A self-consistent model of Γ-X mixing in GaAs/AlAs/GaAs quantum well structures using the quantum transmitting boundary method

Abstract

We present a numerical study of the I-X mixing in GaAs/AlAs/GaAs quantum well structures. A P-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 Schrodinger equations for I' 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 Schriidinger equations, which proves to be very stable and efficient, even for large (> 2000 A) structures. The features of I-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 1-V characteristics for structures exhibiting I-X coupling.

Resonant tunneling diodes: models and properties

“…The physical conditions at the boundaries and interfaces can then be enforced during the entire solution process. For a specific example of how it is implemented, see [56]. The injected distribution function approach is a traveling wave condition in that the boundaries emit a quasicontinuum of eigenstate electrons with their wave vectors distributed according to the thermal equilibrium distribution.…”

The quasibound state model for self-consistent characteristics of semiconductor intersubband devices

“…Snider et al [18] carried out SC simulations of electronic states in quantum wires. A SC model of -X valley electron scattering in GaAs quantum well structures was proposed by Sun et al [19]. Research has also been done in analyzing the self-consistent hole potentials of p-type Si superlattices [20].…”

Hydrostatic pressure effects on the Γ–X conduction band mixing and the binding energy of a donor impurity in GaAs–Ga1–xAlxAs quantum wells

“…There have been several antecedents of the study of the Γ-X mixing phenomenon in GaAs-based systems [1][2][3][4][5][6][7]. In addition, a significant number of works that investigate the effects of the hydrostatic pressure on the optical and electronic properties in this kind of structures have also been put forward [8][9][10][11].…”

“…Several works in the EMA have been reported taking into account the elastic Γ-X intervalley transfer by introducing an additional δ -function scattering potential at each well/barrier heterointerface of GaAs/AlAs/GaAs low dimensional heterostructures [2,3,7].…”