Thermal conductivity in higher-order generalized hydrodynamics: Characterization of nanowires of silicon and gallium nitride

• It is specified a cylindrical geometry in samples of Si and GaN in the macro to nano-scales.
• The study of the thermal conductivity and its influence on the figure-of-merit in thermoelectric devices.
• The thermal conductivity is strongly dependent on the cylinder radius.

An analysis of the influence of geometry and size on the thermal conductivity in semiconductors, particularized to the study in Si and GaN, is presented. This is done in the framework of a higher-order generalized hydrodynamics (HOGH) of phonons in semiconductors, driven away from equilibrium by external sources. This HOGH is derived by the method of moments from a generalized Peierls–Boltzmann kinetic equation built in the framework of a Non-Equilibrium Statistical Ensemble Formalism. We consider the case of wires (cylindrical geometry) exploring the effect of size (radius), particularly in the nanometric scale when comparison with experiment is done. Maxwell times, which are quite relevant to define the hydrodynamic movement, are evidenced and characterized.

The thermal conductivity is strongly dependent on the ratio of the cylinder radius R to a characteristic length ℓ, the latter given approximately by the velocity of sound times a kind of relaxation time (energy Maxwell time) which has values in the order of hundreds of nanometers.Figure optionsDownload as PowerPoint slide