4.3 The SCHRÖDINGER Solver

For the calculation of the transmission coefficient of non-linear energy barriers, the stationary one-dimensional SCHRÖDINGER equation must be solved. To allow an easy extension to two- or three-dimensional problems, a multi-dimensional SCHRÖDINGER solver based on the finite-difference discretization has been developed. For the calculation of the transmission coefficient using the QTBM (see Section 3.5.4) it is necessary to solve SCHRÖDINGER's equation with open boundary conditions, while for the evaluation of tunneling from quasi-bound states as described in Section 3.6.3 it is necessary to solve the same problem with closed boundary conditions. Therefore, a solver which allows flexible treatment of both cases has been developed.

Subsections

• 4.3.1 Open and Closed Boundary conditions
• 4.3.2 System HAMILTONian
• 4.3.3 The Eigenvalue Solver

A. Gehring: Simulation of Tunneling in Semiconductor Devices