Heat dissipation and non-equilibrium phonon distributions in molecular devices

Using a density functional approach we compute vibrations of a styrene molecule adsorbed on a Si(100) substrate and the electron-phonon coupling of these modes. A non-equilibrium Green's function approach is used to compute the partially coherent transmission in molecular junctions due to electron-vibration scattering. The electronic power dissipated into molecular vibrations allows to set a rate equation for the phonon population in the vibrational degrees of freedom of the molecule. The rate of phonon decay is computed using a microscopic approach which includes a first-principle calculation of the coupling of the molecular modes with the vibrations of the contacts. In turn, the calculated phonon lifetime is used to correct the phonon propagator. A self consistent loop allows to compute the steady state non-equilibrium phonon population of the molecular junction under bias condition.