Operator ordering in effective-mass theory for heterostructures.
II. Strained systems
G.T. Einevoll,
Institutt for Fysikk, Norges Teknisk Høgskole,
Universitetet i Trondheim, 7034 Trondheim, Norway
Physical Review B 42, 3497-3502 (1990)
Abstract
For pt.I see ibid., vol.42, p.3485 (1990). A new kinetic-energy
operator -1/2 \hbar^{2} m^{\alpha} a^{\delta} \nabla m^{beta}
a^{-2 \delta} \nabla m^{\alpha} a^{\delta} suitable for
effective-mass treatment of strained heterostructures is introduced. Here,
m(r) is the local effective mass and a(r) is the local lattice constant.
By comparison of exact results with effective-mass results for solvable
test models, values of \alpha , \beta , and \delta , which ensure asymptotic
agreement, are determined. Based on qualitative similarities between the
test models considered and realistic systems, the boundary conditions
((1/a) \phi =continuous), ((a/m) \phi '=continuous) are proposed for abrupt
heterointerfaces for conduction-band states in strained systems. When a
single-band effective-mass equation is applicable to hole states, however,
the authors propose that the continuity of \phi and (1/m) \phi ' should be
imposed instead.