Electron transport in periodic quantum dot arrays in the presence ofinteractions with phonons was investigated using the formalism ofnonequilibrium Green's functions. The self-consistent Born approximation wasused to model the self-energies. Its validity was checked by comparison withthe results obtained by direct diagonalization of the Hamiltonian ofinteracting electrons and longitudinal optical phonons. The nature of chargetransport at electron -- phonon resonances was investigated in detail andcontributions from scattering and coherent tunnelling to the current wereidentified. It was found that at larger values of the structure period the mainpeak in the current -- field characteristics exhibits a doublet structure whichwas shown to be a transport signature of polaron effects. At smaller values ofthe period, electron -- phonon resonances cause multiple peaks in thecharacteristics. A phenomenological model for treatment of nonuniformities of arealistic quantum dot ensemble was also introduced to estimate the influence ofnonuniformities on current -- field characteristics.
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