Two‐Photon Absorption in an Indirect‐Gap Semiconductor Quantum Well System. I. Interband Transitions

Abstract

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 dl), a'", d 3 ) in one-dimensional (lD), 2D, and also 3D (bulk) systems, respectively, are found to vary according to (2hw hQ -EG)p, where hw(hQ) is the photon (phonon) energy and E , is the effective indirect gap. p 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 dl), dzl, and d 3 ) in Si,,,Ge,,, shows that:for polarization parallel to the confinement directions, is four (two) orders of magnitude bigger than d3' for allowed -allowed transitions. Furthermore, dl) is two orders of magnitude larger than d2), for both photon polarizations with respect to the confinement directions in QW systems. This enhancement of dl) over a('' and d 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.

Phonon‐assisted two‐photon magnetoabsorption in an indirect band gap semiconductor quantum well

“…( n is the Landau level quantum number) [19] unlike the direct band gap QWs, where only An = 0 transitions are allowed. Recently, the spectral dependence of the TPA coefficient on (2hw -Eg f ~w Q ) ' is calculated in an indirect band gap semiconductor QW system in zero magnetic field [20]. The exponent s in TPA [20] is found to be different from that in OPA [IS] and dimensionality dependent.…”

“…Recently, the spectral dependence of the TPA coefficient on (2hw -Eg f ~w Q ) ' is calculated in an indirect band gap semiconductor QW system in zero magnetic field [20]. The exponent s in TPA [20] is found to be different from that in OPA [IS] and dimensionality dependent. Moreover, TPA in these QWs is also found to be polarization dependent.…”

One- and two-photon indirect injection of carriers and spins in silicon

“…This approach has been successfully used to describe spin relaxation processes 42 and photoluminescence 13 in bulk silicon. According to investigations on one-15 and two-photon 43,44 indirect gap absorption within the parabolic band approximation, the neglect of the excitonic effects does not change the lineshape at energies more than a few binding energies above the band gap, and we neglect them here. However, since first principle studies of one-photon direct-gap absorption 45 show that the electron-hole interaction plays an important role even for higher photon energies, further work is in order to investigate its role in indirect gap absorption.…”

Two-photon indirect optical injection and two-color coherent control in bulk silicon

“…For two-photon indirect optical carrier injection in bulk silicon, most experimental studies have focused on the two-photon absorption coefficient [29][30][31][32][33][34] and its anisotropy, 33 which is important in optoelectronics de-vices; theoretical studies [35][36][37][38] are mostly based on the parabolic band approximation and on a phenomenological electron-phonon interaction. For the current injection by coherent control, Costa et al 27 and Spasenović et al 28 used THz radiation to detect "1+2" injected current in bulk silicon, and confirmed that the current can be controlled by the phase parameter of the laser beams.…”

“…First principle studies 41 of the direct gap optical absorption shows that the excitonic effect can strongly change the lineshape even for high photon energies in silicon. For indirect one-42 and two-photon injection, 37,38 investigations within the parabolic band approximation show that this neglect does not change the absorption lineshapes at energies more than a few binding energies above the band gap; however, a full band structure investigation is still lacking due to difficulty in numerical calculation of the wave functions of the electron-hole pair. In this paper, as a preliminary calculation, we neglect the excitonic effect.…”