Temperature and doping dependence of the radiative properties of silicon: Drude model revisited

Abstract

Understanding the radiative properties of silicon is crucial to accurate measurement of the temperature of silicon wafer during rapid thermal processing (RTP). Prediction of the radiative properties requires precise knowledge of the dielectric function of silicon in RTP environments. In general, the dielectric function or equivalently optical constants of silicon are complicated functions of the wavelength, temperature, and dopant concentration. To model the free-carrier absorption of doped silicon, the Drude model has been used in many literatures. However, some of the existing Drude model parameters do not agree with other published data. Hence, the present study carefully revisits the Drude model parameters such as carrier concentrations and carrier scattering times. Based on updated Drude model parameters, the absorption coefficients of doped silicon at various dopant concentrations and temperatures are calculated and compared with the available measured data. Reasonably good agreements between the prediction and experimental data are found, suggesting that present Drude model is an efficient way to model the dielectric function of doped silicon