Heat capacity of $\alpha$-GaN: Isotope Effects

TL;DR

This study measures the heat capacity of single-crystal GaN across a wide temperature range, compares it with polycrystalline data, and explores how isotopic masses of Ga and N influence heat capacity through first-principles calculations.

Contribution

It provides the first experimental heat capacity data for single-crystal GaN and investigates isotope effects on heat capacity in a binary semiconductor using first-principles calculations.

Findings

Heat capacity data deviates from polycrystalline values.

Isotopic mass affects acoustic and optical phonons differently.

First-principles calculations confirm isotope dependence on heat capacity.

Abstract

Until recently, the heat capacity of GaN had only been measured for polycrystalline powder samples. Semiempirical as well as \textit{first-principles} calculations have appeared within the past few years. We present in this article measurements of the heat capacity of hexagonal single crystals of GaN in the 20-1400K temperature range. We find that our data deviate significantly from the literature values for polycrystalline materials. The dependence of the heat capacity on the isotopic mass has also been investigated recently for monatomic crystals such as diamond, silicon, and germanium. Multi-atomic crystals are expected to exhibit a different dependence of these heat capacities on the masses of each of the isotopes present. These effects have not been investigated in the past. We also present \textit{first-principles} calculations of the dependence of the heat capacities of GaN, as a canonical binary material, on each of the Ga and N masses. We show that they are indeed different, as expected from the fact that the Ga mass affects mainly the acoustic, that of N the optic phonons. It is hoped that these calculations will encourage experimental measurements of the dependence of the heat capacity on isotopic masses in binary and more complex semiconductors.