Investigations of free electrons in doped silicon crystals derived from Fourier transformed infrared measurements and ab initio calculations

Abstract

The reflection spectra of n- and p-type silicon crystals doped with phosphorus and boron were measured for the free carrier concentrations of 1.1 · 10¹⁵ cm⁻³  − 1.2 · 10²⁰ cm⁻³ in the far- and mid-infrared range between 20–3000 cm⁻¹ using synchrotron radiation and Fourier transformed infrared technique. Transmittance spectra could be measured for lower sample carrier concentrations from the range studied. The measured reflection spectra were fitted by using the Drude relation and the parameters of free electron conductivity (electron effective mass m^* and momentum scattering time τ) were obtained for the n- and p-type-doped silicon. Additionally, the calculations of the band electronic structure and the electric conductivity σ of the crystals were performed in the framework of the density functional theory for different carrier concentrations and temperatures. The study main findings are (1) the substantial decrease of the momentum scattering time τ and (2) the clear increase of the electron effective mass m^* with an increase of the carrier concentrations N_c for both n- and p-type-doped silicon crystals.