Self-consistent solution of schrodinger and poisson equations by means of numerical methods in the LabVIEW development environment

摘要

For the further development of semiconductor heterostructures and devices based on it we have to know precisely the basic parameters such as energy band discontinuities, free carriers distribution, the magnitude of the accumulated charge, etc. Physical description of systems with reduced dimensionality gives the system of Schrodinger and Poisson equations that are too complicated for solving analytically and is usually solved by numerical methods. In this regard, in the paper questions of numerical calculation and energy band offsets determination on the example of quantum well by solving self-consistently Schrodinger and Poisson are considered. The determination of the Schrodinger equation is implemented by the “shooting” algorithm, and the determination of the Poisson equation using Thomas algorithm, in connection with the speed of operation and optimum accuracy of the solution.