Monte Carlo transport simulation of phonons in diamond

Abstract

In this paper, we investigate the degradation of the thermal conductivity of diamond due to the presence of the isotope 13C. We employ a full-band Monte Carlo simulation in which phonons are modeled as semiclassical particles, and the full nonlinear phonon Boltzmann transport equation is solved. The thermal conductivity of diamond with 13C concentrations of 0.005% (isotopically ultrapure), 0.1% (isotopically enriched), and 1.07% (naturally occurring) is computed for a temperature range of 80–500 K, showing good agreement with experimental data. The degradation of thermal conductivity with increasing isotope concentration is observed across the entire temperature range and is significant at low temperatures. At 80 K, the thermal conductivity of the naturally occurring sample is about four times lower than that of the isotopically enriched sample and eleven times lower than that of the isotopically ultrapure one. We further investigate the isotope effect on individual phonon modes and compute their individual contribution to the thermal conductivity. We also calculate the expected value of the mean free path and relaxation time of all phonon modes' population. Acoustic phonons are the principal contributors to thermal conductivity across all isotope concentrations. The optical phonon modes present relaxation times and mean free paths that are affected by the isotope concentration but are fairly constant over the entire temperature range. The acoustic phonon mean free paths decrease with increasing isotope concentration and are temperature-dependent, ranging from 2 mm to 0.5 μm.