  Spectral, optical and transport properties of an anisotropic
three-dimensional Holstein model are studied within the adiabatic
approximation. The parameter regime is appropriate for organic semiconductors
used in single crystal based field effect transistors. Different approaches
have been used to solve the model: self-consistent Born approximation valid for
weak electron-phonon coupling, coherent potential approximation exact for
infinite dimensions, and numerical diagonalization for finite lattices. With
increasing temperature, the width of the spectral functions gets larger and
larger making the approximation of quasi-particle less accurate. On the
contrary, their peak positions are never strongly renormalized in comparison
with the bare ones. As expected, the density of states is characterized by an
exponential tail corresponding to localized states at low temperature. For weak
electron-lattice coupling, the optical conductivity follows a Drude behavior,
while, for intermediate electron-lattice coupling, a temperature dependent peak
is present at low frequency. For high temperatures and low particle densities,
the mobility always exhibits a power-law behavior as function of temperature.
With decreasing the particle density, at low temperature, the mobility shows a
transition from metallic to insulating behavior. Results are discussed in
connection with available experimental data.
