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