Abstract
We have studied the Raman lineshapes of several samples of GaP with appreciable carrier concentrations. There is no feature identifiable as a plasma resonance, but there are pronounced effects of interaction with the LO phonon resonance. For analysis we have developed a model along lines laid down by Barker and Loudon, employing Nyquist relations to calculate infrared fluctuations which scatter light. We introduce a response matrix α(ω) withseveral resonances; and we uncover some points which seem to be new, for coupled-mode scattering systems in general. In the GaP-plasma problem the data do not necessitate inclusion of the scattering amplitude from the plasma; we ascribe this to large plasma damping rates (ωτ≲1). This provides an account for the lack of any apparent plasma resonance in the scattering and for the modified appearance of the LO phonon, relative to the pure crystal. We emphasize that the following parameters suffice: Lorentz parameters measured in linear infrared experiments, the nonlinear parameterC from a visible-infrared mixing experiment, and the plasma frequency and damping fit to each sample.
Beyond treatment of the plasma problem, the theory bears more generally on the conditions under which an LO Raman lineshape measures locally the shape of 〈E 2〉ω. Also it bears upon the analysis of polariton linewidths to infer the variation of the phonon damping Γ(ω).
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The ratio of the area under Im {LO} to that under Im {TO} is 0.1925. In the approximation\(\Gamma<< \Omega \sim \omega _T\), it may be shown analytically that for equal displacements from the respective resonant frequenciesω L andω T we have the ratio Im {LO}=(Ω 2/ω 2 T ) Im {TO}=0.2118 Im {TO}; so the integrals are in this ratio, and the linewidths are equal
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This work was supported by the National Science Foundation Grant No. GH 32401. It is based on a major segment of the thesis of D.T. Hon, submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the Faculty of the Graduate School of the University of Southern California.
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Hon, D.T., Faust, W.L. Dielectric parameterization of raman lineshapes for GaP with a plasma of charge carriers. Appl. Phys. 1, 241–256 (1973). https://doi.org/10.1007/BF00889771
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DOI: https://doi.org/10.1007/BF00889771