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Two‐Photon Absorption in an Indirect‐Gap Semiconductor Quantum Well System. I. Interband Transitions
Author(s) -
Hassan A. R.
Publication year - 1994
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221840225
Subject(s) - photon , quantum well , condensed matter physics , physics , electron , semiconductor , photon energy , phonon , absorption (acoustics) , band gap , quantum dot , two photon absorption , polarization (electrochemistry) , quantum , atomic physics , quantum mechanics , chemistry , optics , laser
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 α (1) , α (2) , α (3) in one‐dimensional (ID), 2D, and also 3D (bulk) systems, respectively, are found to vary according to (2ħω ± ħΩ − E G ) β , where ħω(ħΩ) is the photon (phonon) energy and E G is the effective indirect gap. β 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 α (1) , α (2) , and α (3) in Si 0.5 Ge 0.5 shows that: α (1) (α (2) ), for polarization parallel to the confinement directions, is four (two) orders of magnitude bigger than α (3) for allowed‐allowed transitions. Furthermore, α (1) is two orders of magnitude larger than α (2) , for both photon polarizations with respect to the confinement directions in QW systems. This enhancement of α (1) over α (2) and α (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.