Importance of temperature-dependent optical properties for Raman-temperature measurements for silicon

Abstract

A standard relation of Raman scattering in the resonant regime is that the Raman matrix element $R$ is well represented by $K\frac{d\epsilon }{\mathrm{dE}}$, where $\epsilon$ is the dielectric function, $E$ is the photon energy, and $K$ is a constant. However, the only experimental check of this relationship in silicon [Renucci et al., [Phys. Rev. B 11, 3885 (1975)] concluded that it was only approximately valid. In this paper it is shown for silicon in the resonant regime that the agreement between the measured values of the Raman matrix element squared, $\sigma ={\left|R\right|}^2$ and $K^2{\left|\frac{d\epsilon }{\mathrm{dE}}\right|}^2$, is very good indeed, if accurate values of the dieletric function are used. With the use of recently obtained temperature-dependent optical functions of silicon, the absorption coefficient, the Raman matrix element squared, the index of refraction, and the normal-incidence reflectivity are determined and shown to be strong functions of temperature in the resonant regime. The Stokes to anti-Stokes intensity ratio is calculated and found to compare favorably with values found in the literature for samples held at constant temperature. It is concluded that the temperature dependence of the optical properties must be included in any interpretation of measurements to determine the temperature from the Stokes to anti-Stokes intensity ratio.