Two-photon photoconductivity phenomena in semiconductors and insulators

Abstract

A comprehensive theoretical calculation of the spectral dependences of the two-photon photoconductivity (TPPC) measurements reported previously is given. The band-to-band two-photon absorption (TPA) was calculated by using an average-spherical-band model which was derived from the empirical pseudopotential band structure. The spectral dependences of the TPPC were calculated within the framework of the following three approximation schemes: (i) The $\overrightarrow{\mathrm{k}}$ dependence of the transition-momentum matrix elements (MME) is ignored and real, constant, and equal MME are assumed for all the allowed transitions at $\overrightarrow{\mathrm{k}}=0\mathrm{}$. (ii) The $\overrightarrow{\mathrm{k}}$ dependences of the transition MME are calculated with the aid of the empirical pseudopotential wave functions, and the spherical averages of the absolute values of these MME are used in the calculations of the TPPC. (iii) The exact $\overrightarrow{\mathrm{k}}$-dependent complex MME and energy bands are used, the summations over all the intermediate states are performed, and only the integration over $\overrightarrow{\mathrm{k}}$ space is still carried out by using the average-spherical-band approximation. The results of these spectral TPPC calculations in a hexagonal ZnO crystal and in a mixed cubic and hexagonal ZnS crystal are given. For both crystals, and in all the approximation schemes, good agreement of the calculated TPPC with the experimental results was found, except for the energy region of the second transition in the ZnO crystal (4.25 eV), where only a partial agreement in the spectral shape of the TPPC with the measurements was found. Additional interesting theoretical results in the hexagonal crystals, obtained by a comparison with the experimental results, are that the pseudo-wave-functions of the deeper valence bands give only a poor representation of the real wave functions, and that occupied states should be taken into account as intermediate states in the two-photon transition probability. Alternative two-photon processes which may influence the TPPC, such as TPA by impurities, exciton TPA, and the reabsorption of second-harmonic-generated photons, are also considered, but mainly in a qualitative way.