BANDSTRUCTURE MATCHING AT A HETEROJUNCTION INTERFACE

An analytic theory for the matching of the bandstructure of different crystals at the interface of a heterojunction is presented. The generalized Wannier functions serve as a basis. For a simple uniform band, the Hamiltonian matrix elements then reduce to the k-space Fourier coefficients of the bandstructure along the superlattice direction. The technique therefore accounts for non-effective mass effects and the lower and upper valleys and invokes both the quasi-k-space periodicity together with the spatial variations of the bandstructure. The superlattice Hamiltonian is a system of difference equations taking the form of a band matrix. A new definition of current not based on the effective-mass is introduced for this higher-order Schroedinger equation. The enforcement of the continuity of the elemental currents leads to analytic connection rules for the overlap Hamiltonian matrix elements. A maximum transparency for all energies is achieved only for geometrically related bandstructures. Non-effective-mass effects are demonstrated in resonant-tunneling structures.