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.