In this paper, we mainly consider the global existence of the solutions, large time behavior ofwhereρ, n are electron density and hole density, E is the electric field,the pressure functions p(ρ) =ρm,p(n) = nm(m > 1),ε> 0 is the scaled Planck constant which is small in general andρ±are given constants. Letwhere W is the unique self-similar solution ofρt= (ρm)xx (see [19])and x0 satisfiesOur main result as follows:Theorem Assume thatρ0 > 0, n0 > 0, (g0, h0)∈H3×H3,‖g0‖H3(R)+‖h0‖H3(R)small enough and |ρ+ -ρ-|<< 1,then there is unique global classical solution(ρ, n,E) of the Cauchy problem (1), such that where C,βare positive constants. |