Analysis of critical points in temperature dependent and time resolved ellipsometry spectra of Ge using digital filtering

We analyze critical points (CPs) in the dielectric function (DF) of Ge measured with static and time-resolved spectroscopic ellipsometry. Data were taken between 10 K and 718 K to investigate the temperature dependence of the direct band gap E₀. To obtain lineshape parameters, the second energy derivatives of the DF are calculated using a linear filter technique based on Gaussian kernels introduced by Le et. al.¹ which combines interpolation, noise reduction, and scale change. Taking into account excitonic effects, a Tanguy lineshape is fitted to the second derivatives of the DF. A red shift of energy and an increase in broadening with rising temperature are found and are fitted using a Bose-Einstein factor considering electron-phonon interaction.
The same analysis method is applied to the E₁ and E₁+Δ₁ CPs of Ge dependent on photo-excited charge carrier density obtained from femtosecond pump-probe ellipsometry measurements.² The CP parameters are determined as functions of delay time and a change of the CP energies suggests a laser heating of about 20 K to 40 K.

¹V.L. Le, T.J. Kim, Y.D. Kim, D.E. Aspnes, J. Vac. Sci. & Technol. B 37, 052903 (2019)
²S. Espinoza, S. Richter, M. Rebarz, O. Herrfurth, R. Schmidt-Grund, J. Andreasson, S. Zollner, Appl. Phys. Lett. 115, 052105 (2019)