The Effect of Aluminum Fraction on the Phonon Mean Free Path - Thermal Conductivity Relation of AlxGa1-xN Alloys

Aluminum Gallium Nitride
$(\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}}\mathrm{N})$
is an ultra-wide bandgap alloy popularly used in microwave and radio frequency power amplifier applications. Other uses include light emitting diodes, lasers, and photodiodes. The bandwidth of
$\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}}\mathrm{N}$
in such applications can be tailored from 3.2 eV to 6.2 eV depending on the application needs by changing the Al fraction, x. As in most current semiconductor devices,
$\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}}\mathrm{N}$
layers used in such applications are extremely thin and/or witness localized heating conditions giving rise to nanoscale thermal transport effects. Nanoscale effects slow down the efficient heat removal from the devices. Such effects can be characterized with the proper investigation of the microscopic energy carrier, in this case lattice vibrations (i.e., phonons), properties. One of these properties: the phonon mean free path (MFP) plays a vital role in characterizing the nanoscale thermal behavior of the materials. This study provides an in-depth examination of the phonon MFP and thermal conductivity relation of
$\text{Al}_{\mathrm{x}}\text{Ga}_{1-\mathrm{x}}\mathrm{N}$
alloys changing with the temperature and the Al content. Here, thermal conductivity accumulation spectra of AlGaN for different Al fraction is obtained via ab-initio calculations and lattice dynamics calculations. The novelty of these theoretical calculations is their consideration of third-order force constants, where an opportunity to cover crystal energy expansion at higher order terms emerges.