Global existence and asymptotic behavior for a semiconductor drift-diffusion-poisson model

In this paper a time-dependent as well as a stationary drift-diffusion- Poisson system for semiconductors are studied. Global existence and uniqueness of weak solution of the time-dependent problem are proven and we also prove the existence and uniqueness of the steady state. It is shown that as time tends to infinity, the solution of the time-dependent problem will converge to a unique equilibrium. Due to the presence of recombination-generation rate R in our drift-diffusion-Poisson model, the work of this paper in some sense extends the results in the previous literature (on both time-dependent problem and stationary problem).