Abstract

Recent advances in crystal-growth techniques have allowed fabrication of quantum heterostructures and tailoring of their optical and electronic characteristics. Better understanding of the properties of these structures requires knowledge of their bound and quasi-bound electronic energy levels and their corresponding lifetimes. The purpose of this paper is to present a unified approach for the calculation of electronic states and lifetimes in quantum heterostructures with and without an applied electric field. The present approach is based on the argument principle method (APM) for calculating complex zeros of complex analytic functions. The single-mass time-independent Schrödinger equation is solved within the heterostructure by using the transfer matrix technique, and an eigenvalue equation of the form • (z) = 0 is derived. Then, by using integrations in the complex plane the number of zeros and their approximate values are determined. Finally, by using the Müller method, the exact complex eigenvalues (bound or quasi-bound states) are found. The lifetimes are evaluated from the imaginary part of the complex eigenenergies. Scattering can also be accounted for through application of imaginary potentials. The method can also be applied to virtual energy states. Several examples cases and comparisons with published results are presented.

© 1992 Optical Society of America