硅场发射的WKB法和转移矩阵法比较

硅作为场发射阴极成为可能，硅的场发射研究又重新引起人们的重视．该文将半导体表面的能带弯曲视为一势阱，从而建立了表面势阱作用下硅场致发射的基本方程．并分别应用WKB法和转移矩阵法，求出了垂直于界面的量子能级，并计算了场发射电流．最后对两种方法的结果进行了比较，发现转移矩阵法的结果比WKB近似法更加接近于FN理论的结果，该方法可为复杂势场中的量子化效应及电子特性提供一个有效的分析方法．

Comparison of WKB Method and Transfer Matrix Method Used in Silicon Field Emission

Due to band bending of semiconductor surface applied electric field, the electron emission on silicon surface can be considered as a tunneling process through a potential well. In the article, we calculate the quantum energy levels and emission current,respectively using WKB method and the transfer matrix method .By Comparing the conclusion from WKB method and transfer matrix method, we find that the result from transfer matrix is closer to that from FN theory than WKB method. This method may be useful in the analysis on basic physical qualities and parameters of quantum well, such as the characteristics and the quantization effect of an electron in the complicated potential.