A generalized 3ω method for extraction of thermal conductivity in thin films

摘要

It has been found that in the low-frequency regime, the experimentally determined thermal conductivity of thin dielectric films deviates significantly from the theoretical expectation based on Cahill's 3ω thermal model. It is shown in the present work that this deviation is mainly caused by the heat transport in the heater strip, which is neglected in Cahill's one-dimensional model. By taking this mechanism into account, an analytical model is developed to simultaneously consider the heat transport in the heater strip and the heat flow into the underlying substrate. The validity of this two-dimensional model is confirmed by experiments using specially designed test structures as well as by numerical simulation. The results show that the heat transport along the heater strip, originated from a nonuniform temperature, becomes comparable to that in the substrate at low frequencies. This effect of a nonuniform temperature distribution can also be exploited for extraction of the thermal conductivity of the metallic strip itself.