Coupled quantum – scattering modeling of thermoelectric performance of nanostructured materials using the non-equilibrium Green’s function method

Abstract

Semi-classical transport models based on Boltzmann and Fermi-Dirac statistics have been very effective in identifying the pertinent physical parameters responsible for thermoelectric performance in bulk materials. Reliance on Boltzmann-based models has produced a culture of “smaller is better” research, where the reduction in size is expected to produce limitless increase in performance. Experimental observations especially in the case of thermoelectric performance of nanoscale devices have not exhibited this behavior. The semi-classical Boltzmann models are based on the relaxation-time approximation and cannot model strong non-equilibrium transport. In addition, wave effects in these models are included through correction terms that cannot suitably capture their influence on transport.

A coupled quantum-scattering model to study thermoelectric performance of nanoscale structures is proposed through the nonequilibrium Green’s function method. The model includes all the pertinent physics of the wave nature of electrons while coupling electron-phonon scattering effects. The NEGF method is used to study the performance of silicon nano-films and nanowires as well as strained quantum well Si/Ge/Si superlattices as a function of doping, effective mass and in the case of superlattices, substrate strain and superlattice geometry. Results suggest that the power factor of nanostructured materials is dominated by the electrical conductivity which in turn is strongly influenced by quantum confinement effects and electron-phonon scattering effects. No significant improvement in the Seebeck coefficient is observed due to the decrease in dimensionality of the structure.

The NEGF method can be used as a tool to design structures with optimized values of doping, effective mass, substrate strain and superlattice geometry taking into consideration the effects of electron confinement and scattering. The model developed in this research can be used as a framework to guide further studies on performance of highly scaled thermoelectric devices in order to obtain optimal value of ZT. This effort represents the first reported use of the nonequilibrium Green’s function method to predict thermoelectric performance.