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A quantum transport approach based on the Non-equilibrium Green's Function formalism and the tight-binding method has been developed to investigate the performances of atomistically resolved nanoelectronic devices in the presence of electron-phonon scattering. The model is integrated into a quad-level parallel environment (bias, momentum, energy, and spatial domain decomposition) that scales almost perfectly up to 220k cores in the ballistic limit of electron transport. In this case, the momentum and energy points form a quasi-embarrassingly parallel problem. The novelty in this paper is the inclusion of scattering self-energies that couple all the momenta and several energies together, requiring substantial inter-processor communication. An efficient parallel implementation of electron-phonon scattering is therefore proposed and applied to a realistically extended transistor structure. A good scaling of the simulation walltime up to 95,256 cores and a sustained performance of 142 TFlop/s are reported on the Cray-XT5 Jaguar.