Non-degenerate Two Photon Absorption Spectra of Si Nanocrystallites

The two-photon absorption (TPA) spectrum is an important optical property of semiconductors. It brings valuable information complementary to the one-photon absorption spectrum, gives the limits to the optical transparency of materials, and causes laserinduced damages. Recently, the TPA spectrum of direct-gap nanocrystallites was calculated by Cotter et al. [1] by using the effective-mass approximation to predict a strong effect of the nanocrystallites size. However the experimental result [2] does not support this result. Since then TPA spectra of nanocrystallites has been attracting attention of researchers. In this paper, we develop a new algorithm for calculating TPA spectra by using semiempirical local pseudopotentials [3], finite difference method in real space [4], and a linearscaling time-dependent method which has been applied to the calculation of the linearresponse functions [5, 6, 7, 8]. This efficient algorithm made it possible, for the first time, to calculate the size effect on the TPA spectra of very large nanocrystallites without using effective-mass approximation. In the following we show the effectiveness of this algorithm by applying it to the TPA spectra of indirect-gap nanocrystallites. Though this result does not solve the controversy related to direct-gap nanocrystallites [1, 2], it will be an important step toward it.