Low-temperature lattice thermal conductivity in free-standing GaN thin films

Low-temperature (2 < T < 100 K) lattice thermal conductivity, κp in a semiconducting free-standing thin film (FSTF) is studied using a modified Callaway model. The quantization of acoustic phonons in FSTFs is taken into account and explicit contributions to κp from the shear, dilatational and flexural modes of the confined acoustic phonons are considered. The scattering of phonons is assumed to be by sample boundaries, impurities, dislocations and other phonons via both normal and umklapp processes. Numerical results are presented for the GaN system. The phonon confinement effect, the sample finite size effect and the relative importance of confined phonon modes are investigated. The role of dislocations in limiting κp is also discussed. Results are compared with those based on bulk description of acoustic phonons; bulk phonons are found to underestimate (overestimate) κp in the boundary scattering regime (at higher temperatures). The calculations demonstrate that low-temperature thermal conductivity studies can lead to a better understanding of phonon scattering in FSTFs.