Optical properties of 4H-SiC and 6H-SiC from infrared to vacuum ultraviolet spectral range ellipsometry (0.05–8.5 eV)

Abstract

Complex dielectric function (ɛ = ɛ1 + iɛ2) spectra are obtained from reflection mode spectroscopic ellipsometry and unpolarized transmittance measurements for 4H and 6H stacking sequence silicon carbide (SiC) nitrogen-doped single crystals from the infrared (IR) to vacuum ultraviolet (VUV) spectral range. A single parametric model describing ɛ predominately for the ordinary directions is developed over the 0.05–8.5 eV spectral range from analysis of (0001)-oriented back side roughened 4H-SiC and 6H-SiC single crystals with some contribution from the extraordinary direction of 6H-SiC in the IR region. Indirect bandgaps for 4H-SiC and 6H-SiC are found to be 3.30 and 3.03 eV, respectively, and the corresponding direct optical gaps are at 4.46 and 4.42 eV. A model describing the optical response in the IR spectral range is created using a Drude expression and either transverse optical (TO) and longitudinal optical (LO) (TOLO) or Lorentz oscillator models. Free carrier concentration (N) is optically measured to be 3.7 × 1018 and 3.3 × 1018 cm−3 using TOLO and Lorentz oscillator models, respectively, and the corresponding carrier mobility (μ) is 34 and 39 cm2/V s for 4H-SiC. Under the same assumption for 6H-SiC, N is measured to 8 × 1018 cm−3 using either TOLO or Lorentz oscillator models and μ is 9 and 10 cm2/V s using the TOLO and Lorentz oscillator models, respectively, in the ordinary direction and 5 cm2/V s in the extraordinary direction using either model. For 4H-SiC, using the TOLO oscillator model, TO and LO phonon modes are measured at 797.7 and 992.1 cm−1, respectively, and corresponding modes are found at same locations using the Lorentz oscillator model. In 6H-SiC, using the TOLO model, TO modes in ordinary and extraordinary directions are found at 797.7 and 789.7 cm−1, and corresponding modes are at 796.9 and 788.9 cm−1 using the Lorentz oscillator model. The LO modes using the TOLO model are found at 992 and 984 cm−1 in the ordinary and extraordinary directions, respectively, and the same modes in the corresponding direction using the Lorentz oscillator model are located at 975.9 and 967.9 cm−1.