Lattice thermal conductivity of nanoscale AlN∕GaN∕AlN heterostructures: Effects of partial phonon spatial confinement

Abstract

We report a detailed theoretical modeling of lattice thermal conductivity in nanoscale AlN∕GaN∕AlN heterostructures. Thermal conductivity in such heterostructures is derived based on the solution of the phonon Boltzmann equation in the relaxation-time approximation. Phonon dispersion relations are obtained in the elastic continuum approximation using the finite-difference numerical method. Quasi-two-dimensional (2D) phonon density of states is derived using the actual phonon dispersion. To investigate the effects of partial phonon spatial confinement, numerical simulations are performed for both the three-layer heterostructures and the single GaN thin films. The dependence of the thermal conductivity on the core or cladding layer thickness in an AlN∕GaN∕AlN heterostructure is also discussed. We have demonstrated that partial phonon confinement leads to a higher thermal conductivity in an AlN∕GaN∕AlN heterostructure than that in a single GaN thin film with the same total structure thickness. Such thermal conductivity can also be tuned higher or lower by adjusting the core or cladding layer thickness without changing the total thickness of the structure. Obtained results have quantitatively shown that it is possible to improve heat conduction in semiconductor nanostructures through phonon spectrum engineering, in agreement with other recent studies.