The semiclassical Boltzmann equation for electrons in semiconductors with t
he Kane dispersion law or the parabolic band approximation is considered an
d systems of moment equations with an arbitrary number of moments are deriv
ed. First, the paper deals with spherical harmonics in the formalism of sym
metric trace-free tensors. The collision frequencies are carefully studied
for the physical properties of silicon. Then, for the parabolic band approx
imation, the hierarchy of equations for full moments of the phase density a
nd the corresponding closure problem is discussed. In particular, a set of
2R scalar and vectorial moments is considered. To answer the question which
number R one has to chose in order to retain the physical contents of the
Boltzmann equation, the moment equations are examined in the drift-diffusio
n limit and in an infinite crystal in a homogeneous electric field (transie
nt and stationary cases) for increasing number of moments R. The number R m
ust be considered to be sufficient, if its further increase does not change
the result considerably and the appropriate numbers for the processes are
given. (C) 2000 Elsevier Science B.V. All rights reserved.