Temperature dependence of the thermoreflectance coefficient of gold by the use of a phase-locked single-point measurement approach

Thermoreflectance is a non-contact optical thermography technique that measures the change in the surface temperature of a reflective material, and that has found promising applicability in the characterization of microelectronic devices. As with all temperature measurement approaches, obtaining absolute temperatures requires a calibration step in order to relate the change in reflectance to the change in temperature. In the general literature up to this point, the relation had been assumed to be linear, and the Thermoreflectance Coefficient, C
_TR
, that relates the changes in temperature and reflectance had been assumed to be constant. This study investigates the linear assumption by carefully measuring the variation of C
_TR
of Gold between 25°C and 100°C. The measurements are performed at a fixed wavelength of light using a high precision setup that takes single-point phase-locked differential measurements. The results show that the coefficient is not constant as had been previously assumed, but rather gradually decreases from 4x10
^-4
K
^-1
to 3 x 10
^-4
K
^-1
as the calibration temperature increases in the range from 25°C to 100°C. The effect of this deviation from the linear assumption on the accuracy of microscopy tools is an error in excess of 10°C at 100°C when calibrating between 20°C and 40°C for the studied wavelength.