Thermal Transport in Al_xGa_1-xN—Impact of Mass and Force Field Disorder

Our objective is to determine how disorder related to mass and atomic interactions impacts the thermal conductivity of the Al_xGa_1-xN alloy. While the application of first principles-based lattice dynamics calculations using Abele's virtual crystal approximation (VCA) and Tamura's mass perturbation model has been successful for calculating the thermal conductivity of some alloys, the inclusion of local force-field differences is often overlooked. To address this knowledge gap, we propose a general framework for modeling thermal transport in alloys, with a focus on Al_xGa_1-xN.

Ultra-wide bandgap (UWBG) materials, with electronic band gaps exceeding 4 eV, enable devices that outperform conventional semiconductors in switching frequency, voltage tolerance, and temperature resistance. Among UWBG materials, Al_xGa_1-xN alloys are particularly promising due to their tunable direct bandgap (3.4 - 6 eV), high breakdown electric field, high electron mobility, and easy n-type doping with silicon. These properties make Al_xGa_1-xN ideal for high-power electronic devices operating in extreme conditions.

Although the understanding of the electronic performance of Al_xGa_1-xN-based devices has advanced in recent years, the nanoscale thermal transport properties of Al_xGa_1-xN remain poorly understood. The random occupation of lattice sites by Al or Ga atoms (i.e., compositional disorder) leads to higher phonon scattering rates and reduced thermal conductivity compared to AlN or GaN.

In a typical alloy thermal conductivity calculation, the disorder is initially neglected and phonon-phonon interactions are modeled under the VCA up to third order. The mass disorder is then included as an additional scattering mechanism using Tamura's theory. The impact of force constant disorder (i.e., different interactions between different atom types) is ignored. Our objective is to address this limitation.
We first developed an atomic cluster expansion (ACE) potential for classical molecular dynamics (MD) simulations of Al_xGa_1-xN. The training dataset is generated through ab-initio MD simulations of Al_xGa_1-xN supercells, spanning the full range of compositions, temperatures from 100 K to 1100 K, and lattice strains from 0.95 to 1.05. The ACE potential was validated by comparing its predictions to those from first principle calculations. These properties include the lattice parameters, phonon dispersion curves, and lattice thermal conductivity of wurtzite AlN and wurtzite GaN. The results indicate that the ACE potential effectively captures both harmonic and anharmonic effects across the alloy composition range.

The computational efficiency of MD simulations with the ACE potential enables a rigorous representation of the compositional disorder in a large supercell. We calculated thermal conductivity using the Green-Kubo (GK) method, which accounts for the complete anharmonicity of the potential and does not make any assumptions about the transport mechanisms. To quantify and isolate the effects of mass and force field disorder, we predicted thermal conductivities using four types of GK-MD simulations with the ACE potential: (i) a fully disordered Al_xGa_1-xN supercell, (ii) a supercell with with only force field disorder, where the Al and Ga atoms are assigned a composition-averaged mass, (iii) a supercell with only mass disorder, where the forces on Al and Ga atoms are linearly interpolated based on composition, and (iv) a supercell without mass or force field disorder, simulating the virtual crystal. This MD-based framework can be applied to any alloy, providing a generic tool to assess the accuracy of VCA by quantifying the contributions from various types of disorder to thermal conductivity.