Thermal conductivity of GaN, ${}^{71}\mathrm{GaN}$, and SiC from 150 K to 850 K

The thermal conductivity (Λ) 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 Λ 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 μm grown on $c$-, $m$-, and $a$-plane GaN substrates grown by HVPE; and bulk crystals of 4H and 6H SiC. In low dislocation density ($<{10}^7\mathrm{c}{\mathrm{m}}^{-2}$) bulk and homoepitaxial GaN, Λ is insensitive to crystal orientation and doping concentration (for doping $<{10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$); $\mathrm{\Lambda }\approx 200\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 300 K and $\approx 50\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 850 K. In ${}^{71}\mathrm{GaN}$ epilayers at 300 K, Λ is $\approx 15\%$ higher than in GaN with natural isotope abundance. The measured temperature dependence of Λ 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 Λ of 4H and 6H SiC is anisotropic, in good agreement with first-principles calculations, and larger than GaN by a factor of $\approx 1.5$ in the temperature range $300<T<850\mathrm{K}$. 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.

Figure 1

(a) Thermal conductivity of bulk GaN from literature, from experiments [24, 25, 26, 27, 29, 35, 36, 37], and from first-principles calculations [39], in comparison with representative results of this paper for $c$-plane bulk GaN (AM1) (blue solid triangles). The calculated ${\mathrm{\Lambda }}_{\mathrm{in}}$ and ${\mathrm{\Lambda }}_{\mathrm{out}}$ overlap with each other. (b) In-plane and (c) out-of-plane thermal conductivity of bulk 4H and 6H SiC from previous experimental [49, 50, 51, 52, 53, 54, 55] and theoretical [56] studies. Data from this paper are shown for comparison (blue solid triangles and squares).

Figure 2

XRD rocking curves of (a) $c$-plane [(002) peak] and (b) $m$-plane [(100) peak] bulk GaN grown by HVPE (black lines) and ammonothermal method (blue lines). The curves are shifted along the $\omega$ axis for better visibility. (c) XRD rocking curve of 4H and 6H SiC (006) peaks. (d) Representative cathodoluminescence of the ${}^{71}\mathrm{GaN}$ epilayer of KMiF2 with dark spots corresponding to the locations of threading dislocations.

Figure 3

Raman spectra of bulk $c$-plane (a), (b), and $m$-plane (c), (d) GaN in the low- and high-frequency range. The acoustic and optical combination modes for GaN are labeled by black triangles. The representative peak fittings of the LPP+ modes are shown in (b) and (d). The first-principles calculated phonon density of states (DOS) with frequency expanded by a factor of 2 is included in (c) for comparison.

Figure 4

Raman spectra of the (a) 4H and (b) 6H SiC. The corresponding first-principles calculated phonon density of states with frequency expanded by a factor of 2 is included for comparison.

Figure 5

(a) Thermal conductivity of bulk GaN from 150 to 850 K measured with TDTR using $1/e^2$ laser spot size $w_0\approx 10.2\mu \mathrm{m}$. The first-principles BTE calculation of ${\mathrm{\Lambda }}_{\mathrm{in}}$ and ${\mathrm{\Lambda }}_{\mathrm{out}}$ including three-phonon and phonon-isotope scattering of GaN (mass-disorder parameters $g_{\mathrm{Ga}}=2.0\times {10}^{-4}$, solid lines) is presented for comparison. (b) Same thermal conductivity data as in (a), multiplied by temperature and divided by 300 K to highlight the deviations from a $1/T$ temperature dependence. The solid lines have the same meanings as in (a). In both (a) and (b), the TDTR results obtained with Al transducers are plotted as open symbols; TDTR results obtained with Pt transducers are plotted as solid symbols. Representative error bars are shown in (a).

Figure 6

(a), (b) Thermal conductivity of homoepitaxial GaN and ${}^{71}\mathrm{GaN}$ from 150 to 850 K measured with TDTR using $1/e^2$ laser spot size $w_0\approx 10.2\mu \mathrm{m}$. The first-principles BTE calculation results of ${\mathrm{\Lambda }}_{\mathrm{in}}$ and ${\mathrm{\Lambda }}_{\mathrm{out}}$ including only three-phonon scattering ($g_{\mathrm{Ga}}=0$) [dashed lines in (b)] and three-phonon scattering combined with a total $g_{\mathrm{Ga}}=2.0\times {10}^{-4}$ [solid lines in (b)]. Data for the bulk sample AM1 are included for comparison. (c), (d) Same data as in (a) and (b), respectively, multiplied by temperature and divided by 300 K [solid and dashed lines have the same meanings as in (a) and (b)]. In all panels, the TDTR results obtained with Al transducers are plotted as open symbols while results obtained with Pt transducers are plotted as solid symbols. Representative error bars are shown in (a) and (b).

Figure 7

(a), (b) Thermal conductivity of 4H and 6H SiC along in- and out-of-plane directions from 300 to 850 K measured with TDTR using $1/e^2$ laser spot size $w_0\approx 10.2\mu \mathrm{m}$. The first-principles BTE calculations from [56] are shown for comparison. (c), (d) The same data as plotted in (a) and (b), respectively, multiplied by temperature and divided by 300 K. Solid and dashed lines have the same meaning as in (a) and (b). Representative error bars are shown in (a) and (b).