Thermal conductivity of GaN, GaN71 , and SiC from 150 K to 850 K

The thermal conductivity (\ensuremath{\Lambda}) of wide-band-gap semiconductors GaN and SiC is critical for their application in power devices and optoelectronics. Here, we report time-domain thermoreflectance measurements of \ensuremath{\Lambda} in GaN, $⁷¹\mathrm{GaN}$, and SiC between 150 and 850 K. The samples include bulk $c$- and $m$-plane wurtzite GaN grown by hydride vapor phase epitaxy (HVPE) and ammonothermal methods; homoepitaxial natural isotope abundant GaN and isotopically enriched $⁷¹\mathrm{GaN}$ layers with thickness of 6--12 \ensuremath{\mu}m grown on $c$-, $m$-, and $a$-plane GaN substrates grown by HVPE; and bulk crystals of 4H and 6H SiC. In low dislocation density ($<{10}⁷\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$) bulk and homoepitaxial GaN, \ensuremath{\Lambda} is insensitive to crystal orientation and doping concentration (for doping $<{10}¹⁹\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$); $\mathrm{\ensuremath{\Lambda}}\ensuremath{\approx}200\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 300 K and $\ensuremath{\approx}50\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 850 K. In $⁷¹\mathrm{GaN}$ epilayers at 300 K, \ensuremath{\Lambda} is $\ensuremath{\approx}15%$ higher than in GaN with natural isotope abundance. The measured temperature dependence of \ensuremath{\Lambda} in GaN is stronger than predicted by first-principles based solutions of the Boltzmann transport equation that include anharmonicity up to third order. This discrepancy between theory and experiment suggests possible significant contributions to the thermal resistivity from higher-order phonon scattering that involve interactions between more than three phonons. The measured \ensuremath{\Lambda} of 4H and 6H SiC is anisotropic, in good agreement with first-principles calculations, and larger than GaN by a factor of $\ensuremath{\approx}1.5$ in the temperature range $300<T<850\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This paper provides benchmark knowledge about the thermal conductivity in wide-band-gap semiconductors of GaN, $⁷¹\mathrm{GaN}$, and SiC over a wide temperature range for their applications in power electronics and optoelectronics.