  We have presented a consistent electronic transport framework for the
two-dimensional extended Holstein's organic molecular-crystal based upon
complete quantum-mechanical treatment through the non-equilibrium Green's
function (NEGF) formalism and corresponding one-to-one semi-classical framework
based upon Boltzmann transport theory for the narrow-bandwidth electronic
energy organic semiconductor crystal material and device. In this process, we
have formulated electronic self-energy interaction with acoustic and polar
optical phonon mode with one phonon and two phonon interactions through
Feynman's diagrammatic techniques to investigate combined electronic transport.
Furthermore, the aforementioned can readily expand for the three and four
phonon interactions on choice based upon the particular class of organic
semiconductor crystal and organic polymers for the modern organic device
industry.
