Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires

Abstract

Lattice thermal conductivity (LTC) of Si bulk and nanowires (NWs) with diameter 22, 37, 50, 56, 98 and 115 nm was investigated in the temperature range 3–300 K using a modified Callaway model that contains both longitudinal and transverse modes. Using proper equations, mean bond length, lattice parameter, unit cell volume, mass density, melting temperature, longitudinal and transverse Debye temperature and group velocity for all transverse and longitudinal modes were calculated for each NW diameter mentioned. Surface roughness, Gruneisen parameter and impurity were used as adjustable parameters to fit theoretical results with experimental curves. In addition, values of electron concentration and dislocation density were determined. There are some phonon scattering mechanisms assumed, which are Umklapp and normal processes, imperfections, phonon confinement, NW boundaries, electrons scattering and dislocation. Dislocation density less than 10 $$^{{14}}$$ m $$^{{-2}}$$ for NWs and 10 $$^{{12}}$$ m $$^{{-2}}$$ for bulk has no effect on LTC. Also, electron concentration less than 10 $$^{{22}}$$ m $$^{{-3}}$$ for NWs and 10 $$^{{16}}$$ m $$^{{-3}}$$ for the bulk has no effect. On increasing dislocation density and electron concentration, LTC comparably decreases.