On the theory of the two-photon linear photovoltaic effect in $n$-GaP

A quantitative theory of the diagonal (ballistic) and nondiagonal (shift) band index contributions to the two-photon current of the linear photovoltaic effect in a semiconductor with a complex band due to the asymmetry of events of electron scattering at phonons and photons is developed. It is shown that processes caused by the simultaneous absorption of two photons do not contribute to the ballistic photocurrent in $n$-GaP. This is due to the fact that, in this case, there is no asymmetric distribution of the momentum of electrons excited with photons; this distribution arises upon the sequential absorption of two photons with the involvement of $LO$ phonons. It is demonstrated that the temperature dependence of the shift contribution to the two-photon photocurrent in $n$-GaP is determined by the temperature dependence of the light-absorption coefficient caused by direct optical transitions of electrons between subbands $X_1$ and $X_3$. It is shown that the spectral dependence of the photocurrent has a feature in the light frequency range $\omega\to\Delta/2\hbar$, which is related to the hump-like shape of subband $X_1$ in $n$-GaP1 and the root-type singularity of the state density determined as $k^{-1}_{\omega}=(2\hbar\omega-\Delta)^{-1/2}$, where $\Delta$ is the energy gap between subbands $X_1$ and $X_3$. The spectral and temperature dependences of the coefficient of absorption of linearly polarized light in $n$-GaP are obtained with regard to the cone-shaped lower subband of the conduction band.