Stark shift of the absorption spectra in Ge/Ge1−Sn /Ge type-I single QW cell for mid-wavelength infra-red modulators

Abstract

For mid-wavelength infra-red (MWIR) modulation or detection applications, we propose α-Sn rich Ge/Ge 1-x Sn x /Ge a type-I single quantum wells (SQW) partially strain compensated on Ge 1-y Sn y relaxed layers grown onto (001)-oriented Ge substrate. Such elementary cells with W-like potential profiles of conduction and valence bands have been modeled by solving the one-dimensional Schrödinger equation under an applied external electrical field. First, strain effects on electrons, heavy holes (hh) and light holes (lh) energy bands for strained/relaxed Ge 1-x Sn x /Ge 1-y Sn y heterointerfaces are investigated using the modelsolid theory in the whole ranges (0  x, y  1) of Sn compositions. From the obtained band-discontinuities, band gaps and effective masses, Ge 1-y Sn y /Ge/Ge 0.80 Sn 0.20 /Ge/Ge 1-y Sn y cells are computed as a function of the Ge 0.80 Sn 0.20 well width for three compositions of the Ge 1-y Sn y buffer layer (y=0.05, 0.07 and 0.09) in order to get the optimum quantum confinement of electrons and holes levels while keeping a reasonable amount of averaged strain in the cell. The electric field effect on the absorption spectra is given. An absorption coefficient in the 6  to 3  10 3 cm −1 range is reasonably obtained for a SQW at room temperature with a rather large Stark shift of the direct transition between 0.46 and 0.38 eV (i.e., λ=3.26-2.70 μm) at large external fields (50 kV/cm). These characteristics are attractive for the design of MWIR optical modulators.

Theoretical analysis of direct transition in SiGeSn/GeSn strain balanced QWIP

“…The significant absorption for HH to U-CB transition is observed in infrared range of wavelength (3.6 lm). The peak value of absorption coefficient is 8.3 9 10 3 cm -1 which is in good agreement with reported predicted result (Yahyaoui et al 2014(Yahyaoui et al , 2015. It should be mentioned at this juncture that the transition between HH band and L-CB is not considered in this calculation.…”

“…This absorption is expected to have dependency on parameters like well thickness, band discontinuities which again depends on Sn composition in GeSn well, charge density in well etc. Although the modeling for absorption in GeSn based quantum QWIP have already been reported in literature by several researchers (Gassenq et al 2012;Yahyaoui et al 2014Yahyaoui et al , 2015, to the best of authors knowledge, effect of electron-hole Columbic interaction and position dependent carrier charge density in the well (active region) have not yet been considered in the modeling. Device structure for GeSn based QWIP and theoretical model for Sn composition dependent absorption have already been proposed by the authors elsewhere (Das and Pareek 2015).…”

“…Gaussian line shape function is also considered for inhomogeneity in GeSn alloy (D'costa et al 2009). In this case broadening, r is calculated with the help of interband relaxation time of photo excited carriers in QWIP (Yahyaoui et al 2015). P cv is a momentum matrix element between conduction band and valence band for Bloch states (Chuang 1995).…”

Design of a high-speed germanium-tin absorption modulator at mid-infrared wavelengths

“…On the other hand, only a few studies have been made on the realization of GeSn modulators. Theoretical studies have been mostly focusing on the physical modelling of direct absorption via the quantum confined Stark effect [6], [7] or the Franz-Keldysh effect (FKE) [8], rather than a comprehensive device design relying on a proven fabrication flow. We propose a high-speed and low power consumption FKE GeSn modulator design relying on a strain relaxed Ge 0.875 Sn 0.125 layer grown on a Ge virtual substrate (with a residual compressive strain of -0.4%), as already experimentally realized [3], with a room temperature direct bandgap of 440meV (absorption edge at 2.82m).…”