Spatially-resolved thermoreflectance - basic concepts

Optical modulation spectroscopy techniques measure the response of the optical constants of a solid to a periodic change of an applied perturbation. Depending on the character of the perturbation we distinguish an electric field modulation (electroreflectance-ER), photo induced built-in electric field modulation (photoreflctance-PR) stress modulation (piezoreflctance-PzR) and temperature modtion (thermoreflectance-TR). All optical modulation spectroscopes measure the change of complex dielectric function,

The changes in real and imaginary part of dielectric function, induced by external modulation, result in relative change of reflectivity given by

where a and b are Seraphin coefficients related to the unperturbed dielectric function. In thermoreflectance (TR), the modulation of temperature results in a change De of the dielectric function, which is induced by a shift of the band gap energy E_g and by the change of the broadening parameter G,

Particularly, the principle of the thermoreflectance modulation technique is based on the dependence of the sample’s reflectance on the temperature. Usually an analysing beam is reflected by the sample’s surface, and its intensity is then measured. A variation in the sample reflectance (DR) is related to the temperature variation (DT) through the following relation:

The thermoreflectance coefficient C_TR depends on the sample’s material and on the wavelength. An accurate calibration method is an essential element of any quantitative thermometry techniques.