## 1 Introduction  
Chemical mechanical polishing (CMP) is the process of flattening the wafer by lowering the level of the insulating film. In the CMP process, as shown in Figure 1, the polishing process is achieved via the chemical removal reaction due to the chemical composition in the slurry, which is abrasive particles, and the mechanical polishing action between the pad and the wafer by the applied load from the carrier. It is ideal that the wafer is polished equally at all locations after the CMP process. However, for several reasons, within wafer non-uniformity (WIWNU) occurs and one of the reasons is the rebound phenomenon of the polishing pad [1]. The rebound phenomenon is caused by the release of the pressure applied to the retainer ring, which is a replacement part used for preventing the separation of the wafer during the CMP process, at the edge of the wafer. As a result, the rebound of the pad causes a high contact pressure in the wafer edge area. For this reason, it is impossible to produce semiconductor devices in the edge region, and this edge region of the wafer where the non-uniformity has occurred should be removed. In order to increase the yield of the wafer, it is necessary to predict the material removal rate (MRR) of the wafer and the non-uniformity within the wafer. Several theoretical and empirical studies have been conducted to reduce the wafer non-uniformity and increase the wafer yield [1]. [PERSON]'s equation, expressed as a linear equation of pressure and relative velocity, was presented as a general formula representing the MRR of a wafer in the CMP process [2]. Many studies have been conducted to analyze the MRR based on the Preston equation. [PERSON] et al. [3] studied the effect of the slurry component on the MRR and WIWNU, and [PERSON] et al. [4] conducted a study on the effect of the slurry temperature on the MRR. [PERSON] et al. [5] analyzed the MRR with consideration of the viscoelasticity of the polishing pad made of polyurethane. [PERSON] et al. [6] applied the finite element method to analyze the ratio of the pressure applied to the wafer and the retainer ring, which can minimize WIWNU, using linear regression equations. [PERSON] et al. [7] studied the effect on WIWNU by adjusting the contact angle between the retainer ring and the polishing pad. [PERSON] et al. [8] analyzed the effect of platen speed and pressure on the MRR and the wafer surface roughness. [PERSON] et al. [9] pointed out that even if the pressure distribution on the wafer surface was uniformly applied by the carrier, the contact pressure between the wafer and the polishing pad could be non-uniform. [PERSON] et al. [1] investigated the correlation between the curvature of the polishing pad caused by the pressure applied to the wafer and the contact pressure between the wafer and the polishing pad and thus suggested that non-uniformity can be controlled by adjusting the curvature. In order to reduce the non-uniformity of the MRR, a multi-zone carrier head was developed that can transfer various distributed pressure, unlike the conventional head that transfers the uniform pressure on the wafer [10]. [PERSON] et al. [11; 12] showed that it is possible to control the non-uniformity of the MRR by making the contact pressure between the wafer and the pad uniform by applying the multi-zone carrier head. In addition, it was found that if the number of the multi-zone by the multi-zone carrier head is increased, non-uniformity can be more effectively controlled. Recently, various shapes of retainer rings have been proposed to reduce the polishing deviation, and a retainer ring in which metal is inserted has been developed [13]. Based on this, a study on the effect of the material of the retainer ring and the inner ring on the polishing accuracy was recently published [14; 15]. In this paper, the effect of the shape changes of the retainer ring with metal inserted and pressure changes via a multi-pressure carrier head were studied.