A REVIEW ON THE QUANTUM DRIFT DIFFUSION MODEL

ABSTRACT ABSTRACT We consider the quantum drift diffusion model for semiconductor devices and collect recent results on the stationary and transient equations. The stationary model including generation–recombination terms is studied for bipolar devices and the transient equations are considered in the unipolar case. We cover several topics, such as existence and uniqueness of solutions, asymptotic limits and convergence of a nonlinear iteration scheme in the stationary case as well convergence of a positivity preserving semidiscretization of the transient equations and the linear stability of stationary states. Keywords: Quantum drift diffusionGeneralized Gummel iterationAnalysisNumericsConvergenceFourth order PDEPositivity AMS (MOS) Subject Classification: 35J5535J6035K3565M1265M2076Y05 ACKNOWLEDGMENT The author acknowledges financial support from the TMR Project 'Asymptotic Methods in Kinetic Theory,' grant number ERB FMRX CT97 0157.