We explore phonon decay processes necessary to the design of efficient rough semiconductor nanowire (NW) thermoelectric devices. A novel approach to surface roughness-limited thermal conductivity of Si, Ge, and GaAs NW with diameter D < 500 nm is presented. In particular, a frequency-dependent phonon scattering rate is computed from perturbation theory and related to a description of the surface through the root-mean-square roughness height Δ and autocovariance length L. Using a full phonon dispersion relation, the thermal conductivity varies quadratically with diameter and roughness as (D/Δ)2. Computed results are in agreement with experimental data, and predict remarkably low thermal conductivity below 1 W/m/K in rough-etched 56 nm Ge and GaAs NW at room temperature.
We study phonons produced by transitions between the equivalent X valleys in silicon. We use the Monte Carlo method first to select stochastically the time between phonon collisions, and then to select a final-state pair of phonons from the probability distribution for anharmonic decay. Our results show that intervalley phonons decay into one near-equilibrium transverse acoustic phonon and another intermediate longitudinal phonon either on the acoustic or optical branch. This second phonon has energies between 40 and 50 meV and undergoes another decay before turning into a pair of near-equilibrium transverse acoustic phonons, presenting an additional potential bottleneck.
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