W. Dai et R. Nassar, A 3-DIMENSIONAL NUMERICAL-METHOD FOR THERMAL-ANALYSIS IN X-RAY-LITHOGRAPHY, INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 8(4), 1998, pp. 409
X-ray irradiation of photoresists, such as polymethylmethacrylate (PMM
A), on a silicon substrate is an important technique in micro fabricat
ion used to obtain structures and devices with a high aspect ratio. Th
e process is composed of a mask and a photoresist deposited on a subst
rate (with a gap between mask and resist). Predictions of the temperat
ure distribution in three dimensions in the different layers (mask, ga
p, photoresist and substrate) and of the potential temperature rise ar
e essential for determining the effect of high flux X-ray exposure on
distortions in the photoresist due to thermal expansion. In this study
, we develop a numerical method for obtaining the steady state tempera
ture profile in an X-ray irradiation process by using a preconditioned
Richardson method for the Poisson equation in the micro-scale. A doma
in decomposition algorithm is then obtained based on the parallel ''di
vide and conquer'' procedure for tridiagonal linear systems. Numerical
results show that such a method is efficient.