Finite-element analysis of the miniband structures of semiconductor superlattices with arbitrary periodic potential profiles

The method is based on the Galerkin procedure, and the third-order Hermitian line elements are used for finite elements. The periodic boundary condition is applied to the edges of one period of the periodic potential. A generalized boundary condition at the heterointerface is also introduced by use of the interface matrix. The validity of the method is confirmed by calculating the miniband structures and the envelope functions in rectangular superlattices made of GaAs-AlGaAs and GaSb-InAs. Numerical results for a biperiodic structure, a superlattice with graded interfaces, and a modulation-doped superlattice are presented