Phonon transport unveils the prevalent point defects in GaN

Determining the types and concentrations of vacancies present in intentionally doped GaN is a notoriously difficult and long-debated problem. Here, we use an unconventional approach, based on thermal transport modeling, to determine the prevalence of vacancies in previous measurements. This allows us to provide conclusive evidence of the recent hypothesis that gallium vacancies in ammonothermally grown samples can be complexed with hydrogen. Our calculations for O-doped and Mg-O codoped samples yield a consistent picture interlinking dopant and vacancy concentration, carrier density, and thermal conductivity, in excellent agreement with experimental measurements. These results also highlight the predictive power of ab initio phonon transport modeling, and its value for understanding and quantifying defects in semiconductors.

Figure 1

Lattice thermal conductivity of GaN with ${\mathrm{O}}_{\mathrm{N}}$, ${\mathrm{Mg}}_{\mathrm{Ga}}\text{−}{\mathrm{O}}_{\mathrm{N}}$ defects. O-doped samples also contain gallium vacancies ($V_{\mathrm{Ga}}$), which are included in our calculations. The vacancy concentrations of the respective samples are obtained from the positron annihilation experiments in Ref. [19]. The calculated thermal conductivity results with different concentrations of defects are in good agreement with corresponding measurements from Ref. [27]. The inset shows the local structure of GaN with ${\mathrm{Mg}}_{\mathrm{Ga}}\text{−}{\mathrm{O}}_{\mathrm{N}}$, ${\mathrm{O}}_{\mathrm{N}}$, and $V_{\mathrm{Ga}}$ defects. Defective GaN structures are also included in the SM [39].

Figure 2

Phonon dispersion and density of states for wurtzite GaN. The calculated results are in excellent agreement with the inelastic x-ray scattering results from Ref. [40].

Figure 3

Phonon scattering rates (${\tau }^{-1}$) from different charged defects in GaN plotted with respect to phonon frequencies ($\omega$). The defect concentration of ${10}^{20}{\mathrm{cm}}^{-3}$ is considered here and the corresponding scattering rates are compared to anharmonic scattering at 300 K and isotope scattering. The corresponding defective GaN structures are also included in the SM [39].

Figure 4

GaN thermal conductivity calculated with gallium vacancies and oxygen defects only conserving the free carrier concentrations in the experimental samples. The hydrogen defects are ignored in this test. The predicted $\kappa$ (lines) are much higher than the experiments (circles) [27].