  A recently developed model that unifies the ballistic and diffusive transport
mechanisms is applied in a theoretical study of carrier transport across
potential barriers at grain boundaries in microcrystalline semiconducting
materials. In the unified model, the conductance depends on the detailed
structure of the band edge profile and in a nonlinear way on the carrier mean
free path. Equilibrium band edge profiles are calculated within the trapping
model for samples made up of a linear chain of identical grains. Quantum
corrections allowing for tunneling are included in the calculation of electron
mobilities. The dependence of the mobilities on carrier mean free path, grain
length, number of grains, and temperature is examined, and appreciable
departures from the results of the thermionic-field-emission model are found.
Specifically, the unified model is applied in an analysis of Hall mobility data
for n-type microcrystalline Si thin films in the range of thermally activated
transport. Owing mainly to the effect of tunneling, potential barrier heights
derived from the data are substantially larger than the activation energies of
the Hall mobilities. The specific features of the unified model, however,
cannot be resolved within the rather large uncertainties of the analysis.
