Improvement of Material Removal Rate and Within Wafer Non-Uniformity in Chemical Mechanical Polishing Using Computational Fluid Dynamic Modeling

Abstract

Chemical mechanical polishing (CMP) is a widely used technique in semiconductor manufacturing to achieve a flat and smooth surface on silicon wafers. A key challenge in CMP is enhancing the material removal rate (MRR) while reducing within-wafer non-uniformity (WIWNU). A computational fluid dynamics (CFD) model is employed to analyze the slurry flow between the wafer and the polishing pad. Several factors influence the CMP process, including the type of abrasives, slurry flow rate, pad patterns, and contact pressure distribution. In this study, two polishing pad patterns with concentric and radial grooves are proposed to address how morphology variations influence wafer removal rate and consistency. Under the same operating conditions, the CFD simulations show that (i) the radial grooves have higher wall shear stress, a more significant negative pressure region, and a more evenly distributed mass on the wafer surface than the concentric grooves, and (ii) the radial grooves exhibit superior slurry mass distribution. It is noted that reducing the negative pressure differential field area results in a less pronounced back-mixing effect. A comparison of radial and concentric polishing pad grooves reveals that radial grooves improve slurry distribution, reduce the slurry saturation time (SST), and increase wall shear stress, leading to higher MRR and improved non-uniformity (NU). Precisely, the errors between the experimental SST values of 21.52 s and 16.06 s for concentric circular and radial groove pads, respectively, and the simulated SST values of 22.23 s and 15.73 s are minimal, at 3.33% and 3.35%.

1. Introduction

Chemical Mechanical Polishing (CMP) is a widely used process in the semiconductor and material industries for achieving high-precision polishing of surfaces [1]. The mechanical action of the pad and the chemical interactions from the slurry work synergistically to remove material at a controlled rate, ensuring a uniform and defect-free surface [2]. CMP is essential in creating flat substrates for integrated circuits and other microfabricated devices, as it enables better lithographic accuracy and multilayer integration. It is utilized in various applications, including optical systems, integrated circuits, and hard disk reading and writing [3]. During the CMP process, a wafer is held with the help of a rotating carrier [4], and the surface of the wafer is affected by pressure against the pad’s surface [5]. The slurry flow, made up of abrasive water particles, occurs on the pad’s surface and penetrates the space between the wafer and the pad [6]. The wafer’s surface is planarized, including the effects of the revolving pad, the rotating wafer, the chemical activities of the slurry, and the mechanical abrasions of the abrasive particles [7]. The physical qualities and the polishing process have not been completely comprehended [8]. A correlation exists between the load exerted on the carrier and the gap between the wafer and the pad [9]. A slight slurry coating establishes a barrier between the wafer and pad surfaces when the load is relatively low [10]. This film regulates the amount of material removed from the wafer surface, providing comprehensive support for the load transferred to the carrier. Considering this, the slurry flow is observed as a vital component of the CMP process [11]. Computational fluid dynamics (CFD) is a widely acknowledged method for visualizing fluid flow and investigating tribology, slurry filtration, transportation, and flow [12]. Several factors influence the flow of the grinding fluid in the CMP process. These factors include the flow rate, abrasive concentration (expressed as a weight percentage), grinding particle size, particle deformation, chemical additives, pH value, and temperature. The influence of grinding fluid flow can be studied using mathematical models, numerical models, and experiments [13]. The concentration and size of abrasive particles significantly influence the friction coefficient. A relationship exists between abrasive grains and the formation of scratches on the wafer’s surface [14]. A two-dimensional model can simulate the movement of abrasive grains in the space between the wafer and the polishing pad surfaces. The abrasive particles generate shear stress to meet the objectives of polishing and homogeneity [15]. Using computational fluid dynamics, the method of achieving optimal homogeneity in design is often explored. Jun et al. [16] conducted particle image measuring studies to confirm the uniformity of the flow of the polishing fluid on the polishing pad in terms of particle distribution. Uniformly flowing the polishing fluid enhances the achievement of improved wafer regularity in the polishing process [17]. The volume of fluid (VOF) model is employed to monitor the flow of clean water, whereas the discrete phase model (DPM) is utilized to follow the movement of particles [18]. This research has the potential to significantly contribute to understanding the mechanism behind the flattening process. Wafer surface uniformity is critical for wafer-to-wafer layering technology, which drives three-dimensional integrated circuit applications [19]. CMP is used in the semiconductor manufacturing to make wafer surfaces flat and smooth by combining chemical reactions and mechanical buffing [20]. The demand for electronic equipment, including smartphones and AI devices, is rising, driving significant growth in the market. When analyzing CMP results, factors such as material removal rate (MRR), within-wafer non-uniformity (WIWNU), wafer-to-wafer non-uniformity (WTWNU), and the presence of chemical or physical defects are critical considerations [21].

In addition to incorporating a cleaning stage, ensuring the process’s ultimate quality necessitates using dependable and uninterrupted slurry distribution systems. Initial iterations of tools were limited in their functionality, focusing solely on planarizing [22]. To reduce the cost of the CMP process, the tool evolution has focused on improving the wafer’s quality and dependability [23]. This has been achieved by incorporating bulk chemical distribution (BCD) and reprocessing systems, improving the efficiency and speed of the process through the addition of metrology equipment to the CMP tools, and integrating cleaners to introduce the dry-wafer-in (DWI) and dry-wafer-out (DWO) concept. The DWI-DWO technique involves drying an incoming wafer and subjecting it to CMP processing. One of the benefits of this method is the ability to analyze the internal movement of the polishing fluid on the surfaces of the wafer and polishing pad [24]. This is achieved by incorporating volumetric and discrete phase models into computational fluid dynamics [25]. As a result, this study examines the internal flow characteristics of a polishing pad in the shape of a concentric circle pad and a radial groove pad [26]. Then, it evaluates their effectiveness in the CMP process [27]. The grinding fluid’s fluid dynamics will impact both the rate at which material is removed and the degree of non-uniformity in the process [28]. An analysis was conducted on the dispersion of abrasive particles in the slurry between the surfaces of the wafer and pad using a three-dimensional multiphase CFD model [29]. Two types of polishing pad grooves, concentric and radial, were presented to examine how differing groove morphologies impact MRR and uniformity in the CMP process. Concentric grooves, with their circular pattern, were chosen for their ability to allow homogeneous slurry distribution despite restrictions in wall shear stress and slurry saturation time. Radial grooves extending outward from the center were selected to increase slurry flow, remove negative pressure differential regions, and improve mass distribution over the wafer. CFD simulations were used to evaluate these groove types, and the results showed that radial grooves outperformed concentric grooves by enhancing slurry dispersion, decreasing slurry saturation time, and increasing wall shear stress, resulting in better MRR and enhanced WIWNU.

This study presents a novel approach to improving CMP by examining how different polishing pad designs, specifically concentric and radial grooves, influence the process. Using advanced CFD simulations, we analyze the impact of these groove patterns on critical factors such as the MRR and WIWNU. The research highlights the importance of groove design in controlling slurry flow dynamics, including wall shear stress, pressure distribution, and mass flow. Notably, reducing areas of negative pressure minimizes back-mixing effects, leading to improved slurry distribution and more efficient polishing. Our simulations are validated by experimental results, demonstrating excellent alignment, particularly regarding SST. This work provides valuable insights into how innovative groove designs can optimize CMP processes for enhanced performance and reliability. The aim of this research is to improve the efficiency and consistency of CMP processes by investigating the impact of polishing pad groove designs. Specifically, the study seeks to

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Develop a detailed CFD model to simulate slurry movement during CMP, focusing on critical parameters such as wall shear stress, pressure distribution, and mass flow.

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Compare the performance of radial and concentric groove patterns in terms of their effects on slurry distribution, reduction of back-mixing, and overall process efficiency.

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Validate the accuracy and reliability of the CFD simulations through experimental data.

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Provide practical insights for designing optimized polishing pads to achieve higher material removal rates and improved uniformity across wafers.

2. Methodology

Figure 1 depicts a basic illustration of the polishing equipment and the interaction between the pad and wafer [30]. The primary consumables include slurry, gaskets, adjusters, retaining rings, and films. The slurry is transferred from the slurry distribution arm and enters the confined space between the pad and the wafer. When a batch of wafers has been placed into a CMP tool, it is immersed in deionized (DI) water and remains moist until the entire batch is processed and prepared for post-CMP cleaning [31]. Before planarizing a whole set of wafers using a particular recipe, it is necessary to planarize, clean, and measure a single monitor wafer to determine if the recipe meets the needed parameters [32]. This step is taken before planarizing the rest of the batch. This space contains chemicals and abrasives. Simultaneously, the platform and a specific downward force rotate on separate axes [33]. Ultimately, the slurry removes wreckage, by-products, and frictional heat from the worn gasket. As a result, the rate at which the slurry flows influences the rate at which the wafer’s surface is removed, the wafer’s uniformity, and the number of defects present [34].

2.1. Simulation

The study involved simulating the CMP process with ANSYS FLUENT. The system is partitioned into three components: pre-processing, numerical solution setting, and post-processing. The preprocessing procedures encompass geometric modeling, mesh generation, and defining boundary conditions. The chemical mechanical polishing process was simulated using ANSYS SpaceClaim software, which included various research components. It offers a user-friendly design interface that allows for the efficient creation of geometric models in three dimensions.

After constructing the geometric model, import it into ANSYS for meshing. The computational domain is divided into multiple grids during meshing, enabling the numerical solution of three-dimensional partial differential equations. These meshes can be conceptualized as control volumes, and various sorts of mesh forms exist, including structural meshes, unstructured grids, and multi-block grids [35]. It is a three-dimensional component of the hexahedron. While each piece can deviate from the rectangular shape, the individual elements remain intact [36]. The three-dimensional coordinate axis can be used to determine the labeling sequence. The unstructured grid comprises elements of various shapes, all oriented in the same direction. Unstructured meshes are convenient for creating complicated geometric models, but they have a higher quantity than structured meshes [37]. This abundance of unstructured meshes can lead to lower mesh quality and make achieving convergence more challenging [38]. Given the intricate nature of the design, this study opted for the non-structural grid method for partitioning. When importing the divided model mesh into FLUENT, it is critical to first verify the number of meshes and grid points. Subsequently, the size of the model should be determined before proceeding with additional settings. FLUENT must perform variable initialization before commencing the numerical solver [39]. Essentially, an initial guess is assigned to all variables associated with each element in the grid [26]. By using a reasonable starting estimate, the convergence process can be sped up, iterative computations can be made more stable, and the values of ANSYS Fluent iterative computations can be turned into the solution, which is the first value for each grid. Subsequently, the simulation results are computed iteratively [40]. The obtained values for speed, pressure, concentration import distribution, material flow lines, and vector diagrams can then be imported into CFD POST for observation and analysis.

2.2. CMP Model

The CMP process combines mechanical and chemical actions to remove material from the wafer surface. Mechanically, the wafer is polished against a rotating pad, typically coated with abrasive particles, while a chemical slurry is applied to enhance the material removal rate. The influence of the polishing pad notch design on surface quality is an important aspect in determining CMP efficiency. Notch designs, including changes in groove depth and shape, impact slurry flow dynamics, MRR, and uniformity. These parameters directly influence surface roughness and NU, two important indices of CMP performance. According to the study, deeper or radial grooves increase slurry dispersion, resulting in higher material removal rates and better surface uniformity. However, in real implementations, the efficiency of these notches may be altered by pad wear over time, slurry chemical composition, and changes in wafer material characteristics. The slurry contains reactive chemicals that soften or dissolve the material on the wafer surface, facilitating easier mechanical removal by the abrasives. The polishing pad, positioned on the rotating platen, is critical in this process because it flattens the semiconductor wafer by eliminating superfluous material via mechanical abrasion. Chemical reactions are shown in the Supplementary Material in Figure S2. The device applies regulated pressure to guarantee homogeneous material removal throughout the wafer’s surface, and a slurry comprising fine abrasives and chemical agents improves polishing efficiency [41]. Due to the laminar flow of polishing fluid, pad rotation and wafer shape can regulate fluid flow. The flow of polishing fluid on a polishing pad surface can be calculated by the linear velocity of the polishing pad and wafer [42]. In CMP, the grinding mechanism combines mechanical abrasion and chemical processes to remove material from the wafer surface efficiently. Grinding slurry containing silica particles causes compressive stress on the wafer’s oxide coating, leading to SiO₂ dissolution. The diffusion coefficient increases exponentially under stress. The fundamental chemical interaction is the breakage of siloxane (Si-O-Si) bonds in the oxide layer by hydroxyl groups, which develops a hydrated silica surface. Hydroxyl ions react with silicon atoms, dissolving them into Si(OH)₄ and OH⁻. The slurry then carries them away. Dielectric CMP grinds silica abrasives in deionized water with KOH or NH₄OH to alter pH. The slurry’s alkaline nature (pH 10–11) favors oxidation and the creation of hydroxyl groups, which then react with hydroxyl groups on the wafer surface to produce hydrogen. Following dehydration, the post-grinding silica particles create chemical connections with oxygen atoms on the wafer surface, which aids in atomic-scale material removal. This combination of mechanical and chemical processes guarantees regulated planarization, with the alkaline slurry stabilizing silica abrasives and boosting hydroxyl group reactivity, resulting in efficient material removal. Optimizing these chemical interactions is critical for enhancing CMP performance, reducing defects like dishing and erosion, and enabling high-precision wafer planarization in semiconductor production. More detailed information is in the Supplementary Material Figure S1. Figure 2a,b depicts the linear velocity phase relationship between the wafer surface and the polishing pad, which can be used to calculate the total number of degrees.

The relevant numerical model determines the relative speed between the polishing pad and the wafer using these two Figures. Then, the wafer surface removal rate (RR) is determined using Preston’s equation. The removal rate is the average amount of material thickness eliminated from the surface per unit of time. Preston states that Equation (1) can be expressed as follows [43]:

$$Removalrate\left(RR\right)=Kp\times P\times V$$

(1)

One of these variables is Kp, a constant specific to Preston. It can be influenced by several factors, such as the type of polishing pad, pH adjuster, and the makeup of the polishing fluid. P represents the operational pressure, which applies force to the wafer, utilizing lower pressure (head pressure). V denotes the relative speed between the polishing pad and the wafer [44]. When the angular velocities of the pad and wafer are equal, the relative velocity (V) can be determined using Equation (2) [45].

$$\overrightarrow{\mathrm{V}}={\overrightarrow{\mathrm{V}}}_P-{\overrightarrow{\mathrm{V}}}_w$$

(2)

According to the abovementioned theory, P and V remain constant under the same operating variables. The interaction between the polishing pad and wafer is highly variable. The slurry movement on the polishing pad’s surface is critical for CMP performance. The polishing fluid flow rate on a polishing pad’s surface can be calculated based on the linear velocity between the polishing pad and the wafer. Therefore, we can mathematically represent the rate at which the polishing fluid flows using the following Equations (3)–(5) [45]. The Supplementary Materials include the momentum and turbulent kinetic energy, as shown in Equations (S1)–(S12).

$$\overrightarrow{U}={\displaystyle \frac{1}{2}}\left({\overrightarrow{V}}_p+\overrightarrow{V_w}\right)$$

(3)

$$={\displaystyle \frac{1}{2}}\overrightarrow{{\omega }_p}\times \overrightarrow{{\gamma }_1}-{\overrightarrow{\omega }}_w\times {\overrightarrow{\gamma }}_2$$

(4)

$${\displaystyle \frac{1}{2}}\overrightarrow{{\omega }_p}\times \left(\overrightarrow{{\gamma }_1}-{\overrightarrow{\gamma }}_2\right)if\overrightarrow{{\omega }_p}=\overrightarrow{{\omega }_w}=\overrightarrow{\omega }\&\overrightarrow{{\gamma }_2}=\overrightarrow{{\gamma }_1}-\overrightarrow{{\gamma }_3}$$

(5)

By utilizing these equations, it is possible to compute and forecast the magnitude and direction of the grinding fluid flow, provided that $\overrightarrow{{\gamma }_1}$ is smaller than 0.5$\overrightarrow{{\gamma }_3}$. This implies that, when the linear speed of the wafer is higher, it exerts a more significant influence on the flow of the polishing fluid. Conversely, if the magnitude of vector $\overrightarrow{{\gamma }_1}$ is greater than 0.5 times the magnitude of vector $\overrightarrow{{\gamma }_3}$, it indicates that the polishing pad’s linear speed is higher, and the speed of the polishing fluid flow is dictated by the linear speed of the polishing pad. To ascertain whether $\overrightarrow{{\gamma }_1}$ is less than half of$\overrightarrow{{\gamma }_3}$, it is necessary to assess if the grinding fluid may enter the gap. This, in turn, will impact the performance of the CMP process [45]. Consequently, the flow of the polishing fluid can be regulated by directing it through the groove on the polishing pad. So, guiding it to the surface of the wafer, as depicted in Figure 3a,b, enables a top view of a concentric groove pad. The top view displays the radial groove pad, whereas Figure 3c,d depicts its three-dimensional modeling model.

The parameter values of the reduced model are presented in

Table 1. Parameter settings of a simplified model.

Name	Parameter	Value
Diameter of pad	Dp	400 mm
Diameter of carrier	Dc	150 mm
Diameter of wafer	Dw	100 mm
Distance from pad center to wafer center	L	100 mm
Distance from pad center to inlet	V	160 mm
Distance between wafer and pad	h	0.1 mm
Distance between carrier and pad	hc	0.3 mm

. Regarding the polishing pads and slurry injection, both the wafer and the polishing pad rotate in an anticlockwise direction. The slurry travels from the injection port to the polishing pad’s surface before entering the space between the wafer and the pad due to the pad interface’s rotation. Simplified models of the polishing pad and wafer are depicted in Figure 4 for investigation of the CMP process.

The wafer is positioned on a level grinding table without any tilt. Water and abrasive grains are injected into the system through the injection port at equal velocities. Particles do not interact with each other. The specifications for the grinding fluid particle parameters are displayed in

Table 2. Grinding fluid particle parameter settings.

Parameter	Value	Unit
Density of particle	1110	kg/m3
Diameters of the particles	20~80	nm
Average Diameters of the particle	50	nm
Velocity of water flow	100	mL/min
Velocity of particle flow	100	mL/min
Mass Diffusivity	1 × 10−9	m2/s
Dynamic Viscosity	8.9 × 10−4	kg/m·s

.

Due to the narrow gap thickness between the wafer and the pad surface, achieving excellent mesh quality and minimal skewness in the model is challenging. ANSYS Fluent adheres to specific criteria regarding distortion and orthogonality. If the standards are not satisfied, the simulation outcomes may deviate. As depicted in Figure 5a, the multizone approach is employed to achieve high-quality meshes and distortions suitable for ANSYS Fluent simulations. Given that mesh quality directly influences convergence behavior, computational efficiency, and result reliability, it is critical to determine if these values match the suggested limits for producing valid fluid dynamics and contact mechanics simulations in the context of CMP. For example, a distortion value of less than 0.3 and orthogonality of more than 0.7 are generally considered acceptable in CFD applications; however, in high-precision simulations such as CMP, where thin gaps and complex geometries are involved, even minor grid irregularities can introduce local numerical instabilities or inaccuracies in pressure and velocity distribution. In this study, the Multizone Meshing Method is a hybrid meshing technique used in CFD and FEA to create high-quality meshes for complex geometries. The mesh quality was maximized by carefully selecting element types, improving crucial locations, and guaranteeing seamless transitions between different meshing zones. Key quality indicators such as aspect ratio, skewness, and orthogonality were observed and kept within acceptable ranges to reduce numerical mistakes and increase solution stability. The resulting distortion is generated with an average value of 0.211 and a mesh model with an average orthogonality of 0.780. The grid structure comprises 2,309,718 elements and 569,654 nodes. In Figure 5b, you can see an expanded grid layout of the slurry injection port. In Figure 5c,d, you can see the grid diagrams of concentric circular and radial groove pads.

To examine fluid movement between the pad surface and the wafer surface, it is necessary to investigate the correlation between the pad and the wafer surface. The vertical distance must be partitioned into a minimum of three grid cells. Hence, this article categorizes the concept into three distinct components: wafer, wafer carrier, and other elements. The simulation conditions are set using default values. For modeling purposes, the VOF model uses both the primary phase of air and the secondary phase of water. To represent the movement of particles in a flow, use discrete phase models. Particles are introduced into the inlet at the same velocity as the water. The numerical operational model and simulation condition are presented in

Table 3. Numerical operational model in Ansys.

Model	Discretization
Pressure	PRESTO
Solution Method	SIMPLE
Momentum	Second-order upwind
Viscous	Laminar, Realizable k = ϵ (Standard wall function)

and

Table 4. Parameter condition settings the simulation.

Parameter	Parameter Symbol	Setting
Meshing Method		Multizone
Fluid layer thickness		40 µm
Particle density	ρp	1100 kg/m3
Water density	ρ	998 kg/m3
Average particle diameter	dp	50 nm
Slurry flow rate		200 mL/min
Pressure outlet		Atmospheric
Pad rotation speed	ωp	90 rpm
Head Pressure		2 psi
Wafer rotation speed	ωw	90 rpm

.

In this design, it is assumed that (i) the flow of grinding fluid is typically laminar [46], and (ii) turbulent flow occurs on both the left and right sides [42]. The typical length, denoted as D_h, refers to the overall length of the liquid flow along the polishing pad during the grinding process. The flow between the polishing pads during rotation is not purely laminar but rather turbulent, depending on the Reynolds number of the wafer and the slurry’s total flow lengths [19]. When the polishing pad is removed, the region surrounding the wafer becomes a laminar flow area. During the CMP process, the grinding fluid’s flow is characterized by laminar flow and weak turbulence, as evidenced by tiny eddies and whirlpools. The turbulence model is used to accurately show swirling flows in both concentric circular pads and radial groove pads so that the movement of the slurry between the wafer and the polishing pad can be modeled. Hence, this article employs the realistic k = ϵ(RKM) model to enhance the precision of predicting laminar and swirling flowsPRESTO is Fluent’s default model for mixed or VOF multiphase models. The time step size is set to 0.001 s, and during the 30-s simulation, the maximum number of iterations per time step is 20. n.

2.3. Polishing Pad Groove Forms

Figure 6 illustrates this model’s parameter configurations of the polishing pad groove. The groove width (w) is specified as 0.5 mm, the depth (d) is 0.75 mm, and the spacing (p) is set at 3 mm. The gap between the polishing pad and the wafer is 0.1 mm, and the depth of the groove at the end of the polishing pad’s lifespan is lowered by 0.5 mm, from 0.75 mm to 0.25 mm. The decline in groove depth during the polishing pad’s lifetime substantially impacts the MRR and WIWNU, key considerations in attaining high-quality planarization. The groove depth reduces from 0.75 to 0.25 mm, and the pad’s ability to hold and distribute slurry across the wafer surface declines. This decrease in slurry retention results in the less efficient delivery of abrasive particles and chemical reactants, potentially slowing down the chemical–mechanical interactions necessary for material removal. As a result, the MRR is expected to decrease as the pad wears down, thereby reducing process efficiency and increasing overall polishing time. Furthermore, the decreasing groove depth affects slurry flow dynamics, resulting in uneven distribution throughout the wafer. The variation in slurry supply might cause differences in local polishing velocity, contributing to non-uniformity within the wafers. The areas with less efficient slurry conveyance may suffer lower material removal, whilst areas with comparatively better slurry retention may continue to show greater removal rates, resulting in thickness differences throughout the wafer. Furthermore, when the pad approaches the end of its life, its ability to maintain consistent contact pressure with the wafer may diminish, compounding non-uniformity difficulties.

Upon the polishing pad’s activation, the polishing fluid flow becomes consistent. However, toward the end of the polishing pad’s lifespan, the polishing fluid no longer flows toward the center of the wafer. The formula below can represent the shear stress (τ) on the surface of the wafer: τ = μ/h.

3. Results and Discussion

3.1. Pressure Field Distribution

Taking atmospheric pressure as the reference, Figure 7a, illustrates the distribution of the hydraulic field at the interface between the wafer and the polishing fluid during the polishing process. This field is critical for understanding how fluid dynamics affect the overall polishing performance. In Figure 7b, it is evident that a pressure difference develops between the leading edge and trailing edge of the polishing pad. This difference is significant because it creates areas of negative pressure on the trailing edge of the pad. This negative pressure has significant consequences as it induces a circulation of the older polishing fluid back into the system, delaying the introduction of fresh polishing fluid. This phenomenon, known as the back-mixing effect, disrupts the flow of new polishing slurry, which is crucial for maintaining polishing efficiency. The back-mixing effect refers to the phenomenon where a portion of the fluid within a flow system moves in a direction opposite to the main flow. This effect is commonly observed in systems with significant turbulence, recirculation zones, or poorly designed flow paths. Back-mixing can influence the performance of chemical reactors, separation processes, or fluid transport systems by reducing efficiency, causing uneven distribution of reactants, or altering residence time distributions. The severity of the back-mixing effect is directly related to the magnitude of the negative pressure. The larger the absolute value of the negative pressure, the more substantial the effect. This imbalance in pressure causes the wafer to tilt in the opposite direction of the sliding motion, destabilizing the contact interface between the wafer and the polishing pad. This destabilization results in fluctuations in the thickness of the polishing liquid film across the wafer’s surface, particularly at the wafer edge. As a result, grinding non-uniformity (NU) increases near the wafer edge, which is detrimental to achieving a uniform polish.

In a polishing system with a concentric groove design on the pad, the pressure distribution at the wafer–pad interface is influenced by the circular grooves’ geometry. The concentric grooves create a uniform pattern that aids in distributing slurry across the interface. This design produces a pressure field with relatively consistent variations along the radial direction, ensuring even material removal across the wafer surface. In contrast, a radial groove design introduces grooves that extend outward from the center to the edges of the polishing pad. This configuration significantly influences the pressure field by facilitating more effective slurry transport across the interface. Under identical operating conditions, both concentric and radial groove pads exhibit negative pressures at the trailing edge of the polishing pad. Specifically, the concentric groove pad shows a negative pressure of −8 kPa, while the radial groove pad shows a slightly lower negative pressure of −6 kPa. The extent of the negative pressure area is directly related to the polishing performance; a larger negative pressure area generally correlates with a stronger polishing effect [47]. The liquid slurry that remains trapped in the grooves of the pad reduces the number of effective abrasive particles available for the polishing process. This reduction in effective particles decreases the overall wafer removal rate, which is a key metric for the efficiency of the polishing process. These results indicate that simulations, when conducted under consistent boundary conditions, can be used to predict the behavior of CMP processes. The groove type and the condition or life of the polishing pad play significant roles in determining the polishing outcomes. Therefore, optimizing these factors through simulation can help improve polishing uniformity and efficiency.

3.2. Effect of Wall Shear Stress

The gap between the polishing pad and the wafer measures 0.1 mm throughout the simulation, from the beginning to the polishing process. Upon reaching the end of its usable lifespan, the depth of the groove on the pad decreased from 0.75 mm to 0.25 mm. During the scientific investigation, the polishing fluid is distributed uniformly upon activation of the sanding pad. It is evident from this equation that the flow rate of the grinding fluid is directly related to the shear stress. Inclined furrows are grooves on a polishing pad that are inclined rather than radial or concentric. These angled grooves form an inclined surface, influencing the slurry flow between the pad and the wafer. The furrows’ slope modifies the slurry’s flow dynamics, directing it more uniformly throughout the surface, especially in emphasis with less fluid movements. As the polishing pad is eliminated, the depth of the grooves decreases, affecting the flow of the slurry. When the grooves are sloped, the slurry flows more efficiently, eliminating stagnation and enhancing dispersion. The result is a more consistent material RR, which can help to eliminate problems like scratches and NU on the wafer’s surface. In this study, inclined furrows are mentioned as influencing slurry movement, resulting in a more uniform polishing process, particularly in areas closer to the center of the wafer where flow typically occurs more slowly. Figure 8a,b display the shear stress distribution on the circular pad and the radial groove wall under different groove depths, respectively.

The shear force, as depicted in Figure 9, decreases from the initial simulation value of 0.75mm to the reduced groove depth.

The study presented the impact of various pad groove designs, wafer load, sliding velocity, and slurry flow rate on the slurry distribution beneath the wafer during the polishing process. The DEUVEF measurement approach was implemented and utilized on an industrial-scale polishing tool, enabling a more comprehensive comprehension of the overall hydrodynamics of the CMP process. The existence of inclined furrows will further produce a microscopic impact on slurry movement in the regions of the pad’s surface [48]. Because polyurethane pads have elastoplastic qualities, any load applied to the pad land area will cause partial compression of the land regions, affecting the slurry’s flow path. The results validate that variations in the slurry film distribution under the wafer are caused by varying degrees and directions of groove slanting [49]. From 0.5 mm to the end of the polishing pad’s service life at 0.25 mm, the shear stress reduces due to the reduction in groove depth, as depicted in Figure 10a,b.

According to the velocity streamline diagram and the corresponding wall shear stress, the radial groove experiences higher shear stress than the concentric circular pad. Due to the larger area filled by the concentric circular groove compared to the radial groove, the force between the two interfaces decreases as the number of effective particles in the polishing fluid decreases. As a result, the wafer removal rate is reduced. These findings demonstrate that implementing radial grooves facilitates the rapid flow of the polishing fluid into the space between the polishing pad and the wafer, resulting in an improved removal rate. CMP’s behavior can be predicted by simulating it under identical boundary conditions, considering the groove type and pad life.

The mass distribution of the polishing fluid is more evenly spread in the radial groove pad than in the concentric pad. This occurs because the concentric pad causes the polishing fluid to flow at a slower rate towards the center of the wafer, resulting in a lower supply rate of the polishing fluid. As mentioned earlier, a low supply rate of the polishing fluid can lead to an increased likelihood of wafer scratches, higher NU, and a reduced material RR.

3.3. Validation

Mass Fraction of Slurry

Figure 11a is a schematic diagram of the polishing pad, wafer, and five monitoring points on the wafer surface; Figure 11b,c displays the slurry mass scores at the five monitoring points of the concentric grooves and radial grooves over time [41]. To clearly show the trend, the mass fraction is set from 0.95 as the coordinate starting point. The simulation results show that, when the grinding fluid starts to be supplied, the mass fractions of these five monitoring points all increase significantly,

Point 1: The mass fraction progressively increases over time and exhibits minor fluctuations around the 20-s mark, indicating that it reaches its maximum value at 20 s, corresponding to the optimum slurry mass fraction of 1.0.

Point 2: The mass fraction progressively increases with time and exhibits minor fluctuations around the 20-s mark, indicating that it reaches its maximum value at 20 s, corresponding to the optimum slurry mass fraction of 1.0.

Point 3: The mass fraction progressively increases with time and exhibits minor fluctuations around the 20-s mark, indicating that it reaches its maximum value at 20 s, corresponding to the optimum slurry mass fraction of 1.0.

Point 4: The mass fraction curve exhibits significant fluctuations due to its proximity to the grinding fluid injection port, and the concentric grooves retain the old slurry for an extended period. When fresh grinding fluid is introduced, the previously retained slurry will combine with the incoming fluid, causing more significant variations compared to the others.

Point 5: The mass fraction gradually grows with time, but, since it is located a distance from the injection port, the old slurry rarely reaches this point during the cycle. As a result, it takes longer for the mass fraction to achieve the desired value of 1.0 compared to other monitoring points.

Radial groove pads follow the same idea as concentric pads; however, they achieve equilibrium more rapidly. By the time 25 s elapses, the variations in the distribution of slurry mass begin to decrease gradually. This indicates that, when new slurry is introduced to the wafer, the old slurry within the system continues circulating and is not expelled from the polishing surface until approximately 25 s. The slurry mass fraction in the radial grooves reaches equilibrium following variations in approximately 10–15 s. Upon comparing the two pictures, it is evident that the slurry in the concentric grooves is dispersed unevenly across the entire wafer. The first-order derivative rate, the definition of slurry saturation time (SST), is often Mean Residence Time, Mixing Time, or Blending Time. When the slurry mass fraction of the five monitoring points reaches the ideal target value of 1.0, this side is defined as SST, and the average of the five points is the final value of SST. Figure 12 displays the simulation and the work of Cho, Y., Liu et al. [48] using 100 mm wafer polishing Equipment (Poli-400, GnP Technology, Busan, Republic of Korea). The comparison involves the first-order derivative stack diagrams of the slurry mass distribution obtained from the experiments. According to the literature, the SST values for the concentric circular pad and the radial groove pad are 21.52 s and 16.06 s, respectively. In this simulation, the SST values for the concentric circle pads are 22.23 s and 15.73 s. The contrast between the two is illustrated in

Table 5. Validation of concentric and radial grooves.

	Concentric Groove	Radial Groove
Experiment [48]	21.52 s	15.54s
Simulation	22.23 s	16.06 s
Error	3.33%	3.35%

.

The errors can be computed as 3.33% and 3.35%, respectively. Therefore, it is evident that this simulation approximately aligns with the experimental data, and the simulation method holds a certain degree of reference value. The increasing miniaturization of semiconductor devices, even small deviations in material removal rate, surface topography, or planarization uniformity, can lead to critical defects such as dishing, erosion, and localized stress concentrations, adversely impacting device performance and yield. Modern CMP processes in advanced integrated circuit fabrication often require precise control of WIWNU and total thickness variation (TTV). CMP accuracy is crucial for semiconductor manufacturing, with deviations of 3.33% and 3.35% between simulation and experimental results considered acceptable. The CmpCNN framework achieved an RMSE of 2.7733 Å, highlighting its competitiveness in CMP modeling. The current study’s errors align with accepted standards, indicating that the simulation method holds significant reference value for CMP applications [46].

3.4. Removal Rate and Non-Uniformity

Figure 13a depicts the rate at which material is removed based on the distance from the center of the wafer. This article is derived from the literary works of Yuan Qiwen [46]. The removal rate model formula derived using the least squares method is applied to the simulation data, shown in Equation (S18). These two sections discuss separate parts of the CMP process. The first argument stresses the radial grooves’ ability to improve slurry flow dynamics, which increases material removal rates by ensuring that the polishing fluid is quickly supplied to the wafer surface, decreasing slurry stagnation and increasing the number of abrasive particles participating with the wafer. This process is to optimize the polishing efficiency. The second argument, regarding the necessity for enough time for chemical reactions to occur, focuses on the balance of mechanical and chemical elements of CMP. While the higher flow rate from radial grooves aids in effectively delivering slurry, allowing for quicker material removal, it does not eliminate the need for enough time for chemical reactions between the slurry and the wafer to occur. While the radial grooves increase the flow rate, the polishing pad must still provide adequate time for chemical reactions to contribute efficiently to the material removal process. CMP requires enough time for chemical reactions between slurry and wafer surface to occur effectively. These reactions, like oxidation or etching, break down wafer material, aiding in material removal. Mechanical forces from the polishing pad also contribute to material removal but balancing mechanical and chemical actions is crucial to achieving a uniform, high-quality finish. By analyzing the simulation results, it is evident that the removal rate of the radial groove may be compared to the movement of the concentric circles. The rate of elimination is substantial. The reason for this is that the flow rate of the polishing liquid is greater in the radial groove pad, meaning that the polishing liquid’s supply rate is faster than the concentric circle pad. Consequently, the increased quantity of efficient polishing abrasive grains interacting with the wafer surface enhances the likelihood of the polishing abrasive particles creating dielectric CMP, resulting in a greater removal rate. Figure 13b, displays the average rate at which material is removed and the unevenness caused by grinding along the radial grooves. This unevenness is related to the flow of liquid and can be mitigated by consistently polishing the wafer surface, as supported by the simulation findings.

The simulation findings demonstrate that an increased flow of grinding fluid leads to enhanced homogeneity in the chemical mechanical polishing process. This work replaces the film thickness model formula derived from Yuan Qiwen’s literature [46] using the least squares method. The utilization of radial grooves leads to an enhanced removal rate due to the reduction in the proportion of the surface area occupied by the grooves. The chemical mechanical polishing technique necessitates an adequate amount of time for chemical reactions to occur, while also requiring the polishing pad grooves to sustain and transmit the grinding action throughout the operation. Consequently, the quantity of efficient grinding particles on the real polishing surface is diminished. While the grinding fluid remains in the circular groove for an extended duration, the transmission speed of the radial groove is higher. Radial grooves can enhance the removal rate and reduce unevenness. By optimizing additional process variables in this manner, the chemical mechanical polishing process can achieve its highest level of performance.

4. Conclusions

CMP is widely used in industries, but its slurry flow can affect MRR and NU. A multi-phase 3D CFD model study was conducted to study the slurry distribution between wafer and pad surfaces. The VOF method was used to track water flow, while the discrete DPM was used to calculate wall shear stress, pressure field distribution, and slurry mass distribution. The study investigates that negative pressure causes back mixing, which increases wafer removal rates and NU. The influence of groove form and depth on wall shear stress was evident as the polishing pad wore down. The slurry mass distribution diagram showed that the mass fraction of these points increased with time, with the fluctuation decreasing at 25 s. Concentric grooves had an uneven distribution of slurry on the wafer, while the mean SST of the central circle was slower than that of the radial slot. The radial groove pad performed better in removal rate and unevenness, with a smaller negative pressure difference field area and a reduced back-mixing effect. The simulation results can provide a deeper understanding of the mechanism of chemical mechanical polishing through CFD. Future research aims to add chemical reaction kinetics to the observation of electrochemical reactions during polishing and analyze the agglomeration phenomenon of grinding abrasive grains. The ANSYS model can be applied and verified by comparing simulation results with factory parameters to ensure that they meet operating parameters.