Heating of a uniform wafer disk

The closed-form heating response of a thin uniform circular wafer is obtained, in view of a new processing method for semiconductor materials. A strain energy formulation is obtained expeditiously using Gaussian curvature and associated structural concepts. The method is developed for generally curved wafers, which accounts for flat, spherical, cylindrical and twisted shapes. Solutions for the first two types become available in closed form, and the deformation can exhibit a sudden change in axi-symmetrical response or a snap-through buckling, or both: for the latter two types, a numerical solution points to progressive deformation in both without buckling. All results are shown to compare rather well with finite element analysis.