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# An investigation of the Vickers hardness of polishing pads using simulations based on microtomography model

Le Nam Quoc Huy, Le Ngoc Quynh Hoa

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Le Nam Quoc Huy, Le Ngoc Quynh Hoa. An investigation of the Vickers hardness of polishing pads using simulations based on microtomography model. Japanese Journal of Applied Physics, 2023, 62 (5), pp.056502. 10.35848/1347-4065/acd42a. hal-04162882

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Submitted on 17 Jul 2023

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# An investigation of the Vickers hardness of polishing pads using simulations based on microtomography model

Le Nam Quoc Huy<fnref n="1" />* and Le Ngoc Quynh Hoa<fnref n="2" />*

Received March 30, 2023; revised April 24, 2023; accepted May 10, 2023; published online May 30, 2023

Porous pads used during the chemical mechanical polishing are critical in IC fabrication for achieving consistent throughput. The hardness of thermoplastic polyurethane pads is identified as a crucial parameter in calibrating the amount of material removed during the polishing process. Through micro-CT scanning technology, a three-dimensional micro-topography model of polyurethane IC1000 pad was developed. Nanoindentation measurements were conducted to evaluate the physical properties of IC1000 pad in the manufacture process. In order to investigate the Vickers hardness of the polyurethane IC1000 pad, which widely use in the fabrication of semiconductor manufacturing, the finite element method was employed to simulate the indentation between Vickers indenter diamond tip and the model of IC1000 pad. This study is not only successfully calibrating the Vickers hardness of polyurethane IC1000 pad with a 3 percent error compared to experimental verification, but also developed a novel methodology for investigating the micro-topography structure of polymer foam materials.

© 2023 The Japan Society of Applied Physics

## 1. Introduction

Semiconductors are extensively utilized across diverse applications, not only spanning from automotive to aerospace industries, but also playing a crucial role in the production of ICs, which in turn advances technological innovations. Within the intricate IC fabrication process, chemical mechanical polishing (CMP) constitutes a critical step. This technique involves the use of a porous pad and a tailored slurry to effectively remove nanoscale film materials, thereby enabling the planarization of surfaces in microscale devices such as microcontrollers, integrated chips, and solid-state devices<fnref n="1" />⁻⁷⁾.

Within the scope of CMP, the rate at which material is removed from the wafer is significantly impacted by the hardness and microstructure of the polishing pad. This is a result of the complex interaction between the applied polishing pressure and the rotational velocity of platen during the CMP process, which is heavily influenced by the pad's physical properties and its microscale architecture.⁸⁻¹²⁾ Consequently, thermoplastic polyurethane polymers have emerged as the favored materials for fabricating CMP pads, due to their exceptional energy absorption capabilities, reduced insulating resistance, and thermal properties.¹³,¹⁴⁾

Furthermore, the porosity of CMP pads has been identified as a crucial factor influencing the pad's mechanical attributes, which in turn directly affects the efficiency of material removal throughout the CMP process.¹⁵⁻¹⁸⁾ In the current research, the polyurethane IC1000 pad is extensively utilized in CMP due to its complex porous morphology. This intricate structure introduces significant difficulties in comprehensively analyzing the correlation between the mechanical properties and structural characteristics of CMP pads through traditional techniques.

Expanding on the representative volume elements methodology, which incorporates randomly dispersed cells to represent the three-dimensional (3D) microstructure of foam materials, our prior investigations have explored the 3D microstructure of polyurethane IC1000 pads.¹⁹⁻²¹⁾ However, this approach is time-intensive for analyzing the pore size distribution in the microstructure of polyurethane

IC1000 pad, as it assumes a uniform CMP pad structure with a singular pore created by a bubble and no bubble collapse. To overcome this limitation, Huy et al.²²⁾ utilize micro-CT scanning to reconstruct the 3D microstructure model of the soft polishing pad. The authors investigate the effect of pad asperity on the CMP process for copper thin film wafers.

In the present investigation, the physical attributes of polyurethane IC1000 porous pad are ascertained through nanoindentation measurements. To depict the porous architecture of the polyurethane IC1000 pad, 3D models are generated based on micro-CT scanning of a single cell from the IC1000 pad after the truing process. Following this, finite element method (FEM) simulations are conducted with various down forces to estimate the Vickers hardness of the IC1000 pad of microstructural anisotropy. In addition, Vickers hardness testing is carried out experimentally in order to verify the FEM simulation with the actual results.

## 2. Material properties and microstructure model

### 2.1. Material properties of polishing pad

As part of this study, the experiments on nanoindentation are performed to determine the mechanical properties of the polyurethane IC1000 pad, which is used in the fabrication process. In this study, an experimental setup is employed with a Bruker's Hysitron TI 980 TriboIndent器 instrument, equipped with a Berkovich indenter with a 142.3 degrees, as shown in Fig. 1. The experiments are conducted in a controlled mode with a high load in which the load is gradually increased to its maximum value, and the corresponding depth of contact is measured. The polyurethane IC1000 pad was sliced using a snap-frozen method in liquid nitrogen, resulting in a 200 µm thick blanket specimens for nanoindentation measurements.

Nanoindentation measurements are carried out in this study with high loading values ranging from 1000 to 9000 µN. The Oliver–Pharr method²³,²⁴⁾ is applied to determine the material's hardness and Young's moduli of the material, which is typically used for analyzing the load–displacement data of nanoindentation curves. A mathematical expression for Oliver and Pharr's model is given in Eqs. (1)

<footnote n="1">¹Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taiwan</footnote>

<footnote n="2">²Emerging nanoscience Research Institute (EnRI), Nanyang Technological University, Singapore</footnote>

<footnote>*E-mail: d10903816@mail.ntust.edu.tw; alex.le@ntu.edu.sg</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. The experimental setup for nanoindentation tests.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Berkovich indenter mark and nanoindentation measurements data of polyurethane IC1000 pad.</figcaption></figure>

and (2) below

$$H = \frac{P_{\max}}{A_c} \qquad (1)$$

$$\frac{1}{E_{\text{eff}}} = \frac{1 - \nu^2}{E} + \frac{1 - \nu_i^2}{E_i}, \qquad (2)$$

where the material's hardness (H) is determined by dividing the maximum force ($P_{\max}$) applied during the indentation test by the contact projected area ($A_c$). The Oliver–Pharr method

in Eq. (2) allows for the determination of the effective Young's moduli ($E_{\text{eff}}$) of the material, as well as the reduced Young's moduli ($E$) and the Young's moduli of the Berkovich diamond indenter tip ($E_i$). Furthermore, the Poisson's ratios for the sample ($\nu$) and the diamond indenter tip ($\nu_i$) are taken into account in this calculation. In the Fig. 2, the high-resolution images of Berkovich indent marks are presented, which is obtained using a scanning probe microscope and indentation curves present the mechanical properties of the polyurethane IC1000 porous pad. Average values of polyurethane IC1000 pad hardness and Young's moduli are determined as 0.041 ± 0.0132 GPa and 0.3451 ± 0.01301 GPa, respectively.

For determining the plastic deformation of the IC1000 polyurethane pad, tension tests are conducted using bar specimens made of IC1000 polyurethane pad with a gage length of 70 mm. The quasi-static loading at a cross-head speed of 0.01 mm s⁻¹ until final failure are achieved on a Test Elite 100 tensile testing machine (MTS Systems Corporation). The tensile tests of the IC1000 polyurethane pad are typically conducted by placing the specimen between the upper jaw and lower jaw, as shown in Fig. 3(a). In the calibration process of the stress–strain response, the average value of maximum stress of IC1000 polyurethane pad is taken as the average tensile strength measurement over three experimental results, and the 0.2% offset method is used to calculate the average yield point value. The solid cross-section area of IC1000 polyurethane bar specimens in calibrating is depended on the porosity of IC1000 polyurethane by image processing analysis in our previous research.¹⁹,²¹ The stress–strain tensile behavior curve of IC1000 polyurethane pad is shown in Fig. 3(b).

## 2.2. Micro-topology models of polishing pad

To achieve precise 3D micro-topology model of the polyurethane IC1000 pad, the micro-CT scanning technique is employed to visualize its intricate internal structure. The polishing pad, which is sourced from Dow Corning Corp. in Auburn, MI, USA, is sliced to single cell in Fig. 4(a) and scanned using the SkyScan 1276 micro-CT scanning machine from Bruker in Germany at a micron-level resolution. The resulting micro-CT scanning images, captured from 2000 slices of the polyurethane IC1000 pad, are depicted in Fig. 4(b). The microstructures of the porous IC1000 pad are regenerated using Amira software (Visage Imaging SA, Berlin, Germany), and the red color is used to highlight these features, as shown in Fig. 4(c). Micro-CT scanning images are processed using a median filter to de-noise grayscale images, as well as noise control by segmenting

<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) The experimental setup for the tensile test of the IC1000. (b) The tensile stress–strain curve result of IC1000 polyurethane pad.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** The diagram for generating 3D micro-topology model of polyurethane IC1000 pad.</figcaption></figure>

images based on thresholds. Following this, the image processing techniques are utilized to construct the 3D microstructural model of polyurethane IC1000 pad. Its precision reflects the structural characteristics of the pad, then the obtained results are rendered in the Stereolithography format, allowing for high-resolution visualization and comprehensive analysis of the pad’s intricate cellular architecture. Additionally, the optimization process of the meshing of the 3D micro-topology model of single cell polyurethane IC1000 pad is completed by utilizing the HyperMesh (Altair Company, Troy, MI, USA) software, as demonstrated in Fig. 4(d). The resulting output is a highly optimized mesh that accurately represents the complex geometry of the pad, allowing detailed analysis and simulation of its behavior under various conditions.

### 3. Results and discussion

#### 3.1. Finite element simulations of Vickers indentation

In CMP manufacturing processes, the evaluation of material removal rate is critically dependent on the polishing pad’ hardness. Thus, the finite element simulation techniques are employed to compare the indentation behavior between a Vickers diamond indenter tip and a 3D microstructure model of the pad. The polyurethane IC1000 pad’s Vickers hardness (HV<sub>calibration</sub>) can be calculated by analyzing the recorded load-penetration curves obtained during finite element simulations, which involve both loading and unloading processes. Figure 5 illustrates a typical schematic load-indentation depth curve, wherein parameters commonly measured are utilized for the calculation of HV<sub>calibration</sub>.

In the results of finite element simulations, the highest load applied to the back of the Vickers diamond indenter tip is

denoted by $P_{max\_simulation}$. This load is essentially equivalent to the force values used during experimental procedures. $A_{c\_simulation}$ represents the projected contact area of the Vickers diamond indenter tip on the IC1000 pad surface when it is subjected to the maximum load, and this value is dependent on the maximum contact depth, $h_{c\_simulation}$. The Vickers indenter is characterized by a well-known projected area shape function, which can be expressed as $(A_{c\_simulation} = 24.5h_{c\_simulation}^2)$.²⁵⁻²⁷⁾ The Vickers hardness (HV<sub>calibration</sub>) is computed by utilizing the continuum Oliver–Pharr model,²⁸,²⁹⁾ employing Eq. (3). Equation (4) is utilized to determine the contact depth, $h_{f\_simulation}$, which relies on the maximum depth of indentation simulation. The stiffness of IC1000 pad, denoted as $S$, of the upper section within the elastic unloading phase is ascertained by calculating the slope

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Schematic illustration of Vickers indentation curve of load-displacement data in finite element simulation.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. The boundary conditions for Vickers indentation simulations based on FEM.</figcaption></figure>

of the load-displacement curves at the onset of the unloading process with the slope $S = dP/dh$ being employed in Eq. (4). For a Vickers indenter, the constant value of $\epsilon$ is assumed to be 0.75.30-32)

$$HV_{\text{calibration}} = \frac{P_{\text{max \_simulation}}}{A_{c \_ simulation}(h_{c \_ simulation})} \quad (3)$$

$$h_{c \_ simulation} = h_{f \_ simulation} - \varepsilon \frac{P_{\text{max \_ simulation}}}{S} \quad (4)$$

The FEM software Abaqus version 2020 (ABAQUS Inc., Johnston, RI, USA) is used to simulate the Vickers indentation in this research. The elastic parameters of the material constituting the FEM simulation model in finite element simulations are fine-tuned according to the outcomes of the nanoindentation measurements detailed in Sect. 2.1, which exhibit a mean Young's moduli of 0.3451 GPa and the Poisson's ratio of 0.38. In order to model material behaviors of the damaged plasticity in finite element simulation model of IC1000 polyurethane pad, the conversation between the engineering stress-strain curve on the results of tensile testing is discussed in Sect. 2.1, had been converted into the true stress-strain curve using the calibration option within Abaqus software. The material properties of IC1000 polyurethane pad with the yield strength of 3.86 MPa and ultimate strength of 21.45 MPa is used as input for the plastic model in FEM simulations. The framework of FEM simulation with boundary constraints of the explicit model are depicted in Fig. 6. The Vickers indenter tip contact with the 3D micro-topology model of IC1000 pad surface via the surface to surface contact algorithm approach. The Vickers indenter tip are indented vertically, emulating real experimental conditions, while the polyurethane IC1000 pad 3D micro-topology model have the boundary condition at the bottom surface that is fitted in all directions. The meshing IC1000 porous 3D models is characterized by quadratic tetrahedral elements (C3D10M) with the average element size of 0.01 µm, which are regulated based on factors computation duration time, deviation factor to precisely describe the deformation in simulation.

## 3.2. Experimental verification

To obtain a highly accurate assessment of the macro-scale hardness properties of the polyurethane IC1000 pad, Vickers indentation experiments are performed on the surface of the polishing pad. Utilizing a Vickers diamond tip, produced by

<figure><img src="image_10.png" /><figcaption>Fig. 7. (a) Pyramid Vickers diamond indenter tip. (b) Schematic of Vickers hardness measurement.</figcaption></figure>

Charming, Shanghai Diamond Industry Co., Ltd., with a 136 degrees opening angle, as illustrated in Fig. 7(a), these tests enable the precise determination of the Vickers value. The Vickers hardness value is determined using Eqs. (5) and (6), following the guidelines of ASTM E92-16 (2016) standards. In these equations, $F$ symbolizes the applied load in kilograms-force, and $D$ represents arithmetic mean of the two diagonals lengths of the indentation mark ($D_1$ and $D_2$) measured in millimeters,33-35) as illustrated in Fig. 7(b). This approach allows for a scientifically robust assessment of the material's hardness properties

$$HV = 2 \sin 68^{\circ} \left( \frac{F}{D^2} \right) \quad (5)$$

$$D = \frac{D_1 + D_2}{2} \quad (6)$$

The Vickers hardness of the IC1000 pad is examined using a Vickers micro-hardness tester DVK-1S (Akashi, Corp., Japan), with the experimental setup depicted in Fig. 8. Three distinct applied load values are used: 1 kgf, 5 kgf, and 10 kgf. The loading and unloading speeds are maintained at 50 µm s⁻¹, while the holding time at peak load is set at 10 s. Each applied load is tested three times, and the average hardness is calculated based on the resulting data. Following the application of these indentation load levels, the diagonal length of the indentation is measured using a LEXT OLS5000 confocal laser scanning microscope (Olympus, Inc., Japan). As shown in Fig. 9, the scanning Vickers
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** The experimental platform for determining the Vickers hardness of polyurethane IC1000 pad.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** The average value of diagonal lengths and scanning Vickers indentation marks on the surface of IC1000 polyurethane pad.</figcaption></figure>

indentation marks on the IC1000 polyurethane pad surface and the one-dimensional profiles of diagonals lengths are characterized by three different types of loading forces as well as the average length of two diagonals with a standard variation in Vickers hardness tested three times. The Vickers hardness values of the IC1000 polyurethane pad are calibrated using Eq. (5), in which *D* represents the average length of the diagonal.

A computational simulation of Vickers indentations is performed while varying the down force according to Eq. (3). When the down force applied by the Vickers indenter tip is altered from 1 to 5 kgf, the hardness values experience a substantial reduction, decreasing from 9.27 to 7.6 HV. In contrast, the numerical simulation outcomes indicate that the Vickers hardness value of the IC1000 pad model undergoes a gradual reduction as the down force is incremented from 5 to 10 kgf, ultimately reaching approximately 7.1 HV at 10 kgf. The error value between FEM value and experimental results is slightly increased when down force increases from 1 to

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Experimental verification of Vickers hardness for polyurethane IC1000 pad.</figcaption></figure>

10 kgf, as the error value increases from around 0.6% to approximately 3% when compared to Vickers indentation calibration, as shown in Fig. 10. This is explained by the loss of 3D microstructure during the conversion of the micro-CT scanning images to the meshing model of the polyurethane pad IC1000.

## 4. Conclusions

In this paper, nanoindentation measurements and the tensile test have been performed to determine the material's mechanical properties used in manufacturing the polyurethane IC1000 pad. The geometrical 3D micro-topology of porous IC1000 polishing pad have been precisely reconstructed using a micro-CT scan in order to determine their geometrical characteristics. The simulations of Vickers indentation based FEM has been performed in order to evaluate the feasibility of modeling 3D microstructures in comparison with experimental data. According to the results of this study, it is clear that a Vickers hardness of polyurethane IC1000 pads can be determined by FEM simulation, with an error of 0.6%–3.0% for a change of down loading conditions from 1 to 10 kgf.

## ORCID iDs

Le Nam Quoc Huy https://orcid.org/0000-0002-2015-4272

Le Ngoc Quynh Hoa https://orcid.org/0000-0002-2515-3463

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