Analysis of the temperature evolution from the time resolved thermo-optical interferometric measurements with few Fabry–Pérot peaks

A mathematical method is proposed to calculate the temperature evolution in semiconductor layers from the measurements of Fabry–Pérot (FP) interferences in the reflected or transmitted intensity of a probing laser beam. The changes in the optical intensity are caused by the temperature induced changes in the refractive index and thermal expansion of the semiconductor layer. The method is particularly suitable in cases where the intensity curve exhibits few (at least two) FP intensity extrema. The unknown temperature evolution is obtained from a comparison of mathematical representations of the intensity–time and intensity–temperature dependences and using a symmetry property of the FP intensity–temperature function around the intensity extremum. Expressions for polynomial and exponential approximations of the temperature evolution are given together with empirical rules to maximize the accuracy of output parameters as thermal time constant, polynomial expansion coefficients, and temperature amplitudes. The applicability of the method is demonstrated by time resolved optical reflectivity measurements on semiconductor devices with the active layer forming a FP resonator: smart power devices prepared by silicon-on-insulator technology and power sensors fabricated on GaAs micromachined cantilevers. The temperature evolution in the former and latter devices is studied in the μs and ms time scale up to the temperature increase of 200 and 350 K, respectively. The relative error in both the extracted temperature evolution and time constants is about 15%.