On the stationary quantum drift-diffusion model
On the stationary quantum drift-diffusion model
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DOI：
10.1007/s000330050218
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发表时间：
1998-03
期刊：
影响因子：
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通讯作者：
N. Abdallah;A. Unterreiter
中科院分区：
文献类型：
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作者：
N. Abdallah;A. Unterreiter
考虑了一个包含产生-复合项的双极量子漂移扩散模型。解决方案的存在性证明了一个一般的设置，包括消失的粒子密度在某些部分的边界的情况下。证明是基于Schauder不动点迭代结合最小化过程。证明了与经典的漂移扩散模型相反，真空只能出现在边界处。在非零边界数据的情况下，严格地进行了半经典极限。模型的变分结构允许证明粒子密度、费米能级和静电势的强收敛性。
A bipolar Quantum Drift Diffusion Model including generation-recombination terms is considered. Existence of solutions is proven for a general setting including the case of vanishing particle densities at some parts of the boundary. The proof is based on a Schauder fixed point iteration combined with a minimization procedure. It is proven that, contrary to the classical drift-diffusion model, vacuum can only appear at the boundary. In the case of nonvanishing boundary data, the semiclassical limit is carried out rigorously. The variational structure of the model allows to prove strongconvergence of particle densities, Fermi levels and electrostatic potential.