v of the velocity is not zero. As mentioned above, the open cells on the surface of the pad are all very small, so for the points in the considered cell, their coordinates approximate the coordinates (r, h, z) of the center of the cell. Hereafter, (r, h, z) denote the coordinates of the considered cell. Thereby, the maximum and the minimum of the mass density satisfy the following formulae
qmax ¼ q0 e Ah kr ðsin /þ1Þ ;
ð15Þ
qmin ¼ q0 e Ah kr ðsin /1Þ :
ð16Þ
During polishing, it is assumed that the polishing slurry in the cells is always complemented in time, and thus it will expand with mass density decreasing. Considering that the period of the density’s vibration is very small and the shape of the cells has no time to deform, so a part of the expanded slurry will rush out of the cells and into the contact area between the pad’s flat area and the silicon wafer. Thereby in one period, the cells are filled up with the slurry at the instant of q = qmax and the slurry rushes into the contact area from the cells at the instant of q = qmin. And the volume increment of the slurry in the considered cell due to vibration in one period can be calculated by the following formula,
DXðrÞ ¼
Consider that the mass density of the slurry at time instant (krrh/x) equals to the mass density q0 of the slurry under the condition of no vibration, see Eq. (9). Integrate the Eq. (12) from (krrh/x) to the time instant t,
Z
qðtÞ ¼ q0 eðAh kr Þ½sinðxtkr rhþ/Þsinð/Þ :
qmax ðrÞ X X; qmin ðrÞ
ð17Þ
where X is the volume of the cells. The number of effective polishing particles in the slurry with the mass qmaxX is,
NðrÞ ¼
qmax ðrÞ X n; q0
ð18Þ
where n is the particle density of the polishing slurry without vibration. In one period, the increment of the number of the effective polishing particles due to vibration of the slurry in the considered cell could be calculated as,
DXðrÞ q ðrÞX nX½qmax ðrÞ qmin ðrÞ dNðrÞ ¼ q ðrÞX max n¼ :
q0
max
qmin ðrÞ
q0
ð19Þ
And in unit time, the increment of the number of the effective polishing particles due to the vibration of the considered cell could be calculated as fellows,
DNðrÞ ¼ dNðrÞ
x 2p
:
ð20Þ
Thus the increment of the number of the effective polishing particles due to vibration of the cells in the annulus with radius from r to r + dr, could be calculated as fellows,
RDNðrÞ ¼ DNðrÞ 2prdr r ¼ xrXnrðeAh kr ðsin /þ1Þ eAh kr ðsin /1Þ Þ dr;
ð21Þ
where r is the areal density of the cells on the surface of the pad. 3.3. Contribution of an effective polishing particle
Fig. 7. The schematic diagram of the cylindrical coordinates systems.
During polishing, it is the effective polishing particles that make contact with the silicon wafers and carry out the contact polishing. While working, the effective polishing particles are driven by the
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polishing pad to move with the speed v0 relative to the pad. Generally speaking, the speed v0 should be the function of the speed v of the polishing pad relative to the silicon wafer, and roughly increases with the speed v. It is assumed that v0 is proportional to v, as fellows,
v 0 ¼ lv ;
ð22Þ
where Ah is the amplitude of the displacement in transverse direction, x is angular frequency, x0 is angular speed of the polishing pad and r is the distance between the measured site and the axis of rotation. Under consideration of the high-frequency velocity in Eqs. (28), Eq. (27) could be replaced by
xT 2p
where the adjustable coefficient l is determined by the normal pressure and the characteristics of the contact surfaces such as hardness and roughness, in addition the chemical force of the slurry also has an effect upon l. So the speed (v v0 ) of the effective polishing particles relative to the silicon wafer is also the function of the speed v,
Ds ¼ ð1 lÞ
v v 0 ¼ ð1 lÞv :
and if x0r < Ahx,
ð23Þ
And obviously, the average lifetime T of the effective polishing particles is determined by the average space e between the successive cells of the pad and the speed v0 , as fellows,
T¼
e
¼
v0
e : lv
ð24Þ
Consider that the vibration is periodic movement with zero displacement in a period and the average lifetime is related to the displacement, therefore the average lifetime has nothing to do with the low-amplitude and high-frequency vibration. Generally speaking, the polishing particles with the normal pressure lead to the plastic deformation of the polished silicon wafer, as shown in Fig. 8. And in practice, the depth Dd of the plastic pit of the silicon wafer is very small and determined by the normal pressure and the chemical force of the slurry. Thereby, the volume removed by the considered effective polishing particle could be estimated as the following formula,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 V r ¼ Dd R2 ðR DdÞ Ds;
ð25Þ
where Ds is the distance traveled by the polishing particle relative to the polished silicon wafer, Dd is the depth of the plastic pit of the silicon wafer and should be regarded as minim. The higher order minims in Eq. (25) are ignored, then
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V r ¼ Dd 2R Dd Ds:
ð26Þ
According to the analysis above, the relative distance Ds could be calculated as fellows,
Ds ¼
Z
T
jv v 0 jdt ¼ ð1 lÞ
0
Z
2p
x
jx0 r þ Ah x sinðxtÞjdt:
jv jdt:
ð27Þ
0
ð28Þ
ð29Þ
0
Obviously, if x0r > Ahx,
Ds ¼
ð1 lÞe
l
8
Ahx, the volume Vr removed by an effective polishing particle is determined by the normal pressure and the variables of polishing pad and the polishing slurry, and has nothing to do with vibration and rotation, see Eqs. (26) and (30); whereas if x0r < Ahx, Vr has also correlation with Ah, x and x0 besides the normal pressure and the variables of polishing pad and the polishing slurry, see Eqs. (26) and (31). Meanwhile, it must be noted that Eq. (26) makes logical sense only if the polishing time is considerable larger than the average lifetime T of the effective polishing particles. 3.4. Removal rate For the chemical–mechanical polishing with assisted ultrasonic vibration, from Eq. (8) (or Eq. (7)) and Eq. (21), the total number of effective polishing particles in the annulus with radius from r to r + dr in unit time could be calculated as fellows,
Ntot ðrÞ ¼ NðrÞ þ RDNðrÞ:
ð32Þ
Whereas, if no vibration, the total number of effective polishing particles in the annulus with radius from r to r + dr in unit time should be
N0tot ðrÞ ¼ 4pRrknx0 r2 dr:
T
Under consideration of the contribution of the ultrasonic vibration, v has the following form,
v ¼ x0 r þ Ah x sinðxtÞ;
Z
ð33Þ
And the volume Vr removed by one effective polishing particle could be calculated by Eq. (26). And the removal rate of all effective polishing particles in the annulus with radius from r to r + dr in unit time should be
VRRðrÞ ¼ V r Ntot ðrÞ ¼ V r NðrÞ þ V r RDNðrÞ;
ð34Þ
or
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 lÞe VRR0 ðrÞ ¼ N0tot ðrÞ Dd 2R Dd :
l
ð35Þ
And the removal rate per unit area vrr and vrr0 could be calculated as fellows,
vrr ¼
VRRðrÞ ; 2p rdr
vrr0 ¼
Fig. 8. The schematic diagram of the plastic deformation of the silicon wafer caused by the effective polishing particle.
VRR0 ðrÞ : 2prdr
ð36Þ
ð37Þ
Eqs. (34) and (36) represent the removal rate with assisted ultrasonic vibration, and Eqs. (35) and (37) represent the removal rate without assisted ultrasonic vibration. And it should be pointed out that Vr and N(r) in Eq. (34) both have two series of formulae
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Fig. 9. The calculated results of vrr and vrr0 changing with r. The frequency is 27.99 kHz, and x0r > xAh(r).
respectively and should be calculated by different formula under different conditions as analyzed in Sections 3.1 and 3.3. Furthermore, it is obvious that Eqs. (36) and (37) together with Eqs. (7), (8), (21), (26), (30), (31) could expound the roles played by the polishing variables in the polishing process such as amplitudes, angular frequency and rotary speed etc. 4. Theoretical results In order to make theoretical analysis on the polishing effect, in this paper the removal rate vrr and vrr0 are calculated in a normalized unit, #, which is defined as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 l # ¼ rnDd 2R Dd e;
l
ð38Þ
where r is the areal density of the cells on the surface of the polishing pad, n is the particle number density of the slurry, R is the radius of the polishing particles, e is the average space between the successive cells on the surface of the polishing pad, l and Dd are the adjustable coefficient and the depth of the plastic deformation pit. All these variables are determined by the normal pressure and the characteristics of slurry, pad and silicon wafers. It is clear that if the polishing normal force, the polished silicon wafer, the polishing pad and the polishing slurry all keep unchanged, the normalized unit # is constant, and thus the calcu-
lation in such unit could be used to make theoretical analysis on the polishing effect. As mentioned in Section 3.4, vrr should be calculated with two different groups of formulae for x0r > xAh(r) and x0r < xAh(r). More specifically, for x0r > xAh(r), the calculations should use Eqs. (36), (34), (30), (26), (21), (7); whereas for x0r < xAh(r), the calculations should use Eqs. (36), (34), (31), (26), (21), (8). For the experiments of Section 2, the maximum amplitudes of the vibrators are all about a fraction of a micron and decreases along the reverse of radial direction, whereas the amplitudes of vibrations on the surface of polishing pad are smaller than the vibrators’ and approach 107 m, that is, for experiments in Section 2, x0r > xAh(r). Fig. 9 shows the calculated results of vrr and vrr0 changing along the radial direction on the condition of x0r > xAh(r); wherein, Fig. 9(a) is calculated under the same condition as experimental results of Fig. 4. From these calculated curve surfaces of Fig 9, it could be seen that the ultrasonic vibration has a positive effect to the chemical–mechanical polishing; more specifically, the values of vrr and vrr0 both increase with r but the vrr keeps larger than vrr0, and the absolute contribution (vrr–vrr0) keeps constant along the radial direction. Moreover, the ratio of the minimum vrr to maximum vrr in Fig. 9(a) is about 0.8, which is closer to 1 than that of vrr0, and this ratio could be used to represent the uniform degree of removal rate along the radial direction, thus the calculated results of Fig. 9(a) also indicate that the flatness of the
Fig. 10. The calculated results of vrr and vrr0 changing with r. The frequency is 27.99 kHz, and x0r < xAh(r) .
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Fig. 11. The calculated results of vrr and vrr0 changing with Ah x and x0. kr = 100 m1, r = 0.01 m.
silicon wafers polished with assisted ultrasonic vibration should be superior to that without vibration. These calculated results all accord with the experimental results of Fig. 4. Meanwhile, the comparison between Fig. 9(a) and (b) indicates that the polishing effect becomes a little better with the angular speed x0 increasing and the absolute contribution (vrr–vrr0) of the ultrasonic vibration does not change if x0r > xAh(r). Another experiment shown in Fig. 5 of Section 2 aims at investigating the correlation between the polishing effect and the angular speed x0. The experimental results indicate that the polishing effect becomes better with the angular speed x0 increasing under the experimental condition, and it is clear that this experimental result accords with the calculated results of Fig. 9. Fig. 10 shows the calculated results for x0r < xAh(r). From Fig. 10, it is found that, if x0r < xAh(r), the absolute contribution (vrr–vrr0) of ultrasonic vibration does not change with r but decreases with x0. In addition, it can also be seen from Fig. 10 that vrr also becomes smaller if x0 increasing, which indicates that the polishing effect becomes worse with x0 increasing if x0r < xAh(r). Comparing Fig. 9 and Fig. 10, it must be found that the change of the vrr with x0 is nonlinear, and Fig. 11 shows the calculated results of the vrr and vrr0 changing with x0 and xAh. It is clear that the value of vrr is larger than vrr0; to be specific, for x0r > xAh, vrr increases with xAh and vrr0 increases slowly with x0, whereas (vrr-vrr0) hardly changes with x0; whereas for x0r < xAh, the vrr increases with the increasing xAh and the decreasing x0. Therefore, for practical chemical–mechanical polishing, the angular speed x0 must have a reasonable range rather than the bigger the better. On the other hand, it must be noted that the chemical force of the slurry is ignored in these calculation and the difficulties of the polishing slurry rushing into the effective polishing area might increase with x0 decreasing. Thus the angular speed’s unreasonable decreasing might also have negative influence on the polishing effect. So the optimal range of the angular speed x0 needs more accurate experiments to determine. 5. Conclusions The ultrasonic traveling wave generated by the ultrasonic vibrators is combined with the chemical–mechanical polishing aiming at investigating the effect of the ultrasonic vibration on the polishing. The experimental results indicate that the ultrasonic vibration is beneficial to improvement of the morphology of the polished silicon wafer, and the flatness of the silicon wafer polished with assisted ultrasonic vibration is superior to that without assisted vibration. In addition, if the amplitude of vibration is small, the polishing effect increases with rotary speed of the silicon wafer relative to the polishing pad.
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Meanwhile the model of the chemical–mechanical polishing with assisted ultrasonic vibration is established in order to understand the contribution of the ultrasonic vibration to the chemical– mechanical polishing in detail. In this model, the definition of the effective polishing particle is used to establish the relationship between the removal rate and the polishing variables; and the equation of continuity is applied to the polishing slurry to derive the function of the mass density of the slurry changing with time, which could be used to explain the increment of the number of the effective polishing particles due to the ultrasonic vibration, and then to elucidate the effect of the ultrasonic vibration on the polishing. The model not only could be used to analyze the experimental results but also to illuminate the roles played by the polishing variables in detail. The calculated results indicate that the ultrasonic vibration has a positive effect to the polishing effect, and the contribution of the ultrasonic vibration increases with the amplitude and angular frequency of the vibration. Whereas, the role played by rotary speed of silicon wafer relative to the polishing pad is related to the ratio of the line speed of rotation and the amplitude of the vibration velocity, and there is a reasonable range of rotary speed which needs more accurate experiments to determine. Acknowledgement This paper is supported by the National Natural Science Foundation of China (51075195). This support is gratefully acknowledged. References [1] Markus Forsberg. Chemical Mechanical Polishing of Silicon and Silicon Dioxide in Front End Processing. Acta Universitatis Upsaliensis Uppsala, 2004. [2] M.R. Oliver, Chemical–Mechanical Planarization of Semiconductor Materials, Springer-Verlag, Berlin Heideberg, 2004. [3] R. Dejule, CMP challenge below a quarter micron, Semicond. Int. 20 (1997) 54– 60. [4] F.G. Shi, B. Zhao, Modeling of chemical–mechanical polishing with soft pads, Appl. Phys. A 67 (1998) 249–252. [5] P.L. Kuo, C.L. Liao, S.K. Ghosh, Superior chemical–mechanical polishing performance of silica slurry made of surface-active siloxane/acrylic polymers, Colloid Polym. Sci. 279 (2001) 1212–1218. [6] F.W. Preston, The theory and design of plate glass polishing machine, J. Soc. Glass Technol. 11 (44) (1927) 214–256. [7] V.H. Nguyen, F.G. Shi, Modeling of the removal rate in chemical mechanical polishing, Proc. SPIE Int. Soc. Opt. Eng. 4181 (2000) 161–167. [8] G. Fu, A. Chandra, S. Guha, et al., A Plasticity-based model of material removal in chemical–mechanical polishing (CMP), IEEE Trans. Semicond. Manuf. 14 (4) (2001) 406–417. [9] J.F. Luo, D.A. Dornfeld, Effects of abrasive size distribution in chemical mechanical planarization–modeling and verification, IEEE Trans. Semicond. Manuf. 16 (3) (2003) 469–476. [10] S.R. Runnels, I. Kim, J. Schleuter, et al., Modeling tool for chemical–mechanical polishing design and evaluation, IEEE Trans. Semicond. Manuf. 11 (3) (1998) 501–510. [11] D.A. Litton, S.H. Garofalini, Modeling of hydrophilic wafer bonding by molecular dynamics simulations, J. Appl. Phys. 89 (11) (2001) 6013–6023. [12] Toshi Kasai, Bharat Bhushan, Physics and tribology of chemical mechanical planarization, J. Phys.: Condens. Matter 20 (2008). [13] K.H. Park, H.J. Kim, O.M. Chang, H.D. Jeong, Effects of pad properties on material removal in chemical mechanical polishing, J. Mater. Process. Technol. 187–188 (2007) 73–76. [14] J.M. Steigerwald, S.P. Murarka, R.J. Gutmann, Chemical Mechanical Planarization of Microelectronic Materials, J. Wiley, New York, 1997. [15] T.B. Thoe, D.K. Aspinwall, M.L.H. Wise, Review on ultrasonic machining, Int. J. Mech. Tools Manuf. 38 (4) (1988) 239–255. [16] Z.J. Pei, N. Khana, P.M. Ferria, Rotary ultrasonic machining of structural ceramics – a review, Ceram. Eng. Sci. Proc. 16 (1) (1995) 259–278. [17] P. Legge, Machining without abrasive slurry, Ultrasonic 4 (7) (1966) 157–162. [18] P. Legge, Ultrasonic drilling of ceramics, Ind. Diamond Rev. 24 (1964) 20–24. [19] K.I. Ishikawa, H. Suwabe, T. Nishide, A study on combined vibration drilling by ultrasonic and low-frequency vibrations for hard and brittle materials, Prec. Eng. 22 (4) (1998) 196–205. [20] Z.J. Per, P.M. Ferreira, S.G. Kapoor, et al., Rotary ultrasonic machining for face milling of ceramics, Int. J. Mach. Tool Manuf. 35 (7) (1995) 1033–1046. [21] K.P. Rajurkar, Z.Y. Wang, A. Kuppattan, Micro removal of ceramic material (Al203) in the precision ultrasonic machining, Prec. Eng. 23 (1999) 73–78.
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[22] Ming-Yi Tsain, Wei-Zheng Yang, Combined ultrasonic vibration and chemical mechanical polishing of copper substrates, Int. J. Mach. Tools Manuf 53 (2012) 69–76. [23] W.H. Xu, X.C. Lu, G.S. Pan, Y.Z. Lei, J.B. Luo, Ultrasonic flexural vibration assisted chemical mechanical polishing for sapphire substrate, Appl. Surf. Sci. 256 (2010) 3936–3940. [24] Pei-Lum Tso, Yao-Cheng Chang, Study on chemical mechanical polishing with ultrasonic vibration, Adv. Mater. Res. 126–128 (2010) 311–315.
[25] H. Suzuki, S. Hamada, T. Okino, M. Kondo, Y. Yamagata, T. Higuchi, Ultraprecision finishing of micro-aspheric surface by ultrasonic two-axis vibration assisted polishing, CIRP Annals – Manuf. Technol. 59 (2010) 347– 350. [26] John McGrath, Chris Davis, Polishing pad surface characterisation in chemical mechanical planarisation, J. Mater. Process. Technol. 153–154 (2004) 666–673.
Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Contribution of ultrasonic traveling wave to chemical–mechanical polishing Li Liang a,⇑, He Qing b, Zheng Mian a, Liu Zheng b a b
College of Science, Liaoning University of Technology, Liaoning 121001, China Institute of Vibration Engineering, Liaoning University of Technology, Liaoning 121001, China
a r t i c l e
i n f o
Article history: Received 10 February 2014 Received in revised form 8 June 2014 Accepted 3 October 2014 Available online 13 October 2014 Keywords: Ultrasonic Vibrator Chemical–mechanical polishing Silicon wafer Morphology
a b s t r a c t The ultrasonic vibrators are introduced into the chemical–mechanical polishing devices, and in this polishing system, the ultrasonic vibrators generate ultrasonic traveling wave and keep coaxial with the polished silicon wafer rotating at given speed so as to compare the texture of the polished silicon wafers. And the experiments on the chemical–mechanical polishing with assisted ultrasonic vibration are accomplished in order to investigate the effect of the ultrasonic vibration on the chemical–mechanical polishing. Via comparing the roughness average of the two silicon wafers polished with assisted ultrasonic vibration and without assisted vibration, it is found that the morphology of the silicon wafer polished with assisted vibration is superior to that without assisted vibration, that is, this series of experiments indicate that the ultrasonic vibration is beneficial to the chemical–mechanical polishing. Aiming at understanding the contribution of the ultrasonic vibration to chemical–mechanical polishing in detail, the model of the chemical–mechanical polishing with the assisted ultrasonic vibration is built up, which establishes the relationship of the removal rate and the polishing variables such as the rotary speed of silicon wafers, the amplitude and the frequency of vibrators, the particle density of polishing slurry and the characteristics of polishing pad etc. This model not only could be used to explain the experimental results but also to illuminate the roles played by the polishing variables. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The chemical–mechanical polishing is a physicochemical process used to make wafer surfaces locally and globally flat [1]. It can be regarded as a hybrid of chemical etching and free abrasive polishing. With the development of semiconductor technology, it has been accepted wildly [2], and as the rising of ultra large scale integration chips in recent years, it gains ever increasing attentions [3] and appears to be the only available method for global planarization [4,5]. In order to widen the application area and lower the manufacturing cost of chemical–mechanical polishing, many scholars have made efforts to research this polishing technology experimentally and theoretically [6–11], to date, it is also the point at issue [4,12]. Generally, in process of chemical–mechanical polishing, the slurry with abrasive particles suspending makes the surface of the polished object produce chemical change and the relative ⇑ Corresponding author at: Liaoning University of Technology, 169 Shiying Street, Guta District, Jinzhou, Liaoning 121001, China. Tel.: +86 416 4199830. E-mail addresses: [email protected] (L. Li), [email protected] (Q. He), [email protected] (M. Zheng), [email protected] (Z. Liu). http://dx.doi.org/10.1016/j.ultras.2014.10.006 0041-624X/Ó 2014 Elsevier B.V. All rights reserved.
movement between the polishing pad and the surface of the polished object also makes the abrasive particles grind the surface of the object [13]. These two processes are the main mechanism of the chemical–mechanical polishing. Thus, the variables describing this system roughly consist of the following four categories, namely, tool process parameters, wafer variables, slurry variables and pad variables. The tool process parameters include pressure applied to the wafer and pad, relative speed between wafer and pad, polishing time, etc; the wafer variables refer to film type and pattern density; the slurry variables involve chemistry, particle size, and other properties; and the pad variables are hardness, roughness, and other properties of the pad [14]. The further development of the chemical–mechanical polishing requires an insight into the roles played by these parameters in the polishing process, which is still ongoing work at this moment [4,12] and also the aim of this paper. The engineering application of ultrasonic technology arose in 1920s [15], it is the synthesis technology consisting of the electric technique, measurement technique, mechanical vibration and material science etc [15]. It has been attempted for many years to introduce the ultrasonic technology into the process of the hard and brittle material’s planarization [16–19]. The early ultrasonic machining mostly relies on the ultrasonic vibration of the
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instrument which makes the suspending abrasive particles gain sufficient energy to impact the polishing object aiming at removing the rougher part of the surface. But the efficiency of this type of technology is very low. In recent years, a type of advanced instrument combining the vibration of ultrasonic frequency and the rotation at high speed of 1000–5000 r s1 came into being, which have been wildly applied in the areas of aviation and atomic energy [16,17]. Then more and more technologies of the ultrasonic combined machining emerge in response to the need of times, which are regarded as the most effective method to machine the hard and brittle material and rapidly become a research hotspot [20,21]. The chemical–mechanical polishing with ultrasonic vibration assisted discussed in this paper just belongs to this type of technology. As a promising polishing technology, the chemical–mechanical polishing with ultrasonic vibration assisted has become an important subject of many researchers and be applied to the polishing of silicon wafer, copper and sapphire and so on [22–25]. However, at present the effects of the ultrasonic vibration on the polishing process are still being discussing on basis of the experimental researches, and there is not an exhaustive theory to analyze the roles played by the ultrasonic vibration in the chemical–mechanical polishing so far. In this paper, the experiments of chemical– mechanical polishing with assisted ultrasonic vibration is analyzed, and the roughness average of the silicon wafers polished with assisted ultrasonic vibration was compared with that without assisted vibration so as to investigate the role played by the ultrasonic vibration. In addition, the contribution of the ultrasonic vibration to the chemical–mechanical polishing is also theoretically analyzed in detail, and it is found that the theoretical results qualitatively agree with the experimental results.
2. Experiments 2.1. Experimental devices
to
Aim at investigating the contribution of the ultrasonic vibration the chemical–mechanical polishing, the author’s team
Precise grinding and polishing machine
conducted a series of polishing experiments. In these experiments, the ultrasonic vibrators are introduced into the chemical–mechanical polishing system. The polishing effect with assisted ultrasonic vibration was compared with that without assisted vibration, so as to analyze the role of the ultrasonic vibration in the chemical– mechanical polishing. The polishing experiments were accomplished on the precise grinding and polishing machine UNIPOL-802, as shown in Fig. 1. During polishing, the silicon wafer fixed on the platen rotates synchronously with the platen, and the polishing pad adheres to the working face of vibrator which generates ultrasonic traveling wave without macroscopic rotation and swing. The polishing slurry is injected into the area between the silicon wafer and the polishing pad in advance, and further injected into the polishing pad in the process of the polishing experiment. The gravity of the vibrator and the weights serves as the polishing normal force, which can be precisely measured. Considering that the polishing pad and the vibrator must not rotate freely due to high-frequency voltage loaded on the vibrator, three clamps are used to ensure that vibrator don’t rotate and swing. The axis of the vibrator approximately coincides with the axis of the silicon wafer in order to compare the polishing texture of the corresponding area. The other conditions of these experiments are listed in Table 1. 2.2. Experimental results The first experiment is conducted to investigate the polishing effect varying with the measured sites. In this experiment, the vibrator is shown as Vibrator I in Fig. 1, which has a diameter of 0.02 m and could generate a traveling wave composed by a series of second-order bending vibrations and a series of first-order longitudinal vibrations. During experiment, the input voltage is 100 V, the frequency is 27.99 kHz, the polishing normal force is 8.212 N, the rotary speed is 60 r min1 and the polishing time is 4 min. The morphology of the silicon wafers polished with assisted ultrasonic vibration and without vibration is both measured by NV5000 5022S 3-D surface profiler, and the schematic diagram of the measured sites is shown in Fig. 2. The effective measurement
Vibrator II
Vibrator I Normal Force
Vibrator Polishing pad Polishing Pad
Vibrator
Silicon wafer
Fig. 1. The photos and schematic diagrams of the experimental devices.
Slurry
Platen
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Table 1 The conditions of experiments. Parameters
Polishing pad
Polyurethane polishing pad with application of gum, 0.5 mm in thickness CMP slurry for UPP/SS010 silicon material, PH = 10–12, SiO2 particles with the diameter 60–80 nm 70 mL/min 24 °C
Polishing slurry Slurry supply Temperature
0.7
without assisted ultrasonic vibration with assisted ultrasonic vibration
0.6 0.5
Ra (µm)
Item
0.4 0.3 0.2 0.1 0.0
1
2 3 4 5 The ordinal of the measured sites
6
7
Fig. 4. The experimental values of Ra varying with the measured sites. The results were directly measured by NV5000 5022S 3-D surface profiler of which the step height accuracy is not more than 0.75% and the vertical resolution is up to 0.1 nm.
Fig. 2. The schematic diagram of measured sites on the polished silicon wafer.
area of every measured site is the rectangle with 1.79 mm in length and 1.34 mm in width, the central measured site is exhibited by 3D morphological picture in Fig. 3. From Fig. 3, it is easy to see that the polishing effect of the silicon wafer polished with assisted ultrasonic vibration is superior to that without assisted vibration. Furthermore, the roughness average Ra of the measured sites is represented by the curves in Fig. 4. It is clear that the roughness average of the silicon wafer polished with assisted ultrasonic vibration is lower than that without vibration; and the former is more uniform than the latter, which indicates that the flatness of the silicon wafer polished with assisted ultrasonic vibration is better than that without assisted vibration. Another experiment was also accomplished to study the contribution of the ultrasonic vibration to the polishing effect when the rotary speed of the silicon wafers changes. The ultrasonic vibrator of this experiment has an outer diameter of 30 mm, and the width of its teeth is 5.1 mm, as is shown by Vibrator II in Fig. 1. This vibrator could generate a rotary traveling wave. During polishing, the input voltage is 15 V, the frequency is 50 kHz, the polishing time is 5 min and the polishing normal force is 5.223 N. And the experimental results measured by JB-4C surface roughometer are represented by the curves in Fig. 5. From Fig. 5 it is found that the
positive effect of the ultrasonic vibration keeps obvious all the time with the rotary speeds varying. To sum up, the conclusion could be drawn that the ultrasonic vibration has a positive effect on the chemical–mechanical polishing. In addition, it must be pointed out that these experiments just qualitatively indicate that the ultrasonic vibration is helpful for the chemical–mechanical polishing, and it is difficult to obtain the accurate quantitative results due to the randomness of the morphology of the silicon wafer and the uncontrollability of the experimental conditions. 3. Methods and theories The experimental results indicate that the ultrasonic traveling wave has positive effect on the chemical–mechanical polishing when the silicon wafer rotates relative to the polishing pad. But the current experiments cannot quantitatively explain the mechanism of improvement of the polishing effect. In order to understand the contribution of the ultrasonic traveling wave, a theoretical model is proposed in this section. 3.1. Effective polishing particles The polishing pads are usually made of some soft material with a large number of open or closed cells and its surface consists of lots of open cells and the relative flat area, shown as Fig. 6. Under the action of the external normal pressure, the relative flat area sufficiently makes contact with surface of the silicon wafer and
Fig. 3. The 3-D morphology of the central sites of the polished silicon wafers; (a) the silicon wafer polished without assisted vibration; (b) the silicon wafer polished with assisted ultrasonic vibration.
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0.38 0.36 0.34 0.32
Ra (µm)
0.30 0.28 0.26 0.24 0.22 0.20
with assisted ultrasonic vibration without assisted ultrasonic vibration
0.18 0.16 60
70
80 90 100 Rotary speed (r min-1)
110
120
Fig. 5. The measured values of Ra changing with rotary speed of the silicon wafer. The measured site is 12 mm away from the center of the silicon wafer. The results were directly measured by JB-4C surface roughometer of which the indication error is ±5% and the resolution is 1 nm.
polishing particle is defined as the effective polishing particle from the time instant when it come into the contact area between the pad’s flat area and the silicon wafer until it leaves this contact area. Since a large number of cells are randomly distributed on the surface of the polishing pad, the polishing particles always come into the contact area from a certain cells and then leave this area and come into another cell. Thus, an effective polishing particle must come into being at the edge of some cell and annihilate at the edge of the other cell. Because the effective polishing particles are sandwiched between the polishing pad and the silicon wafer during contact polishing, the thickness of the thin film of the slurry should approach the diameter of the polishing particles. Hence, if the speed of some cell is v relative to the silicon wafer, the number of effective polishing particles generated at its moving leading edge in unit time could be estimated as fellows,
dNðv Þ ¼ 2Rkn
Z
1
jv jdt;
ð1Þ
0
where R the radius of the polishing particles, n the particle number density of the polishing slurry and the integral term is the distance traveled by the considered cell in unit time. If the number of the cells with speed v is M(v), the number of the effective polishing particles generated due to the movement of all the cells with speed v in unit time is given by
Nðv Þ ¼ Mðv Þ2Rkn
Z
1
jv jdt:
ð2Þ
0
Consider that the polished silicon wafer rotates relative to the polishing pad, and the sites with speed v = x0r are distributed in the annulus with radius from r to r + dr. So the number of the cells with speed v could be estimated as
M½v ðrÞ ¼ 2prdr r; Fig. 6. The surface of the polishing pad mentioned in Table 1, (a) the photo, (b) the microscopic photo.
could be regarded as flat area; in addition, those open cells on surface would deform due to the normal pressure. In order to facilitate modeling, the surface of polishing pad under the action of normal pressure is considered as the collection of the open cells scattering on the flat surface, that is to say, the surface of the polishing pad consists of a large number of open cells and the flat area. Generally speaking, the shape of the cells is irregular and the size is also nonuniform [26], which present difficulties in modeling. In this work, the cells on the surface of the pad are further idealized as the columnar cells with the average diameter k and average depth l. During polishing, the thin film of the polishing slurry between the flat area of the pad and the silicon wafer is effective for polishing. Whereas, the open cells and the surface of the polished silicon wafer form many closed cells which is filled up with the polishing slurry and will burst with the increasing internal pressure of the slurry. The slurry in such cells is the good store and necessary complement for the effective slurry of the thin film between the flat area of the pad and the surface of the silicon wafer. Considering that the external polishing pressure is large enough, the flat area of the polishing pad sufficiently touches the surface of silicon wafer and drives the abrasive particles to carry out contact polishing. Whereas if the ultrasonic vibration is not too strong, the impact force upon the silicon wafer of the polishing particles in the slurry of the cells is very small in comparison to the external pressure, so its effects on the polishing could be ignored. That is, only polishing particles, between the flat area of the pad and the silicon wafer, contribute to the polishing. Hereafter, a
ð3Þ
where r is the distance between the measured site and the axis of rotation and r is the areal density of the cells. Hence, Eq. (2) has the following form,
NðrÞ ¼ 2Rkn
Z
1
jv jdt r 2prdr:
ð4Þ
0
Under consideration of the contribution of the ultrasonic vibration v has the following form,
v ¼ x0 r þ Ah x sinðxtÞ;
ð5Þ
where Ah is the amplitude of the displacement in transverse direction, x is angular frequency, x0 is angular speed of the polishing pad, and r is the distance between the measured site and the axis of rotation. Because the velocity in Eq. (5) has a very small period, Eq. (4) could be replaced by
NðrÞ ¼
x 2p
Z
2p
x
jx0 r þ Ah x sinðxtÞjdt 4pRrknrdr:
ð6Þ
0
Obviously, if x0r > Ah x,
NðrÞ ¼ x0 r 4pRrknrdr;
ð7Þ
And if x0r < Ah x,
2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 5
x4 x0 r x0 r x0 r NðrÞ ¼ 4 arcsin þ 4Ah 1 Ah x x Ah x 2p 4pRrknrdr:
ð8Þ
It is easy to understand that N(r) has the same form as Eq. (7) if no assisted vibration.
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then the following equation is obtained, which represents the time evolution of the mass density of the polishing slurry,
3.2. Increment of number of effective polishing particles due to ultrasonic vibration See Fig. 7, the cylindrical coordinate systems is established, of which the origin is on the center of the vibrator. During working, the traveling waves along the transverse direction vibrate in both axial direction and transverse direction in the polishing pad. In that the cells is very small, the velocity of the slurry in such cells could be approximated as
~ v ðr; h; z; tÞ ¼ ~eh Ah x sinðxt kr rh þ /Þ ~ez Az x sinðxt kr rh þ wÞ;
ð9Þ
where r, h, z are coordinates, ~ eh and ~ ez are the unit vectors in transverse direction and axial direction, Ah and Az are the amplitudes of the displacements in transverse direction and axial direction, x is angular frequency, kr is the angular wavenumber changing with radial coordinate r, / and w the initial phases of vibrations in transverse direction and axial direction, t is time. The polishing slurry is considered as the perfect fluid which obeys the equation of continuity as fellows,
@q þ r ðq~ v Þ ¼ 0; @t
ð10Þ
where q is the mass density of polishing slurry. Now only slurry in the small cells is considered and the gradient of mass density of the slurry in such cells could be ignored, hence
dq þ qr ~ v ¼ 0: dt
ð11Þ
So
dq
q
¼ ðr ~ v Þdt:
ð12Þ
qðtÞ
q0
dq
q
Z
t
kr rh
r v dt;
x
ð13Þ
ð14Þ
From Eq. (14), it is clear that the mass density of the slurry in a specific small cell varies with time periodically if divergence r v of the velocity is not zero. As mentioned above, the open cells on the surface of the pad are all very small, so for the points in the considered cell, their coordinates approximate the coordinates (r, h, z) of the center of the cell. Hereafter, (r, h, z) denote the coordinates of the considered cell. Thereby, the maximum and the minimum of the mass density satisfy the following formulae
qmax ¼ q0 e Ah kr ðsin /þ1Þ ;
ð15Þ
qmin ¼ q0 e Ah kr ðsin /1Þ :
ð16Þ
During polishing, it is assumed that the polishing slurry in the cells is always complemented in time, and thus it will expand with mass density decreasing. Considering that the period of the density’s vibration is very small and the shape of the cells has no time to deform, so a part of the expanded slurry will rush out of the cells and into the contact area between the pad’s flat area and the silicon wafer. Thereby in one period, the cells are filled up with the slurry at the instant of q = qmax and the slurry rushes into the contact area from the cells at the instant of q = qmin. And the volume increment of the slurry in the considered cell due to vibration in one period can be calculated by the following formula,
DXðrÞ ¼
Consider that the mass density of the slurry at time instant (krrh/x) equals to the mass density q0 of the slurry under the condition of no vibration, see Eq. (9). Integrate the Eq. (12) from (krrh/x) to the time instant t,
Z
qðtÞ ¼ q0 eðAh kr Þ½sinðxtkr rhþ/Þsinð/Þ :
qmax ðrÞ X X; qmin ðrÞ
ð17Þ
where X is the volume of the cells. The number of effective polishing particles in the slurry with the mass qmaxX is,
NðrÞ ¼
qmax ðrÞ X n; q0
ð18Þ
where n is the particle density of the polishing slurry without vibration. In one period, the increment of the number of the effective polishing particles due to vibration of the slurry in the considered cell could be calculated as,
DXðrÞ q ðrÞX nX½qmax ðrÞ qmin ðrÞ dNðrÞ ¼ q ðrÞX max n¼ :
q0
max
qmin ðrÞ
q0
ð19Þ
And in unit time, the increment of the number of the effective polishing particles due to the vibration of the considered cell could be calculated as fellows,
DNðrÞ ¼ dNðrÞ
x 2p
:
ð20Þ
Thus the increment of the number of the effective polishing particles due to vibration of the cells in the annulus with radius from r to r + dr, could be calculated as fellows,
RDNðrÞ ¼ DNðrÞ 2prdr r ¼ xrXnrðeAh kr ðsin /þ1Þ eAh kr ðsin /1Þ Þ dr;
ð21Þ
where r is the areal density of the cells on the surface of the pad. 3.3. Contribution of an effective polishing particle
Fig. 7. The schematic diagram of the cylindrical coordinates systems.
During polishing, it is the effective polishing particles that make contact with the silicon wafers and carry out the contact polishing. While working, the effective polishing particles are driven by the
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polishing pad to move with the speed v0 relative to the pad. Generally speaking, the speed v0 should be the function of the speed v of the polishing pad relative to the silicon wafer, and roughly increases with the speed v. It is assumed that v0 is proportional to v, as fellows,
v 0 ¼ lv ;
ð22Þ
where Ah is the amplitude of the displacement in transverse direction, x is angular frequency, x0 is angular speed of the polishing pad and r is the distance between the measured site and the axis of rotation. Under consideration of the high-frequency velocity in Eqs. (28), Eq. (27) could be replaced by
xT 2p
where the adjustable coefficient l is determined by the normal pressure and the characteristics of the contact surfaces such as hardness and roughness, in addition the chemical force of the slurry also has an effect upon l. So the speed (v v0 ) of the effective polishing particles relative to the silicon wafer is also the function of the speed v,
Ds ¼ ð1 lÞ
v v 0 ¼ ð1 lÞv :
and if x0r < Ahx,
ð23Þ
And obviously, the average lifetime T of the effective polishing particles is determined by the average space e between the successive cells of the pad and the speed v0 , as fellows,
T¼
e
¼
v0
e : lv
ð24Þ
Consider that the vibration is periodic movement with zero displacement in a period and the average lifetime is related to the displacement, therefore the average lifetime has nothing to do with the low-amplitude and high-frequency vibration. Generally speaking, the polishing particles with the normal pressure lead to the plastic deformation of the polished silicon wafer, as shown in Fig. 8. And in practice, the depth Dd of the plastic pit of the silicon wafer is very small and determined by the normal pressure and the chemical force of the slurry. Thereby, the volume removed by the considered effective polishing particle could be estimated as the following formula,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 V r ¼ Dd R2 ðR DdÞ Ds;
ð25Þ
where Ds is the distance traveled by the polishing particle relative to the polished silicon wafer, Dd is the depth of the plastic pit of the silicon wafer and should be regarded as minim. The higher order minims in Eq. (25) are ignored, then
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V r ¼ Dd 2R Dd Ds:
ð26Þ
According to the analysis above, the relative distance Ds could be calculated as fellows,
Ds ¼
Z
T
jv v 0 jdt ¼ ð1 lÞ
0
Z
2p
x
jx0 r þ Ah x sinðxtÞjdt:
jv jdt:
ð27Þ
0
ð28Þ
ð29Þ
0
Obviously, if x0r > Ahx,
Ds ¼
ð1 lÞe
l
8
Ahx, the volume Vr removed by an effective polishing particle is determined by the normal pressure and the variables of polishing pad and the polishing slurry, and has nothing to do with vibration and rotation, see Eqs. (26) and (30); whereas if x0r < Ahx, Vr has also correlation with Ah, x and x0 besides the normal pressure and the variables of polishing pad and the polishing slurry, see Eqs. (26) and (31). Meanwhile, it must be noted that Eq. (26) makes logical sense only if the polishing time is considerable larger than the average lifetime T of the effective polishing particles. 3.4. Removal rate For the chemical–mechanical polishing with assisted ultrasonic vibration, from Eq. (8) (or Eq. (7)) and Eq. (21), the total number of effective polishing particles in the annulus with radius from r to r + dr in unit time could be calculated as fellows,
Ntot ðrÞ ¼ NðrÞ þ RDNðrÞ:
ð32Þ
Whereas, if no vibration, the total number of effective polishing particles in the annulus with radius from r to r + dr in unit time should be
N0tot ðrÞ ¼ 4pRrknx0 r2 dr:
T
Under consideration of the contribution of the ultrasonic vibration, v has the following form,
v ¼ x0 r þ Ah x sinðxtÞ;
Z
ð33Þ
And the volume Vr removed by one effective polishing particle could be calculated by Eq. (26). And the removal rate of all effective polishing particles in the annulus with radius from r to r + dr in unit time should be
VRRðrÞ ¼ V r Ntot ðrÞ ¼ V r NðrÞ þ V r RDNðrÞ;
ð34Þ
or
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 lÞe VRR0 ðrÞ ¼ N0tot ðrÞ Dd 2R Dd :
l
ð35Þ
And the removal rate per unit area vrr and vrr0 could be calculated as fellows,
vrr ¼
VRRðrÞ ; 2p rdr
vrr0 ¼
Fig. 8. The schematic diagram of the plastic deformation of the silicon wafer caused by the effective polishing particle.
VRR0 ðrÞ : 2prdr
ð36Þ
ð37Þ
Eqs. (34) and (36) represent the removal rate with assisted ultrasonic vibration, and Eqs. (35) and (37) represent the removal rate without assisted ultrasonic vibration. And it should be pointed out that Vr and N(r) in Eq. (34) both have two series of formulae
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Fig. 9. The calculated results of vrr and vrr0 changing with r. The frequency is 27.99 kHz, and x0r > xAh(r).
respectively and should be calculated by different formula under different conditions as analyzed in Sections 3.1 and 3.3. Furthermore, it is obvious that Eqs. (36) and (37) together with Eqs. (7), (8), (21), (26), (30), (31) could expound the roles played by the polishing variables in the polishing process such as amplitudes, angular frequency and rotary speed etc. 4. Theoretical results In order to make theoretical analysis on the polishing effect, in this paper the removal rate vrr and vrr0 are calculated in a normalized unit, #, which is defined as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 l # ¼ rnDd 2R Dd e;
l
ð38Þ
where r is the areal density of the cells on the surface of the polishing pad, n is the particle number density of the slurry, R is the radius of the polishing particles, e is the average space between the successive cells on the surface of the polishing pad, l and Dd are the adjustable coefficient and the depth of the plastic deformation pit. All these variables are determined by the normal pressure and the characteristics of slurry, pad and silicon wafers. It is clear that if the polishing normal force, the polished silicon wafer, the polishing pad and the polishing slurry all keep unchanged, the normalized unit # is constant, and thus the calcu-
lation in such unit could be used to make theoretical analysis on the polishing effect. As mentioned in Section 3.4, vrr should be calculated with two different groups of formulae for x0r > xAh(r) and x0r < xAh(r). More specifically, for x0r > xAh(r), the calculations should use Eqs. (36), (34), (30), (26), (21), (7); whereas for x0r < xAh(r), the calculations should use Eqs. (36), (34), (31), (26), (21), (8). For the experiments of Section 2, the maximum amplitudes of the vibrators are all about a fraction of a micron and decreases along the reverse of radial direction, whereas the amplitudes of vibrations on the surface of polishing pad are smaller than the vibrators’ and approach 107 m, that is, for experiments in Section 2, x0r > xAh(r). Fig. 9 shows the calculated results of vrr and vrr0 changing along the radial direction on the condition of x0r > xAh(r); wherein, Fig. 9(a) is calculated under the same condition as experimental results of Fig. 4. From these calculated curve surfaces of Fig 9, it could be seen that the ultrasonic vibration has a positive effect to the chemical–mechanical polishing; more specifically, the values of vrr and vrr0 both increase with r but the vrr keeps larger than vrr0, and the absolute contribution (vrr–vrr0) keeps constant along the radial direction. Moreover, the ratio of the minimum vrr to maximum vrr in Fig. 9(a) is about 0.8, which is closer to 1 than that of vrr0, and this ratio could be used to represent the uniform degree of removal rate along the radial direction, thus the calculated results of Fig. 9(a) also indicate that the flatness of the
Fig. 10. The calculated results of vrr and vrr0 changing with r. The frequency is 27.99 kHz, and x0r < xAh(r) .
L. Li et al. / Ultrasonics 56 (2015) 530–538
Fig. 11. The calculated results of vrr and vrr0 changing with Ah x and x0. kr = 100 m1, r = 0.01 m.
silicon wafers polished with assisted ultrasonic vibration should be superior to that without vibration. These calculated results all accord with the experimental results of Fig. 4. Meanwhile, the comparison between Fig. 9(a) and (b) indicates that the polishing effect becomes a little better with the angular speed x0 increasing and the absolute contribution (vrr–vrr0) of the ultrasonic vibration does not change if x0r > xAh(r). Another experiment shown in Fig. 5 of Section 2 aims at investigating the correlation between the polishing effect and the angular speed x0. The experimental results indicate that the polishing effect becomes better with the angular speed x0 increasing under the experimental condition, and it is clear that this experimental result accords with the calculated results of Fig. 9. Fig. 10 shows the calculated results for x0r < xAh(r). From Fig. 10, it is found that, if x0r < xAh(r), the absolute contribution (vrr–vrr0) of ultrasonic vibration does not change with r but decreases with x0. In addition, it can also be seen from Fig. 10 that vrr also becomes smaller if x0 increasing, which indicates that the polishing effect becomes worse with x0 increasing if x0r < xAh(r). Comparing Fig. 9 and Fig. 10, it must be found that the change of the vrr with x0 is nonlinear, and Fig. 11 shows the calculated results of the vrr and vrr0 changing with x0 and xAh. It is clear that the value of vrr is larger than vrr0; to be specific, for x0r > xAh, vrr increases with xAh and vrr0 increases slowly with x0, whereas (vrr-vrr0) hardly changes with x0; whereas for x0r < xAh, the vrr increases with the increasing xAh and the decreasing x0. Therefore, for practical chemical–mechanical polishing, the angular speed x0 must have a reasonable range rather than the bigger the better. On the other hand, it must be noted that the chemical force of the slurry is ignored in these calculation and the difficulties of the polishing slurry rushing into the effective polishing area might increase with x0 decreasing. Thus the angular speed’s unreasonable decreasing might also have negative influence on the polishing effect. So the optimal range of the angular speed x0 needs more accurate experiments to determine. 5. Conclusions The ultrasonic traveling wave generated by the ultrasonic vibrators is combined with the chemical–mechanical polishing aiming at investigating the effect of the ultrasonic vibration on the polishing. The experimental results indicate that the ultrasonic vibration is beneficial to improvement of the morphology of the polished silicon wafer, and the flatness of the silicon wafer polished with assisted ultrasonic vibration is superior to that without assisted vibration. In addition, if the amplitude of vibration is small, the polishing effect increases with rotary speed of the silicon wafer relative to the polishing pad.
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Meanwhile the model of the chemical–mechanical polishing with assisted ultrasonic vibration is established in order to understand the contribution of the ultrasonic vibration to the chemical– mechanical polishing in detail. In this model, the definition of the effective polishing particle is used to establish the relationship between the removal rate and the polishing variables; and the equation of continuity is applied to the polishing slurry to derive the function of the mass density of the slurry changing with time, which could be used to explain the increment of the number of the effective polishing particles due to the ultrasonic vibration, and then to elucidate the effect of the ultrasonic vibration on the polishing. The model not only could be used to analyze the experimental results but also to illuminate the roles played by the polishing variables in detail. The calculated results indicate that the ultrasonic vibration has a positive effect to the polishing effect, and the contribution of the ultrasonic vibration increases with the amplitude and angular frequency of the vibration. Whereas, the role played by rotary speed of silicon wafer relative to the polishing pad is related to the ratio of the line speed of rotation and the amplitude of the vibration velocity, and there is a reasonable range of rotary speed which needs more accurate experiments to determine. Acknowledgement This paper is supported by the National Natural Science Foundation of China (51075195). This support is gratefully acknowledged. References [1] Markus Forsberg. Chemical Mechanical Polishing of Silicon and Silicon Dioxide in Front End Processing. Acta Universitatis Upsaliensis Uppsala, 2004. [2] M.R. Oliver, Chemical–Mechanical Planarization of Semiconductor Materials, Springer-Verlag, Berlin Heideberg, 2004. [3] R. Dejule, CMP challenge below a quarter micron, Semicond. Int. 20 (1997) 54– 60. [4] F.G. Shi, B. Zhao, Modeling of chemical–mechanical polishing with soft pads, Appl. Phys. A 67 (1998) 249–252. [5] P.L. Kuo, C.L. Liao, S.K. Ghosh, Superior chemical–mechanical polishing performance of silica slurry made of surface-active siloxane/acrylic polymers, Colloid Polym. Sci. 279 (2001) 1212–1218. [6] F.W. Preston, The theory and design of plate glass polishing machine, J. Soc. Glass Technol. 11 (44) (1927) 214–256. [7] V.H. Nguyen, F.G. Shi, Modeling of the removal rate in chemical mechanical polishing, Proc. SPIE Int. Soc. Opt. Eng. 4181 (2000) 161–167. [8] G. Fu, A. Chandra, S. Guha, et al., A Plasticity-based model of material removal in chemical–mechanical polishing (CMP), IEEE Trans. Semicond. Manuf. 14 (4) (2001) 406–417. [9] J.F. Luo, D.A. Dornfeld, Effects of abrasive size distribution in chemical mechanical planarization–modeling and verification, IEEE Trans. Semicond. Manuf. 16 (3) (2003) 469–476. [10] S.R. Runnels, I. Kim, J. Schleuter, et al., Modeling tool for chemical–mechanical polishing design and evaluation, IEEE Trans. Semicond. Manuf. 11 (3) (1998) 501–510. [11] D.A. Litton, S.H. Garofalini, Modeling of hydrophilic wafer bonding by molecular dynamics simulations, J. Appl. Phys. 89 (11) (2001) 6013–6023. [12] Toshi Kasai, Bharat Bhushan, Physics and tribology of chemical mechanical planarization, J. Phys.: Condens. Matter 20 (2008). [13] K.H. Park, H.J. Kim, O.M. Chang, H.D. Jeong, Effects of pad properties on material removal in chemical mechanical polishing, J. Mater. Process. Technol. 187–188 (2007) 73–76. [14] J.M. Steigerwald, S.P. Murarka, R.J. Gutmann, Chemical Mechanical Planarization of Microelectronic Materials, J. Wiley, New York, 1997. [15] T.B. Thoe, D.K. Aspinwall, M.L.H. Wise, Review on ultrasonic machining, Int. J. Mech. Tools Manuf. 38 (4) (1988) 239–255. [16] Z.J. Pei, N. Khana, P.M. Ferria, Rotary ultrasonic machining of structural ceramics – a review, Ceram. Eng. Sci. Proc. 16 (1) (1995) 259–278. [17] P. Legge, Machining without abrasive slurry, Ultrasonic 4 (7) (1966) 157–162. [18] P. Legge, Ultrasonic drilling of ceramics, Ind. Diamond Rev. 24 (1964) 20–24. [19] K.I. Ishikawa, H. Suwabe, T. Nishide, A study on combined vibration drilling by ultrasonic and low-frequency vibrations for hard and brittle materials, Prec. Eng. 22 (4) (1998) 196–205. [20] Z.J. Per, P.M. Ferreira, S.G. Kapoor, et al., Rotary ultrasonic machining for face milling of ceramics, Int. J. Mach. Tool Manuf. 35 (7) (1995) 1033–1046. [21] K.P. Rajurkar, Z.Y. Wang, A. Kuppattan, Micro removal of ceramic material (Al203) in the precision ultrasonic machining, Prec. Eng. 23 (1999) 73–78.
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