Hamiltonian and Boundary Conditions for Electrons in Semiconductor Heterostructures

In using the equivalent Hamiltonian approach for the simulation of semiconductor heterostructures two aspects are discussed controversially in the present literature: firstly the form of the equivalent Hamiltonian and secondly the appropriate boundary conditions. In this paper both aspects are investigated in the framework of the envelope‐function formalism especially for non‐parabolic band structures. Appropriate forms of the equivalent Hamiltonian and the boundary conditions are suggested and compared. The expected deviations are presented using theoretical calculations for type I and type II heterostructures. In accordance to theoretical evidence, the differences may be important in the case of type II heterostructures. From a theoretical point of view the use of the energy mass should be preferred. But for final evidence further experimental investigations and comparison with calculations based on different models are necessary.