Pad Asperity Parameters for CMP Process Simulation
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Pad Asperity Parameters for CMP Process Simulation Takafumi Yoshida YNT-jp.Com 2-10-17 Asae, Hikari, Yamaguchi 743-0021, Japan ABSTRACT This paper reviews the contact mechanics between the surface of a wafer and the asperity of the polishing pad for CMP from basic asperity such as spherical, rectangular, and conical shapes to more general asperity with a height distribution. This paper also proposes a practical method to bridge a measured profile of pad asperity in microscopic scale to a set of simple parameters which describe the elastic behavior for CMP process simulation in larger scale. We show a scalable CMP simulation using the proposed pad asperity parameters. INTRODUCTION The recent accelerated trends for the miniaturization of ULSI are placing great burdens on the CMP process [1]. To support this situation, the role of the CMP process model is becoming more important. The CMP process model we previously proposed by the boundary element method (BEM) methodology treated the elastic modulus of the polishing pad as the fitting parameter and the adjusted values are much lower than the real modulus in most cases [2]. To avoid this problem, we propose a set of pad asperity parameters which take into consideration the contact mechanics on the pad surface using an equivalent asperity model by BEM. Figure 1 shows a CMP process and feature scale pad asperity schematically. It is well known that the pad asperity is relevant to both the removal rate and the topographical quality. The effect of asperity on the removal rate has been studied extensively at slurry particle scale and taken into the material removal rate (MRR) equation by several institutes [3, 4]. On the other hand, the attempts to relate the pad asperity to the topographical results at feature scale were limited only to spherical asperities with an exponential height distribution [5]. In this paper, firstly, we prepare the equivalent asperity model by BEM to review the asperity deformation of basic shapes. Secondly, we introduce a new method to get the asperity parameters for the practical CMP simulations in feature scale. Thirdly, we apply the method for the real pad asperity. Finally, we show a scalable CMP simulation with the parameters. Wafer Holder
Slurry Supply
Relative Velocity
Wafer
Surface Structure Wafer Surface Topography
Slurry
Pad Asperity
Pores Pad
• Removal Rate • Pad Deformation
Figure 1. Schematic of CMP with Pad Asperity
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MODEL FORMULATION In this paper, wafers are assumed to be rigid. To calculate the asperity deformation, we use the well-known theory from contact mechanics, “the contact stresses depend only upon the shape of the gap before loading,” and replace the system of a pad with asperities and a flat rigid wafer by a flat elastic pad in contact with a rigid body having the equivalent asperities [6]. We begin with the comparison of the asperity model by BEM with the Hertz model for a single spherical asperity having a curvature radius R as in figure 2a. EPad Bulk and νPad Bulk denote the elastic modulus an
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