Chemically-induced active micro-nano bubbles assisting chemical mechanical polishing: Modeling and experiments

The material loss caused by bubble collapse during the micro-nano bubbles auxiliary chemical mechanical polishing (CMP) process cannot be ignored. In this study, the material removal mechanism of cavitation in the polishing process was investigated in detail. Based on the mixed lubrication or thin film lubrication, bubble-wafer plastic deformation, spherical indentation theory, Johnson-Cook (J-C) constitutive model, and the assumption of periodic distribution of pad asperities, a new model suitable for micro-nano bubble auxiliary material removal in CMP was developed. The model integrates many parameters, including the reactant concentration, wafer hardness, polishing pad roughness, strain hardening, strain rate, micro-jet radius, and bubble radius. The model reflects the influence of active bubbles on material removal. A new and simple chemical reaction method was used to form a controllable number of micro-nano bubbles during the polishing process to assist in polishing silicon oxide wafers. The experimental results show that micro-nano bubbles can greatly increase the material removal rate (MRR) by about 400% and result in a lower surface roughness of 0.17 nm. The experimental results are consistent with the established model. In the process of verifying the model, a better understanding of the material removal mechanism involved in micro-nano bubbles in CMP was obtained.


Introduction
Chemical mechanical polishing (CMP) is one of the ultra-precision machining technologies that is currently widely accepted worldwide [1]. CMP mainly combines the chemical corrosion effect of chemical reagents in the slurry and the mechanical grinding effect of a polishing pad and abrasives to realize global planarization of the oxide dielectric layer and metal layer. With the development of semiconductor technology, its application in very large scale integrated circuits has received increased attention. In order to continue to follow Moore's Law [2], more efficient (higher material removal rate (MRR) and lower surface roughness) CMP has become the research focus of many scholars.
Nowadays, more and more researchers have introduced auxiliary methods such as ultrasonic [3,4], plasma [5], photocatalysis [6,7], micro-bubbles [8,9], and other auxiliary methods to improve the polishing www.Springer.com/journal/40544 | Friction efficiency. Among them, the ultrasonic and microbubble auxiliary methods both involve micro-level and nano-level bubbles. Xu et al. [3,4] used piezoelectric transducers to combine traditional CMP and ultrasonic flexural vibration (UFV) to improve the polishing of sapphire. Li et al. [10] designed a low-amplitude megasonic vibration, which generates nano-amplitude vibration on the surface of the silicon wafer to improve the polishing effect. However, they did not explore cavitation in the ultrasonic field in great detail. Aida et al. [8] used a micro-nano bubble device to prepare a micro-nano bubble slurry to improve the dispersibility of diamond abrasives, and thereby increase the removal rate of GaN. Uneda and Fujii [9] designed a micro-nano bubble system to generate a slurry containing ozone bubbles to improve the oxidation of the slurry to achieve efficient removal of SiC. Similarly, they did not explore the mechanism of bubble collapse during the polishing process.
In fact, when two solid walls move horizontally relative to each other (such as bearings and similar equipment) or when the fluid in a thin film liquid layer flows at high speeds, cavitation occurs [11]. This is the hydraulic cavitation in the thin film liquid layer, as shown in Fig. 1. The collapse of cavitation bubbles will form rapid micro-jets and strong shock waves, which will impose higher stress on objects Fig. 1 Hydrodynamic cavitation in thin liquid layers: (a) visualized hydraulic cavitation equipment and (b) cavitation between glass surfaces in relative motion. Reproduced with permission from Ref. [11], © Elsevier B.V. 2020. near the bubbles [12]. When the stress formed by the collapse of the bubble is higher than the elastic limit of the material, it will cause brittle deformation of the material [13]. This is exactly the reason why researchers want to use cavitation to assist processing and manufacturing.
However, to realize the autonomous formation and collapse of bubbles (i.e., cavitation), it is necessary to have a sufficiently high energy (such as ultrasonic or ultra-high-speed shear). Although Xin et al. [14] proposed that under the conditions of mixed lubrication or boundary lubrication, the high shear rate of the slurry at the local removal point can form strong shear stress to achieve material removal on the wafer surface. Relying only on conventional polishing conditions is not enough to directly form a large number of cavitation bubbles during the polishing process. For this reason, we need to introduce bubbles by other means, and then realize the collapse of the bubbles through the high shear stress during the polishing process.
Sodium borohydride (NaBH 4 ) is a commonly used raw material for hydrogen storage and generation, and has a relatively high theoretical hydrogen storage capacity of 10.8% [15]. It has good stability and mild reaction conditions, and can also react with water to produce pure hydrogen at room temperature (298 K). The rate of hydrolysis can often be stabilized by adding sodium hydroxide (NaOH), and the hydrolysis of sodium borohydride is a spontaneous and exothermic process (−210 kJ/mol) [16]. The hydrolysis process are shown by Reactions (1) and (2).
Therefore, a large amount of hydrogen gas can be obtained by the hydrolysis reactions of sodium borohydride, which provide a gas source for bubbles. In addition, this method can control the total amount of gas by controlling the chemical reaction, thereby controlling the number of bubbles.
In this article, we used sodium borohydride as a chemical gas source for bubbles to achieve the purpose of generating micro-nano bubbles in situ during the polishing process to assist polishing. We propose the basic mechanism of material removal caused by 1626 Friction 11(9): 1624-1640 (2023) | https://mc03.manuscriptcentral.com/friction microbubble cavitation in CMP. Based on the plastic contact between the micro-nano bubbles and wafer, the Johnson-Cook (J-C) constitutive model, the micro-nano bubble and micro-jet radii, the chemical reaction rate (number of micro-nano bubbles), etc., a simple mathematical formula was established to explain the mechanism. At the same time, the proposed mathematical model was verified through the polishing experiments. The experimental results show that compared to traditional CMP, microbubble-assisted CMP can indeed increase the removal rate and improve the quality of the display.

Preparation of silica slurry with NaBH 4
We added an appropriate amount of deionized water (DI) to the silica sol (ACS Nano 2050s; Ace Nanochem Co., Ltd., Republic of Korea) with a particle size of 50 nm to dilute the solution to 5 wt%. Then, a certain content (0.1-0.7 wt%) of sodium borohydride (NaBH 4 , purity 98% AAS, KANTO) was added, and a 3.0 wt% NaOH solution was used to adjust the pH value of the slurry to 10 for the polishing experiments.

Polishing tests
For the convenience of the experiments, the silicon oxide wafer was cut into 3.9 cm × 3.9 cm samples before polishing. All the polishing experiments were performed using a 4-inch wafer polisher (Poli-400, GnP Technology, Republic of Korea), as shown in Fig. S1 in the Electronic Supplementary Material (ESM). The polishing pad was a porous polyurethane polishing pad (HW-300 K-Groove, KPX Chemical Co., Ltd., Republic of Korea). The specific polishing experiment conditions are shown in Table 1. Before polishing, pretreatment with DI water and slurry was carried out for 10 and 5 min, respectively. Each silicon oxide wafer was polished for 1 min, and the process was repeated 3 times.

Characterizations
The thicknesses of the silicon oxide wafer before and after polishing were measured by a thin film thickness Head-left (Head-L) speed 87 r/min Head-L pressure 3.0 psi Slurry feed speed 100 mL/min measurement system (ST5030-SL, K-MAC Co., Republic of Korea) to calculate the MRR. The bubbles in the slurry were observed and photographed by an optical microscope (UMSSP4, Olympus Co., Japan). The particle size distribution and zeta potential of the abrasives as well as the size distribution of the bubbles were measured by a particle size analyzer (ELSZ-2000, Otsuka Electronics Co., Japan) using the dynamic light scattering (DLS) method. The morphology of abrasives was measured by a scanning electron microscope (SEM; JSM7500F, JEOL Co., Japan) at an accelerating voltage of 15 kV. The surface roughness of the polishing pad was measured by an optical profiler (ContourGT-1, Bruker Co., USA). The X-ray photoelectron spectrometer (ESCALAB250, Thermo Fisher Scientific, USA) was used to measure the surface elements of the wafer under different conditions. The surface roughness of the silicon oxide wafer before and after polishing was measured by an atomic force microscope (AFM; NX10, Park Systems Corp., Republic of Korea).

Mathematical model
Due to the unobservable nature of the polishing process, the use of a calculation model for the MRR is controversial. To clarify the mechanism of material removal in the micro-nano bubble auxiliary CMP process, we integrated the removal mechanism of traditional CMP and the removal mechanism caused by bubble collapse. MRR is the MRR caused by bubble collapse. Generally, the Preston equation, MRR = k p PV (k p is the Preston's coefficient, P is the pressure, and V is the rotation speed), as the original model is considered to be the most basic formula of traditional CMP. This equation expresses the relationship between the removal rate and the polishing parameters (P and V) from a macro perspective. However, the experimental results show that there are many influencing factors in CMP. In particular, the hardness of the wafer and the microscopic morphology of the pad have large impacts on the MRR [17]. The removal rate model proposed by Luo and Dornfeld [18][19][20] seems to be the most comprehensive. The model is based on the assumptions of plastic contact between the wafer-abrasives and abrasives-pad, a Gaussian distribution of the abrasive size, and periodic distribution of the pad surface. In a sense, almost all of the factors involved in the polishing process are included. But because CMP is a very complicated process, both mechanical abrasion and chemical corrosion play very important roles. Xin et al. [14] introduced the concept of a chemical reaction layer on the wafer surface, combined with the continuous removal of the newly formed metamorphic layer by the shear stress of the slurry, and proposed a more uniform material removal mechanism for each wafer. It can be said that although the removal mechanism of traditional CMP has not been completely unified, research on the mechanism is very detailed and close to the actual polishing effect. In the polishing process, the material removal caused by bubble collapse does not yet have one model to explain its mechanism.
In this experiment, no additional high-energy output items are provided. But in CMP, the gap between the wafer and pad can actually be regarded as mixed lubrication or thin film lubrication. The classic CMP experiment conducted by Shan et al. [21] showed that the average thickness of the fluid liquid film is about 15 μm, while the liquid film at the highest point of the pad can only exist with a thickness of 1 μm or less. Lortz et al. [22] pointed out that under conventional CMP conditions, the slurry film has a high shear rate. When the linear velocity of the slurry is 0.5 m/s, and the thickness of the liquid film is 10 μm, the corresponding shear rate is 200,000 s −1 . When the linear velocity of the slurry is 1 m/s, and the thickness of the liquid film is 1 μm, the corresponding shear rate is 1,000,000 s −1 . Such a high shear rate is sufficient to cause the collapse of micro-nano bubbles in the slurry. Therefore, the effect caused by bubble collapse in the CMP process cannot be ignored.
The cavitation damage of materials is mainly caused by micro-jets and shock waves caused by bubble collapse, where the former is the primary factor [12,23]. In the past, most bubble collapse was caused by ultrasonic pressure. According to the polishing results in Section 4.3, the MRR caused by micro-nano bubbles is significantly higher than the removal rate of pure slurry. This indicates that the material removal caused by bubble collapse occupies the main part of MRR, so the material removal caused by bubble collapse can be regarded as brittle deformation. In the short polishing process, two micro-jets almost never impact the same spot at the same time, and it can be considered that a single cavitation pit is completely caused by a single micro-jet, as shown in Fig. 2. In addition, the micro-jet in this paper is a micro-jet with abrasives.
The shape of the cavitation pit is similar to the material deformation in the spherical indentation, such that the spherical indentation theory combined with the geometric characteristics of the cavitation pit can be used to infer the cavitation stress and strain. In the indentation experiment proposed by Tabor [24], the relationship between the equivalent strain and the geometric characteristics of the cavitation pit, p  , is described by Eq. (4): where p d is the diameter of the cavitation pit, and p h is the depth of the cavitation pit. In this experiment, the hardness of silicon oxide is relatively large, and the depth of the cavitation pit is much lower than the diameter of the cavitation pit. As a result, Eq. (4) can be modified as Eq. (5) The plastic deformation of the cavitation pit is caused by the impact load of the micro-jet in a short time, and the deformation often occurs in the peak pressure stage, which is about a few nanoseconds [25]. Therefore, the strain effect of plastic deformation of the material needs to be considered. The typical J-C constitutive model considers the strain hardening, strain rate hardening, and thermal softening effects of the material [26]. In this study, the temperature of the slurry changed little, and the temperature effect was negligible. Based on the J-C model, the equivalent stress of the cavitation pit, JC  , can be obtained.
where 0  is the yield strength, B and 1 n are the strain hardening parameters, C is the strain rate strengthening parameter, and p  and 0  are the equivalent strain rate and the reference strain rate, respectively. Francis [27] introduced the constraint factor, ψ, and established the cavitation load, p L , based on the equivalent stress. When the material is fully elastically deformed, ψ is 1.11. When the material is plastically deformed, ψ is 2.87. The cavitation pit here is considered to be plastic deformation (Eq. (7)): where p S is the area of the cavitation pit. Since the depth of the cavitation pit is much smaller than the diameter, it can be regarded as the projected area of the pit, . We believe that the cavitation pit is completely formed by the micro-jet, so the diameter of the cavitation pit is related to the diameter of the micro-jet, j d . Here, we assume that p j d d  , and the impact pressure formed by the micro-jet is As mentioned above, the micro-jet forms a plastic deformation zone near the cavitation pit. When a material undergoes plastic deformation, it means that the pressure on its surface has reached the pressure value that defines the "hardness" of the material [18]. Therefore, the average pressure exerted by the micro-jet on the wafer surface is equal to its hardness, w H .
Combined with Eq. (5), the relationship between the depth of the cavitation pit and diameter of the micro-jet is obtained.
The MRR caused by bubble collapse is the total volume of all effective bubbles removed in the polishing area per unit time.
Here, vol MRR is the material volume removal rate caused by bubble collapse, and b N  is the number of bubbles that can effectively form microjets in the polishing area per unit time. The total number of bubbles in the polishing area per unit time is related to the hydrolysis rate of NaBH 4 and the volume of the slurry thin film between the wafer and the pad.
It is well known that when the concentration of NaBH 4 is low, a first-order reaction is observed; and when the concentration of NaBH 4 is high, a zero-order reaction is observed [28]. From the experimental section, the concentration of NaBH 4 (0.1-0.7 wt%) is relatively low compared to other studies showing zero-order reaction kinetics. As a result, in this concentration range, it follows first-order reaction kinetics. According to Reaction (1) or (2), the rate of hydrogen generation can be expressed by Eq. (14): where 2 H C  is the amount of substances that generate hydrogen per unit time, 1 c is the concentration of NaBH 4 , 2 c is the concentration of H 2 O, and k is the reaction rate constant, which can be obtained by Arrhenius' law (Eq. (15)).
Here, a E is the reaction activation energy, A is the prefactor, R is the gas constant, and T is the temperature.
The contact mechanics in CMP shows that the contact between the wafer and pad is discontinuous. The actual contact area is only a part of the apparent area [18]. When the two objects are in contact, the surface roughness of the wafer is much lower than that of the pad. Therefore, the surface of the wafer can be regarded as a flat surface, while the surface of the pad that appears is a rough surface, as shown in Fig. 3.
In the model of Luo and Dornfeld [18], it is believed that the known uniform density, number of asperities per unit area, SUM D , of the asperity is distributed on the surface of the pad. All asperities have similar shapes and sizes. In our model, it is assumed that all asperities that can contact the wafer follow a periodic distribution with approximately uniform heights. Because the elastic modulus of the | https://mc03.manuscriptcentral.com/friction pad is low, it is possible that asperities with the same or similar heights are in contact with the wafer. The total volume of the polishing area is t 0 V A l  , where l is the gap between the wafer and the pad (also the average height of asperity), and 0 A is the area of the wafer. However, asperities also occupy a part of the volume, a , where a is the area occupied by a single asperity. Therefore, the actual volume of the slurry thin film, s V , in the polishing area is shown by Eq. (16): Rayleigh [29] and Plesset [30] proposed the famous Rayleigh-Plesset equation, which expresses the change of bubble radius with time.
Here, B ( ) P t is the pressure inside the bubble; ( ) P t  is the pressure outside the infinite bubble; L  is the density of the liquid; R is the radius of the bubble; R  and R  are the speed and acceleration of the bubble expansion, respectively; L  is the kinematic viscosity of the liquid; and S is the surface tension of the bubble. In fact, the bubbles in this experiment do not exist in such an ideal environment. However, as the basic theory of the bubble radius, it still provides a good reference value for the experiments. As mentioned above, due to limitations of the high shear rate and liquid film thickness, the bubble size will be limited to a relatively uniform size during a short polishing time. Therefore, we chose the average radius, b avg R  , as the radius of the micro-nano bubbles in the polishing process. Combining Eqs. (14)-(16), the total number of bubbles per unit time, all N  , in the polishing process is shown as Eq. (18): where b M and b  are the relative molecular mass and density of hydrogen, respectively. However, only a portion of the bubbles that can form micro-jets per unit time are called active bubbles. The proportion of active bubbles is a k , which is proportional to the density of the asperity, Therefore, Eq. (20) for the volume of material removed by bubble collapse per unit time is expressed as The MRR of conventional CMP is often estimated by the thickness of the material removed per unit time, In addition to the generation of micro-jets, the collapse of bubbles will also form hydroxyl radicals [31]. The hydroxyl radicals will slightly change the surface of the wafer and the surface of the pad. Such changes will increase the friction coefficient of the traditional CMP system, thereby increasing the MRR of the traditional CMP [32]. The MRR of the traditional CMP is proportional to the friction coefficient. Therefore, in order to further improve the a MRR , a correction coefficient, f k , is introduced.
Next, the polishing experiments were conducted to verify the accuracy of this mathematical model.

Results and analysis 4.1 Micro-nano bubbles
Sodium borohydride reacts with water to form hydrogen, and apart from the small amount of gas dissolved in the solution, most of it exists in the solution in the form of bubbles. Because the polishing process cannot be observed on a micro-level in situ, an off-line method is used to observe and characterize the hydrogen bubbles formed by the hydrolysis of sodium borohydride. We placed a small amount of NaBH 4 dissolved in an aqueous solution under an optical microscope and found that it can indeed be hydrolyzed to form numerous bubbles at room temperature, as shown in Fig. 4(a). In order to preliminarily determine the size of these bubbles, this was combined with the DLS method to measure the bubble size distribution in the solution. Figure 4(b) shows that the bubbles present a multi-size distribution under normal conditions with sizes of about 20 nm, 200 nm, 1.5 μm, and 26 μm. This shows that numerous micro-nano bubbles can be formed during the polishing process. Endo et al. [33] and Bai et al. [34] showed that for a larger liquid film thickness, the bubbles are larger; while for a smaller layer thickness, a large number of smaller bubbles were observed. In the actual polishing process, in addition to the lower slurry film thickness, other factors, such as the short polishing time, limit the growth time of the bubbles. In addition, the asperity size of the pad is limited to the micron level, which will further limit the size of the bubbles within a certain range. The surface profile of the pad is shown in Fig. 5. It is not difficult to see that the width between the surface rough peaks of the pad is only about 100 μm, and the depth is about 30 μm. Therefore, the average bubble radius used in the mathematical model is reasonable. In addition, the existence of micro-nano bubbles in the slurry provides the most important prerequisite for bubble collapse to form micro-jets.

Influencing factors of MRR
This study involved the use of a new chemical (NaBH 4 ) in the slurry, so a brief analysis of its possible impact on CMP is required. From Reaction (2), it can be seen that NaBH 4 is hydrolyzed to form a strongly basic metaborate ion 4 B(OH)  , which causes the whole slurry to be alkaline. After adjustment, the pH value can finally be controlled at 10, which is in line with the normal pH range of conventional alkaline slurries. In addition to the impact of micro-jets caused by bubble collapse mentioned above, the dispersibility of abrasives [35] and the chemical corrosion of reagents [36] will also have a great impact on MRR.

Dispersity of abrasives
The morphology of the silica abrasives in the two slurries (with or without NaBH 4 ) is shown in Fig. 6. It can be found that the size of the particles is uniform, and the morphology and distribution of the abrasives in the two slurries show no obvious changes. Figure 7(a) shows the size distributions of the abrasives in the two slurries. It can be seen in Fig. 7(a) that there is only a single peak, and the particle sizes are similar at about 55 nm. Figure 7(b) shows the corresponding zeta potentials of the two slurries. The zeta potential of pure silica sol is −81.7 mV, and the zeta potential of the silica sol with NaBH 4 is −78.9 mV. Their absolute values are similar and very high, representing good dispersibility. Therefore, sodium borohydride has little effect on the size and dispersibility of the abrasives.

Corrosiveness of chemicals
In addition to the formation of alkaline ions by the  www.Springer.com/journal/40544 | Friction hydrolysis reaction of NaBH 4 , its own H − has strong reducibility, so the influence of the chemical reducibility of H − on the silicon oxide wafer has to be considered. For this reason, the wafer was deliberately immersed in two slurries for 24 h to evaluate the static corrosion degree of the slurry. In order to ensure the accuracy of the measurement, 10 points on the middle axis of the wafer were selected. The specific corrosion rate is shown in Fig. 8. The average static corrosion rates of pure silica sol and the silica sol with NaBH 4 are 1.14 and 1.20 Å/h, respectively, which are approximately equal. This result shows that the addition of NaBH 4 does not increase the chemical corrosion rate of the wafer. In addition, considering the influence of chemical reagents on the wafer surface morphology, the wafer surface morphology before and after corrosion was evaluated, as shown in Fig. 9. It can be seen in Fig. 9 that the surface roughness of the initial wafer is 0.302 nm, while the surface roughness of the wafer after corrosion by pure silica sol and the silica sol with NaBH 4 decreased slightly to 0.263 and 0.255 nm, respectively. Therefore, after corrosion by different slurries, the surface roughnesses of the wafer were not significantly different, demonstrating that the surface morphology of the wafer does not change much.
In order to analyze the chemical interaction between NaBH 4 and the silicon oxide wafer, the X-ray spectroscopy (XPS) analysis was performed on the surface elements of the wafer before and after corrosion. It can be seen in Fig. 10 that the surface of the initial wafer shows conventional silicon oxide peaks. However, the element peaks of the wafer immersed in different slurries did not show any obvious changes from the initial wafer, and no new peaks appeared, indicating that the silica sol containing NaBH 4 will not undergo additional chemical reactions with the oxide wafer. Although the chemical corrosion effect of the dynamic polishing process is more complicated, static corrosion can still provide a good reference value.

Polishing performance and verification
Silicon oxide wafers were polished with different slurries (with and without NaBH 4 ), and the MRR was calculated using Eq. (23) in units of the thickness difference, Thickness  , per time, T, before and after polishing. In order to reduce the error, each sample was polished 3 times, and 10 points on the middle axis of the wafer were selected for the measurements to compute the average MRR values. thickness

MRR
Thickness / T   (23) Fig. 9 Surface morphologies (the 3D images are embedded) of (a) initial wafer, (b) wafer in the silica sol, and (c) wafer in the silica sol with NaBH 4 .

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Friction 11(9): 1624-1640 (2023) | https://mc03.manuscriptcentral.com/friction Figure 11(a) shows the average MRR values of pure silica sol and silica sol with different concentrations of NaBH 4 . Compared to the MRR of pure silica sol (127.60 Å/min), the MRR of the silica sol with NaBH 4 is generally higher, with up to a 400% increase (642.37 Å/min). Furthermore, the MRR values increase with increasing NaBH 4 concentrations, and then tend to be flat after increasing to a certain extent. The previous growth trend is consistent with the inferred Eq. (22), and the MRR is directly proportional to the concentration of NaBH 4 . We believe that this is mainly because the increase of the concentration of NaBH 4 promotes the hydrolysis reaction, which increases the number of hydrogen micro-nano bubbles in the system, and the subsequent material loss caused by the micro-jets resulting from bubble collapse increases. The MRR tends to be flat because the number of effective micro-nano bubbles in the system reached its peak, and no amount of bubbles will cause additional material removal.
Using the calculation method in Ref. [37], the main parameters of the J-C constitutive model are calculated,  www.Springer.com/journal/40544 | Friction according to the results of the silica strain-stress curve at different strain rates reported in Ref. [38]. The inherent physical properties of amorphous silica determine its J-C constitutive model parameters, so it is suitable for the silica wafers in this study. The detailed calculation process is recorded in the ESM. The parameters of the NaBH 4 hydrolysis reaction in Eq. (22) are provided by Ref. [39]. The parameters of the polishing pad are obtained from Fig. 5. The average radius of micro-nano bubbles is calculated from the results in Fig. 4. Figure S2 in the ESM shows the surface of the wafer after polishing by the silica sol with 0.6 wt% NaBH 4 for 5 s. It can be found that there are still cavitation pits formed by micro-jets on the surface of the silica wafer. This is because the chemical and mechanical effects of traditional CMP are weak due to short polishing time, while the cavitation effect formed by micro-nano bubbles is relatively strong. On the one hand, the cavitation effect of the micro-jet is confirmed. On the other hand, it can estimate the average radius of the micro-jet based on the cavitation pits on the wafer surface. The friction coefficients of each slurry during the polishing process were measured and calculated by the GnP polishing machine, as shown in Table S1 in the ESM. Compared with the friction coefficient of pure silica sol of 0.431, the friction coefficients of the silica sol with NaBH 4 range from 0.633 to 0.690 (the average value is 0.672). Therefore, the correction coefficient is about 1.56. When the concentration of NaBH 4 is 0.1 wt%, the MRR value is 271.3 Å/min. Thus, the effective collapse coefficient * k is obtained, 0.823. All the parameters are recorded in Table 2. The  fitting line in Fig. 11(a) is consistent with the actual measured MRR, which illustrates the reliability of the mathematical model. In addition, it can be found that the error bars shown in Fig. 11(a) are relatively small in the initial and final stages. The error value first increases and then decreases as the concentration increases. This is consistent with the slight deviation between the actual measured MRR and the fitting line at medium concentration. In order to clarify the reason for this behavior, a trend of the MRR obtained by polishing three times for all slurries was made, as shown in Fig. 11(b). The slurry used for the three polishing times of each wafer was the same, and each polishing was about 3 min apart. For the silica sol with 0.1 wt% NaBH 4 , the MRR of the three polishing times is almost the same. This is because when the NaBH 4 concentration is too low, the reaction rate is low and stable, and the number of bubbles remains constant. Furthermore, the MRR at each concentration showed a trend of increasing greatly at first and then gradually. This is mainly because when the concentration of NaBH 4 is constant, the hydrolysis reaction of NaBH 4 has different reaction stages, and the reaction rates in different stages are different [28]. The relationship between the mass of NaBH 4 and the rate of hydrogen generation was studied, as shown in Fig. 12. The corresponding concentration of 0.5 g NaBH 4 is 0.1 wt%. It can be found that the rate trend of hydrogen generation is consistent with the trend of MRR, which also increased first and then leveled off. This also shows that MRR is related to the amount of hydrogen (the number of active bubbles). As the concentration increases, the hydrogen generation rate in the initial stage of the hydrolysis reaction increases. As a result, the numbers of active bubbles generated at the same time at different concentrations are different, and the growth of the number of bubbles at the same polishing time of different slurries increases with increasing concentration, thus forming the trend of the error bars (first increase and then decrease). When the concentration is high enough, the rate of the hydrolysis reaction is too fast, and the rate of hydrogen generation quickly reaches its peak; so that at a high concentration, the MRR of slurry tends to be stable, and the error is reduced. Moreover, the  deviation between the actual measured MRR and the fitting line is within the error bar of the actual measured MRR and can be ignored. In summary, the MRR in the actual polishing process is consistent with Eq. (22), which proves the correctness of the mathematical model.
Of course, the average surface roughness, R a , of the silicon oxide wafer is also very important. The surface morphology and R a of the polished wafer corresponding to different slurries are shown in Fig. 13. Compared to the surface morphology of the initial wafer shown in Fig. 9(a), the surface of the polished wafer was improved. The R a of the wafer polished by pure silica sol and the silica sol with NaBH 4 are about 0.19 and 0.17 nm, respectively, with little difference between them. This means that micro-nano bubbles can also effectively reduce the roughness of the wafer. This is because on the one hand, the micro-jets cause a higher removal rate, so that the silica sol with NaBH 4 can remove more rough peaks. On the other hand, the impact of the micro-jet in the actual polishing process is not always perpendicular to the wafer surface. The impact of the micro-jet in oblique or horizontal direction has a great effect on removing the rough peaks on the wafer surface, so that the wafer surface tends to be flat. In addition, the surface quality of the wafer is not affected by the cavitation effect of micro-nano bubbles. This is because as the polishing time increases, the chemical and mechanical effects in CMP are enhanced until they reach a state of equilibrium with the cavitation effect, so that the cavitation pits can be removed in time. This is why cavitation pits are not visible after polishing. Furthermore, there is no subsurface damage on the wafer because CFP is one of the main methods to eliminate subsurface damage [40,41].

Conclusions
In this work, combined with the traditional CMP material removal mechanism, the material removal model of micro-nano bubbles in the auxiliary polishing process was established for the first time. The result reveal the auxiliary mechanism of activated micro-nano bubbles on CMP. The basic idea of the model is   MRR is the material removal rate of traditional CMP, p V is the volume of material removed by a single bubble, b N  is the number of active bubbles per unit time, and 0 A is the area of the wafer. The model is consistent with the experimental results. The main conclusions are drawn as follows.
1) Based on theories such as mixed lubrication, brittle deformation, the spherical indentation theory, and J-C constitutive model, the model proposed in this paper integrates many important parameters in the polishing process (wafer hardness, pad roughness, reactant concentration, asperity density, micro-jet radius, bubble radius, strain rate, strain hardening, etc.) to represent the MRR.
2) MRR is proportional to the number of active micro-nano bubbles. The micro-jet caused by the collapse of micro-nano bubbles causes additional cavitation damage to the wafer, which can increase the MRR.
3) The chemical reaction method was used to form micro-nano bubbles in the polishing process. Based on factors such as thin film lubrication and growth time limitation, combined with the size of the bubbles detected by the off-line method (showing a multi-scale distribution of micrometers and nanometers), it is inferred that the bubbles during the polishing process are at the nanometer or micrometer scale. 4) We used a sodium borohydride hydrolysis method to induce micro-nano bubbles. Compared to that of conventional silica sol, the MRR of silica sol with NaBH 4 can be increased by about 400%, and the surface roughness can be lowered by 0.17 nm.
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