Heat Transfer Model to Estimate Temperature Distribution on a Wafer Surface During a Steady State CMP Process

摘要

A conduction heat transfer model using Bessel functions has been developed to estimate the temperature rise in the wafer during the CMP process. The current model estimates the distribution of temperature along the radial direction and along the thickness of the wafer after a steady state has been reached. An insulation boundary condition has been assumed at the back side of the wafer which is in contact with the backing film. The model is solved analytically and various plots of wafer temperature with changing slurry flow rate and relative linear velocity of the wafer with the pad are plotted. The convection heat transfer coefficients necessary for the analytical solution are estimated from the finite element analysis of convection adjacent to a rotating disk (wafer). The slurry (working fluid) used for this simulation included water with Alumina as abrasive particles. The results from the analytical solution show that the temperature at the center of the wafer is much higher than the temperature towards the edge. The surface temperature on the wafer varied from 293K to 325K. The change in surface temperature and local temperature profile with respect to the radius and thickness of the wafer are plotted for various slurry flow rates and relative linear velocities.