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

We present a detailed Monte Carlo simulation of electron transport incorporating both Gamma- and X-valley states in GaAs-based quantum cascade lasers (QCLs). Gamma states are calculated using the K center dot 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 J(X). The magnitude of J(X) depends on the temperature and occupation of the X subbands, which are populated primarily by the same-stage scattering from the Gamma-continuum (Gamma(c)) states. At 77 K, J(X) is small up to very high fields in both QCLs. However, at room temperature the 33% QCL shows a much higher J(X) than the 45% QCL even at low fields. The reason is that in the 33% QCL the coupling between the Gamma-localized (Gamma(l)) states and the next-stage Gamma(c) states is strong, which facilitates subsequent filling of the X states through efficient intrastage Gamma(c)-> X scattering; with high X-valley population and high temperature, efficient interstage X -> X scattering yields a large J(X). In contrast, good localization of the Gamma(l) 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. (c) 2007 American Institute of Physics.