Thermal analysis of an x-ray mask membrane in a plasma environment

Quantifying the temperatures of a membrane while the mask is in a plasma environment is essential in controlling absorber stress due to deposition, and both etch rate and feature profile due to etching. Temperature gradients across the membrane during deposition lead to nonuniform stress across the absorber resulting in large distortions during pattern transfer [W. Dauksher et al., J. Vac. Sci. Technol. B 13, 3103 (1995)]. This article presents a procedure to obtain the steady state temperature profile of a mask/membrane while in a plasma environment (deposition or etch) subjected to different cooling configurations. Membrane heat fluxes and heat transfer coefficients were determined using a thermal transient technique which compares analytical solutions to experimental results. The steady state temperature profile of the membrane was then obtained by using these fluxes and heat transfer coefficients in a three-dimensional finite element model. The analysis procedure was demonstrated on a mask subjected to no helium backside cooling and a mask subjected to flowing helium backside cooling. Good agreement was obtained between the finite element solution, analytical solution, and the experimental results. (C) 1995 American Vacuum Society.