The role of the spatial dependence of the electron effective mass in forming the Wannier-Stark spectrum

We have shown that in the effective mass approach the spatial dependence of the effective mass significantly influences electron properties in the Wannier-Stark problem. That is, if the effective mass of an electron in the infinite periodic structure is uniform everywhere, then its inherent energy spectrum is continuous. But if the effective mass in the adjacent layers of the periodic structure is different, then the energy spectrum must be discrete and consist of so-called Wannier-Stark ladders. To calculate the Wannier-Stark spectrum and the corresponding wavefunctions, we proposed a formalism based on the transfer-matrix method. The formalism is used to investigate anticrossing of the levels of the different Wannier-Stark ladders.