Comparative investigation between complex energy and transfer matrix techniques for quasi-energy states in heterostructure materials

Abstract

A comparative analysis is performed to study the resonant tunneling through symmetric multiple double-barrier resonant tunneling heterostructure materials composed of nanoscale semiconductors ZnSe/BeTe, AlAs/GaAs, InGaAs/AlInAs, and AlGaAs/GaAs. Two techniques are applied in the present investigation for calculating the quasi-resonant energy states and their associated lifetimes in nanoscale double-barrier quantum well heterostructures. The first technique is based on the complex energy solution of the time-dependent Schrödinger equation with the time–energy uncertainty condition. The second one is employing the transfer matrix method. The quasi-resonant energies, lifetimes, and frequencies in nanoscale double-barrier quantum well heterostructures are calculated by both methods and compared. The validity and accuracy of both techniques are tested and compared extensively with various current numerical methods. Excellent agreements are obtained between our results and the available experimental and theoretical values. It is also found that the complex energy technique is recommended when handling the quasi-energy states and quasi-lifetimes of novel nanoscale devices.