Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector

The variation of two-photon absorption (TPA) coefficient β TPA ( ω ) of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An equivalent RC circuit model was adapted to derive the TPA coefficient β TPA ( ω ) . The results showed that β TPA ( ω ) varied from 4.2 × 10 - 4 to 1.17 × 10 - 3 cm/GW in the transparent wavelength region 1.80 < λ < 1.36 μ m of Si. The increasing tendency of β TPA ( ω ) with the incident photon energy can be qualitatively interpreted as the photon energy increases from E ig / 2 to nearly E ig , the electrons excited from the valance band find an increasing availability of conduction band states. Comparing with the high-energy side transitions, the TPA coefficient in low-energy side is about 10 times too small. This can be attributed that the TPA transition in low-energy side is the process of photon-assisted electron transitions from valence to conduction band occurring between different points in k -space, while is direct transition in high-energy side.