Lock-in photothermal method for in-plane thermal diffusivity measurements using arrayed temperature sensors on suspended SiN_x membranes

A device consisting of a line- or spiral-shaped temperature sensor array on a two-dimensional (2D) silicon nitride (SiNx) membrane of thickness 50 or 150 nm is developed for use in the lock-in photothermal method to determine the in-plane thermal diffusivity of SiNx membranes in air and in vacuum. The results of 2D heat diffusion are analyzed by the quadrupole method, and the system is approximated to the one-dimensional (1D) fin standing in a surrounding media (the fin approximation). The results show that 2D thermal diffusion on the membrane is affected not only by heat exchange with the surrounding environment but also by parallel thermal diffusion caused by heat conduction in the air along the membrane surface. The measurement using photothermal heating and contact detection of the temperature response enables the phenomenon to be detected consistently at a wide frequency range of temperature waves (50-1000 Hz). The measured thermal diffusivity values of the SiNx membrane are much smaller than those of bulk material, which can be reasonably considered an effect of the confined state of the phonon in the nanoscale geometry of the membrane.