物理学报2018，Vol.67Issue(2)：242-248,7.DOI:10.7498/aps.67.20171827
InAlN/GaN异质结二维电子气波函数的变分法研究
Variational study of the 2DEG wave function in InAlN/GaN heterostructures
摘要
Abstract
The variational method has been widely used to study the electronic structures of heterostructure materials in spite of this method being less accurate than the numerical method,because analytical formulas for some electrical parameters can be derived using this method. However, effects of surface states on the two-dimensional electron gas (2DEG) have not been taken into account in the variational studies of GaN-based heterostructures. In the present study, analytical formulas for the electron wave function and ground state energy level of the 2DEG in InAlN/GaN heterostructures are derived using the variational method, and the influences of structural parameters of InAlN/GaN heterostructures on the electrical properties are discussed. In the theoretical model, evenly distributed surface states below the conduction band are assumed to be the origin of the 2DEG,and the polarization charges at the InAlN surface and the InAlN/GaN interface due to spontaneous and piezoelectric polarization effects in InAlN/GaN heterostructures are taken into account. A trial envelope wave function with two variational parameters is used to derive the expectation value of the total energy per electron. The variational parameters are determined by minimizing the expectation value. The model predicts a linear conduction band profile in InAlN barrier layer and an approximately triangular-shaped potential well on the GaN side of the InAlN/GaN interface. Electrons released from the surface states are confined in the potential well, forming the 2DEG. The 2DEG sheet density for the lattice-matched InAlN/GaN heterostructure with a 15 nm InAlN layer is 1.96×1013cm?2, and the average distance from the InAlN/GaN interface of electrons is 2.23 nm. The 2DEG sheet density increases rapidly with InAlN thickness increasing when the InAlN layer exceeds the critical thickness,and starts to be saturated above 15 nm. The dependence of the calculated 2DEG sheet density on the InAlN thickness quantitatively agrees with recently reported experimental data. The increasing 2DEG sheet density results in increasing the ground state energy level and Fermi energy, and the energy spacing between the two also increases for containing more electrons. The polarization discontinuity at the InAlN/GaN interface decreases with increasing In mole fraction, causing the 2DEG sheet density to decrease, and thus the ground state energy level and the Fermi energy to decrease. This model is conducive to understanding the electrical behaviors of InAlN/GaN heterostructures and providing readily applicable formulas for studying the electron transport and optical transitions.关键词
InAlN/GaN异质结/二维电子气/变分法/波函数Key words
InAlN/GaN heterostructure/two-dimensional electron gas/variational method/wave function引用本文复制引用
李群,陈谦,种景..InAlN/GaN异质结二维电子气波函数的变分法研究[J].物理学报,2018,67(2):242-248,7.基金项目
国家自然科学基金(批准号:11647053)和陕西省教育厅科学研究计划项目(批准号:17JK0552)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No. 11647053)and the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 17JK0552). （批准号:11647053）
