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In this paper, we study the generalized polynomial chaos (gPC) basedstochastic Galerkin method for the linear semiconductor Boltzmann equationunder diffusive scaling and with random inputs from an anisotropic collisionkernel and the random initial condition. While the numerical scheme and theproof of uniform-in-Knudsen-number regularity of the distribution function inthe random space has been introduced in [Jin-Liu-16'], the main goal of thispaper is to first obtain a sharper estimate on the regularity of thesolution-an exponential decay towards its local equilibrium, which then lead tothe uniform spectral convergence of the stochastic Galerkin method for theproblem under study.

Uniform Spectral Convergence of the Stochastic Galerkin Method for the  Linear Semiconductor Boltzmann Equation with Random Inputs and Diffusive  Scalings