  Electron transport in periodic quantum dot arrays in the presence of
interactions with phonons was investigated using the formalism of
nonequilibrium Green's functions. The self-consistent Born approximation was
used to model the self-energies. Its validity was checked by comparison with
the results obtained by direct diagonalization of the Hamiltonian of
interacting electrons and longitudinal optical phonons. The nature of charge
transport at electron -- phonon resonances was investigated in detail and
contributions from scattering and coherent tunnelling to the current were
identified. It was found that at larger values of the structure period the main
peak in the current -- field characteristics exhibits a doublet structure which
was shown to be a transport signature of polaron effects. At smaller values of
the period, electron -- phonon resonances cause multiple peaks in the
characteristics. A phenomenological model for treatment of nonuniformities of a
realistic quantum dot ensemble was also introduced to estimate the influence of
nonuniformities on current -- field characteristics.
