Numerical simulation of temperature distributions during electron beam annealing of multilayer semiconductor structures

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Abstract
A finite element method has been used to study temperature profiles in multilayer semiconductor structures. Of particular interest is the modeling of a continuous wave energy beam similar to those typically used for electron, laser, or ion beam annealing of semiconductor layers. The intensity of the heat source has been modeled in the form of a Gaussian disk on the surface of the structure. Using experimental data and appropriate curve fitting, mathematical expressions are derived that model both thermal conductivity and specific heat as a function of both temperature and sample composition. The resulting expressions give interpolation errors of less than 1% when compared with tabulated experimental values. The simulated temperature distributions are obtained by numerically solving the Helmholtz equation in cylindrical coordinates. Results are presented of simulations involving multilayer structures consisting of metal, insulating, and semiconducting films typically used in both silicon and gallium arsenide technology. The calculated temperature distributions point to possible large variations in substrate temperature as a consequence of lack of thorough control over the beam parameters. More specifically, the diameter of the energy beam is found to strongly affect the resultant peak temperature. The presence of either metal and/or dielectric layers on the surface of the semiconducting substrates is found to have a profound effect on the simulated temperature distributions.