外电场下应变量子阱中电子与空穴的本征态

考虑自发与压电极化引起的内建电场,自由电子-空穴气屏蔽效应和外加电场,基于常微分数值计算,自洽求解电子与空穴的薛定谔方程和泊松方程以获得基态能级。以典型的GaN/A lxGa1-xN纤锌矿氮化物应变量子阱为例,通过数值求解,得到电子与空穴的本征基态能和相应本征波函数。计算结果表明:沿量子阱生长方向所施加的外加电场将抵消阱中内建电场的作用,阱结构的弯曲程度略显平缓,使电子(空穴)本征波函数逆(顺)着外电场方向移动,且均向阱中心移动,波峰峰值增加,隧穿几率减小;在固定外电场情况下,电子与空穴基态能级随阱宽的增加而减小,随掺杂组分的增加而增加,表明外加电场对内建电场有所削弱以及量子限制作用对电子(空穴)基态能有显著的影响。

Eigen-states of Electron and Hole in Strained Quantum Well under External Electric Field

The Schrdinger equations of electron and hole and Poisson equations are solved self-consistently to obtain the ground-state energies on the basis of the numerical computation of ordinary differential equations. The built-in electric field induced by spontaneous and piezoelectric polarization, the screening effect due to the free electron-hole gas and the applied external electric field are considered. For example, a typical GaN/AlxGa1-xN wurtzite nitride strained quantum well is taken to calculate the eigen energies of electron and hole as well as the corresponding eigen-wavefunctions. The results show that the built-in electric field is offset by the electric field applied along the same direction as the growth of quantum well. The bending degree of the well structure is slightly reduced. The electron or hole wave function then moves along or away from the electric field direction to the center of the well leading to the increase of wave peak value and decrease of tunneling probability. It is also found that in a fixed external electric field case, the ground-state energy levels of electron and hole in the quantum well significantly decrease with increasing the well width and prominently increase as the Al component increases. That is to say, the external electric field certainly weakens the built-in electric field and the quantum confinement has a significant impact on the electronic (hole) ground-state energy.