Two-photon absorption in direct bandgap semiconductors quantum dots

We present degenerate and nondegenerate two-photon absorption spectra in a series of CdSe and CdTe quantum dots. The measurements show that the two-photon absorption (2PA) spectrum is strongly dependent on the quantum dot size and that the 2PA coefficient decreases as the quantum dot size decreases, and it is larger for the frequency nondegenerate process. Previously we had shown a theoretical analysis of these results based on a simple model using the effective mass approximation. Although this model works well for larger quantum dots, it fails for the smaller ones. Here we use the more realistic model kp for the band structure and consider the hole band mixing in quantum dots to describe our data. This theory better describes the spectral structures for smaller quantum dots and also predicts the decrease of the 2PA coefficient with the decrease of quantum dot size. This is due to the reduction of the number of possible transitions and the blue shift of the optical bandgap from quantum confinement. This theory predicts the reduction of the 2PA coefficient with size, although our experimental results show an even stronger reduction.