Phonon mean free path and thermal conductivity analysis of wide and ultra-wide bandgap materials

As the Knudsen number (defined as the as the ratio of the molecular mean free path length to length scale of the device) increases, materials' thermal properties are compromised due to disruption of phonon movement. If the thermal conductivity and mean free path relationship of the phonons is known, interference of size effects at small scales can be predicted as well as thermal conductivity reductions. To do this, thermal accumulation spectra of four wurtzite semiconductor materials: gallium nitride, aluminum nitride, aluminum gallium nitride, and beta form gallium oxide were calculated at different temperatures. As these materials are usually employed in high power electronic applications in confined structures, a method was devised in order to infer their conductivities at small scales from accumulation spectra. Third-order force constants, which are the expanded coefficients of crystal ground energy, are used directly for mentioned calculations.It was observed that this approach is very useful at high anharmonicity where MFP range is short and temperature is high. This work concluded that MFP spectra contributing to thermal conductivity were 1661.7 nm, 1648.8 nm, 442.3 nm and 467.3 nm respectively for GaN, AlN, AlGaN and beta-form Ga_2O_3 at 300 K. Hence, size effects are expected to dominate conductivity at scales smaller than these values.