  In this paper, we study the bipolar Boltzmann-Poisson model, both for the
deterministic system and the system with uncertainties, with asymptotic
behavior leading to the drift diffusion-Poisson system as the Knudsen number
goes to zero. The random inputs can arise from collision kernels, doping
profile and initial data. We adopt a generalized polynomial chaos approach
based stochastic Galerkin (gPC-SG) method. Sensitivity analysis is conducted
using hypocoercivity theory for both the analytical solution and the gPC
solution for a simpler model that ignores the electric field, and it gives
their convergence toward the global Maxwellian exponentially in time. A formal
proof of the stochastic asymptotic-preserving (s-AP) property and a uniform
spectral convergence with error exponentially decaying in time in the random
space of the scheme is given. Numerical experiments are conducted to validate
the accuracy, efficiency and asymptotic properties of the proposed method.
