A Study to Estimate the Number of Active Particles in CMP
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A Study to Estimate the Number of Active Particles in CMP Jeremiah N. Mpagazehe1, Geo Thukalil1, C. Fred Higgs III1 1 Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213 ABSTRACT To improve yield rates during integrated circuit fabrication, a better understanding of the material removal process during CMP is sought. Many material removal models have been generated to predict the material removal rate (MRR) during CMP. The majority of such models estimate that the MRR is equal to the material removed by a single particle multiplied by the total number of particles contributing to the wear process. Particles contributing to the wear process are known as βactive particlesβ. While several authors have proposed analytical models to estimate this quantity, this work introduces a new method for estimating the number of active particles in CMP by deducing it from the polish results of a multi-physics CMP model. By employing The Particle-Augmented Mixed Lubrication model (PAML) developed by Terrell and Higgs (2008), it is possible to determine the number of active particles in CMP. The predictions of PAML are compared with two popular analytical approaches which have been commonly used to predict the number of active particles during CMP.
INTRODUCTION CMP is the primary method for planarization in integrated circuit fabrication. A greater understanding of CMP is desired as inconsistent polishing leads to degradation in circuit performance. Many authors have posited models to predict material removal rates (MRRs) during CMP [1],[6],[9]. However, these material removal models have employed a wide range of physical phenomena to predict wear mechanisms. Strikingly, despite the range of hypotheses and approximations developed to predict wear, many of the methods used to model CMP base the MRR formulation on the number of particles which take part in the wear process, multiplied by the volume per time removed by each of these particles. The number of particles taking part in the wear process is defined as Na.
πππππππππ Eqn. (1) ππ‘ The purpose of this work is to gain a better understanding of Na by comparing the results from several models. Two analytical models were selected because of their difference in underlying assumptions and their pervasive use in the field of MRR prediction. A third model is a new computational approach which can, for the first time, provide an in-situ prediction of the number of active particles during a multi-physics CMP simulation. Each of these models predicts the number of active particles in a fundamentally different manner. The resultant number of active particles is a difficult parameter to verify experimentally. Thus, in the absence of experimental results which directly measure Na, the comparison of these three different approaches to predict Na will help to verify this common parameter in CMP modeling. ππ
π
ππππππ = ππ Γ
Approaches to Predict Na This work compares three different techniques for predicting the number of active particles during CMP: The Particle Dis
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