AlGaN/GaN势垒层异质结构与二维电子气密度的相互作用

Interaction between Two-dimensional Electron Gas Density and Heterostructure of Barrier Layer in AlGaN/GaN Heterojunction

在忽略二维电子气波函数对势垒层渗透的前提下提出了直接求解无电子势垒层泊松方程来计算势垒层能带的新思路,提出了把势垒层以外的极化电荷、杂质电荷及电子电荷作为势垒层边界上的界面电荷来解势垒层泊松方程的新方法。由此计算出的势垒层能带和自洽能带计算结果相吻合。用电子气密度多项式来拟合沟道阱子带能级随电子气密度变化的曲线,推算出新的二维电子气密度的超越方程。对于各种不同异质结构,从超越方程解出的电子气密度和势垒层能带同自洽能带计算结果相吻合,从而创立了一种自洽求解沟道阱泊松方程和薛定谔方程的新方法。研究了二维电子气密度与势垒层异质结构的相互作用,讨论了电子气密度随异质结构的变化,提出了异质结能带剪裁的新思路。

By ignoring the permeating of the electron wave function into the barrier layer,a new train of thought of solving the Poisson equation to obtain the energy band in barrier layer without electron is proposed.A new method is put forward that the Poisson equation in barrier layer could be solved by treating the polarization charge,impurity charge,and electron charge outside the barrier layer as interface charge at the boundary of barrier layer.The energy band in barrier layer calculated by the Poisson equation agrees with the self-consistent energy band solution.A polynomial of electron density is used to fit the energy level of fundamental sub-band calculated by the self-consistent energy band software,from which a transcendental equation of electron density is derived.For four different heterostructures,the electron density and energy band in barrier layer calculated by the mentioned transcendental equation of electron density agree with the self-consistent energy band solution,from which a new method to self-consistently solve the Poisson equation and Schrodinger equation is established.The interaction between the electron density in channel well and the heterostructure band in barrier layer is investigated by the mentioned Poisson equation in barrier layer,and thus the variation of electron density with the heterostructure in barrier layer is discussed and a new idea of band tailoring is proposed.