Theory of the lattice thermal conductivity in bulk and films of GaN

摘要

We report on a systematic theoretical investigation of the lattice thermal conductivity of several GaN samples (bulk and films) over a wide range of temperature, by applying Callaway's relaxation-time theory in its full form and Srivastava's scheme for anharmonic three-phonon scattering processes. The role of the usually neglected three-phonon normal-drift term has been quantified. We have attempted to quantify the role of phonon scattering by various defects and imperfections, present in the film samples, in controlling the temperature dependence of thermal conductivity. We find that except for the purest sample, the phonon-impurity scattering plays a significant role in controlling the thermal conductivity of GaN not only around the thermal-conductivity peak region but also over a very large range of temperature. It can also be predicted from our numerical study, and with available experimental results, that the highest possible thermal conductivity of bulk GaN can only be realized when point impurities such as oxygen and silicon are in small concentration (approx=10~(16) cm~(-3) or less) and other defects are either absent (from experimental study) or present in very small concentration (our numerical study). The highest value of the room-temperature thermal conductivity is achieved for samples grown by the high-temperature and high-pressure growth technique.