Heat dissipation and non-equilibrium phonon distributions in molecular devices

Abstract

Using a density functional approach we compute vibrations of molecules adsorbed on metal and semiconducting substrates and the electronphonon 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 [1], [2]. 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 equation includes the phonon emission rate and phonon decay due to absorption, electron-hole pair production and dissipation into the contacting leads, which are assumed to behave as reservoirs. 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. As the power dissipated in the molecular junction depends nontrivially on the phonon populations, the equilibrium distribution under bias condition is a complex issue. A self consitent loop allows to compute the steady state non-equilibrium phonon population of the molecular junction under bias condition. We find that the resulting average population is far from the equilibrium thermal distribution, frequently assumed in such calculations, which allows to obtain a mean temperature of the junction. As expected the deviations increase with applied bias. As molecular electronics is moving to semiconducting substrates, it is relevant to explore and understand thermal issues. Metallic substrates have in fact a very efficient channel of phonon damping into electron-hole pairs, while vibrational coupling to the substrate may not be very efficient due to ionic mass mismatch and a weaker bond. On the other hand the the electron-hole generation is prevented on semiconducting substrates, where instead vibrational coupling is stronger.We compare thermal behavior of organic molecules adsorbed on Si with molecules adsorbed on metallic substrates (Au or Cu) and determine the molecular temperature as a function of applied bias and for different temperatures of the termostats.