Impact of anharmonic effects on the phase stability, thermal transport, and electronic properties of AlN

Wurtzite aluminium nitride (AlN) is a technologically important wide-band-gap semiconductor with an unusually high thermal conductivity, used in optical applications and as a heatsink substrate. Explaining many of its properties depends on an accurate description of its lattice dynamics, which have thus far only been captured in the quasiharmonic approximation. In this work, we show that anharmonic effects have a considerable impact on its phase stability and transport properties, since they are much stronger in the rocksalt phase. We construct a theoretical pressure-temperature phase diagram of AlN, demonstrating that the rocksalt phase is stabilized by increasing temperature, with respect to the wurtzite phase. We recover the thermal conductivity of the wurtzite phase ($320{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ under ambient conditions) and compute the hitherto unknown thermal conductivity of the rocksalt phase ($81{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$). We also show that the electronic band gap decreases with temperature. These findings provide further evidence that anharmonic effects cannot be ignored in simulations of materials intended for high-temperature applications.

Figure 1

Temperature-pressure phase diagram of AlN. Experimental data are collected from Refs. [1, 3, 4, 11, 22]. Theoretical data are extracted from Refs. [11, 12] and show the difference in the boundary line between the wurtzite and rocksalt phases depending on a choice of the functional. Our anharmonic phase boundary is in good agreement with previous QHA calculations at low temperatures. There is considerable uncertainty in the actual transition boundary, as evidenced by the experimental data points, and it is sensitive to the experimental details and in the case of simulations, the choice of exchange-correlation functional.

Figure 2

(a) Comparison of volume as a function of temperature computed anharmonically using TDEP and quasiharmonically. (b) $c/a$ ratio as a function of temperature for wurtzite AlN, computed anharmonically and quasiharmonically. Red points are from experiments [30]. (c) Comparison of the relative volume expansion as a function of temperature with experimental data [30]. $V_0$ is the room temperature equilibrium volume.

Figure 3

Total phonon density of states and partial phonon density of states per Al and N atoms at room temperature for (a) rocksalt AlN and (b) wurtzite AlN. Total phonon density of states as a function of temperature (c) rocksalt AlN (d) wurtzite AlN.

Figure 4

Phonon lineshapes for rocksalt (left) and wurtzite (right) AlN at 300 K and 2400 K and ambient pressure. There is insignificant broadening at 300 K. From the broadening at 2400 K, it is clear that the anharmonicity in the rocksalt phase is significantly stronger than for wurtzite across all branches.

Figure 5

Thermal conductivity of rocksalt and wurtzite phases as a function of temperature at ambient pressure. Experimental data are taken from Ref. [2] correspond to in-plane thermal conductivity for the wurtzite phase.

Figure 6

Cumulative thermal conductivity as a function of the mean free path for the rocksalt and wurtzite phases of AlN at room temperature.

Figure 7

Spectral function for the rocksalt phase at 300 K and 2400 K and ambient pressure, showing the broadening of electronic bands due to thermal disorder. The lines indicate the band structures computed at zero temperature for thermally expanded cells in the absence of the thermal atomic displacements and compares them with band structures that include both volume expansion and thermal disorder.

Figure 8

Direct electronic band gap as a function of temperature for the rocksalt and wurtzite phases at ambient pressure.