Weak effects of electron-phonon interactions on the lattice thermal conductivity of wurtzite GaN with high electron concentrations

Wurtzite gallium nitride (GaN) has great potential for high-frequency and high-power applications due to its excellent electrical and thermal transport properties. However, enhancing the performance of GaN-based power electronics relies on heavy doping. Previous studies showed that electron-phonon interactions have strong effects on the lattice thermal conductivity of GaN due to the Fröhlich interaction. Surprisingly, our investigation reveals weak effects of electron-phonon interactions on the lattice thermal conductivity of $\mathit{n}$-type GaN at ultrahigh electron concentrations and the impact of the Fröhlich interaction can be ignored. The small phonon-electron scattering rate is attributed to the limited scattering channels, quantified by the Fermi surface nesting function. In contrast, there is a significant reduction in the lattice thermal conductivity of $\mathit{p}$-type GaN at high hole concentrations due to the relatively larger Fermi surface nesting function. Meanwhile, as $\mathit{p}$-type GaN has relatively smaller electron-phonon matrix elements, the reduction in lattice thermal conductivity is still weaker than that observed in $\mathit{p}$-type silicon. Our work provides a deep understanding of thermal transport in doped GaN and the conclusions can be further extended to other wide-band-gap semiconductors, including $\beta -{\mathrm{Ga}}_2{\mathrm{O}}_3$, AlN, and ZnO.

Figure 1

(a) Band structures of GaN along the high-symmetry paths. The horizontal lines are Fermi energy related to the carrier concentrations of ${10}^{17}$ (green), ${10}^{18}$ (orange), ${10}^{19}$ (yellow), ${10}^{20}$ (light purple), and ${10}^{21}$ (light pink) ${\text{cm}}^{-3}$ at room temperature. The electron energy is normalized to the VBM. (b) ${\kappa }_{1\text{at},a}$ as a function of carrier concentration at room temperature for undoped, $\mathit{n}$-type, and $\mathit{p}$-type GaN. The scatters are experimental results, reported by Beechem et al. [17] and Simon et al. [18], respectively.

Figure 2

$1/{\tau }_{\lambda }^{\mathrm{ph}-\text{ph}}, 1/{\tau }_{\lambda }^{\mathrm{ph}-\text{iso}}$, (a) $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{el}}$, and (b) $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{hole}}$ at room temperature with carrier concentration of ${10}^{21}{\text{cm}}^{-3}$.

Figure 3

(a) Electron DOS near the valence- and conduction-band edges. The purple dotted curve represents the Fermi window. The electron energy is normalized to the VBM. The position of the Fermi energy for electron and hole concentrations of ${10}^{21}{\text{cm}}^{-3}$ is indicated with black dashed lines. Room-temperature phonon linewidth ${\mathrm{\Gamma }}_{\mathrm{pe}}$ of TA1, TA2, and LA along the high-symmetry path due to (b) phonon-electron and (c) phonon-hole scattering with carrier concentration of ${10}^{21}{\text{cm}}^{-3}$. The Fermi surface nesting function is inserted to the top left in (b) and (c).

Figure 4

(a) The ratio of $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{el}}$ to $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{ph}}$ with ${10}^{21}{\text{cm}}^{-3}$ electron concentration of GaN and Si, which is used to identify the dominant scattering term in phonon thermal transport. The horizon green line marks the equal importance of $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{el}}$ and $1/{\tau }_{\lambda }^{\mathrm{ph}-\text{ph}}$. (b) The DOS for GaN and Si. The positions of the Fermi energy for the electron and hole concentrations of ${10}^{21}{\text{cm}}^{-3}$ are indicated with black dashed lines for GaN and Si. The purple and red dotted curves represent Fermi windows. (c) Absolute value of electron-phonon matrix elements $\left|\mathit{g}\right|$ of GaN and Si.