Chemical Mechanical Polishing Model Research Articles

Material removal rate model for chemical–mechanical polishing of single-crystal SiC substrates using agglomerated diamond abrasive

Material removal mechanisms are essential for the selection of polishing slurries and parameter optimization of chemical–mechanical polishing (CMP) processes. This study established a material removal rate (MRR) model for CMP of single-crystal SiC substrates using a fixed agglomerated diamond (AD) abrasive pad (FADAP). The distribution of the polishing pressure between the AD abrasive and FADAP matrix was examined, and the influence of the abrasive and polishing parameters on the MRR was revealed. Furthermore, single-factor experiments were conducted to validate the rationality of the MRR model. The experiments demonstrated that when the thickness of the surface-affected layer of the single-crystal SiC substrate in the MRR model was set to 5 nm, the error between the calculated and experimental values of the model could be controlled to within 20%. This result experimentally verified the validity of the MRR model and its associated assumptions. Moreover, the MRR of the CMP process of a single-crystal SiC substrate reached 36.26 μm/h with a polishing pressure of 27.6 kPa and an AD abrasive primary particle size range of 7–10 μm. Therefore, the feasibility of efficiently processing single-crystal SiC substrates using an FADAP was theoretically confirmed.

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

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

Characterization of Pad–Wafer Contact Area and Distance in Chemical-Mechanical Polishing

Chemical-mechanical polishing (CMP) has been an important process step in microelectronic device manufacturing for more than three decades. Physical CMP modeling utilizes the interactions between the polishing pad and the wafer. This requires data on important physical properties such as the real contact area and the effective pad-to-wafer distance under near-process conditions, as these are directly related to the removal rate, defects, etc. In the present study, a FTIR spectrometer and a custom ATR equipment with micro-structured single reflection elements (mSRE) were used to quantify the volume fraction and contact area of a IC1000 polishing pad in dry and wet state under different static loads. No stable contact over time was observed even at very high pressures of up to 350 kPa. Viscoelastic behavior of air-dried and water-soaked pad was proven on a microscale by using load response, creep-recovery and stress relaxation tests. This leads to a memory effect of the pad that should be taken into account during dynamic loading as the wafer-pad contact has a direct impact on the material removal. The presented method can therefore provide valuable information about dynamic effects of the pad behavior in near-process environment and thus help to improve the CMP modelling.

CmpCNN: CMP Modeling with Transfer Learning CNN Architecture

Performing chemical mechanical polishing (CMP) modeling for physical verification on an integrated circuit (IC) chip is vital to minimize its manufacturing yield loss. Traditional CMP models calculate post-CMP topography height of the IC’s layout based on physical principles and empirical experiments, which is computationally costly and time-consuming. In this work, we propose a CmpCNN framework based on convolutional neural networks (CNNs) with a transfer learning method to accelerate the CMP modeling process. It utilizes a multi-input strategy by feeding the binary image of layout and its density into our CNN-based model to extract features more efficiently. The transfer learning method is adopted to different CMP process parameters and different categories of circuits to further improve its prediction accuracy and convergence speed. Experimental results show that our CmpCNN framework achieves a competitive root mean square error ( RMSE ) of 2.7733Å with 1.89× reduction compared to the prior work, and a 57× speedup compared to the commercial CMP simulation tool.

A Fine-Grained, End-to-End Feature-Scale CMP Modeling Paradigm Based on Fully Convolutional Neural Networks

Chemical mechanical polishing (CMP) planarizes the chip surface through a synergistic effect of chemical etching and abrasive polishing, and has become increasingly essential in modern semiconductor manufacturing. For better production yield, the industry seeks an accurate CMP model to identify, localize and control surface unevenness caused by the layout dependent effect (LDE) prior to fabrication, which provides valuable information for manufacturing-friendly designs, such as accurate hotspot prediction, design-rule optimization, and smart dummy fill. However, existing models are often overly coarse-grained and inaccurate: They are unable to utilize or analyze detailed topology information in a layout design, and can only characterize the post-CMP chip surface into a rough step-height model. The prediction resolution is also constrained by the featuring window size. In this paper, we propose a novel fine-grained and end-to-end feature-scale CMP modeling paradigm based on fully convolutional neural networks. The model directly analyzes the detailed layout topology without an explicit step of featuring parameter extraction, accurately predicts the rich chip surface micro-topography at a feature-scale precision. We designed and taped-out test chips under 28nm and 40nm processes. Experiments on silicon data demonstrated our model’s accuracy improvements of 65% to 76%, as well as its cross-process-node adaptability.

Analysis of the error of the optical material removal function in a multivariate mathematical model for controlling the shaping processlarge optical parts

The features of technological processes for controlling the shaping of the optical surfaces of large-sized flat parts at the stages of grinding and polishing on modern machines of continu-ous shaping with a full-size tool.The substantiation of the structure of a multifactorial mathe-matical model of the processes of grinding and polishing of flat optical surfaces is given on the basis of studying the laws of motion of actuators and the processing zone of optical machines of continuous shaping with a full-size tool. The analysis of the influence of technological fac-tors and physicochemical features of the processes of processing surfaces of flat optical parts on the function of removing the optical material of a model of chemical mechanical polishing (CMP) is presented. The analysis of the study of the error of the optical material removal func-tion of the presented multivariate mathematical model with the recommendation for fixing cer-tain values of the main kinematic parameters of machine equipment is carried out.

A Study on the Pattern Effects of Chemical Mechanical Planarization with CNN-Based Models

Chemical mechanical polishing (CMP) has become one of the most important process stages in the fabrication of advanced integrated circuits (IC). The CMP pattern effect strongly influences the planarization of the chip surface morphology after CMP, degrading the performance and the yield of the circuits. In this paper, we introduce a method to predict the post-CMP surface morphology with a convolutional neural network (CNN)-based CMP model. Then, CNN-based, density step height (DSH)-based, and common neural-network-based CMP models are built to compare the accuracy of the predictions. The test chips are designed and taped out and the predictions of the three models are compared with experimental results measured by an atomic force profiler (AFP) and scanning electron microscope (SEM). The results show that CNN-based CMP models have better accuracy by taking advantage of the CNN networks to extract features from images instead of the traditional equivalent pattern parameters. The effective planarization length (EPL) is introduced and defined to make better predictions with real-time CMP models and in dummy filling tasks. Experiments are designed to show a method to solve the EPL.

An efficient material removal rate prediction model for cemented carbide inserts chemical mechanical polishing

Aiming at the defects of cemented carbide inserts surfaces produced in the conventional grinding process, a cemented carbide inserts chemical mechanical polishing (CMP) process is developed to reduce the insert rake face roughness for the improvement of cutting performance. Especially, an efficient material removal rate (MRR) prediction model for cemented carbide inserts CMP is established considering synthesized effects of multi-factors characteristics such as abrasive particles, the polishing pad, and cemented carbide inserts. Firstly, the contact mechanism between the cemented carbide insert and the polishing pad is analyzed by using the Greenwood and Williamson elastic model. Then the contact model between the abrasive particle and the polishing pad is established based on the Sneddon's hyper-elastic micro-contact mechanics, and the contact model between the abrasive particle and the cemented carbide insert is built by applying the elastic-plastic micro-contact mechanics. Finally, an efficient MRR prediction model is proposed. The experimental results show that when changing the polishing pressure and the polishing disk rotational speed individually, the MRR average error between the predicted value and the experimental value is 1.65% and 2.18%, respectively. This study demonstrates that the proposed model can contribute to CMP preparation of high-performance cemented carbide tools/inserts.

Development of an Ultra-Precision Annular Polishing Machine Tool with Full Gas Static Pressure

In order to improve chemical mechanical polishing (CMP) efficiency and accuracy in the fabrication of planar optics, CMP models and machine tools have been developed. A three-dimensional contour map of the surface of the polishing plate was established by measuring the runout error of several circles on the polishing plate. Based on the Preston equation and the three-dimensional contour map, a CMP model that simulates material removal at any point on the work piece is proposed. This model shows that higher motion accuracy can improve efficiency and accuracy. Then, based on this point of view, a new CMP machine tool was designed, and the ultra-precision gas static pressure guide rail and turntable and Siemens 840Dsl numerical control system were applied to the new CMP machine tool. In order to validate the new machine, a series of testing and processing experiments were carried out. The straightness error of the gas static pressure guide rail can be less than 1.1 μm. The axial runout error of the gas turntable can be less than ±0.4 μm. The surface profile of the experimental workpiece can be less than 0.01λ, and the processing efficiency of the new CMP machine can reach 4 times of the processing efficiency of the conventional CMP machine. In addition, the repeatability and stability of the CMP process is improved on new machines.

A CNN-Based CMP Planarization Model Considering LDE Effect

As integrated circuit (IC) industry advances to the nanometer scale, layout pattern plays more and more important role on chip fabrication. Layout-dependent effect (LDE) studies how different patterns influence the fabrication results. Chemical–mechanical polishing (CMP), one of the most important processes during IC fabrication, is strongly influenced by LDE. The purpose of this article is to show a convolutional neural network (CNN)-based method to model post-CMP surface topography problem. The method accurately predicts the topological height of the chip surface after CMP by using CNN to abstract features from layout patterns, aiming to analyze defects that may cause failure. This article first addresses about the principles and practicability of using the CNN method to build a CMP model, then builds up a complete CNN structure, and compares the CNN-based model with a traditional pressure-distribution-based CMP model. We designed test chips containing different structures and fabricated them with 28- and 45-nm process nodes. Surface topography is measured using atomic force profiler (AFP) and scanning electron microscope (SEM). The result shows that the total root-mean-squared error (RMSE) of the CNN-based model is 22.41 A, whereas the RMSE of the pressure-distribution-based model is 65.54 A. The CNN-based CMP model shows better accuracy.

Review on modeling and application of chemical mechanical polishing

Abstract With the development of integrated circuit technology, especially after entering the sub-micron process, the reduction of critical dimensions and the realization of high-density devices, the flatness between integrated circuit material layers is becoming more and more critical. Because conventional mechanical polishing methods inevitably produce scratches of the same size as the device in metal or even dielectric layers, resulting in depth of field and focus problems in lithography. The first planarization technique to achieve application is spin on glass (SOG) technology. However, this technology will not only introduce new material layers, but will also fail to achieve the global flattening required by VLSI and ULSI technologies. Moreover, the process instability and uniformity during spin coating do not meet the high flatness requirements of the wafer surface. Also, while some techniques such as reverse etching and glass reflow can achieve submicron level regional planarization. After the critical dimension reaches 0.35 microns (sub-micron process), the above methods cannot meet the requirements of lithography and interconnect fabrication. In the 1980s, IBM first introduced the chemical mechanical polishing (CMP) technology used to manufacture precision optical instruments into its DRAM manufacturing [1]. With the development of technology nodes and critical dimensions, CMP technology has been widely used in the Front End Of Line (FEOL) and Back End Of Line (BEOL) processes [2]. Since the invention of chemical mechanical polishing, scientists have not stopped studying its internal mechanism. From the earliest Preston Formula (1927) to today’s wafer scale, chip scale, polishing pad contact, polishing pad - abrasive - wafer contact and material removal models, there are five different scale models from macro to the micro [3]. Many research methods, such as contact mechanics, multiphase flow kinetics, chemical reaction kinetics, molecular dynamics, etc., have been applied to explain the principles of chemical mechanical polishing to establish models. This paper mainly introduces and summarizes the different models of chemical mechanical polishing technology. The various application scenarios and advantages and dis-advantages of the model are discussed, and the development of modeling technology is introduced.

Wafer Flatness Modeling in Chemical Mechanical Polishing

Flatness is an important criteria for evaluating wafer quality. Chemical mechanical polishing (CMP) is an effective method to process wafers and to improve the wafer flatness. Therefore, a flatness model is necessary for optimizing CMP process variables through investigating the wafer surface formation mechanism as well as the influences of CMP parameters on the wafer flatness. However, most studies pay attention to the roughness change of a wafer surface. Besides, there is little literature about the flatness of CMP modeling wafers. In this study, a wafer flatness model based on the material removal during CMP was established. The surface pressure distribution of the wafer surface was obtained by finite element simulation. The relative velocity distribution of the abrasive particles and the wafer surface during polishing were acquired by the numerical simulation, introduced to develop the flatness model. Finally, the influences of different process parameters on flatness were investigated. The flatness model established agreement between the calculated and the experimental results.

Design of an ultraprecision computerized numerical control chemical mechanical polishing machine and its implementation

The chemical mechanical polishing (CMP) is a key process during the machining route of plane optics. To improve the polishing efficiency and accuracy, a CMP model and machine tool were developed. Based on the Preston equation and the axial run-out error measurement results of the m circles on the tin plate, a CMP model that could simulate the material removal at any point on the workpiece was presented. An analysis of the model indicated that lower axial run-out error led to lower material removal but better polishing efficiency and accuracy. Based on this conclusion, the CMP machine was designed, and the ultraprecision gas hydrostatic guideway and rotary table as well as the Siemens 840Dsl numerical control system were incorporated in the CMP machine. To verify the design principles of machine, a series of detection and machining experiments were conducted. The LK-G5000 laser sensor was employed for detecting the straightness error of the gas hydrostatic guideway and the axial run-out error of the gas hydrostatic rotary table. A 300-mm-diameter optic was chosen for the surface profile machining experiments performed to determine the CMP efficiency and accuracy.

Establishing a theoretical model for abrasive removal depth of silicon wafer chemical mechanical polishing by integrating a polishing times analytical model and specific down force energy theory

This study uses the polishing pad with cross pattern, and it is supposed that the contact area between polishing pad surface of cross pattern and wafer is Gaussian distribution to establish and analyze an innovative abrasive removal depth theoretical model of chemical mechanical polishing (CMP) silicon wafer. In this model, it uses the binary image pixel division to calculate polishing times and it derives the contact force of each abrasive particle and uses the specific down force energy (SDFE) theoretical equation to calculate the abrasive removal depth on each abrasive particle after down force being applied. This study carries out CMP silicon wafer experiment as well as atomic force microscopy (AFM) measurement experiment of SDFE of silicon wafer. The abrasive removal depth of silicon wafer acquired from simulation analysis is compared with the abrasive removal depth of silicon wafer obtained from CMP experiment of silicon wafer, and the difference in between will also be analyzed. It shows that the difference between the results of simulation and experiment is in the acceptable range.

Material removal model of chemical mechanical polishing for fused silica using soft nanoparticles

Fiber arrays are used to connect arrayed waveguide chips. The end-faces of fiber array components are multi-materials non-uniform surfaces. Their low polishing quality has become a bottleneck that restricts coupling performance of integrated photo-electronic devices. The chemical mechanical polishing (CMP) is normally used to improve the polishing quality of the end-faces of fiber array components. It is very important to optimize process parameters by researching the mechanical behavior of nanoparticles and material microstructure evolution on the CMP interfaces. Based on the elastic and hyper-elastic contact of the soft polishing nanoparticles with fused silica and polishing pad, respectively, the material removal mechanism at molecular scale of polishing process for fused silica using nanoparticles is investigated, and the material removal rate model is also derived by using Arrhenius theory and molecule vibration theory. Theoretical and experimental results show that the material is mainly removed by the interfacial tribo-chemical effect between polishing nanoparticles and fused silica during CMP process. The penetration depth of a single nanoparticle inside the fused silica is at molecular scale, and the superficial molecules of fused silica are removed by chemical reactions because of enough energy obtained. The material removal rate of fused silica during CMP process is determined by the polishing pressure, the chemical reagents and its concentration, and the relative movement speed between the fused silica workpiece and the polishing pad.

Effect of photocatalytic oxidation technology on GaN CMP

GaN is so hard and so chemically inert that it is difficult to obtain a high material removal rate (MRR) in the chemical mechanical polishing (CMP) process. This paper discusses the application of photocatalytic oxidation technology in GaN planarization. Three N-type semiconductor particles (TiO2, SnO2, and Fe2O3) are used as catalysts and added to the H2O2–SiO2-based slurry. By optical excitation, highly reactive photoinduced holes are produced on the surface of the particles, which can oxidize OH− and H2O absorbed on the surface of the catalysts; therefore, more OH* will be generated. As a result, GaN MRRs in an H2O2–SiO2-based polishing system combined with catalysts are improved significantly, especially when using TiO2, the MRR of which is 122nm/h. The X-ray photoelectron spectroscopy (XPS) analysis shows the variation trend of chemical composition on the GaN surface after polishing, revealing the planarization process. Besides, the effect of pH on photocatalytic oxidation combined with TiO2 is analyzed deeply. Furthermore, the physical model of GaN CMP combined with photocatalytic oxidation technology is proposed to describe the removal mechanism of GaN.

Modeling of chemical mechanical polishing processes by cellular automata and finite element/matlab integration methods

In this work, novel chemical-mechanical polishing modeling schemes in both wafer and device levels are proposed and analyzed. The cellular automata method, based on Preston equation and contact mechanics, are used for analyzing the wafer level material removing rate. On the other hand, a finite element and Matlab integration scheme is also developed, primarily for addressing the structural integrity of interconnected structures after polishing. These methods are validated by comparing the previous reported analysis and experimental data. Finally, these schemes are used for parametric studies for guiding process optimization.

Influence of the Molecular Adhesion Force on the Indentation Depth of a Particle into the Wafer Surface in the CMP Process

By theoretical calculation, the external force on the particle conveyed by pad asperities and the molecular adhesion force between particle and wafer are compared and analyzed quantitatively. It is confirmed that the molecular adhesion force between particle and wafer has a great influence on the chemical mechanical polishing (CMP) material removal process. Considering the molecular adhesion force between particle and wafer, a more precise model for the indentation of a particle into the wafer surface is developed in this paper, and the new model is compared with the former model which neglected the molecular adhesion force. Through theoretical analyses, an approach and corresponding critical values are applied to estimate whether the molecular adhesion force in CMP can be neglected. These methods can improve the precision of the material removal model of CMP.

Chemical mechanical polishing: Theory and experiment

Abstract For several decades, chemical mechanical polishing (CMP) has been the most widely used planarization method in integrated circuits manufacturing. The final polishing results are affected by many factors related to the carrier structure, the polishing pad, the slurry, and the process parameters. As both chemical and mechanical actions affect the effectiveness of CMP, and these actions are themselves affected by many factors, the CMP mechanism is complex and has been a hot research area for many years. This review provides a basic description of the development, challenges, and key technologies associated with CMP. We summarize theoretical CMP models from the perspectives of kinematics, empirical, its mechanism (from the viewpoint of the atomic scale, particle scale, and wafer scale), and its chemical-mechanical synergy. Experimental approaches to the CMP mechanism of material removal and planarization are further discussed from the viewpoint of the particle wear effect, chemical-mechanical synergy, and wafer-pad interfacial interaction.

研磨パッドの微細凹凸接触を考慮したCMPプロセスのEHL解析

A soft EHL analysis model of Chemical Mechanical Polishing (CMP) is developed in the present study. Since a surface of a polishing pad is filled with micro asperities due to conditioning, the polishing pad deforms in a nonlinear manner by contacting to a wafer. A viscosity of the polishing pad also affects stress concentration beneath the edge of the wafer. In order to take into account both effects, damping behavior of the polishing pad and macroscopic characteristics of the polishing pad asperity deformation are considered at the same time in the proposed analysis. Based on the traditional contact model, i.e., Greenwood-Williamson model, nonlinear elasticity of the surface asperity layer of the polishing pad is formulated, and Arbitrary Lagrangian-Eulerian (ALE) method is applied to deal with dynamic structure analysis. A series of three-dimensional EHL analysis was conducted using the proposed model. Effects of viscosity of the polishing pad and the nonlinear elasticity caused by the polishing pad asperities on distributions of contact stress and fluid pressure were examined. Analytical results indicated that both distributions greatly depend on the viscosity and the nonlinear elasticity of the polishing pad, and thus the consideration of nonlinear viscoelastic behavior in the pad-wafer contact is important to predict the polishing pressure distribution, especially beneath wafer leading edge.