The effective-mass Hamitonian for abrupt heterostructures

G.T. Einevoll; P.C. Hemmer, Institutt for Fysikk, Norges Teknisk Høgskole, Universitetet i Trondheim, 7034 Trondheim, Norway

Journal of Physics C: Solid State Physics 21, L1193-L1198 (1988)


Abstract

The effective-mass Hamiltonian H= 1/2 m^{\alpha} p m^{\beta} p m^{\alpha} +V_c + v for non-homogeneous semiconductors is studied. Here m is the position-dependent effective mass, 2 \alpha + \beta =-1. V_c is the position-dependent conduction band edge and v is a localised potential. Through an exact model calculation the authors show that when effective-mass theory is applicable, \alpha =0 and \beta =-1.