A self‐consistent model of Γ‐Xmixing in GaAs/AlAs/GaAs quantum well structures using the quantum transmitting boundary method

摘要

We present a numerical study of the Γ‐X mixing in GaAs/AlAs/GaAs quantum well structures. A Γ‐X mixing model proposed by Liu [Appl. Phys. Lett. 51, 1019 (1987)] is extended to include the effects of self‐consistency and nonzero transverse momentum. In the present model, the coupled Schrödinger equations for Γ and X electron envelope wave functions are solved self‐consistently with Poisson’s equation to calculate the electron transmission probability and wave functions, which lead to the current‐voltage (I‐V) characteristics of single barrier and double barrier resonant tunneling diode structures. The quantum transmitting boundary method is employed in the model for numerical solution of the coupled Schrödinger equations, which proves to be very stable and efficient, even for large (≳2000 Å) structures. The features of Γ‐X mixing, such as the resonance/antiresonance in the transmission probability and the virtual bound states, are clearly demonstrated. Additional physical features are observed in the transmission probability and the wave functions under applied bias conditions. Our work shows that inclusion of transverse momentum, variable effective mass, and the self‐consistent potential is important in the realistic modeling of I‐V characteristics for structures exhibiting Γ‐X coupling.