A three-valley model of a GaAs/AlAs heterostructure has been developed
by a pseudopotential method. The construction is based on results of
a multiband calculation of the joining matrices J(ij) (i and j specify
the valleys) at a GaAs/AlAs (001) heterojunction and the transmission
coefficients of a two-barrier GaAs/AlAs(4a)/GaAs(8a)/AlAs(4a)/GaAs st
ructure, where a is the lattice constant. This model correctly describ
es electronic processes near the heterojunction. In this model, the mo
st important elements, corresponding to the interaction of states whic
h derive from the Gamma(1), X(1), and X(3) valleys of the lower conduc
tion band, are incorporated in the matrix J(ij). The electron wave fun
ctions in the GaAs and AlAs layers are approximated in a limited basis
of states corresponding to extrema of the conduction and valence band
s. Parametric expressions are derived for the matrix elements J(ij) Th
ese expressions retain all features of the energy dependence of these
elements contained in the exact expressions.