THERMAL-ANALYSIS OF AN X-RAY MASK MEMBRANE IN A PLASMA ENVIRONMENT

Quantifying the temperatures of a membrane while the mask is in a plas ma environment is essential in controlling absorber stress due to depo sition, and both etch rate and feature profile due to etching. Tempera ture gradients across the membrane during deposition lead to nonunifor m stress across the absorber resulting in large distortions during pat tern transfer [W. Dauksher et al., J. Vac. Sci. Technol. B 13, 3103 (1 995)]. This article presents a procedure to obtain the steady state te mperature profile of a mask/membrane while in a plasma environment (de position or etch) subjected to different cooling configurations. Membr ane heat fluxes and heat transfer coefficients were determined using a thermal transient technique which compares analytical solutions to ex perimental results. The steady state temperature profile of the membra ne was then obtained by using these fluxes and heat transfer coefficie nts in a three-dimensional finite element model. The analysis procedur e was demonstrated on a mask subjected to no helium backside cooling a nd 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.