Non-degenerate two-photon absorption (ND-2PA) across the indirect gap of silicon is theoretically and experimentally investigated in the current work. We present measurements of the 2PA coefficient of bulk silicon using femtosecond pump and probe pulses in the IR and mid-IR range. Enhancement of ND-2PA was observed from the results of our measurements with increasing non-degeneracy. This can be utilized when designing sensitive silicon-based mid-IR detectors. Modeling of the 2PA was performed by considering three theoretical pathways across the band structure of silicon for the two photons and a phonon, and the most dominant processes are determined by comparison to our measurements.
Semiconductors have long been known to exhibit large two photon absorption (2PA) coefficients. It has also been shown that for extremely nondegenerate pairs of photons (energy ratios of approximately 10:1) the 2PA in direct gap semiconductors (e.g. GaAs, CdTe, ZnSe, ZnO, GaN) is enhanced over the degenerate value by up to 3 orders of magnitude. Silicon has always been a material of interest for photonics applications due to its low cost and possibility for integration with electronics, but its indirect bandgap provides a challenge since 2PA requires a phonon scattering process. Despite this, the degenerate 2PA in Silicon has been shown to be comparable to that of direct gap semiconductors with similar band gap energy. We present a model for nondegenerate 2PA (ND-2PA) in indirect semiconductors that is nearly identical to the direct gap theory with a phonon transition added as a perturbation step. We also experimentally investigate the enhancement of ND-2PA in Silicon for the extremely nondegenerate case using a femtosecond pump-probe arrangement. In these experiments, the transmittance of a tunable near infrared probe pulse is monitored in the presence of a mid-IR pump pulse generated by difference frequency generation while varying the relative delay between pump and probe pulses. Measurement results reveal that the 2PA enhancements due to nondegeneracy are similar to those seen in direct-gap semiconductors. As with direct gap semiconductors, these enhancements indicate the applicability of using nondegenerate 2PA as possible method for ultrafast, gated mid-IR detection using off-the-shelf Silicon photodiodes.
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