Cyclotron mass of electrons in GaN-Al xGa1-xN heterostructures

Abstract

The quasi-two-dimensional electron cyclotron mass in GaN-AlxGa1,xN heterostructures is theoretically calculated. The shifting in Landau Levels due to the electron Longitudinal Optical phonon interaction is calculated through the Second Order Improved Wigner Brillouin Perturbation Theory IWBPT. Experimental results recently obtained for GaN heterojunction are well described by the theory. W e h a ve also investigated the e ects of the electronic density on the Cyclotron Resonance frequency. I IntroductionCyclotron Resonance CR is a powerful experimental technique to investigate the e ective mass of quasitwo dimensional Q2D electron systems in semiconductor structures of reduced dimensionality. In the past, InSb inversion layer of the metal-oxide-semiconductor MOS and GaAs-AlGaAs heterostructures have been intensively studied by several authors 1 . In GaAsbased heterostructures the cyclotron resonance experiments have shown that the polaronic e ects are reduced in comparison with the results for the semiconductor bulk.More recently, the Cyclotron Resonance CR mass of quasi-two-dimensional electrons con ned in a GaN AlGaN heterojunction was experimentally investigated 2; 3 . Gallium Nitrite GaN and related III-V ternary alloys as Al x Ga 1,x N and Ga x In 1,x N are wide direct bandgap semiconductors, and the GaN is a moderately polar material with Fr ohlich coupling constant = 0 :49. Since the rst report by Dingle et al. 4 on GaN optical properties numerous investigations have been made, motivated by the potential technological applications of this material for construction of the optoelectronic devices. However, little is still known about the basic properties of these materials, and only in the recent y ears there appeared some theoretical and experimental investigations.In this paper we calculate the electron cyclotron mass in a GaN AlGaN heterojunction and in a GaN Quantum Well QW with in nite potential barrier for the electronic con nement. We take i n to account the electron-phonon-longitudinal optical LO interaction polaronic e ects through the Improved WignerBrillouin Perturbation Theory IWBPT. The IWBPT has been successfully applied to GaAs-AlGaAs heterostructures 5 , 7 . For the GaN heterojunction our theoretical results for CR frequency were compared with the experimental results presented in Ref. 2 . We also investigate the e ects of the electronic density o n the CR frequency. II TheoryThe Hamiltonian describing one electron con ned in the GaN side, in the heterojunction or QW, in the presence of a magnetic eld applied perpendicular to interface and interacting with the bulk LO phonons, can be written as in the e ective mass approximation,