Pulsed Raman Measurements of Phonon Populations: Time Reversal, Correction Factors, and All That
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PULSED RAMAN MEASUREMENTS OF PHDNON POPULATIONS: TIME REVERSAL, CORRECTION FACTORS, AND ALL THAT A. COMPAAN*, Max-Planck-Institut f1r Festk6rperforschung, Heisenbergstrasse 1, 7000 Stuttgart 80, Federal Republic of Germany, H.W. LO, A. AYDINLI** AND M.C. LEE, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA ABSTRACT Transient optic phonon populations are measured in crystalline Si as a function of 532 nm laser energy density. The use of a continuously tunable pulsed dye laser as the Raman probe allows us to obtain, under exact experimental conditions, all correction factors necessary to extract the phonon population without the necessity of relying on room temperature or oven-heated conditions. We find the shift of the 520 cm- Raman-line to be consistent with the observed Stokes/anti-Stokes ratios indicating a maximum optic phonon temperature of 450 ± 100 0 C. A discussion is also given of the errors in several recent criticisms of the Raman results. In this paper we describe new experiments which exploit the time reversal invariance of the Raman effect [1] in order to obtain directly all of the temperature-dependent corrections which are needed, in addition to the readily measured instrumental throughput corrections. Thus we are able to infer unambiguously the optic phonon population in silicon under laser annealing conditions. We demonstrate that these corrections may be obtained without requiring the assumption of thermal equilibrium conditions in the semiconductor. We thus avoid sane of the difficulties which confuse the interpretation of other time-resolved measurements performed under laser annealing conditions. In addition,
in
this paper we describe measurements of the shift of the Stokes
Raman line and show that it is consistent with the 450 0 C temperature rise inferred from the Stokes/anti-Stokes ratio. Finally we critically evaluate some of the recent attempts made to reinterpret the Raman measurements. TIME REVERSAL INVARIANCE AND THE RAMAN RATIO The Raman technique has generated much interest because of the fact that the Stokes/anti-Stokes ratio is directly related to a phonon population, and because the Raman probe is non-destructive, is easily used on a nanosecond or picosecond time scale, and for sane wavelengths samples less than 100 9 of the crystal surface [2]. It is thus an attractive probe for examining phonon populations (lattice temperatures) during pulsed laser annealing (PLA). However, a propos of laser annealing conditions, there exist almost no data at all on the necessary corrections to the Raman ratio. In this paper we describe how we have used the time reversal invariance of the Raman cross section to obtain, via an additional Raman measurement, the required corrections under exactly the conditions for which the temperature or phonon population is sought. The technique involves a set of three Raman intensity measurements - only one more than needed for the temperature measurement itself. The method requires the On sabbatical leave fram Kansas State Univer
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