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

Abstract

The variation of two-photon absorption (TPA) coefficient $\beta _{\mathrm{TPA}} (\omega )$ 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 $\beta _{\mathrm{TPA}} (\omega )$. The results showed that $\beta _{\mathrm{TPA}} (\omega )$ varied from $4.2 \times 10^{-4}$ to $1.17 \times 10^{-3 }$ cm/GW in the transparent wavelength region $1.80<\lambda <1.36\,\upmu$m of Si. The increasing tendency of $\beta _{\mathrm{TPA}} (\omega )$ with the incident photon energy can be qualitatively interpreted as the photon energy increases from $E_{\mathrm{ig}}/2$ to nearly $E_{\mathrm{ig}}$, 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.