Temperature Distribution and Stresses in Circular Wafers in a Row During Radiative Cooling

Abstract

A model is proposed in which transient temperature profiles in circular wafers in a row during cooling are analyzed. Various effects such as the number of wafers in a row, the position of the wafer in a row, the ratio of the wafer radius to the wafer spacing, multiple reflections, and the contribution of conduction are considered. It is shown that drastic radial variations of temperature can occur because of the geometrical factor affecting the efficiency of radiative transfer in various parts of a wafer. Thermal stresses thus induced in the cooling wafer can often exceed the yield stress in silicon wafers, causing plastic deformation. The phenomenon of ``thermal warping'' is briefly discussed.