Interband and free charge carrier absorption in silicon at 800 nm: experiments and model calculations

Abstract

The average transmitted power of a Ti:sapphire femtosecond (fs) laser beam through thin, oxidized silicon (Si) membranes in the 10–30 \(\, \upmu \text{m}\) thickness range at \(45{^\circ }\) external angle of incidence at first increases with the incident average laser power and then decreases considerably. This stationary state behavior is quantitatively reproduced by a recently derived model using an effective absorption coefficient \(\alpha _{\text {eff}} = \alpha _{1} + \alpha _{\text {FCA}}\), adding the coefficients of two independent linear absorption processes, \(\alpha _{1}\) of the indirect interband transition and \(\alpha _{\text {FCA}}\) of free charge carrier absorption (FCA). The relations between the empirical parameter \(\alpha _{\text {FCA}}\) and the model parameters \(n_{\text {eh}}\) (density of free charge carriers) and \(\sigma _{\text {eh}}\) (absorption cross section of free charge carriers) are found to depend on the Si membrane thickness and are briefly discussed. Using different sample thicknesses, experimental evidence has been found for a nonlinear intensity dependence of \(\alpha _{\text {FCA}}\)∼\(I_{0}^{n}\), where \(1\le n \le 3\) shows systematic variation. The FCA model in combination with its empirical fit parameters allowed to fully calculate the transmission behavior of the Si membranes within the investigated sample thickness and laser power regimes.