Theoretical analysis of thermal conductivity of GaN containing defects using machine learning potential

<p>Gallium Nitride (GaN) is a wide-bandgap semiconductor used in electronic and optoelectronic devices. In these applications, heat management is important to achieve high performance and long lifetime, and thus deep understanding of thermal conduction behavior is required. Because the computational cost of ab initio calculations is often too high to obtain such understanding, especially in examining the effects of defects, machine learning potentials have been attracting attention in recent years, which are expected to achieve low computational cost and accuracy comparable to ab initio calculations simultaneously. In this study, we have constructed a machine learning potential for investigating the effects of defects on thermal conduction behavior in GaN, and examined its prediction accuracy.</p><p></p><p>As for the type of machine learning potential, we adopted the high-dimensional neural network potential (HDNNP) [1]. In fact, our group developed a modified scheme of HDNNP [2] that can take account of multiple charge states of defects. Note that the stable charge state of a defect can vary depending on the Fermi level of the system. The modified scheme was applied to bulk GaN crystals with N vacancies, and the results showed insufficient prediction accuracy for defect formation energies [2]. In this study, we have generated structural data for the training dataset in addition to those generated previously in our group [2] to improve the prediction accuracy: The former has been obtained from ab initio molecular dynamics (AIMD) calculations based on density functional theory (DFT) performed using the VASP package on structures containing +1 to +3 valence N vacancy defects at low temperatures, while the latter from molecular dynamics calculations using classical potentials on the Ga₁₆N₁₆, Ga₃₂N₃₂ and Ga₆₄N₆₄ models, and structures where several N atoms were removed from these models using the LAMMPS package. Phonon band structures and thermal conductivities were calculated for GaN structures containing N vacancy defects using the open-source program Phonopy/Phono3py, and compared with the DFT calculations.</p><p></p><p>Figure 1 shows the phonon bands of Ga₆₄N₆₃ with the charge state of 3+ calculated by HDNNP and DFT. The red curves in the figure denote phonon bands of the perfect crystal for comparison. The phonon bands calculated with the HDNNP agree those calculated by DFT well, including the band split near the Γ point and the appearance of flat bands at frequencies near 500 cm^-1. The root mean square error of force prediction for slightly displaced structures to calculate phonon bands was 192.9meV/Å for the previous HDNNP [2] and 109.5meV/Å for the HDNNP constructed in this study. Thus, we can say that the force and phonon prediction accuracies have been improved much. On the other hand, preliminary calculations show that the errors of thermal conductivities compared with the DFT results were larger for the present HDNNP than the previous one. In the presentation, we discuss the prediction accuracy comparison between the previous and present HDNNPs in more detail. This work was supported by the JST CREST Program “Novel electronic devices based on nanospaces near interfaces” and JSPS KAKENHI Grants Nos. 19H02544, 19K15397, 20K15013, 20H05285, 21H05552, 22H04607 and 23H04100.</p><p></p><p>References</p><p>[1] J. Behler et al., Phys. Rev. Lett. 98, 146401 (2007)</p><p>[2] K. Shimizu et al., Phys. Rev. B. 106, 054108 (2022)</p>