ANALYSIS OF THE TEMPERATURE EVOLUTION FROM THE TIME-RESOLVED THERMOOPTICAL INTERFEROMETRIC MEASUREMENTS WITH FEW FABRY-PEROT PEAKS

A mathematical method is proposed to calculate the temperature evoluti on in semiconductor layers from the measurements of Fabry-Perot (FP) i nterferences in the reflected or transmitted intensity of a probing la ser beam. The changes in the optical intensity are caused by the tempe rature induced changes in the refractive index and thermal expansion o f the semiconductor layer. The method is particularly suitable in case s where the intensity curve exhibits few (at least two) FP intensity e xtrema. The unknown temperature evolution is obtained from a compariso n of mathematical representations of the intensity-time and intensity- temperature dependences and using a symmetry property of the FP intens ity-temperature function around the intensity extremum. Expressions fo r polynomial and exponential approximations of the temperature evoluti on are given together with empirical rules to maximize the accuracy of output parameters as thermal time constant, polynomial expansion coef ficients, 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: sm art power devices prepared by silicon-on-insulator technology and powe r sensors fabricated on GaAs micromachined cantilevers. The temperatur e evolution in the former and latter devices is studied in the ms and ms time scale up to the temperature increase of 200 and 350 K, respect ively. The relative error in both the extracted temperature evolution and time constants is about 15%. (C) 1998 American Institute of Physic s. [S0021-8979(98)01720-4].