Simultaneous measurement of the two-photon coefficient and free-carrier cross section above the bandgap of crystalline silicon

We report what is to our knowledge the first simultaneous measurement of the two-photon absorption coefficient and the free-carrier cross section above the bandgap in a semiconductor. This is also the first observation of two-photon absorption of 1 μm radiation in single-crystal Si at room temperature in a regime where a two-photon stepwise process involving indirect absorption followed by free-carrier absorption is usually dominant. A critical pulsewidth (and fluence) is established below (and above) which two-photon absorption cannot be neglected. Pulses that range from 4 to 100 ps in duration are then used to isolate the irradiance-dependent two-photon absorption from the fluence-dependent free-carrier absorption. We obtain an indirect two-photon absorption coefficient of 1.5 cm/GW and extract a free-carrier cross section of 5 \times 10^{-18} cm ² by using a simple technique that does not require a knowledge of the actual carrier density.