Al composition dependency of interface phonon in the wurtzite quantum cascade laser

Abstract

The interface (IF) phonons of the wurtzite quantum cascade lasers (QCL) are investigated using the transfer-matrix method (TMM). The IF modes are presented in the longitudinal optical-phonon frequency for the Al 0.2 Ga 0.8 N/GaN and Al 0.15 Ga 0.85 N/ GaN QCLs, and two IF modes can be changed into other modes if their wave numbers are less than the special values. Owing to the more dispersive properties of IF phonons with the increasing Al composition, the scattering rates in both QCLs increase with the Al composition.The quantum cascade laser (QCL) is an important semiconductor laser source in basic reseach and potential applications [1][2][3] . Its structure is composed of many periods, in which a special type of semiconductor heterostructrue is grown with some alternating layers of different materials and various thicknesses. Sun [4] and Huang [5] proposed to use a GaN-based system with large longitudinal-optical (LO)-phonon energy (~90 meV) for THz QCLs to achieve the high temperature operation. The GaN-based material usually crystallizes in the hexagonal wurtzite structure [6,7] . Every primitive cell in wurtzite contains four atoms, and nine optical and three acoustical branches are presented. Only two optical phonons are both Raman and infrared active, which correspond to the A 1 and E 1 modes [8] . The two modes both split into LO and transverse-optical (TO) components.Up to now, several theoretical investigations based on the dielectric continuum (DC) model and London's uniaxial model have been presented to the polar optical phonons in wurtzite GaN-based heterojunctions, for example, SQW, MQW, and superlattices (SL) [9][10][11][12][13][14][15] . Among them, Chen [11,15] utilized the macroscopic dielectric continuum (MDC) approach, and Lu [12,13] utilized the transfer-matrix method (TMM) to study the interface and confined phonons of GaN/ ZnO QW. TMM was also adopted by Gleize [9] to describe the interface and confined phonons of GaN QW and GaN/ AlN SL. In this paper, TMM is used to investigate the interface phonon spectra of the AlGaN/GaN QCL proposed by Sun [4] and Huang [5] . The active region of QCL is composed of many heterojun-ctions with arbitrary layer widths and numbers, which is suitable for TMM to treat with. The interface phonon spectra in Sun's and Huang's QCL are achieved by TMM, and the scattering rates in both QCLs induced by the IF phonon are also investigated.The wurtzite Al 0.15 Ga 0.85 N/GaN QCLs [4] proposed by Huang and Sun are considered here, and the width of each layer in one period is 3.0, 4.0, 3.0, 2.5, 2.0 and 2.5 nm, respectively, where the boldface numbers stand for the widths of wells. The width of each layer in both QCLs is the same, but Al composition of the barrier in Huang's QCL is 0.20, while that in Sun's QCL is 0.15. The electron energy levels and wavefunctions of the subband in one period are shown in Fig.1, which can be obtained by solving the effective mass Schrodinger and Poisson's equations self-consistently.The phonon mode in each layer can be regarded as the li...

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