X -valley leakage in GaAs-based midinfrared quantum cascade lasers: A Monte Carlo study

Abstract

We present a detailed Monte Carlo simulation of electron transport incorporating both Γ- and X-valley states in GaAs-based quantum cascade lasers (QCLs). Γ states are calculated using the K⋅p method, while X states are obtained within the effective mass framework. All the relevant electron-phonon, electron-electron, and intervalley scattering mechanisms are included. We investigate the X-valley leakage in two equivalent-design GaAs/AlGaAs QCLs with 33% and 45% Al-barrier compositions. We find that the dominant X-valley leakage path in both laser structures is through interstage X→X intervalley scattering, leading to a parallel leakage current JX. The magnitude of JX depends on the temperature and occupation of the X subbands, which are populated primarily by the same-stage scattering from the Γ-continuum (Γc) states. At 77 K, JX is small up to very high fields in both QCLs. However, at room temperature the 33% QCL shows a much higher JX than the 45% QCL even at low fields. The reason is that in the 33% QCL the coupling between the Γ-localized (Γl) states and the next-stage Γc states is strong, which facilitates subsequent filling of the X states through efficient intrastage Γc→X scattering; with high X-valley population and high temperature, efficient interstage X→X scattering yields a large JX. In contrast, good localization of the Γl states in the 45% QCL ultimately leads to low X-valley leakage current up to high fields. Very good agreement with experiment is obtained at both cryogenic and room temperatures.