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

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 ) were obtained for the n- and p-typedoped silicon. Additionally, the calculations of the band electronic structure and the electric conductivity 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 and (2) the clear increase of the electron effective mass m* with an increase of the carrier concentrations Nc for both n- and p-type-doped silicon crystals.

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1. Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).

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2. Experimental measurements were performed with infrared synchrotron radiation at the IRIS beamline of the electron storage ring BESSY II at the Helmholtz-Zentrum Berlin für Materialien und Energie in the framework of the BESSY proposal 232-12203-ST. Computer calculations were performed at ICM of Warsaw University, Poland (projects nos. g93-1636 and g96-1832) and WCSS of Wrocław University of Science and Technology, Poland (project no. 053).