Bandstructure calculation using the k∙p method for arbitrary potentials with open boundary conditions

Abstract

We present a method to calculate the quantum-mechanical bandstructure of semiconductor heterostructures for open boundary conditions using k∙p theory. The method is efficient, numerically stable, and easy to implement. The open boundary conditions are derived from a perfectly matched layer (PML) formalism resulting in a complex coordinate stretching. Compared with previous methods like the transfer-matrix method and the quantum transmitting boundary method, the PML formalism reduces the computational costs several orders of magnitude without noticeable reduction of accuracy.

Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

“…It might also be valuable to extent the presented work to systems of Schrödinger equations that arise as so-called multiband effective mass approximations (MEMAs) to model electronic states in modern semiconductor nanostructures, cf. [41,42,43]. Let us finally remark that applications to generalized Schrödinger equations could also be developed by adapting the methods developed in [2,44].…”

Efficient calculation of lifetime based direct tunneling through stacked dielectrics

“…Recently, a method based on absorbing boundary conditions (called the Perfectly Matched Layer (PML) method) for SCHRÖDINGER'S equation has been applied for band structure calculations in III-V heterostructure devices [16]. In the present work the PML formalism, which is often used in electromagnetics, has been applied to determine the energy levels and the lifetime broadening of QBS in MOS inversion layers.…”

Efficient simulation of quantum cascade lasers using the Pauli master equation

“…To describe the openness of the quantum system we make use of the perfectly matched layer (PML) boundary conditions for the Schrödinger equation [11]. Perfectly matched layers were originally used as boundary conditions for electromagnetic and waveguide problems [12].…”