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

Abstract

The quasibound state model (QBSM) for determining the self-consistent conduction band profile and space charge density of semiconductor intersubband devices is presented. This new method is based on the quasibound (QB) state resonances of quantum structures. For heterostructures, the traditional self-consistent energy continuum model (ECM) calculates space charge by integration over the entire energy continuum, weighted by Fermi–Dirac statistics. In the present approach, the continuum of energy states of the heterostructure is accurately represented by a small number of QB states, and the space charge calculations are performed only at these eigen-energies. This approach significantly reduces the computational burden associated with all self-consistent algorithms. Theoretical formulation of QBSM is compared with the traditional ECM approach. The bound (B) and QB eigenenergies of the structure are obtained by solving the single-band effective-mass Schrödinger equation using the argument principle method. The performance and the accuracy of the QBSM are evaluated for a double-barrier resonant structure and an asymmetric Fabry–Perot electron-wave interference filter. The self-consistent electron density and potential profiles calculated by the present method are shown to be in excellent agreement with the results obtained from the traditional ECM model. In addition to requiring less computational time, the present method is easily implemented and may be applied equally well to biased/unbiased, symmetric/asymmetric heterostructures.