Two-band finite difference method for the bandstructure calculation with nonparabolicity effects in quantum cascade lasers

We present a two-band finite difference method for the bandstructure calculation of quantum cascade lasers (QCLs) based on the equivalent two-band model of the nonparabolic Schrödinger equation. Particular backward and forward difference forms are employed in the discretization procedure instead of the common central difference form. In comparison with the linearization approach of the nonparabolic Schrödinger equation, the method is as accurate and reliable as the linearization approach, while the velocity of the method is faster and the matrix elements are more concise, therefore making the method more practical for QCLs simulations.