Photoluminescence, recombination rate, and gain spectra in optically excited n-type and tensile strained germanium layers

Abstract

We theoretically investigate the optical properties of photo-excited biaxially strained intrinsic and n-type doped Ge semi-infinite layers using a multi-valley effective mass model. Spatial inhomogeneity of the excess carrier density generated near the sample surface is considered. Strain effects on the band edges, on the band dispersions, and on the orbital compositions of the near gap states involved in radiative recombinations are fully taken into account. We obtain, as a function of the distance from the sample surface, the energy resolved absorption/gain spectra resulting from the contribution of the radiative direct and phonon-assisted band-to-band transitions and from the intra-band free carrier absorption. Photoluminescence spectra are calculated from the spatially dependent spontaneous radiative recombination rate, taking into account energy-dependent selfabsorption effects. For suitable combinations of doping density, strain magnitude, pump power, and emitted photon polarization, we find gain values up to 5800 cm-1

Carrier lifetime assessment in integrated Ge waveguide devices

“…From this fitting, we estimate the extracted recombination velocity for the Ge/Si interface to be less than 2×10 4 cm/s and the recombination velocity for the Ge/SiO 2 to be the range 1-5×10 3 cm/s. The recombination velocities for Ge/Si interface are in good agreement with those reported in [7,9]. The contribution to carrier recombination at Ge/SiO 2 sidewall layers can be suppressed in future devices by using better passivation coatings.…”

Group IV Direct Band Gap Photonics: Methods, Challenges, and Opportunities

“…Due to the fact that the Γ-valley energy reduces faster than the one of the L-valley, Ge transforms into a direct band gap semiconductor at ~4.7% uniaxial strain along [100] when the direct transition (black line) decreases below the energy of the indirect recombination (green line). For Ge under biaxial tensile strain or GeSn alloys, the band edges behave similarly with an indirect-to-direct band gap crossover at ~1.6-2.0% strain (El Kurdi et al, 2010;Virgilio et al, 2013;Wen and Bellotti, 2015) or and at a Sn-content of ~9% (Low et al, 2012;Gupta et al, 2013b;Wirths et al, 2015) for a fully relaxed layer.…”

“…The gain was calculated via Fermi's golden rule, assuming cylindrical symmetry for the valence bands to simplify the calculation of the joint density of states (JDOS), c.f. Virgilio et al (2013). More details of the calculation can be found in Süess et al (2013), supplementary information.…”

“…The energetic order of the heavy and light hole bands is reverted when moving from the uniaxial to the biaxial case. Most of the theoretical work concerning Ge light emission utilizes k·p theory including 6 bands (Aldaghri et al, 2012;Chang and Cheng, 2013;Virgilio et al, 2013), 8 bands (Zhu et al, 2010;Wirths et al, 2013b), or 30 bands (El Kurdi et al, 2010). The latter is not restricted to the Brillouin-zone center but describes the full energy dispersion.…”

Direct and indirect band gaps in Ge under biaxial tensile strain investigated by photoluminescence and photoreflectance studies

“…Bright emission can be explained via the compounding effects of strain-dependent gain enhancement, prohibitively large energy separations between the L and conduction band minima, and momentum contribution to the indirect L-valley light holes (lh) recombination path from exciton-generated longitudinal acoustic (LA) phonons [39]. In the former case, several theoretical [54][55][56] As/GaAs (sample C) under ε = 0.95% biaxial tensile strain depending on temperature; (b) experimental (circles) and calculated (triangles) peak energy (black line) and normalized integrated intensity (red line) versus temperature. [57,58] studies have demonstrated the effects of increasing tensile strain and doping concentrations on optical gain (or absorption) in Ge films.…”