In contrast to known Raman-thermometric measurements of thermal conductivity (k) of suspended Si nano-membranes, here we apply Raman thermometry for k measurement of mono- and nano-crystalline Si films on quartz, which is important for applications in thermoelectricity and nanoelectronics. Experimentally, we measure linear dependence of the laser-induced Raman band downshift, which is proportional to the moderate heating ΔT, on the laser power P. Then we convert the downshift to ΔT and determine the ratio ΔT/P. The actual power absorbed by the film is calculated theoretically and controlled experimentally by the reflection/transmission measurement. Then we calculate ΔTcalc/P for arbitrary film k assuming diffusive phonon transport (DPT). Film k is determined from the condition ΔT/P = ΔTcalc/P. We show that this method works well for films with thickness h > Λ where Λ is phonon-mean-free path, even for low-k films like nano-crystalline Si and SiGe. For h < Λ despite ballistic phonon transport contribution, this approach works when the in-plane DPT dominates, e.g. in Si films on quartz with h ≥ 60 nm. We also show that the influence of thermal boundary resistance on the determined k is negligible at this condition. The proposed method is simple and time efficient, as dozen of films can be examined in one hour.
|Журнал||International Journal of Heat and Mass Transfer|
|Состояние||Опубликовано - 1 авг. 2018|