摘要
The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.
研究了半导体器件中量子漂移扩散模型(QDD)的一维稳态模型.通过指数变量代换,把原问题转化成一个非线性四阶方程的边值问题,然后利用不动点定理的理论方法和先验估计的技巧,证明了问题弱解的存在性.在此基础上,还证明了电流充分小的情形下该问题的解的惟一性和当Planck常数δ→0时,QDD的解收敛于经典的漂移扩散模型(DD)的解.
