Heat-transfer modeling of the gas gap under a wafer

Abstract

The wafer temperature is a critical observable in semiconductor manufacturing. One of the various mechanisms determining this temperature is the heat transfer in a gas gap between the wafer and the electrostatic chuck (ESC). Various correlations for this heat transfer are available. However, to calculate more accurately the spatial distribution of this temperature, computing the flow in this gap is necessary. With this motivation in mind, this paper presents a computational fluid dynamics model (CFD) for the flow in the wafer-ESC gap that is designed to be easy to implement in industrial CFD codes. This model is tested in various channel-flow problems and then applied to a generic wafer-ESC configuration. For this configuration, CFD results show that varying the flow rate split between three zones, or the total flow rate, or the rugosity of the wafer affect the heat transfer coefficient and its spatial variation. This is important since controlling this variation would allow to maintain a uniform wafer temperature. The model could be used in more realistic wafer-ESC configurations to consider many other parameter variations, such as the size of injection holes, a radially varying gap distance, or the use of many injection zones. From a broader viewpoint, the model is applicable to vacuum problems other than the wafer-ESC configuration.