对含有A1N插入层纤锌矿A1xGal-xN／A1N／GaN异质结构，考虑有限厚势垒和导带弯曲的实际异质结势，同时计入自发极化和压电极化效应产生的内建电场作用，采用数值自洽求解薛定谔方程和泊松方程，获得二维电子气（2DEG）中电子的本征态和本征能级．依据介电连续模型和Loudon单轴晶体模型，用转移矩阵法分析该体系中可能存在的光学声子模及三元混晶效应．进一步，在室温下计及各种可能存在的光学声子散射，推广雷．丁平衡方程方法，讨论2DEG分布及二维电子迁移率的尺寸效应和三元混晶效应．结果显示：A1N插入层厚度和A1xGal-xN势垒层中A1组分的增加均会增强GaN层中的内建电场强度，致使2DEG的分布更靠近异质结界面，使界面光学声子强于其他类型的光学声子对电子的散射作用而成为影响电子迁移率的主导因素．适当调整A1N插入层的厚度和A1组分，可获得较高的电子迁移率．%Adopting a numerical method of solving self-consistently the Schr6dinger equation and Poisson equation through taking into account the realistic heterostructure potential, which includes the influences of energy band bending and the finite thickness of barriers, and through considering the built-in electric field induced by spontaneous and piezoelectric polarization, the eigenstates and eigenenergies of electrons in two-dimensional electron gas （2DEG） are obtained for wurtzite AIxGal_xN/A1N/GaN heterostructures with an inserted A1N layer. Based on the continuous dielectric model and the Loudon＇s uniaxial crystal model, optical-phonon modes and their ternary mixed crystals effect are discussed using the transfer matrix method. Furthermore, the Lei-Ting balance equation is extended in order to investigate the distribution of 2DEG and its size effect as well as ternary mixed crystals effect on electron mobility, which under the influence of each branch of optical-phonon modes are analyzed at room temperature. The results show that the increases of the thickness of inserted A1N layer and the A1 component of AlxGal-xN in the barrier enhance the built-in electric field in the GaN layer, leading 2DEG to be much closer to the interface of a heterostrncture. In addition, it can also be found that the scattering from the interface phonons is stronger than from other optical-phonons, the interface phonons play a dominant role in the total mobility. A higher electron mobility can be obtained by adjusting appropriately the thickness of inserted A1N layer and A1 component.
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