A novel atomic removal model for chemical mechanical polishing using developed mesoporous shell/core abrasives based on molecular dynamics

Abstract

To improve polishing performance and reduce the environmental pollution of chemical mechanical polishing (CMP) tests, mesoporous shell/core silica abrasives were prepared, and a novel green CMP slurry was developed, including sorbitol, hydrogen peroxide and sodium carbonate. Prior to CMP, fused silica was roughly polished with ceria slurry. Using developed mesoporous abrasives, surface roughness S_a is reduced from 0.347 to 0.253 nm for a scanning area of 200 × 200 μm², and the material removal rate (MRR) is increased from 70 to 127 nm min⁻¹, compared with traditional solid abrasives. Based on molecular dynamics (MD) simulations, a novel atomic removal model is proposed for mesoporous abrasives through the immediate elastic recovery of atoms. MD simulations suggest that the formation of convex peaks and pits was inhibited by the mesoporous structure, promoting uniform distribution of surface atoms and atomic removal. This is different from a conventional simple increase of polishing times. In addition, more bridge bonds of Si–O–Si and a lower average Si–O bond order are produced in fused silica samples due to their mesoporous structure, contributing to a higher MRR.

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Introduction

Chemical mechanical polishing (CMP) is an ultra-precision processing technology that integrates chemical corrosion and mechanical removal.^1–6 This synergy serves to effectively diminish surface roughness and sub-surface damage, ultimately yielding an impeccably smooth and unblemished surface.⁷ In particular, abrasives in CMP play an important role in both fundamental mechanical force and bonding force on account of their advantages for material removal, and thus polishing performance is significantly affected by the morphology, structure, size and chemical composition of abrasives.^8,9

For decades, a series of research studies have been conducted to investigate the influence of abrasive morphology^10,11 and the micro-topological structure^12–15 on polishing performance. Liang et al. synthesized necklace-shaped silica particles which exhibited a superior material removal rate (MRR) from 13.4 nm min⁻¹ to 22.2 nm min⁻¹ compared with conventional silica particles.¹⁰ Compared with spherical particles, the MRR can be improved by 117.4% utilizing flower-shaped particles synthesized by Xu et al.¹¹ While the above nanoparticles undeniably yield a substantial elevation in polishing efficiency, their discernible impact on enhancing the quality of the workpiece surface remains less pronounced. By contrast, the mesoporous structure exhibits a dual advantage, notably augmenting both polishing efficiency and surface quality, which has been confirmed in some reports.^16–20 Ryu et al. discovered that the mesoporous structure of wrinkled silica nanoparticles increased the MRR by 89.3% and reduced root-mean-square (RMS) roughness from 0.226 nm to 0.164 nm compared to silica nanospheres.¹⁶ Chen et al. utilized the mesoporous structure to obtain superior polishing efficiency increasing from 21.1% to 163.9% and polishing quality improving from 32.2% to 60% in RMS relative to solid silica particles (sSiO₂).^17,18 Lei et al. prepared mesoporous structure alumina abrasives and obtained a higher MRR from 1.75 mg min⁻¹ to 4.25 mg min⁻¹ and reduced surface roughness by 12.2% compared with solid alumina abrasives.¹⁹ From the perspective of microstructure, mesoporous structure can be considered a normal abrasive with holes on its surface, akin to nanoscale cutting edges that encompass minute gaps.²¹ This intriguing attribute leads to the presence of what can be termed nanoscale gap multi-edges (NGMEs), which wield a dual advantage by positively influencing both surface roughness and the MRR in CMP. While a plethora of studies have concentrated on elucidating its efficacy and practical utility in polishing performance, the nuanced microscopic effects and underlying removal mechanisms intrinsic to the mesoporous structure in CMP have yet to receive unequivocal explication.

At present, due to the limitations of testing techniques, the mesoporous structure action mechanism during CMP remains elusive and cannot be directly observed or documented. Most previous reports concentrated on conducting various types of experimental characterization methods to infer the material removal mechanism, which is still hard and expensive.^17,22 Molecular dynamics (MD) simulation provides an alternative solution, which has been proven effective in exploring the material removal mechanism.²³ As a computational approach that explores atomic dynamic behaviors, MD simulations can intuitively reflect the dynamic evolution process of materials.^24–27 Chen et al. explored the atomic adhesive behavior of silicon under impact processing of porous silica clusters based on classical MD, which mainly depended on the elastic–plastic deformation of abrasives during impact.²⁴ Vo et al. utilized ReaxFF MD to investigate the influence of pore shape and porosity on the mechanical properties of abrasives.²⁸ Regrettably, the atomic-scale mechanical and chemical removal effects of NGMEs pertaining to the mesoporous structure abrasives in CMP have received limited attention in the current work. Consequently, the specific way that NGMEs contribute to material removal remains an enigma, posing a substantial impediment to the advancement of subsequent nano/atomic-level processing methodologies. Through the meter per second (m s⁻¹) level of polishing speed, the contact interval between two edges with a nanogap is just picosecond scale, which is consistent with MD. Thus, MD simulations stand as a judicious approach for investigating the intricate action mechanism underlying NGMEs and have the potential to elucidate the uncharted terrain of NGME-driven material removal.

Herein, to realize the complementarity of different structures and utilize the surface smoothing effect of spherical shape,^1,29 mesoporous core/shell silica nanosphere abrasives (sSiO₂@mSiO₂) were synthesized and applied in CMP. According to CMP experiment results, sSiO₂@mSiO₂ manifest superior potential in both polishing efficiency and quality compared with sSiO₂. After that, MD simulations were conducted to explore the chemical–mechanical cutting mechanism of NGMEs. In simulations, both classical and ReaxFF MD models with special double-tips representing the multiple edges of the mesoporous structure were established to synergistically investigate the action mechanism. This proposed approach provides a valuable analytical approach for nano/atomic scale processing and theoretical guidance for subsequent related work.

Methodology

Experiment details

Synthesis of silica abrasives. The sSiO₂@mSiO₂ particles were synthesized by a modified Stöber method,^22,30 and all correlative chemicals were purchased from Sinopharm Chemical Reagent Co., Ltd (China). Firstly, deionized water (DI, 50 mL), absolute ethanol (EtOH, 50 mL) and ammonium hydroxide aqueous solution (NH₄OH, 6 mL) were thoroughly mixed using a magnetic stirrer (350 rpm) for 10 min at room temperature. Next tetraethyl orthosilicate (TEOS, 5 mL) was rapidly injected into the previous solution and stirred for 3 h. Then, after adding EtOH (250 mL), DI (550 mL) and hexadecyltrimethylammonium bromide (CTAB, 3.2 g) sequentially, the mixed solution was stirred for 30 min and sonicated for 15 min. EtOH (30 mL) and TEOS (13.4 mL) were stirred (600 rpm) for 30 min for complete mixing and then added dropwise to the previous solution. After dripping, the mixture was stirred (600 rpm) for 2 h. Subsequently, silica particles from the solution were centrifuged (7000 rpm) and washed with EtOH and DI, and then dried overnight at 80 °C. Finally, the particles were ground and calcined at 550 °C for 8 h to obtain sSiO₂@mSiO₂ (Fig. 1(a)).

Fig. 1 Schematic diagram and characterization of silica abrasives: (a) synthesis process of sSiO₂@mSiO₂ and sSiO₂, (b) SEM of cSiO₂, (c) SEM of sSiO₂, (d) particle size distribution of sSiO₂, (e) TEM of sSiO₂@mSiO₂, (f) SEM of sSiO₂@mSiO₂, and (g) particle size distribution and pore size distribution of sSiO₂@mSiO₂.

Since the sizes of commercial silica abrasives (cSiO₂) from Jinan Zhongye New Materials Co., Ltd (China) were inconsistent (Fig. 1(b)), it was impossible to form a control experiment with a similar particle size, morphology and structure between sSiO₂@mSiO₂ and cSiO₂, so the synthesis of sSiO₂ was still required. Briefly, DI (45 mL), EtOH (45 mL) and NH₄OH (14 mL) were mixed at room temperature. Next, TEOS (10 mL) was fast-injected into the mixed solution and stirred (600 rpm) for 4 h. Then silica particles from the solution were centrifuged (7000 rpm) and washed with EtOH and DI several times, and dried overnight at 80 °C. Finally, the sSiO₂ was obtained after grinding and calcining at 550 °C for 8 h.

Chemical mechanical polishing tests. The fused silica samples (10 mm × 10 mm × 4 mm) purchased from Donghai County Weida Quartz Products Co., Ltd (China) were applied in CMP tests. All CMP experiments were performed on a UNIPOL-1502 polishing machine from Shenyang Kejing Auto-instrument Co., Ltd (China). In this experiment, D-sorbitol from Shanghai Aladdin Biochemical Technology Co., Ltd (China), sodium carbonate (Na₂CO₃) and 30% hydrogen peroxide solution (H₂O₂) from Sinopharm Chemical Reagent Co., Ltd (China) were employed as a dispersant, a pH regulator and an oxidant, respectively. Before CMP, three samples were evenly distributed and glued on a cast iron disc (8 cm in diameter). Then 500 mL of rough polishing slurry with ceria abrasives (3 μm CeO₂) from Jinan Zhongye New Materials Co., Ltd (China) was utilized to roughly polish the samples for 1 h to obtain flat silica surfaces with reduced sub-surface damage. Then, cSiO₂, sSiO₂, and sSiO₂@mSiO₂ were employed respectively to prepare a fine polishing slurry for subsequent CMP experiments. The detailed polishing slurry compositions and process parameters are shown in Table 1.

Table 1 CMP test parameters

Tests	Polishing slurry parameters			Process parameters
	Abrasive	Oxidant	pH regulator	Pressure	Speed	Flow rate
Rough polishing	4 wt% CeO2	—	—	27.5 kPa	90 rpm	15 mL min^−1
Fine polishing	3 wt% cSiO2	5 wt% H2O2	0.4 wt% Na2CO3	37.5 kPa	80 rpm	20 mL min^−1
	3 wt% sSiO2
	3 wt% sSiO2@mSiO2

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Characterization

The morphology of silica abrasives was characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Nitrogen (N₂) adsorption/desorption and X-ray diffraction (XRD) were utilized to investigate the aperture distribution of sSiO₂@mSiO₂. An optical surface profiler (Zygo NewView™ 9000, USA) was applied to measure the surface roughness of silica samples. The surface topography of the silica samples was investigated using an optical microscope (BX53M, Olympus, Japan). The surface chemical information of fused silica was characterized by Fourier-transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. A precision balance (Lichen, China) was utilized to weigh the mass of the silica samples before and after CMP. And the MRR of the samples was calculated using eqn (1):where Δm (g) is the mass difference of the samples before and after CMP, ρ (g cm⁻³) is the material density of fused silica, S (cm²) is the contact area between the samples and the polishing pad in CMP, and τ (min) is the polishing duration.

Molecular dynamics models

Due to the limitations of both classical MD and ReaxFF MD, it is difficult to comprehensively describe the NGME effect based on a single force field. In this work, two types of different force fields were combined to complement each other based on microscopic atoms. For classical MD, the influences under the mechanical effects of NGMEs on large area fused silica surfaces were investigated. On the other hand, chemical reactions and interatomic dynamic behaviors between the abrasive-slurry and the substrate in different systems were researched through the formation and breaking of chemical bonds by ReaxFF MD. The details of the model establishment are in the ESI.†

Results and discussion

Experiment results

The micromorphologies of various silica abrasives utilized in CMP experiments are shown in Fig. 1(b)–(g). It can be found that cSiO₂ has a much wider size distribution range (Fig. 1(b)), while both synthetic particles manifest outstanding size uniformity (Fig. 1(c), (e) and (f)). Furthermore, Fig. 1(d) and (g) illustrate the particle diameter distribution of sSiO₂ and sSiO₂@mSiO₂ and the average particle sizes are 361.5 ± 37.2 nm and 353.3 ± 29.2 nm. Therefore, the influence of both particle size and shape on the CMP process is minimized and the comparison between abrasives is reasonable.

To investigate the atomic arrangement and structure orderliness, wide-angle and small-angle XRD tests were conducted on two types of abrasives respectively (Fig. 2(a) and (b)). Fig. 2(a) shows that the diffraction intensity trends of double abrasives are basically identical, and both have feature peaks with a large distribution range around 2θ ≈ 22° instead of sharp diffraction peaks. Such peaks are attributed to atomic arrangement, which manifests that both particles belong to the amorphous silica structure.³¹ And that corresponds to the construction of molecular dynamics models. It can be seen from the small-angle diffraction pattern (Fig. 2(b)) that sSiO₂@mSiO₂ has an obvious feature peak near 2θ ≈ 2.82°, while the diffraction curve of sSiO₂ is smooth as a whole. And the feature peak is associated with ordered pores of sSiO₂@mSiO₂.³² According to Bragg's equation (eqn (2)),³³ the aperture corresponding to the feature peak value is 3.13 nm. Moreover, based on N₂ desorption branching, the most probable aperture of synthetic sSiO₂@mSiO₂ analyzed by the Barrett–Joyner–Halenda (BJH) method is 3.069 nm (top right of Fig. 1(g)), which is consistent with the results of small-angle XRD. Therefore, sSiO₂ and sSiO₂@mSiO₂ are consistent in atomic arrangement, and sSiO₂@mSiO₂ particles have an ordered mesoporous shell.

nλ = 2d sin θ (2)

Fig. 2 Characterization results of abrasives and the workpiece: (a) wide-angle and (b) small-angle XRD patterns of different abrasives, (c) FTIR and (d) Raman spectroscopy of fused silica before and after 12 h slurry immersion, XPS (e) full spectrum and (f) O 1s fine spectrum of fused silica before (origin) and after polishing (sSiO₂ and sSiO₂@mSiO₂).

To explore the possible chemical reactions during CMP, FTIR, XPS and Raman spectroscopy were performed on fused silica samples (Fig. 2(c)–(f)). Fig. 2(c) displays the transmittance difference before and after 12 h slurry immersion, and the difference occurs only in the yellow region. The infrared bands at 1137 cm⁻¹ and 776 cm⁻¹ are contributed by the antisymmetric and symmetric stretching vibrations of Si–O bonds,^34,35 and the feature peak centered at 954 cm⁻¹ corresponds to the Si–O antisymmetric tensile vibration from the silanol structure (≡Si–OH).³⁶ Under the influence of the slurry, chemical reactions such as hydrogenation and hydroxylation occurred on the workpiece surface, which facilitated the increase of the oxidation degree and silanol content (eqn (3)–(7)). Therefore, the yellow region transmittance of fused silica is greatly reduced after immersion.³⁷ The results of Raman spectroscopy and XPS also illustrate this point. Fig. 2(d) displays the Raman spectrum after subtracting the baseline. The main peak (ω₁) centered at 433 cm⁻¹ corresponds to the bond angle distribution of Si–O–Si, the bands at 490 cm⁻¹ (D₁) and 602 cm⁻¹ (D₂) are attributed to the vibrations of quaternary and ternary Si–O rings, respectively, and ω₃ and ω₄ are associated with the Si–O stretching vibration.^38–40 After immersion, the feature peaks corresponding to ω₁ and D₁ were significantly enhanced, indicating an increase of oxygen content in fused silica. Fig. 2(e) shows that except for a few Na elements, no other impurity elements pollute the workpiece surface after CMP, which avoids serious damage to material properties. And the oxygen content of the workpiece surface increased slightly after polishing (Fig. 2(f)).

NaCO₃ + H₂O ⇌ 2Na⁺ + HCO₃⁻ + OH⁻ (3)

HCO₃⁻ + H₂O ⇌ H₂CO₃ + OH⁻ (4)

H₂O ⇌ H⁺ + OH⁻ (5)

(≡Si)⁺ + OH⁻ ⇌ (≡Si–OH) (6)

(≡Si–O)⁻ + H⁺ ⇌ (≡Si–OH) (7)

The surface morphology of fused silica after rough polishing is shown in Fig. 3(a) and (b). It can be seen that there are numerous scratches and pits on the workpiece surface after rough polishing and the surface roughness S_a is 4.805 nm. After fine polishing (Fig. 3(g)–(i)), the workpiece surface still manifests some defects such as pits and scratches in the cSiO₂ system, while sSiO₂ and sSiO₂@mSiO₂ induced samples are relatively smooth. This discrepancy can be attributed to the highly uneven particle sizes of cSiO₂, whereas sSiO₂ and sSiO₂@mSiO₂ demonstrate a more uniform particle size distribution. For consistent particles, the load from the workpiece will be evenly distributed on each particle during CMP. However, for inconsistent particles, the load is concentrated on a small fraction of particles with larger diameters. This concentration of load presses particles to a greater depth, leading to the formation of scratches and pits on the workpiece surface.

Fig. 3 Microscopic topography of the fused silica surface after rough and fine polishing: (a) optical surface morphology and (b) surface roughness in the 200 × 200 μm² area after rough polishing, (c) MRR curve, (d–f) surface morphology and (g–i) optical images of the fused silica surface induced by cSiO₂, sSiO₂ and sSiO₂@mSiO₂ after fine polishing.

According to CMP characterization tests as shown in Fig. 3(c)–(f), the system induced by sSiO₂@mSiO₂ exhibits a higher MRR and better S_a. For CMP systems with cSiO₂, sSiO₂ and sSiO₂@mSiO₂, MRRs of fused silica are 76 ± 19 nm min⁻¹, 70 ± 12 nm min⁻¹ and 127 ± 28 nm min⁻¹, respectively. And the S_a of cSiO₂, sSiO₂ and sSiO₂@mSiO₂ are 0.409 nm, 0.347 nm and 0.253 nm with a scanning area of 200 × 200 μm², respectively. Compared to sSiO₂, sSiO₂@mSiO₂ can induce an 81.4% higher MRR and lower the surface roughness by 27.1%. Since the size and shape of abrasives are identical and other polishing parameters are the same, these improvements are solely contributed by the mesoporous structure.

Influence of the removal of immediate elastic recovery atoms

To reveal the mesoporous structure effect of sSiO₂@mSiO₂ abrasives, a series of CMP simulations induced by abrasives with different d₁ (Fig. S1†) at 50 m s⁻¹ were conducted and three simulations were carried out for each process parameter. Compared to the sSiO₂ system, the system induced by 3 nm sSiO₂@mSiO₂ exhibits a 13.9% lower S_a and 383 more removed atoms (Fig. 4(a) and (b)), which matches the experiment results. Through further simulation, it is discovered that the surface roughness becomes lower as the aperture increases, and the number of removed atoms increases first from 0 to 3 nm and then decreases sharply (even less than the sSiO₂ system), which indicates that superior S_a and MRR are both contributed by the mesoporous structure with an appropriate aperture.

Fig. 4 Simulated polishing performance of fused silica: (a) roughness comparison of abrasives with different d₁, (b) comparison of the number of removed atoms of abrasives with different d₁, and (c–e) extracted atoms and the surface of the workpiece induced by sSiO₂, sSiO₂@mSiO₂ (1.5 nm) and sSiO₂@mSiO₂ (3 nm) at 50 m s⁻¹ (the yellow curved area indicates pit defects).

To investigate what causes the decrease in surface roughness, processed systems induced by both abrasives were explored (Fig. 5(a)–(c)). No accumulated atoms were formed in front of both abrasives while some atoms were embedded in the mesoporous gap as shown in Fig. 5(b). Fig. 5(c) illustrates that the top accumulated atoms were carried from a further distance, while the below ones were from adjacent spots. According to trajectory lines (Fig. 5(d)), the accumulated atoms experienced two stages of compression and rebound relative to the abrasive under continuous scratching, and a series of dynamic snapshots about some atoms were recorded (Fig. 5(e)–(j)). During MD simulations, the elastoplastic deformation occurred on the substrate surface. Firstly, only some atoms in the right direction were compressed (hydrostatic stress in blue, Fig. 5(e)). As scratching progressed, the left atoms were also pressed down and all atoms slipped slightly to the negative X axis (Fig. 5(f) and (g)). After the external load disappeared (abrasive leaving), immediate elastic recovery occurred under the action of interatomic repulsion on the substrate surface (hydrostatic stress turns pink)^41–43 which was manifested by an upward bulge of the substrate relative to the abrasive bottom. For the presence of pores, the bulge would be embedded in the pores (Fig. 5(h) and (i)). As the abrasive moved, tips continued to squeeze and scratch the bulge, and then part of the bulge was removed (Fig. 5(j)), which inhibits the formation of convex peaks and promotes uniform distribution of surface atoms. Moreover, the removed atoms would accumulate gradually and the initial accumulated atoms would continue to rise during the removal of immediate elastic recovery atoms (RERA) subsequently (Fig. 5(c) and (d)), which is different from the adhesion removal of common abrasives in CMP.^44,45

Fig. 5 Atomic dynamic behavior: slice image of (a) sSiO₂ and (b) sSiO₂@mSiO₂ (3 nm) systems, (the red part represents accumulated atoms after CMP), (c) X-direction position cloud image of the sSiO₂@mSiO₂ (3 nm) system colored based on the atomic position before CMP, (d) complete displacement trajectory of atoms with the abrasive as the reference frame, (e–j) dynamic behavior of some atoms and their corresponding displacement vectors and hydrostatic stress states from 400 to 600 ps.

In addition to convex peaks, the formation of pits is also an important factor affecting roughness. As d₁ increases, the pit region on the surface gradually becomes smaller (Fig. 4(c)–(e)). When d₁ reaches 3 nm, large pits disappear and surface uniformity becomes better, which is consistent with the CMP experiments (Fig. 3(e) and (f)). Moreover, since the original surface after modeling was relatively smooth and S_a was near 0 (0.6853 Å), such pits were formed during the scratching process.

To investigate the reason for the formation of the pit region, the hydrostatic stress distribution and atomic displacement vector of the substrate were analyzed during CMP (Fig. 6). During sliding, workpiece atoms before and below the abrasive were squeezed to develop a compressive stress area. After the abrasive left, elastic recovery occurred behind the abrasive, and a tensile stress region was formed under the friction and adhesion of the abrasives. Meanwhile, under the friction effect, the plastic flow appeared on workpiece surface atoms below the abrasive. For the sSiO₂ system, the contact atoms were subjected to violent friction and adhesion to form a wide range of tensile stress zones (Fig. 6(a)), which caused a large section of tensile fracture behind the abrasive and thus pits were formed (Fig. 6(d)). As the aperture increases, the friction and adhesion between the abrasive and the workpiece surface weaken continuously, and the high tensile stressed zone gradually approaches the workpiece surface (Fig. 6(a)–(c)). When d₁ reaches 3 nm, the number of highly stressed atoms decreases significantly (Fig. 6(b)). Under the influence of nanoscale gaps, the REAR effect inhibits the formation of surface convex peaks and releases some stress from contact atoms, which reduces friction and adhesion below the second cutting edge. As a result, the range of the tensile stress region is obviously reduced (Fig. 6(b)), some atoms are accumulated before the second cutting edge by the RERA effect, and the depth of atomic flow behind the second edge is remarkably reduced (Fig. 6(e)). Therefore, inter-atomic tensile fracture can only occur in a few layers of surface atoms, which inhibits the formation of pits. In the 5 nm NGME system, the friction and adhesion are further weakened, and the distribution depth of high tensile stress atoms is pronouncedly lowered (Fig. 6(c)). Moreover, double almost independent atomic flow regions were formed below the two cutting edges and the atomic flow range was greatly reduced (Fig. 6(f)), which further improved surface quality.

Fig. 6 Atomic stress and displacement information: (a–c) hydrostatic stress distribution at 440 ps, the atoms with stress beyond 10 GPa or below −7.5 GPa were extracted as highly stressed atoms, and (d–f) atomic displacement vector at 460 ps in 0 nm, 3 nm and 5 nm NGME systems.

Notably impacting S_a, the influence of RERA extends to the MRR as well. The MRR is mainly contributed by two parts, namely, adhesive removal of the abrasive and the RERA effect. The accumulated atoms with more than 5 nm displacement in the X direction are defined as RERA atoms, which reflect the intensity of the RERA effect (Fig. 7(a)). From 0 to 3 nm systems, the RERA effect is continuously enhanced, which compensates for the slight decrease in abrasive adhesion, and a continuous increase in the number of removed atoms was observed (Fig. 4(b)). In the range of 3–5 nm, the RERA effect experiences substantial attenuation (Fig. 7(a) and (b)), concomitant with a diminishing adhesive influence of the abrasive. This brings about a pronounced decrease in the number of removed atoms, even less than that of the sSiO₂ system. When d₁ reaches 50 nm, scarcely any RERA atomic formation is observed (Fig. 7(c)), which illustrates that the RERA effect fundamentally differs from mere increasing in cutting number. This indicates that there is an optimal aperture size for RERA action, and too large or too small d₁ will both weaken RERA action. For smaller pore sizes, the elastic recovery of atoms is limited and the RERA effect is weakened. For larger apertures, surface atoms complete elastic recovery and re-enter equilibrium, and the second cutting edge will return to adhesion removal mode, greatly reducing or even making RERA not occur. According to simulation results, the RERA effect is most significant when d₁ is about 3 nm.

Fig. 7 Comparison of the RERA effect: (a) number of removed atoms by RERA in different systems, (b) and (c) slice images of the final system states when the gap is too small (1.5 nm), or the second edge comes 50 nm behind the first edge.

From the above analysis, the special atomic scale cutting effect (RERA) explained the better surface roughness and higher MRR induced by the mesoporous structure. And it was discovered that the RERA effect induced by 3 nm NGMEs was most significant and RERA bears an inherent distinction from the simple augmentation of cutting times. Such an effect is a vital factor in understanding mesoporous abrasive removal mechanisms and can be used in studying the benefits of porous abrasives in polishing more materials like sapphire and even SiC.

Effect of nanoscale gap multi-edges in chemical reactions

Though classical MD has successfully revealed the above special material removal mechanism that promotes the MRR utilizing porous abrasives, the chemical reaction aspect of such a process is still unknown. Whether NGMEs are capable of also promoting chemical reactions and leading to a higher MRR based on MD urgently needs to be investigated.

Based on previous research,^46,47 two essential stages in the process of removing atoms from fused silica exist: namely the formation of Si (substrate)–O–Si (abrasive) bridge bonds and the breaking of surrounding chemical bonds under the pull of bridge bonds.

(≡Si)⁺ + (≡Si–OH) ⇌ (≡Si–O–Si≡) + H⁺ (8)

H₃O⁺ ⇌ H⁺ + H₂O (9)

A group of atoms at the interface were tracked during scratching and a series of snapshots were captured as presented in Fig. 8 based on ReaxFF MD, which perfectly reveals the atomic removal process. Fig. 8(a)–(d) illustrate the formation of bridge bonds. Under the influence of the sliding process and surrounding atoms, Si¹ and Si² undergo dehydroxylation and dehydrogenation reactions, respectively, to form Si¹–O⁵–Si² bridge bonds. Fig. 8(e) and (f) indicate the breaking of surrounding chemical bonds under the pull of Si¹–O⁵–Si². The chemical reaction eqn (5)–(9) are involved in the whole process. According to the above dynamic process, the number of bridge bonds and the chemical bond stability are vital factors affecting material removal. Therefore, these two factors are the focus of the following exploration.

Fig. 8 Dynamic removal process of atoms from the substrate, where white fonts represent Si atoms, black fonts represent O atoms, and red fonts represent H atoms: (a–d) illustrates the forming of bridge bonds, and (e and f) the breaking of surrounding chemical bonds.

The number of Si (substrate)–O–Si (abrasive) bonds during the sliding process was counted as shown in Fig. 9(a), and it was found that more bridge bonds were commonly formed in sSiO₂@mSiO₂ systems, which means there were more atoms with a tendency to be removed.

Fig. 9 Information of bridge bonds and bond order in different abrasive systems: (a) number of Si (substrate)–O–Si (abrasive) bridge bonds, (b) pressing force on the abrasive along the Z axis direction; (I) is the relaxation stage and (II) is the down-pressing stage, (c) penetration depth and the surface atoms of systems with different d₂ under F₀ (100 nN), (d) average bond order of the Si–O bond of the substrate, (e) number of adsorbed O after the sliding process, (f) number of removed atoms of fused silica, and (g–i) the dynamic oxidation process.

To further explain the above difference, the information about pressing force and depth was processed and analyzed (Fig. 9(b) and (c)), and the Z-direction mean coordinate value difference of the abrasive bottom between the after-relaxation stage and under loading force F₀ (100 nN) was defined as penetration depth. As d₂ (Fig. S3†) increases, pressing force (F_z) decreases and penetration depth rises (Fig. 9(b) and (c)). The reason is that the effective contact area of sSiO₂@mSiO₂ samples is smaller than that of sSiO₂ under the influence of NGMEs, resulting in a single substrate contact atom bearing a larger load under the same loading force. To balance the extra load, the contact area atoms of the substrate are further compressed to create greater interatomic forces and thus contribute to a deeper penetration depth. This indicates that the contact atoms of the substrate will be more strongly squeezed under the influence of NGMEs.

In fact, the slurry layer would hinder the contact between the abrasive and the substrate to form bridge bonds, and a stronger compression effect would encourage abrasives to break through the slurry layer and contact the substrate, facilitating the formation of more Si–O–Si bridge bonds.⁴⁸ Furthermore, a nanoscale gap will inevitably reduce the compression area between the abrasive and the substrate, and thus the advantage of stronger compression in increasing bridge bonds is not obvious at the beginning of the sliding process. As abrasives slide, an under-compressed region corresponding to the original nanoscale gap is gradually compressed, and more bridge bonds in the sSiO₂@mSiO₂ system are formed under stronger compression (Fig. 9(a)).

Bond order is a numerical value that represents the strength of chemical bonds between atoms. The larger the bond order value is, the more stable the bond between atoms is, and the less likely the bond is to break.⁴⁹ As shown in Fig. 9(d), the average Si–O bond order of the substrate of the sSiO₂@mSiO₂ system is generally lower than that of sSiO₂, which indicates that the Si–O bonds of the substrate in the sSiO₂@mSiO₂ system are more unstable and it is easier to obtain enough energy to break through the energy barrier under external force to prompt atomic detachment and removal.

To further explore the reason for the difference in bond order, the number of substrate surface atoms was counted as presented in Fig. 9(c). It can be observed that the number of atoms on the workpiece surface is higher in the sSiO₂@mSiO₂ system, and this number increases with the growth of the nanoscale gap. Under the compression of a solid abrasive, the substrate surface atoms were squeezed evenly to form a flat surface. However, in the sSiO₂@mSiO₂ system, an under-compressed region was formed due to the nanoscale gap, which facilitated the formation of convex peaks on the surface and increased the number of surface atoms. For more surface atoms and stronger compression on contact atoms, more O atoms were adsorbed on the substrate surface for the oxidation reaction in the sSiO₂@mSiO₂ system (Fig. 9(e)), which is consistent with XPS results (Fig. 2(f)). Fig. 9(g)–(i) illustrate a common adsorption form of O atoms, which is consistent with the results of FTIR and Raman spectroscopy (eqn (5)–(7)). After the oxidation reaction (Fig. 9(e)), the coordination number of Si¹ increases (from 3 to 4), which lowers the stability and average bond order value of Si–O.^50,51

From the microscopic dynamic behavior of atoms, it can be found that more Si (substrate)–O–Si (abrasive) bridge bonds and a lower average bond order of Si–O bonds were formed in the sSiO₂@mSiO₂ system. The more bridge bonds indicate a tendency to remove more atoms, while the lower bond order value suggests that chemical bonds between atoms are more likely to break under the influence of an external force. Both factors contribute to the removal of a greater number of atoms. Therefore, the number of removed atoms in the sSiO₂@mSiO₂ system is universally higher than that in the sSiO₂ system (Fig. 9(f)), which is consistent with the CMP experiments.

Conclusions

This work explored the NGME effect of sSiO₂@mSiO₂ on fused silica by MD simulations combined with correlative experiments. Experiment results illustrate that fused silica samples manifest superior surface quality and polishing efficiency induced by sSiO₂@mSiO₂ compared with sSiO₂. Then based on a special material removal model caused by sSiO₂@mSiO₂, RERA was proposed. According to MD results, the RERA effect promotes atomic uniform distribution and removal and contributes to obtaining better surface quality and polishing efficiency compared with sSiO₂, which is similar to CMP experiment results. After further analysis, the strength of RERA exhibits a close correlation with nanoscale apertures. The RERA effect is most significant when d₁ equals 3 nm. And when the gap increases to a certain extent (i.e., 50 nm), the RERA effect almost disappears. Moreover, under the influence of sSiO₂@mSiO₂, more bridging bonds (from 20.7% to 41.4%) and lower average Si–O bond order values of fused silica were formed, which contributed to the removal of more atoms (from 13.3% to 60%). Therefore, the superiority of a mesoporous structure is well explained. This proposed approach offers a significant analytical method and theoretical guidance for related research work.

Author contributions

Z. Y. Z. conceived the projects. Z. S. L. performed the experiments and simulation. Z. S. L. and J. Y. F. analyzed the mechanism and completed the manuscript. X. Y., C. J. S. and F. Z. revised the manuscript. Y. G., S. H. L. and J. R. L. characterized the samples. All authors discussed the results.

Conflicts of interest

The authors declare no competing interests.

Acknowledgements

The authors acknowledge the financial support from the National Key Research and Development Program of China (2018YFA0703400), the Basic Research Expenses for Provincial Colleges and Universities – Research and Innovation Project for Young Teachers (GK239909299001-021), the Young Scientists Fund of the National Natural Science Foundation of China (52205447), and the Changjiang Scholars Program of the Chinese Ministry of Education.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nr04420c

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