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In this paper, we study the bipolar Boltzmann-Poisson model, both for thedeterministic system and the system with uncertainties, with asymptoticbehavior leading to the drift diffusion-Poisson system as the Knudsen numbergoes to zero. The random inputs can arise from collision kernels, dopingprofile and initial data. We adopt a generalized polynomial chaos approachbased stochastic Galerkin (gPC-SG) method. Sensitivity analysis is conductedusing hypocoercivity theory for both the analytical solution and the gPCsolution for a simpler model that ignores the electric field, and it givestheir convergence toward the global Maxwellian exponentially in time. A formalproof of the stochastic asymptotic-preserving (s-AP) property and a uniformspectral convergence with error exponentially decaying in time in the randomspace of the scheme is given. Numerical experiments are conducted to validatethe accuracy, efficiency and asymptotic properties of the proposed method.

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings