  Both the semi-classical and quantum transport properties of F-doped SnO$_2$
thick films ($\sim$1\,$\mu$m) were investigated experimentally. It is found
that the resistivity caused by the thermal phonons obeys Bloch-Gr\"{u}neisen
law from $\sim$90 to 300\,K, while only the diffusive thermopower, which varies
linearly with temperature from 300 down to 10\,K, can be observed.The
phonon-drag thermopower is completely suppressed due to the long
electron-phonon relaxation time in the compound. These observations, together
with the temperature independent characteristic of carrier concentration,
indicate that the conduction electron in F-doped SnO$_2$ films behaves
essentially like a free electron. At low temperatures, the electron-electron
scattering dominates over the electron-phonon scattering and governs the
inelastic scattering process. The theoretical predicated scattering rates for
both large- and small-energy-transfer electron-electron scattering processes,
which are negligibly weak in three-dimensional disordered conventional
conductors, are quantitatively tested in this lower carrier concentration and
free-electron-like highly degenerate semiconductor.
