  A consistent methodology is presented to extract carrier concentrations in
n-type Ge from measurements of the infrared dielectric function and the Hall
effect. In the case of the optical measurements, usually carried out using
spectroscopic ellipsometry, the carrier concentration is affected by the doping
dependence of the conductivity effective mass, which is computed using a model
of the electronic density of states that accounts for non-parabolicity and is
fit to electronic structure calculations. Carrier concentrations obtained from
Hall measurements require a knowledge of the Hall factor, which is arbitrarily
set equal to unit in most practical applications. We have calculated the Hall
factor for n-Ge using a model that accounts for scattering with phonons and
with ionized impurities. We show that determinations of the carrier
concentration n using our computed effective mass and Hall factor virtually
eliminates any systematic discrepancy between the two types of measurement. We
then use these results to compute majority carrier mobilities from measured
resistivity values, to compare with measurements of minority carrier
mobilities, and to fit empirical expressions to the doping dependence of the
mobilities that can be used to model Ge devices.
