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. The one-dimensional steady-state model of quantum drift diffusion model (QDD) in semiconductor devices is studied. By exponential variable substitution, the original problem is transformed into a boundary value problem for a nonlinear fourth-order equation. Then, by using the theorem of fixed point theorem And priori estimation techniques, the existence of weak solutions to the problem is proved.On the basis of this, the uniqueness of the solution of the problem under the condition of sufficiently small current is also proved and when the Planck constant δ → 0, the solution of QDD Solution to classical drift diffusion model (DD).