Molecular dynamics simulation of abrasive characteristics and interfaces in chemical mechanical polishing

Journal Pre-proofs Full Length Article Molecular dynamics simulation of abrasive characteristics and interfaces in chemical mechanical polishing Van-Thuc Nguyen, Te-Hua Fang PII: DOI: Reference:

S0169-4332(19)33492-0 https://doi.org/10.1016/j.apsusc.2019.144676 APSUSC 144676

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Applied Surface Science

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15 August 2019 20 October 2019 11 November 2019

Please cite this article as: V-T. Nguyen, T-H. Fang, Molecular dynamics simulation of abrasive characteristics and interfaces in chemical mechanical polishing, Applied Surface Science (2019), doi: https://doi.org/10.1016/ j.apsusc.2019.144676

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Molecular dynamics simulation of abrasive characteristics and interfaces in chemical mechanical polishing Van-Thuc Nguyen1,2, Te-Hua Fang1,* 1

Department of Mechanical Engineering, National Kaohsiung University of Science and Technology,

Kaohsiung 807, Taiwan 2

Faculty of Mechanical Engineering, HCMC University of Technology and Education, Ho Chi Minh City,

Vietnam

*

Corresponding author. Email address: [email protected] (T.-H. Fang).

1

Abstract Molecular dynamics simulation is employed to analyze the effect of sliding, rolling and oscillating movements on nanotribology properties of diamond abrasive on a silicon substrate. The abrasive oscillating mechanism is achieved by simulating megasonic-assisted on planarization process. In this paper, the effects of abrasive size, sliding velocity, depths of polishing, rolling velocity, rolling direction, oscillating amplitude and oscillating frequency on material removal are considered. The results showed that the rolling mechanism reaches the highest number of atoms removed while the suitable oscillating mechanism gains the lowest height of asperity. The oscillating movement has remarkable results in wiping out asperity atoms, although at high amplitude and low frequency causing some atoms from the flat substrate stuck to the abrasive and left some surface defects. Moreover, the multi-asperities model is set up to simulate the global-scale ability of sliding, oscillating and rolling mechanisms on polishing. This model indicates the saturated behavior of the rolling mechanism, while the lowest value of surface roughness attained by the sliding mechanism. Combining three types of removing mechanisms could create a smooth surface with a high effective removal rate on both local and global scale.

Keywords: Molecular dynamics, Diamond, Nanotribology, Sliding, Rolling, Oscillating.

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1. Introduction The demand of both local and global surface qualities of silicon wafer has greatly increased in recent years due to the development of the semiconductor industry, especially as the interconnections have overcome 10 layers and the lithography process has decreased to less than 10 nm [1]. Therefore, the chemical mechanical polishing (CMP) has to evolve synchronously to satisfy these requirements by applying multi-solutions such as finding better abrasive particle, pad, slurry or developing hi-end CMP equipment like endpoint detection, pressure control or ultra-sonic vibration assisting [2-5]. Agrawal et al. [6] reported the sliding behavior and figured out the effective removal distance between the abrasive and the asperity. To simulate the final stage of polishing with gentle force, monoatomic layer removal mechanism was carried by removing one monoatomic layer after another, so that a smooth and defect-free surface is achieved [7]. The chemical reaction between abrasive and asperity atoms such as oxidation of the diamond surface and formation of SiC in the removal process showing that improving pressure leading to more atoms removed [8,9]. Moreover, high hydrostatic pressure on a local area creates Si-phase transformation from α silicon to β silicon and facilitates the ductile fracture of silicon [10-12]. Considering the geography of a wafer, polishing a textured surface produces lower friction than a planar surface [13]. On the slurry aspect, the slurry chemical composition dramatically affects the quality of the polished surface [14-16]. Yang et al. [17] investigated the rolling effect of an abrasive on material removal and surface finish and showed that both sliding and rolling play important roles in material removal rate (MRR) of a silicon substrate. Furthermore, Si et al. [18] studied molecular dynamics (MD) simulation with various down forces and argued that increasing the force result in rising the number of atoms removed, but too much force applied on the abrasive creates pits and others kind of surface defects. The removal regimes of rolling can be separated into two kinds: cutting and plowing depend on the rotation speed [19]. Hu et al. [20] and Xu et al. [21] applied mechanical wave on ultrasonic experiments combined with ultrasonic lapping to a reach higher MRR, a lower peak-to-valley value of roughness and a lower depth of the damaged layer at a micro-level. The ultrasonic vibration is 3

not only used on wafer polishing but also on the pad conditioning method to gain a greater MRR and a better surface roughness [22]. Li et al. [23] surveyed the high performance of megasonic wave on micro-scale polishing and showed a better choice compared to ultrasonic wave which has a lower frequency. In addition, megasonic vibration-assisted CMP is applied on nano-scale in precision polishing and prove that the quality and quantity of material removal are superior to traditional CMP [24]. Molecular dynamics (MD) simulation is well known for the ability to rebuild nanoscale details of the CMP process from various specific input parameters with consistently output data, from which the improvement of wafer quality can be achieved. MD simulation in wafer polishing could give a hand and be updated with the development of the CMP machine. A large numbers of MD simulations have been carried out to investigate the CMP polishing process [2528]. Some authors focus on the physical aspects to investigate material removal mechanisms [29,30], while others study in chemical aspects to analyze the role of slurry on the polishing process [31,32]. This paper analyzes the material removal in associated with sliding, rolling and for the first time oscillating movements. The sliding mechanism simulations survey the effect of abrasive size, depths of penetration of the abrasive to the asperity surface, the velocity of sliding to calculate the number of atoms removed, probability of atoms removed on the pathway, asperity height, and other aspects. The rolling mechanism simulations study the effect of rotating velocities and divide them into 4 principal stages. Especially, the oscillating mechanism simulations are examined and the results are not only some parameters of the asperity but also some information from the substrate. After that, three mechanisms: sliding, rolling and oscillating for the single-asperity model are compared. Finally, overall-scale polishing simulations are considered by creating multi-asperities model polished by sliding, rolling and oscillating, respectively.

2. Computational method Fig. 1 shows the simulation models with single or multi-asperities, with a diamond abrasive in gray color, silicon asperities in blue color, and a silicon substrate in red color. The upper 4

surface of the monocrystalline silicon substrate is ordered in the (100) crystallographic plane. The diamond abrasive particles with radius 10 Å, 15 Å and 20 Å, a substrate with 10.8 Å (thickness) x 108 Å (length) x 64.8 Å (width) contains 4320 atoms and rectangular parallelepiped asperity with 10 Å (thickness) x 27 Å (length) x 16.2 Å (width) contains 210 atoms have been examined. To investigate the issue of polishing depths, we adjust the distance between the highest point of the silicon asperity and the lowest point of the diamond abrasive particle at the initial state in range of 2-6 Å, so that there is always a tiny distance between the abrasive and the substrate as an inter-layer of slurry [33,34]. At the beginning, the abrasive is posited far from the asperity and the substrate so that the interaction between them is ignored. The abrasive mainly moves across x-axis in [100] crystallographic direction. The diamond abrasive is much harder than the silicon substrate so it is treated as a rigid body and does not perform any deformation during the polishing process. To survey the effect of sliding velocity, some simulations are conducted in a speed range of 0.25-3 Å/ps (25-300 m/s) with three sizes of abrasive radius 10 Å, 15 Å and 20 Å. In the rolling mechanism, 15 Å radius abrasive with rolling velocities from 16.7 rad/ns to 1600 rad/ns, moving across x-axis at 1 Å/ps is considered. The oscillating mechanism of 15 Å abrasive is simulated with a variety of amplitude (1-3 Å) and frequency (0.07-0.33 cycle/ps), moving across x-axis at 1 Å/ps. Furthermore, the results of these types of mechanisms are compared and displayed. Lastly, a multi-asperities model is constructed with three asperities to inspect the global-scale effect of sliding, rolling and oscillating on the quality of the wafer surface. All the simulations are performed by Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). A software called open visualization tool (OVITO) was adopted to observe, analyze and illustrate the simulation results. A Tersoff potential is used for the interaction between C-C, Si-Si, and C-Si; the simulations run at 300 K under the microcanonical ensemble (NVE) [35]. The lowest bottom layer is fixed while the upper layer is treated as a thermostat slab. The time step of this simulation is 1 femtosecond.

3. Results and discussion

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In the sliding movement, the effects of depths, abrasive sizes at a specific velocity, the crystalline directions and the effects of sliding velocity are considered in section 3.1 and 3.2, respectively. Section 3.3 pays attention to the rolling mechanism while section 3.4 focuses on the oscillating mechanism. Finally, two comparisons of these mechanisms for single-asperity and multi-asperities are carried out in section 3.5 and 3.6, respectively.

3.1 Sliding mechanism: effect of depth, abrasive size and crystalline direction Fig. 2 and Fig. 3 represent four principal stages of thrusting force in the sliding process when 15 Å abrasive slides over the asperity with 4 Å depth and 1 Å/ps velocity: initial thrusting, middle of thrusting, critical thrusting and finished thrusting. These stages are divided due to the relative position between the abrasive and the asperity. In general, the absolute value of the thrusting force (Fy-normal force) increases to a critical value and then reduces gradually. Meanwhile, the thrusting force (Fx-friction force) goes up, thereafter reaches the highest point. After that, the thrusting force decreases to minus value, then reaches the lowest point, then goes up again to obtain a balanced state. At stage one, the abrasive touches and thrusts the asperity down. Stage two displays a reversion of the thrusting force, after the abrasive moves over the center of the asperity, the force changed from a positive value to negative. This phenomenon indicates a redirection of the force from pressing to pulling like a tension test [6]. On stage three, critical thrusting force appears at about 40 ps as the asperity is pressed heavily and marked by the lowest peak in Fig. 2. In Fig. 3, the fourth stage demonstrates the splitting phenomenon of the asperity into two parts: one part stuck to the substrate and another one stuck to the abrasive. At the same time, both Fx and Fy force slowly come back to initial stabilize state. The number of atoms removed is a good parameter to evaluate the material removal rate. For 10 Å radius abrasive, the numbers of atoms erased from the asperity are 62, 68 and 74 atoms corresponding to three depth levels: 2, 4 and 6 Å, respectively. For 15 Å radius abrasive, the numbers of atoms wiped out are 65, 77, 102 atoms corresponding to 2, 4 and 6 Å depths, respectively. Lastly, for 20 Å radius abrasive, the numbers of atoms erased are 62, 106 and 98 atoms corresponding to 2, 4 and 6 Å depths, respectively. Generally, the number of atoms erased from the asperity rises as the depth and the radius of the abrasive increase. Mostly, the bigger the 6

abrasive the higher the real contact area appears leading to a higher number of atoms removed [36]. For 20 Å abrasive, the number of atoms pulled out firstly rises from 62 to 106 as the depth increasing from 2 Å to 4 Å. However, Fig. 4 shows that as the depth increases from 4 to 6 Å or the slot between the abrasive and the substrate is too thin, the number of atoms pulled out decreases from 106 to 98 due to the removed atoms is pressed and stuck again to the substrate. Generally, when the abrasive is too big and too close to the silicon substrate, some removed atoms come back to stick to the substrate. In addition, the results are consistent with the results in [37,38] researches, confirming that the abrasive and asperity size should have a proportionate ratio to achieve good removal and surface quality. For a more technical parameter, the asperity heights are calculated and reported. For 10 Å radius abrasive, the heights are 7.83, 5.98 and 4.91 Å corresponding to 2, 4 and 6 Å depths, respectively. For 15 Å radius abrasive, the asperity heights are 7.36, 5.40 and 3.87 Å corresponding to 2, 4 and 6 Å depths, respectively. Finally, for 20 Å radius abrasive the calculated heights are 6.34, 5.59 and 3.59 Å corresponding to 2, 4 and 6 Å depths, respectively. Those numbers point out that the final height of an initial 10 Å height asperity reduces as the depth and the abrasive radius increasing. The bigger abrasive mostly creates a lower asperity than the smaller one as it removes more atoms than the smaller one. It means that improving the abrasive size and the depth leading to a smoother surface. Fig. 5 presents the asperity atoms outside the pathway bonded to the abrasive to appear a neck during the sliding process, similar to a tensile test of ductile materials at a nanoscale machining [39-41]. While one part of the asperity stuck to the abrasive, another part stuck to the substrate, pulling the asperity and causing a reduction in the middle area of the asperity. Table 1 shows the dependence of the number and percentage of the silicon atoms removed from the pathway on the depth and the abrasive size. The results show that increasing the depth results in improving the number of atoms removed, but decreasing the percentage of removing atoms. The deceleration of the proportion of atoms removed varies from 1.88 to 0.59, is a result of decreasing the distance between the abrasive and the substrate. As increasing the depth, the thrusting effect is much stronger and then presses the asperity stuck to its substrate. Furthermore, the removing ability of the abrasive is gradually saturated or have a limitation depends on its surface area and the mechanisms of removing. 7

The crystalline directions of the Si diamond structure are also considered in this study. Many prior studies have focused on the [100] and [110] crystalline directions of Si (001) plane on scratching or cutting processes [42,43]. Besides simulating the model in the [100] direction, some simulations are conducted on the model with [110] direction as shown in Fig. 1(c). With the same size, the asperity organized along [110] direction contains 230 atoms or 9.5% more atoms than the [100] one. The 15 Å abrasive particle slides across the [110] crystalline direction at a velocity of 1 Å/ps at 2, 4 and 6 Å depths. The number of atoms removed in the [110] direction are 81, 66 and 97 atoms corresponding to 2, 4 and 6 Å depths, respectively. The number of atoms removed in the [100] direction are 65, 77 and 102 atoms corresponding to 2, 4 and 6 Å depths, respectively. There are different results between these directions, even if the difference of atom numbers in these asperities are considered. This is because different directions present different behaviors due to the anisotropy of a single crystal. Despite having higher number of atoms erased at an upper layer with 2 Å depth than [100] direction, the [110] direction has lower number of atoms removed at 4 and 6 Å depths. The reason is that direction [110] is harder to deform than [100] direction [42]. The asperity height of the [110] direction are 6.62, 5.80 and 3.97 Å corresponding to 2, 4 and 6 Å depths, respectively. The asperity height of the [100] direction are 7.36, 5.40 and 3.87 Å corresponding to 2, 4 and 6 Å depths, respectively. At 2 Å depth, the asperity height in [110] direction is lower than [100] one. At 4 and 6 Å depths, the asperity heights in [110] crystalline direction are higher than [100] direction. These results are suitable with the number of atoms removed as a higher number of atoms removed creates a lower asperity height. Conclusion, the number of atoms removed from the asperity is in direct proportion to the depth and the abrasive size as the abrasive is not too near to the substrate. However, the asperity height is in inverse proportion to the depth and the abrasive size. The abrasive particle moving in [100] crystalline direction removes the asperity atoms more efficient than moving in [110] direction as the depth is deeper than 2 Å.

3.2 Sliding mechanism: effect of velocity

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To investigate the effect of sliding speeds on the material removal, diamond abrasives of 10 Å, 15 Å and 20 Å radius and 4 Å depths are simulated with sliding speeds in the range of 0.25-3 Å/ps. The numbers of atoms erased from the asperity by 10 Å radius abrasive are 66, 62, 61, 62 and 49 atoms corresponding to the sliding speeds of 0.25. 0.5, 1.0, 2.0 and 3.0 Å/ps, respectively. For 15 Å radius abrasive, these values are 77, 83, 77, 71 and 68 atoms corresponding to the sliding speeds of 0.25. 0.5, 1.0, 2.0 and 3.0 Å/ps, respectively. Lastly, for 20 Å radius abrasive these values are 87, 92, 106, 91 and 84 atoms corresponding to the sliding speeds of 0.25. 0.5, 1.0, 2.0 and 3.0 Å/ps, respectively. These numbers present the dependence of the number of asperity atoms removed on the sliding speed and the abrasive size. The numbers of atoms removed fluctuate, but generally decrease as the sliding speeds increase, and increase with the increase of the abrasive size. The fluctuating amplitude of these numbers is relatively small meaning the number of atoms removed is not too sensitive to the abrasive velocity, showing a consistent result as Agrawal et al. [6] and Chen et al. [13] simulations. Increasing the velocity will reduce the contact time, causing a decreasing in adhesion so that the number of atoms removed decrease. Moreover, the numbers of atoms removed increase as the abrasive size increase. Because a bigger abrasive always erases a higher number of atoms than a smaller one as a larger surface area can attach more atoms. Fig. 6 represents the total kinetic energy at different velocities with 15 Å radius abrasive. The diagram indicates that the total kinetic energy increases as the velocity increases. Moreover, the highest peaks of these energies rise higher at a faster speed due to higher impact effect between the abrasive and the asperity. The length of time of these kinetic energy diagrams is in reverse to the sliding velocity. Besides, the deviation of the kinetic energy values among 0.25-1 Å/ps range is minor compared to the range of 2 and 3 Å/ps. Increasing the velocity lead to improving the kinetic energy rapidly. However, the effect of this improvement on the number of atoms removed and the asperity height is not so strong. Fig. 7 presents the dependence of the final height of asperity on the sliding velocity. The diagrams show that the asperity heights fluctuate slightly in a range of 0.25-3 Å/ps. The difference of the asperity heights on 0.25-1 Å/ps range is small due to the closed value of the kinetic energies between these cases. The difference in higher velocity range is clearer because of a larger difference between their kinetic energies. 9

Furthermore, despite the difference in the velocity, the bigger abrasive mainly creates a lower asperity than the smaller one as the bigger abrasive removes more atoms than the smaller abrasive. In general, improving the sliding velocity results in declining the number of atoms removed. The asperity heights made by the bigger abrasive mostly lower than the smaller abrasive in spite of the difference in the velocity.

3.3 Rolling mechanism: effect of velocity The tribo-pairs contacts between a asperity, a pad, and a spherical abrasive surface prefer to perform the rolling mechanism rather than slide mechanism, especially with a hard surface, a low friction coefficient and a low press pressure [44,45]. Previous papers used to simulate the rolling mechanism with narrow range of rotating velocity [17,19]. The rolling velocities are selected to simulate how much the asperity rolls as it contacts with the pad and the substrate. The moving velocity creates a relative rolling movement at different speed depending on the position of the polishing area from the center of the wafer. The speeds of rolling are chosen so that they have a suitable ratio of the moving speed and are divided into four levels in this research: from slower than moving speed to a few times faster. In this section, we investigate the effect of the rolling velocity of 15 Å radius abrasive on the material removal with a wide range of rolling velocities from 16.7 rad/ns to 1600 rad/ns across x-axis at 1 Å/ps moving velocity. The rolling velocity value of the abrasive that is equal to sliding speed is 66.7 rad/ns. The circumference of the longest circle on 15 Å radius abrasive is 94.2 Å, because of that the abrasive needs to rotate 5.8 times faster than the sliding velocity or 387 rad/ns for the whole circumference to roll over all the width of the asperity which is 16.2 Å. The maximum rolling speed in the simulations is about 4 times higher than the speed that roll over all the asperity width. Fig. 8 displays the dependence of the number of atoms removed and the asperity height on the rolling velocity. The diagram figures out that this number initially increases as the rolling velocity increases and peaks at 166.7 rad/ns, which is mainly much higher than sliding only. After peaking at 166.7 rad/ns, this number decreases as the rolling velocity increases. The rolling velocities are divided into four stages: the first stage is mainly sliding in the range of 16.7-66.7 10

rad/ns, the second stage is rolling-plus-sliding in the range of 100-333.3 rad/ns, the third stage is rolling in the range of 400-800 rad/ns, and the fourth stage is fast-rolling in the range of 12001600 rad/ns. In the first stage, the rotation velocity is slower than the moving velocity along the x-axis, so the sliding behavior of the abrasive is much stronger than the rolling effect [17]. The average number of atoms removed at this stage is 55 atoms, slightly lower than 77 atoms in the sliding mechanism. In the second stage, the rolling velocity approaches the moving velocity so that the rotational effect is sharper than the first stage. The average number of atoms removed on stage 2 is 112 atoms, and reaches the maximum value of 139 atoms at 166.7 rad/ns. The ratio of the abrasive surface that takes part in removing asperity atoms increases as the rolling velocity increases. Therefore, increasing the rolling speed on the first two stages leads to improving the number of atoms removed, a similar result as Zhang et al. [46] experiments. At the third stage, the rolling velocity is higher than the moving velocity but does not exceed two times of moving velocity. In the first rolling round, the asperity atoms stuck to the diamond abrasive effectively. Meanwhile, in the second round of the abrasive, some removed atoms are stuck back to the asperity, causing a declination on the average number of atoms removed from the asperity from maximum 139 to 121 atoms. In the fourth stage, the average number of atoms removed from the asperity is 86 atoms, lower than two previous stages. According to Yang et al. [19], abrasive with too high rolling velocity is not good for removing asperity atoms and reducing the asperity height. Consequently, the rolling mechanism needs abrasive to rolling for about its whole circumference on the asperity width to achieve the highest surface quality. Fig. 9 shows the dependence of the asperity height on rolling velocity. The diagrams represent that the asperity height increases from 5.7 Å to 13.7 Å in stage 1. In stage 2, the asperity height decreases from 13.7 Å to 7.6 Å and then fluctuates around 7 Å. In stage 3 and stage 4, the asperity height increases greatly from 6.6 Å to 25.5 Å. The abrasive in the fourth stage rolls so rapidly that the asperity is rolled up, creating a higher asperity. In general, whenever the number of atoms removed reduces, the height of asperity will arise. Fig. 10 demonstrates the adhering portion of the atoms removed on the circumference of the abrasive with a variety of rolling velocity. This figure indicates that increase the rolling velocity from the first stage to the third stage leads to a higher adhering portion of atoms removed. Moreover, Fig. 11

10(f) illustrates that at stage fourth, some high-energy atoms absorbed from the abrasive appear to “fly away” when their kinetic energy is more severe than the adhering energy. Another aspect that this study surveyed is rotating in reverse direction. While other papers only concentrate on normal rotating direction, as polishing pad moves in opposing direction to the wafer [17,18], this study investigates the states that the pad moves in the same direction of the silicon wafer for the first time in literature. Fig. 11 shows the dependence of the number of atoms removed and asperity height on rolling velocity in reverse direction. The diagram points out that the number of atoms removed surpasses both the previous case and the sliding case. The number of atoms removed mainly increases as the rolling velocity increases to 1200 rad/ns, peaks at 1200 rad/ns with 172 atoms removed. This rising trend is a result of more abrasive surface joins in removing asperity atoms as the rolling speed increases. Thereafter, this number declines to 152 atoms at 1600 rad/ns due to fast-rolling effect like rolling in normal direction at stage 4. From Fig. 11, it can be seen that the asperity height varies around the average number 4.8 Å and generally lower than in normal direction. Initially, increasing the rolling speed to 1200 rad/ns lead to decreasing the asperity height. As the abrasive rolls faster than 1200 rad/ns, the asperity height increases but with much lower value than the normal direction case. This height is synchronous with the number of atoms removed, showing a good symmetry between “asperity height” line and “number of atoms removed” line. Fig. 12 shows the adhering portion of the atoms removed on the circumference of the abrasive with a variety of rolling velocity in reverse direction. Similar to rolling at normal direction, increasing the rolling velocity from 16.7 rad/ns to 400 rad/ns results in a higher portion of atoms adhered on the circumference of the abrasive. Additionally, Fig. 12(f) displays that the “fly away” circumstance repeats in the reverse rolling direction as in the normal rolling direction at very high rotational velocity at 1600 rad/ns, marking a moment that the weakening of rolling effect on removing atoms and reducing asperity height. In conclusion, the rolling mechanism removes the asperity atoms effectively by improving the ration of the abrasive surface joining in removing asperity atoms. Removing mechanism in rolling in the reverse direction is pulling up the asperity atoms, not thrusting down the atoms as rolling in the normal direction, results in a higher number of atoms removed and a lower asperity height. 12

3.4 Oscillating mechanism: effect of amplitude and frequency To investigate the effect of ultrasonic wave on the polishing process, a series of simulations are executed with an abrasive that vibrates at some specific frequency and amplitude. Although there are some experimental studies of ultra-sonic and mega-sonic assisted [20-24], this is the first time an oscillating simulation model is built and analyzed. The diamond abrasive in this simulation has a 15 Å radius and moves with 1 Å/ps velocity with 4 Å depth, oscillates with a range of period 3-15 ps or frequency 0.07-0.33 cycles/ps, and a range of 1-3 Å amplitude. With the presence of vibration, some substrate atoms with red color are removed unexpectedly. Fig. 13 presents the dependence of the number of substrate atoms removed on oscillating amplitude and frequency. This diagram indicates that the abrasive oscillates with higher amplitude removes a higher number of substrate atoms. At higher amplitude, the abrasive penetrates deeper into the asperity as it oscillates down, leading to a higher number of substrate atoms adhere to it as it oscillates up. The diagram also shows that at 1 Å amplitude, this number fluctuates around 9 atoms when increases the frequency. At 2 Å and 3 Å amplitude, the number of substrate atoms removed fluctuates in a range of 0.07-0.11 cycles/ps. Thereafter, at a higher frequency range of 0.11-0.33 cycles/ps this number increases as the frequency increases. Specifically, as the abrasive vibrates at 3 Å amplitude and high-frequency range of 0.11-0.33 cycles/ps, the number of substrate atoms escalates quickly. Fig. 14 represents the image of silicon atoms removed from asperity and substrate with different frequency at 3 Å amplitude. The picture shows that at high frequency, the substrate is affected more serious than lower one, leaving some defects on the substrate surface. Fig. 15 appears to show that the asperity height fluctuates around 5.5 Å when changing the frequency and amplitude, meaning the asperity height is not so sensitive to amplitude and frequency. Fig. 16 presents the total kinetic energy of different amplitude and frequency on the oscillating mechanism. The total kinetic energy demonstrated in Fig. 16(a) indicates that with the same frequency at 0.33 rad/ns, the higher the amplitude, the higher the vibration of kinetic energy. In Fig. 16(b), the diagrams exposes that with the same amplitude at 1 Å, the higher the frequency the higher the fluctuation of the kinetic energy. 13

Generally, the number of atoms removed from the substrate and the asperity height fluctuate as increasing the amplitude and the frequency. The addition pushing force from the oscillating movement causes the substrate atoms attached to the asperity, specifically at high amplitude and low frequency.

3.5 Comparing sliding, rolling and oscillating: single-asperity model To compare the effect of three mechanisms: sliding, oscillating and rolling with 15 Å abrasive, 4 Å depth, 1 Å/ps moving velocity, we organized some previous results and present them in this section. The diamond abrasive slides at 1 Å/ps or rolls in the normal direction at 166.7 rad/ns or vibrates at 1 Å amplitude and 0.07 cycles/ps. The number of atoms removed of these mechanisms is 77, 139 and 82 atoms corresponding to sliding, rolling and oscillating, respectively. The rolling mechanism has the best effect on removing the asperity atoms while sliding and oscillating have equal results. For asperity height, the height values are 5.4, 7.6 and 5.0 Å corresponding to the sliding, rolling and oscillating mechanism, respectively. The results implied that the oscillating mechanism has a better effect than the sliding mechanism while rolling has modest results. Despite the efficiency in removing silicon atoms, the rolling mechanism is not actually very good at reducing the asperity height as sliding and oscillating. However, when the abrasive rotates in the reverse direction, the rolling mechanism is the best for both removing atoms and reducing the asperity height as shown in Fig. 11. Fig. 17 presents the cross-section of the simulation models with the atomic strain of some atoms under the initial flat surface of the substrate. It can be seen that the atomic strain concentrates on some atoms at the interfaces between the asperity and the flat substrate due to the collision between the abrasive and the asperity. Along the substrate, there are also some clear marks of the atomic strain due to the collision between the adhered atoms on the abrasive and the substrate. These sensitivity areas create some point defects on the substrate surface. Fig. 18 exhibits the RDF diagram of sliding, rolling and oscillating mechanisms. The heights of the highest peaks of sliding and oscillating processes reduce greatly compare to before polishing. It means that an appreciable number of diamond cubic structures of Si atoms have been changing. 14

After these mechanical processes, the asperity ordering structure reduced dramatically. Meanwhile, the crystal structure of rolled asperity remained better than the structure of slid asperity and oscillated asperity as a result of removing atoms gently, slowly and gradually of the rolling mechanism. In Fig. 19, the total kinetic energies of three types of polishing process are displayed. The kinetic energy of the oscillating mechanism has a great vibration amplitude showing its oscillating behavior. While the kinetic energy of the rolling mechanism has a clear peak at about 20 ps when the abrasive rolls over the asperity atoms, showing a consistent outcome as Si et al. [47] simulations. The advantage of the rolling mechanism is a greater rate of material removal. Meanwhile, the advantage of the oscillating mechanism is lower asperity height.

3.6 Comparing sliding, rolling and oscillating: multi-asperities model To investigate the quality of global scale surface after using three mechanisms: sliding, oscillating and rolling in the normal direction with 15 Å abrasive, 4 Å depth, 1 Å/ps moving velocity we constructed a multi-asperities model with 3 similar asperities presented in Fig. 1(b) and Fig. 20. The diamond abrasive rolls in the normal direction at a speed of 166.7 rad/ns or vibrates at 1 Å amplitude and 0.07 cycles/ps. These asperities having a distance of 13.8 Å intend to display a pattern of wafer scratches after the grinding process [13,48]. The final heights of the highest asperity of these mechanisms are considered and calculated. For the sliding mechanism, the heights are 8.09, 7.12 and 5.10 Å corresponding to 2, 4 and 6 Å depths, respectively. For oscillating movement, the asperity heights are 7.64, 6.21 and 5.74 Å corresponding to 2, 4 and 6 Å depths, respectively. Moreover, for rolling movement, the final heights are 10.33, 10.14 and 11.32 corresponding to 2, 4 and 6 Å depths, respectively. These numbers show that in the sliding and oscillating mechanism, increasing the depth will help to reduce the asperity height. In the sliding mechanism, at 2-4 Å depth, the effect of increasing the depth on the reduction of the asperity height is not as strong as oscillating. However, at 6 Å depth, the removal effect of the oscillating mechanism is lower due to the adhering effect: the asperity atoms attached to the abrasive particle and pulled up while the abrasive oscillates. In the 15

rolling mechanism, the effect is inverse compared to sliding and oscillating mechanisms due to the atoms rolled up during the rolling process as seen in Fig. 10. The numbers of atoms removed of these mechanisms are also investigated. For the sliding mechanism, the number of atoms wiped out is 77, 116 and 179 atoms corresponding to 2, 4 and 6 Å depths, respectively. For oscillating movement, the number of atoms removed is 92, 135 and 186 atoms corresponding to 2, 4 and 6 Å depths, respectively. Lastly, for rolling movement, the number of atoms removed is 266, 269 and 257 atoms corresponding to 2, 4 and 6 Å depths, respectively. Those numbers display that for both sliding and oscillating mechanisms, the increasing in the depth leads to having more atoms wiped out from asperities. The oscillating mechanism has a higher number of atoms removed than the sliding one. In the rolling mechanism, the number of atoms removed is dramatically higher than the sliding and oscillating mechanisms due to the higher rate of the abrasive surface takes part in removing the asperity atoms. However, increases the depth does not improve the number of atoms removed steadily as there is a limitation for the abrasive to adhere and detach the asperity atoms. When the touching area of the abrasive surface entirely covered by the removed atoms, the abrasive cannot hold more atoms or its removing capacity is saturated. This is a reason for smaller abrasives gain better removal rate due to its high specific surface [49,50]. Beside the asperity heights and the number of atoms removed, the surface roughness of silicon substrate after polishing is also calculated. The equation of root-mean-square (RMS) roughness is given by: ∑𝑛 ̅)2 𝑖=1(𝑦𝑖 − 𝑦

𝑅𝑅𝑀𝑆 = √

𝑛

(1)

where yi indicates the height of ith exposed atom on the surface; 𝑦̅ denotes the mean height of n exposed atoms; n is the number of atoms on the exposed surface [51]. For the sliding mechanism, RMS roughness are 1.28, 1.21 and 1.01 Å corresponding to 2, 4 and 6 Å depths, respectively. The RMS roughness of oscillating are 1.49, 1.12 and 1.20 Å corresponding to 2, 4 and 6 Å depths, respectively. Lastly, the RMS roughness of rolling are 1.97, 1.88 and 1.83 Å corresponding to 2, 4 and 6 Å depths, respectively. Generally, these numbers show that increasing the depth results in reducing the RMS roughness. The roughness of sliding 16

is always better than rolling [52,53]. The roughness of oscillating is also better than rolling. The surface roughness of sliding at 2 and 6 Å depth are better than oscillating. Although at 4 Å depth, the surface roughness of oscillating is better than sliding mechanism. According to Han et al. [54], the cooperation between these types of mechanisms generates high-quality surfaces and high rate of material removal as all the advantages of three mechanisms are all contributed. To have an overview of other studies on experimental CMP technology, Table 2 is built to compare some specific parameters: the MRR improvement and the average roughness. The MRR improvement of this simulation is calculated by comparing the number of atoms removed between the sliding and the oscillating mechanisms in multi-asperities model. Using mechanical vibration in [21,22,24] experiments increases from 15 to 250 percent of MRR compares to traditional CMP without using it. The values in these experimental researches are often higher than this research (3.9-19.5%) because the existence of slurry in experiment facilitates the removing of wafer atoms. Additionally, the average surface roughness Ra of other experimental studies present in Table 2 are often slightly lower than this study due to the aid of the chemical reaction of the slurry. On the aspect of simulation, the results of other researchers are showed in “number of atoms removed” column in Table 2, their studies also simulate the single abrasive and single asperity model. There are some small differences in the number of atoms removed among these simulation models. In this study, the numbers of atoms removed by 15 Å radius abrasive and 4 Å depth with a variety of velocities are 68-83 atoms for the sliding mechanism and 46-139 atoms for the rolling mechanism. In the sliding mechanism, Agrawal et al. [6] used smaller asperity with 52 atoms than this research with 210 atoms so the number of atoms removed is smaller. In rolling mechanism, Si et al. [18] simulate silica abrasive rolling on a flat surface without any asperity so there is only adhering force that contributes to the removing substrate atoms. Because thrusting force does not appear in that model as this research so the number of atoms removed is lower with 17-25 atoms compare to 46-139 atoms in this research. Moreover, Chen et al. [36] study the effect of silica abrasive impacts on a flat substrate without any asperity, focusing on the adhesion force between silica and silicon atoms. There is also a lack of thrusting force in Chen et al. [36] model leading to a lower number of atoms removed than this research.

17

The asperities height is reduced effectively by the oscillating mechanism while the rolling mechanism always clears the highest number of atoms. The surface roughness of sliding is similar to oscillating and definitely better than the rolling mechanism.

4. Conclusion MD simulation has been applied to analyze the material removal for all of three mechanisms: sliding, rolling and oscillating of a diamond abrasive on a silicon substrate. Consequently, the afterward conclusions can be extracted: (1) The number of atoms wiped out from the asperity in the sliding mechanism is in direct proportion to the depth and the abrasive size as the abrasive is not too close to the substrate; on the contrary, the asperity height is in inverse proportion to the depth and the abrasive size. The probability of atoms removed from the pathway decreases from 1.88 to 0.59 as the depth and the abrasive size increase. The abrasive moving in [100] direction removes the asperity atoms better than moving in [110] direction as the depth is deeper than 2 Å. (2) In general, improving the sliding speeds leads to declining the number of atoms removed. Despite the difference in the velocity, the asperity heights made by the bigger abrasive mostly lower than the smaller abrasive. (3) The relationships between rolling velocity, moving velocity and asperity width are able to divide into four stages and decide the number of atoms wiped out and the asperity height. If the abrasive rolls on the asperity so that it rolls about one cycle on the asperity width, the asperity will be removed with the highest number of atoms. Rolling in reverse direction removes more asperity atoms and creates lower asperity than rolling in normal direction. (4) In the oscillating mechanism, the number of atoms and the asperity height fluctuate when changing the amplitude and the frequency. The pushing force causes the substrate atoms attached to the asperity, especially at high amplitude and low frequency. (5) To consider the global surface, a model with three asperities is constructed and investigated. The rolling mechanism always gains the highest number of atoms removed but having the saturated signal as the circumference of the abrasive is full of adhered atoms from the asperities. The asperities height is reduced effectively by the oscillating mechanism on low 18

amplitude case. The surface roughness of sliding is close to the oscillating mechanism and definitely lower than the rolling mechanism. (6) In general, the benefits of the rolling mechanism are a greater rate of material removal while still preserve substrate quality; oscillating mechanism could produce the lowest surface; sliding mechanism gains the smoothest surface. Combining these three types of removing mechanisms could create a smoother surface at both local and saturated with a high material removal rate.

Acknowledgments The authors acknowledge the support by Ministry of Science and Technology, Taiwan under grant numbers MOST106-2221-E-992-333-MY3 and MOST106-2221-E-992-343-MY3.

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25

Tables Table 1 Dependence of the number and percentage of silicon atoms removed from the pathway on the depth and abrasive size (v = 3 Å/ps) Depth (Å)

R = 10 Å

R = 15 Å

R = 20 Å

No. of atoms

No. of atoms

No. of atoms

No. of atoms

No. of atoms

No. of atoms

on pathway

erased

on pathway

erased

on pathway

erased

2

27

41 (152%)

33

62 (188%)

42

66 (157%)

4

54

49 (91%)

75

68 (91% )

93

84 (90%)

6

123

72 (59%)

126

86 (68%)

153

104 (68%)

26

Table 2 The comparison of some specific parameters of the simulation and experimental CMP Methods

Experimental

Experimental

MRR

Number of

improvement

atoms removed

-

-

-

-

Average roughness Ra (nm)

Materials of

References

abrasive/wafer 0.22-1.28

0.73-1.30

SiO2/Ni-P

Mu et al.

alloy

[16]

CeO2/SiO2

Zhang et al.

(0.815-1.44 RMS

[57]

roughness) Experimental

-

-

0.15-0.39

CeO2/SiO2

Chen et al. [56]

Experimental

-

-

0.503±0.067

SiO2/Cu

Zhang et al. [55]

Experimental

250%

-

0.75-1.91 (0.83-2.12 RMS

SiO2/Al2O3

Xu et al. [21]

Al2O3 /Cu

Tsai et al.

roughness) Experimental

50-90%

-

1.448-2.378

[22] Experimental

15-25%

-

0.387-0.509

SiO2/Si

Zhai et al. [24]

Simulation

-

12-60

-

SiO2/Si

Chen et al. [36]

Simulation

-

17-25

-

SiO2/Si

Si et al. [18]

Simulation

-

45-47

-

Diamond/Si

Agrawal et al. [6]

Simulation

3.9-19.5%

68-83 (sliding)

0.91-1.77

46-139 (rolling)

(1.01-1.97 RMS roughness)

27

Diamond/Si

This research

Figure captions Fig. 1 Simulation models: (a) Si diamond structure, (b) single-asperity in [100] direction, (c) single-asperity in [110] direction, (d) multi-asperities Fig. 2 Force of four interaction stages between abrasive and asperity: (1) initial thrusting, (2) middle of thrusting, (3) critical thrusting, (4) finished thrusting Fig. 3 Four interaction stages between abrasive and asperity with atomic strain: (a) initial thrusting, (b) middle of thrusting, (c) critical thrusting, (d) finished thrusting Fig. 4 The sticking phenomenon between asperity atoms and substrate atoms with different depths and abrasive sizes with atomic strain: (a1) 2 Å-R10, (b1) 4 Å-R10, (c1) 6 Å-R10; (a2) 2 Å-R15, (b2) 4 Å-R15, (c2) 6 Å-R15; (a3) 2 Å-R20, (b3) 4 Å-R20, (c3) 6 Å-R20 Fig. 5 The necking process of sliding removed mechanism with atomic strain: (a) initial position, (b) 30 ps, (c) 50 ps, (d) 60 ps, (e) 70 ps. Fig. 6 The total kinetic energy at different sliding velocities: 0.25 Å/ps, 0.5 Å/ps, 1 Å/ps, 2 Å/ps, 3 Å/ps Fig. 7 Dependence of the final height of asperity on sliding velocity Fig. 8 Dependence of the number of silicon atoms removed on rolling velocity (moving velocity 1Å/ps) Fig. 9 Dependence of the asperity height on rolling velocity (sliding velocity 1Å/ps) Fig. 10 The adhering portion of the atoms removed on the circumference of the abrasive with a variety of rolling velocity with atomic strain: (a) 66.7 rad/ns, (b) 133.3 rad/ns, (c) 200 rad/ns, (d) 400 rad/ns, (e) 800 rad/ns, (f) 1600 rad/ns Fig. 11 Dependence of the number of atoms removed and asperity height on rolling velocity in reverse direction (sliding velocity 1Å/ps) Fig. 12 The adhering portion of the atoms removed on the circumference of the abrasive with variety of rolling velocity in reverse direction with atomic strain: (a) 66.7 rad/ns, (b) 133.3 rad/ns, (c) 200 rad/ns, (d) 400 rad/ns, (e) 800 rad/ns, (f) 1600 rad/ns Fig. 13 Dependence of the number of substrate atoms removed on oscillating amplitude and frequency Fig. 14 Silicon atoms removed from asperity and substrate with different frequency: (a) 0.07 rad/ns 28

(b) 0.08 rad/ns (c) 0.11 rad/ns (d) 0.17 rad/ns (e) 0.33 rad/ns Fig. 15 Dependence of the final height of asperity on oscillating amplitude and frequencies Fig. 16 The total kinetic energy of different amplitude and frequency on oscillating mechanism: (a) amplitude, (b) frequency Fig. 17 Cross-section with atomic strain of three atoms removed mechanisms: (a) sliding, (b) rolling, (c) oscillating Fig. 18 The radial distribution function of Si-Si bond of single-asperity of 3 mechanisms: sliding, rolling, oscillating after polishing compared to the initial state Fig. 19 The total kinetic energy of different mechanisms sliding, oscillating and rolling for single-asperity Fig. 20 Multi-asperity with 3 mechanisms after polishing: (a) sliding, (b) oscillating, (c) rolling

29

Figures

Fig. 1 Simulation models: (a) Si diamond structure, (b) single-asperity in [100] direction, (c) single-asperity in [110] direction, (d) multi-asperities

30

Fig. 2 Force of four interaction stages between abrasive and asperity: (1) initial thrusting, (2) middle of thrusting, (3) critical thrusting, (4) finished thrusting

31

Fig. 3 Four interaction stages between abrasive and asperity with atomic strain: (a) initial thrusting, (b) middle of thrusting, (c) critical thrusting, (d) finished thrusting

32

Fig. 4 The sticking phenomenon between asperity atoms and substrate atoms with different depths and abrasive sizes with atomic strain: (a1) 2 Å-R10, (b1) 4 Å-R10, (c1) 6 Å-R10; (a2) 2 Å-R15, (b2) 4 Å-R15, (c2) 6 Å-R15; (a3) 2 Å-R20, (b3) 4 Å-R20, (c3) 6 Å-R20

33

Fig. 5 The necking process of sliding removed mechanism with atomic strain: (a) initial position, (b) 30 ps, (c) 50 ps, (d) 60 ps, (e) 70 ps

34

Fig. 6 The total kinetic energy at different sliding velocities: 0.25 Å/ps, 0.5 Å/ps, 1 Å/ps, 2 Å/ps, 3 Å/ps

35

Fig. 7 Dependence of the final height of asperity on sliding velocity

36

Fig. 8 Dependence of the number of silicon atoms removed on rolling velocity (sliding velocity 1Å/ps)

37

Fig. 9 Dependence of the asperity height on rolling velocity (sliding velocity 1Å/ps)

38

Fig. 10 The adhering portion of the atoms removed on the circumference of the abrasive with a variety of rolling velocity with atomic strain: (a) 66.7 rad/ns, (b) 133.3 rad/ns, (c) 200 rad/ns, (d) 400 rad/ns, (e) 800 rad/ns, (f) 1600 rad/ns

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Fig. 11 Dependence of the number of atoms removed and asperity height on rolling velocity in reverse direction (sliding velocity 1Å/ps)

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Fig. 12 The adhering portion of the atoms removed on the circumference of the abrasive with variety of rolling velocity in reverse direction with atomic strain: (a) 66.7 rad/ns, (b) 133.3 rad/ns, (c) 200 rad/ns, (d) 400 rad/ns, (e) 800 rad/ns, (f) 1600 rad/ns

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Fig. 13 Dependence of the number of substrate atoms removed on oscillating amplitude and frequency

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Fig. 14 Silicon atoms removed from asperity and substrate with different frequencies: (a) 0.07 cycles/ps (b) 0.08 cycles/ps (c) 0.11 cycles/ps (d) 0.17 cycles/ps (e) 0.33 cycles/ps

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Fig. 15 Dependence of the final height of asperity on oscillating amplitude and frequency

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Fig. 16 The total kinetic energy of different amplitude and frequency on oscillating mechanism: (a) amplitude, (b) frequency

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Fig. 17 Cross-section with atomic strain of three atoms removed mechanisms: (a) sliding, (b) rolling, (c) oscillating

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Fig. 18 The radial distribution function of Si-Si bond of single-asperity of 3 mechanisms: sliding, rolling, oscillating after polishing compared to the initial state

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Fig. 19 The total kinetic energy of different mechanisms sliding, oscillating and rolling for single-asperity

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Fig. 20 Multi-asperity with 3 mechanisms after polishing: (a) sliding, (b) rolling, (c) oscillating

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Cross-section with atomic strain and total kinetic energy of three mechanisms: (a) sliding, (b) rolling, and (c) oscillating of removing silicon substrate atoms by diamond abrasive at a moving velocity of 1Å/ps.

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Highlights:



In sliding, the probability of atoms removed from the pathway is calculated.

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Rolling achieves the highest number of atoms removed.

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Oscillating removes some atoms from the substrate.

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Combining sliding, rolling and oscillating mechanisms gains high-quality surface.

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CRediT authorship contribution statement: Van-Thuc Nguyen: Formal analysis, Investigation, Software, Writing - original draft, Visualization Conceptualization, Writing - review & editing. Te-Hua Fang: Data curation, Funding acquisition, Methodology, Project administration, Resources, Validation.

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