对自恰求解薛定谔方程和泊松方程的数值迭代方法的研究

本文比较了用在自洽求解薛定谔方程和泊松方程中的改变松弛因子的一般迭代方法和predictor-corrector 迭代方法。数值试验表明，使用一般迭代方法求解时，收敛速度慢或迭代过程中解振荡从而不能得到收敛的结果，而使用predictor-corrector 迭代方法时，会加快方程的收敛速度，提高数值的稳定性。本文最后求解了几个常用于高电子迁移率晶体管的异质结的能带图和电子浓度的分布，并解释其物理意义。

Study On The Numerical Iteration Method For Self-consistently Solving Poisson And Schrodinger Equation

In this work, we compare the changing relaxation factor and predictor-corrector iteration method which are used in self-consistently solving Poisson and Schrodinger equation. The numerical experiments illustrate that using the iteration method of changing relaxation factor will lead to the slow convergence speed or numerical oscillation resulting in non-convergent results, while predictor-corrector iteration method can accelerate the convergence speed and improve the numerical stability. At last, the energy band and electron distribution of several heterostructures which are usually used in high electron mobility transistors (HEMTs) are solved and the physical meanings are explained.