Simulation and Experimental Investigation of the Radial Groove Effect on Slurry Flow in Oxide Chemical Mechanical Polishing

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This research predicted the slurry saturation time with simulations, which were verified with experiments. This work will help guide polishing recipe development to save costs.

Abstract

Slurry flow on the pad surface and its effects on oxide chemical mechanical polishing (CMP) performance were investigated in simulations and experiments. A concentric groove pad and the same pad with radial grooves were used to quantitatively compare the slurry saturation time (SST), material removal rate (MRR), and non-uniformity (NU) in polishing. The monitored coefficient of friction (COF) and its slope were analyzed and used to determine SSTs of 25.52 s for the concentric groove pad and 16.06 s for a certain radial groove pad. These values were well correlated with the simulation prediction, with around 5% error. Both the laminar flow and turbulent flow were included in the sliding mesh model. The back mixing effect, which delays fresh slurry supply, was found in the pressure distribution of the wafer–pad interface.

1. Introduction

As nodes are shrinking in semiconductor fabrication, chemical mechanical polishing (CMP), the process to achieve global and local planarization of the wafer surface, is also facing some emerging problems, such as defect control, novel material CMP, and green CMP [1,2,3,4]. Continuous optimization of the consumables, polishing recipe, and post-processing is needed to solve contemporary challenges. Innovative consumables and manufacturing processes are also being proposed for the future CMP [5]. Computational fluid dynamics (CFD) is a well-recognized tool to visualize fluid flow and study the tribology, slurry filtration, transportation, and flow [6,7,8].

Shallow trench isolation (STI) and inter-level dielectric (ILD) CMP are two main steps for multi-layer stacking on the substrate. The over-deposited oxide film was removed by silica or ceria slurries based on a combination of a chemical reaction and mechanical buffing. Simple graphics of the polisher equipment and the pad–wafer interface are shown in Figure 1. The slurry, pad, conditioner, retainer ring, and membrane are the main consumables. The slurry is pumped out of the slurry dispenser arm and then flows into the narrow gap with chemicals and abrasives in the pad–wafer interface while the platen and the head rotate on different axes. Finally, the used slurry takes away worn pad debris, byproducts, and friction heat. Therefore, slurry flow can affect the MRR, NU, and number of defects [9,10,11].

The huge amounts of waste chemicals produced result in environmental pollution, so green CMPs that use fewer chemicals are desired. In addition, the disposable slurry expense covers a high percentage of the consumables [12]. Slurry expenditures represent almost 50% of all CMP-related costs [13]. Optimized slurry flow in terms of the polishing performance and slurry consumption trade-off can precisely control the supplement amount and improve the utilization efficiency. Moreover, sufficient and uniform slurry flow can lower the NU of the polished wafer. Several kinds of defects, dishing, and erosion were identified as being related to the NU [14]. The cost of ownership can be reduced by saving the slurry cost and improving the yield rate.

In general, more fresh slurry means better polishing but the pad–wafer gap limits the flow in one end and out the other [15]. A traditional CMP pad normally has concentric pad grooves to accommodate the slurry. Furthermore, the radial groove pad was designed to improve the slurry refresh rate [16]. Different pads and certain polishing recipes have different SSTs, which means there is a critical amount of supplemental slurry, and excess slurry cannot flow into the pad–wafer gap.

Many researchers have made use of different simulation methods to investigate the slurry behavior in CMP. Mueller et al. varied the applied load, wafer rotation, slurry injection, and pad types and showed the fluid flow fields [17]. Rogers et al. investigated the effects of pad conditioning on slurry transport and mixing [18]. Zhou et al. reported changes in the slurry film thickness with the interfacial fluid pressure distribution and contact conditions [19]. Li et al. optimized the pad groove design to realize uniform slurry velocity and high surface quality for polished CaF₂ crystals [20]. Rosales-Yeomans et al. explored the effect of slanted concentric grooves on slurry film thickness during polishing [21]. Nevertheless, these studies lack the quantitative analysis of the in situ polishing conditions with combined turbulent flow in the pad grooves and laminar flow in the pad–wafer interface.

In the present study, both simulations and experimental approaches are used to investigate the slurry flow at a wafer–pad interface with concentric groove pads and radial groove pads. The preliminary flow conditions were derived using fluid mechanics equations. Then, the simulation was carried out with a combination of commercial software and original coding. The slurry flow simulation was carried out on a 100 mm polisher modeling for computational convenience. Next, experiments were performed using a 100 mm wafer polisher and a 300 mm wafer polisher to confirm the simulation results. Finally, the simulated and experimental results were compared, and high consistency was found. This study provides insight into the slurry distribution at the contact interface and a new way to predict the SST of a newly designed CMP pad.

2. Simulation Methodology

2.1. Simulation Target

The pad surface is the main flow region in the polishing process. When the slurry is supplied at a certain flow rate, it is transported along the pad grooves. The geometries of the pad and the sunken grooves directly determine the slurry distribution and the flowing conditions. However, it is difficult to characterize these experimentally due to the thin slurry film and micro-scale gap between the pad and wafer. This simulation aims to compute the slurry flow to estimate the MRR variation with different pads.

Commercial computational fluid dynamics (CFD) software (Fluent 2020 R1, ANSYS, Inc., Wayzata, MN, USA) was used for the simulation. Two kinds of commercial polyurethane CMP pads (IC 1000) were used: a concentric groove pad (R0) and a radial groove pad (R8, R32). The number following the letter ‘R’ indicates the number of radial grooves on the pad. Top views of the R0 pad and R32 pad are shown in Figure 2. The solid black lines represent the pad grooves. The R0 pad represents a pad with concentric grooves, while the R32 pad means a concentrically grooved pad with 32 radial grooves.

2.2. Governing Equations

Reynolds-Averaged Navier–Stokes (RANS) Equations [22]—Equations (1) and (2) are RANS equations commonly used in commercial CFD codes [18]:

$$\frac{\partial \rho }{\partial t}+\frac{\partial \rho }{{\partial }_{x_i}}\left(\rho u_i\right)=0$$

(1)

$$\frac{\partial }{{\partial }_t}\left(\rho u_i\right)+\frac{\partial \rho }{{\partial }_{x_j}}\left(\rho u_i{u}_j\right)=-\frac{\partial p}{{\partial }_{x_i}}+\frac{\partial }{{\partial }_{x_j}}\left[\mu \left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}-\frac{2}{3}{\delta }_{ij}\frac{\partial u_l}{\partial x_l}\right)\right]+\frac{\partial }{{\partial }_{x_j}}\left(-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(2)

Here, t is a basic mathematical promise representing the partial derivative with respect to the time variable. ${\delta }_{ij}$ is the “Kronecker delta” function for two variables i and j. If the i and j have the same value, it becomes 1, then it becomes 0. $\rho$ is the density of the slurry. $p$ represents the slurry pressure. $\mu$ represents the dynamic viscosity of the slurry, and $u_i$ represents the velocity of the slurry. $x_i$, $x_j$ are Cartesian coordinates in index notation. $u_l$ is the vector of averaged velocity field. $u_i$, $u_j$ are Cartesian velocity in index notation. $\overline{u_i^{\prime }}$, $\overline{u_j^{\prime }}$ are mean and fluctuating velocity components. $-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ is Reynolds stresses tensor.

Species Transport Equation [22]—Equation (3) is a conservation equation for calculating the local mass fraction of slurry ($Y_i$) by convection and diffusion [22].

$$\frac{\partial }{\partial t}\left(\rho Y_i\right)+\nabla ·\left(\rho \overrightarrow{v}{Y}_i\right)=-\nabla ·{\overrightarrow{J}}_i+R_i+S_i$$

(3)

where $\overrightarrow{v}$ is mass averaged velocity vector; $R_i$ is the net rate of production of the species i, which is zero in this simulation; $S_i$ is the volume of the supplied slurry, which is generated every time step by a volume flow rate of 160 mL/min; and $J_i$ is the diffusion flux for the species i, which is determined by the mass diffusion equations below.

Mass Diffusion Equations [22]—There are significant differences in mass diffusion flux between the laminar and turbulent regions. In this study, the laminar region and turbulent region were modeled simultaneously.

$${\overrightarrow{J}}_i=-\rho D_{i,m}\nabla Y_i-D_{T,i}\frac{\nabla T}{T}$$

(4)

$${\overrightarrow{J}}_i=-\left(\rho D_{i,m}+\frac{{\mu }_t}{S{c}_t}\right)\nabla Y_i-D_{T,i}\frac{\nabla T}{T} , \left(S{c}_t=\frac{{\mu }_t}{\rho D_t}\right)$$

(5)

$D_{i,m}$ and $D_{T,i}$ represent the mass diffusion coefficient for species i and thermal diffusion coefficient, respectively. Only $D_{i,m}$ was considered in the laminar region, while a stronger diffusion effect was applied in the turbulent region because $S_{ct}=0.7$. ${\mu }_t$ is turbulent viscosity. $D_t$ is turbulent diffusion coefficient. $S_{ct}$ is turbulent Schmidt number. $\frac{\nabla T}{T}$ is temperature gradient. $D_{T,i}$ was set to zero so that the effect of temperature could be ignored.

2.3. Laminar and Turbulent Reacting Flows

The Reynolds number equation in the internal flow is:

$$Re=\frac{\rho VL}{\mu }=\frac{\rho V{D}_h}{\mu }, (D_h=\frac{4A_c}{p})$$

(6)

Here, Re, $\rho$, V, L, and $\mu$ are the Reynolds number, density of the fluid, velocity of the fluid, characteristic length, and dynamic viscosity of the fluid, respectively. Additionally, $D_h$, $A_c$, and $p$ are the hydraulic diameter, cross-sectional area of the fluid flow, and wetted perimeter that is in contact with the fluid, respectively.

In previous research, the slurry flow was normally treated as laminar flow [18,20,23]. The transition from laminar flow to turbulent flow is generally known to occur around Re = 2300 [24,25]. The characteristic length can be defined as the hydraulic diameter ($D_h$) of the slurry flow along the pad groove. According to the Reynolds numbers calculated for different hydraulic diameters, the slurry flow between a wafer and a pad is not fully laminar, but is turbulent vortex flow while rotating. Other exposed surfaces of the pad belong to the open laminar flow regime. Briefly, the slurry flow during the CMP process exhibits both laminar flow and weak turbulent flow, showing small eddies and vortices. To simulate the slurry flow between the wafer and the pad for pads with different geometric shapes, the turbulence model was chosen to capture the swirl flows and vortices. In addition, the realizable k-ε model (RKM) was used to show more accurate predictions of the separation flow and rotational flow [22,26].

2.4. Simulation Model Description

A flowchart summarizing the simulation steps is shown in Figure 3. ANSYS Fluent supports the Multiple Reference Frame (MRF), Sliding Mesh Model (SMM), Overset Mesh, and other methods for characterizing rotating flow. The MRF method is the most frequently used because it can show the time-averaged flow, but the analysis reliability is extremely low when rotational and non-rotational domains exist simultaneously, or when there are dependencies on the geometric angle. Thus, the SMM method was applied in this simulation due to the geometric angle dependencies caused by the radial groove patterns. Then, the species transport equations were solved, and the SST was calculated with the converged flow field. All the residual values dropped to below 1 × 10⁻⁵ and satisfied mass conservation.

The defined SST is also called mean residence time, blend time, or mixing time. These are the primary concerns when developing agitators or stirrers. The simulation is helpful to predict the temperature and concentration variation with time for each monitoring point. For example, the required mixing time to homogenize the solution in the stirred tank was calculated by tracking the tracer concentration with CFD [27,28,29]. In addition, the fluid mixing speed of the helical impeller was predicted by the CFD technique with the tracer tracking method [30].

2.5. Meshing and Calculation

A cross-sectional view and boundary conditions of polishing parts are presented in Figure 4. The no-shear wall condition was used as the upper boundary condition for slurry flow. Figure 4b shows a magnified view of an intersection between grooves. A total of 71,325,554 polyhedral meshes were generated using the non-conformal method to match the SMM. Figure 5a provides meshed models in several sections as below. In addition, Figure 5b gives the mesh size distribution.

Laminar flow and turbulent flow were calculated simultaneously. Simulation and slurry properties are listed in

Table 1. Fluid simulation settings.

Model	Discretization
P-V Coupling	Coupled
Gradient	Least Squares Cell-Based
Pressure	PRESTO!
Momentum	Second Order Upwind
Motion	Sliding Mesh
Viscous	Laminar, Realizable k = ε (Standard wall function)

and

Table 2. Slurry simulation settings.

Parameter	Method	Value	Unit
Density	Constant	1110	kg/m3
Mass Diffusivity	Constant	1 × 10−9	m2/s
Dynamic Viscosity	Constant	8.9 × 10−4	$\mathrm{kg}/\mathrm{m}·$s

. The calculation was simplified because of the limited computing power. The simulation was run based on the 100 mm wafer CMP machine, and the fluid domain of the slurry flow was modeled without the external flow. Figure 6 shows the pad, wafer dimensions, slurry injection position, and five monitoring points that are used for calculating the slurry mass fraction to obtain the SST. Their coordinates are listed in

Table 3. The coordinates of five monitoring points.

	X (mm)	Y (mm)	Z (mm)
P1	100.0	0.8	0.0
P2	74.6	0.8	0.0
P3	125.4	0.8	0.0
P4	100.0	0.8	−25.4
P5	100.0	0.8	25.4

.

3. Experimental

The experiments were initially conducted using a 100 mm wafer polisher (Poli-400, GnP Technology, Korea) and then scaled-up using a 300 mm wafer polisher (Poli-762, GnP Technology) with the same recipe.

The 4 cm × 4 cm plasma-enhanced tetraethyl orthosilicate (PE-TEOS) coupon wafers and 300 mm PE-TEOS wafers were polished with a commercial colloidal silica slurry with a mean abrasive size of 121 nm. The pH and mass concentration of the slurry were 11 and 16 wt%, respectively. The single-abrasive scenario of an oxide film polished with a silica slurry is depicted in Figure 1. When one silica particle scratches the oxide surface, the compressive stress causes dissolution of SiO₂ at the contact spot [31,32,33,34,35]. The diffusion coefficient of water increased exponentially with the tensile stress [32,36]. Next, the siloxane bonds (Si-O-Si) of the particle and oxide film were broken by hydroxyl groups and formed hydrated silica surfaces. After adsorbing hydroxyl ions, silicon atoms were dissolved with silicon ions Si(OH)₄ and OH- [35,36], and the slurry abraded the hydrolytic surface. Three kinds of pads were used in the 300 mm wafer polisher: a concentric groove pad (R0) and two radial groove pads (R8, R32). The polishing pressure and rotation speed of the platen/head were set to 21 kPa and 93/87 rpm, respectively, and the slurry flow rate was set to 160 mL/min. The rotation speed of the conditioning disk was 101 rpm.

Before experiments, the new pad break-in was conducted with ex situ pre-conditioning for 30 min with deionized water (DIW) and ex situ preconditioning for 20 min with the slurry. Next, two dummy wafers and three experimental wafers were polished with in situ conditioning. The polishing processes used for the 100 mm and 300 mm wafer polishers are shown in Figure 6. A 30 s or 60 s pre-conditioning period was carried out with DIW, then a polishing period with DIW (30 s or 80 s) was carried out until the coefficient of friction (COF) curve converged. Finally, an additional period (30 s or 70 s) of polishing with silica slurry continued until the COF curve converged again. The experiments were repeated four times to obtain a universal law. The real-time COF was measured using the integrated monitoring system (CMP-Eye) in the polisher [37]. COF data post-processing was performed to smooth the curve.

The MRR and NU of the 300 mm wafers were only checked to verify the practical application of the simulation model in a real manufacturing process. The film thickness was measured before and after polishing using a reflectometer (ST5030-SL, K-Mac, Republic of Korea). In the measurement, 50 points on the same line of the wafers were characterized for the 300 mm wafer.

4. Results and Discussion

4.1. Numerical Simulation Results

The mass fraction of each monitoring point as described above is shown in Figure 7 for the R0 and R32 pads. The whole process of simulated fluid flow included 30 s DIW flow and 30 s slurry flow. Thus, the slurry mass fraction only shows the data from the last 30 s. As the slurry was supplied, the mass fraction of these five points all rose rapidly for both the R0 and R32 pads. Values below 0.95 are hidden to make the trends more obvious. The slope of the slurry mass fraction with time is presented in Figure 8 by taking the first derivative of data in Figure 7. The SSTs of the five monitoring points are labeled with double-headed arrows. The time at which each monitoring point reached the ideal target mass fraction of 1.00 was defined as the SST, and the average SST of the five points was regarded as the final value. In the case of the R0 pad, the mass fraction slope of the fresh slurry fluctuated significantly because the old slurry was recirculated beneath the wafer surface. Even if fresh slurry is supplied continuously, it cannot escape from the polishing interface completely until around 50 s. As for the R32 pad, the mass fraction slope of the fresh slurry fluctuated slightly around 45 s, which means there is little old slurry recirculation. Compared to the R32 pad, the fresh slurry is not evenly supplied throughout the wafer for the R0 pad, and the average SST is 4.90 s slower.

Taking atmospheric pressure as a reference, the gauge pressure of the slurry at the wafer–pad interface is depicted in Figure 9. The pressure difference between the two cases occurs on the trailing edge and the leading edge in dynamic conditions. This is consistent with reported experiment results [19]. Quantitatively, the R0 pad and R32 pad showed negative pressures of −8 kPa and −6 kPa, respectively, at the trailing edge. The negative pressure caused recirculation of the old slurry and delayed the supply of fresh slurry, a phenomenon known as the back mixing effect [38,39,40]. The greater the absolute value of negative pressure, the more obvious the back mixing. This suction caused by the uneven pressure distribution can tilt the wafer opposite to the sliding direction, making the wafer–pad contact unstable and causing variations in slurry film thickness [41]. This phenomenon eventually acts as a destabilizing NU near the wafer edge.

In terms of the overall slurry distribution beneath the wafer, Figure 10 shows the mass fraction of the fresh slurry as a function of time at the surface of Y = 0.9 mm. The slurry mass fraction of the R32 pad had a more uniform distribution than that of the R0 pad because the fresh slurry supply was slower when using the R0 pad, as discussed above. The confirmed theory revealed that the slow feed rate and discharge rate of fresh slurry increased the scratching and NU, but reduced the MRR [42,43].

4.2. Experimental Results

The fresh slurry supplied into the pad–wafer interface increased with the number of pad grooves [16]. More pad grooves allow the newly injected slurry to flow through the interface faster and prevent the used slurry from flowing back with the wafer rotation, as discussed in the numerical simulation results. The global pad/wafer contact ratio also decreased when the original land area was occupied by the radial grooves. The local pad–abrasive–wafer pressure can then be increased, leading to a slightly larger single silica particle indentation depth and higher MRR. The 300 mm wafer polisher had a faster relative velocity between the pad and wafer. To confirm the results, the experiment was run with a 300 mm wafer polisher. In the scaled-up experiment, an additional R8 pad was added. As shown in Figure 11a, the MRR of the 300 mm polisher was higher and NU was lower in the R32 pad than in the R0 pad. The R8 pad showed almost the same MRR as the R32 pad but was slightly lower. The NU of the polished wafer was improved with the increased radial grooves on the pad. Brief MRR profiles across the wafer are shown in Figure 11b. The NU value decreased with increasing numbers of radial grooves (4.65%, 2.67%, and 1.56% for rR0, R8, and R32, respectively), and the MRR was more stable at the wafer edges than at the wafer center. Regarding the resolved unstable pressure distribution observed for more radial grooves, the wafer edge contact was stabilized and the MRR increased.

Despite the improvements in MRR and NU with increasing numbers of grooves, there was not an obvious change when the radial groove count was increased from 8 to 32, especially in the MRR. The pressure distribution of the pad–wafer interface was expected to improve even with only a few radial grooves. The changes of the R0 pad to R8 and R8 to R32 were a qualitative change and a quantitative change, illustrating the diminishing marginal effect.

Figure 12 shows the COF curves and COF slopes of the polishing processes. The SST was determined using the same method used in the simulation, but the first SST point was chosen within a 3% margin of error compared to the average COF value from 50 to 60 s. As a result, the R0 and R32 pads required 21.52 s and 16.06 s, respectively, for slurry saturation, which is defined as the time when DIW was fully replaced by fresh slurry and the COF reached a stable state.

The SSTs of different pads were quantitatively analyzed and proved with the simulation and COF convergence. The slurry consumption efficiency is only around 10%, and most was wasted because of the high centrifugal force and narrow flow channel [44]. Since insufficient slurry transportation, the bow wave can form around the retainer ring and CMP pad interface, as shown in Figure 13. Moreover, the thickness is sensitively dependent on the pad groove pattern [21]. To qualitatively compare the slurry transportation ability, the slurry bow wave near the retainer ring was recorded with a high-speed camera. As shown in Figure 14, the bow wave on the R32 pad was significantly reduced, and the gap between the retainer ring and pad was more clearly visible than on the R0 pad. It proves that the R32 pad owns the enhanced ability to transport slurry into the pad–wafer interface than the R0 pad, and the SST is also shorter.

4.3. Comparison of the Experiments and Simulations

A comparison of the simulation and experimental results is shown in

Table 4. Comparison of simulated and measured slurry saturation time of 100 mm wafer polisher.

	R0 pad	R32 pad
Simulation (s)	20.44	15.54
Experiment (s)	21.52	16.06
Difference (s)	1.08	0.52
Difference (%)	−5.02	−3.24

. For the simulation and experiments with the 100 mm polisher, the simulation results underestimated the experimental results of the R0 and R32 pads by 5.04% and 3.25%, respectively. Furthermore, the R32 pad was proved to own stronger slurry transportation ability with the evidence of eliminated bow wave. It can be concluded that the simulation results are consistent with the experiment and the error is acceptable. As for the 300 mm wafer polisher, the R32 pad had the advantage of an SST that was 13.57 s shorter than that of the R0 pad. The shorter SST can result in a higher updating speed of the slurry, which can be used to explain the increased MRR and NU.

5. Conclusions

The slurry flow on a concentric groove and radial groove pad was simulated and experimentally verified. A simulation was performed with turbulent vortex flow in the groove trench and laminar flow in the pad–wafer gap while rotating. A shorter SST and slurry refresh rate were proved in terms of slurry mass fraction variation in the simulation and COF in the experiment. We confirmed that a radial groove pad improved the MRR and NU of the polished wafer. The fluid pressure and fresh slurry mass fraction distribution were shown to explain the mechanism. The precise simulation of SST, whose error was around 5%, was expected to be an effective tool to optimize the slurry supply amount and reduce cost.