2-PHOTON ABSORPTION IN AN INDIRECT-GAP SEMICONDUCTOR QUANTUM-WELL SYSTEM .1. INTERBAND-TRANSITIONS

Phonon-assisted two-photon interband transitions in an indirect-band-gap semiconductor layered quantum well (QW) and quantum well wire (QWW) are theoretically studied. The spectral dependence of the two-photon absorption (TPA) coefficients alpha(1), alpha(2), alpha(3) in one-dimensional (1D), 2D, and also 3D (bulk) systems, respectively, are found to vary according to (2homegaBAR +/- hOMEGABAR - E(G))beta, where homegaBAR(hOMEGABAR) is the photon (phonon) energy and E(G) is the effective indirect gap. Beta takes the values 0, 1, 2, and 3 depending on the dimension of the system and the form of momentum matrix elements. The analytical expressions of the electron-photon and electron-phonon matrix elements in QW systems are given. The numerical calculation of the TPA coefficients alpha(1), alpha(2), and alpha(3) in Si0.5Ge0.5 shows that: alpha(1)(alpha(2)), for polarization parallel to the confinement directions, is four (two) orders of magnitude bigger than alpha(3) for allowed-allowed transitions. Furthermore, alpha(1) is two orders of magnitude larger than alpha(2), for both photon polarizations with respect to the confinement directions in QW systems. This enhancement of alpha(1) over alpha(2) and alpha(3) is interpreted as due to the additional lateral quantum confinement of the carriers in QWW and also due to the intra-subband momentum matrix elements.