Raman Spectroscopy as a Simple yet Effective Analytical Tool for Determining Fermi Energy and Temperature Dependent Fermi Shift in Silicon

The Fermi energy is known to be dependent on doping and temperature, but finding its value and corresponding thermal Fermi shift experimentally is not only difficult but is virtually impossible if one attempts their simultaneous determination. We report that temperature dependent Raman spectromicroscopy solves the purpose easily and proves to be a powerful technique to determine the position and temperature associated Fermi shift in an extrinsic semiconductor as demonstrated for silicon in the present study. The typical asymmetrically broadened Raman spectral line-shape from sufficiently doped n- and p-type silicon contains the information about the Fermi level position through its known association with the Fano-coupling strength. Thus, Raman line-shape parameters, the terms quantify the Fano-coupling, have been used as experimental observables to reveal the value of the Fermi energy and consequent thermal Fermi shift. A simple formula has been developed based on existing established theoretical frameworks that can be used to calculate the position of the Fermi level. The proposed Raman spectroscopy-based formulation applies well for n- and p-type silicon. The calculated Fermi level position and its temperature dependent variation are consistent with the existing reports.