We have investigated the band structure of tensile-strained germanium using a 30 band k • p formalism. This multiband formalism allows to simultaneously describe the valence and conduction bands, including the L, ⌬, and ⌫ valleys. We calculate the energy band variation as a function of strain and obtain that the crossover from indirect to direct band gap occurs for a tensile in-plane strain of 1.9%. The effective masses of density of states are deduced from the calculated conduction and valence band density of states. Significant deviations are observed as compared to the effective masses of density of states values of unstrained bulk germanium. We finally calculate the optical gain that can be achieved with tensile-strained bulk germanium. An optical gain larger than 3000 cm −1 is predicted for a carrier density of 1 ϫ 10 18 cm −3 and a 3% in-plane biaxial strain. This optical gain is larger than the one of GaAs calculated with the same formalism and is much larger than the experimental free-carrier absorption losses. This gain should be sufficient to achieve lasing in these structures.

GeSn alloys are the most promising semiconductors for light emitters entirely based on group IV elements. Alloys containing more than 8 at. % Sn have fundamental direct band-gaps, similar to conventional III-V semiconductors and thus can be employed for light emitting devices. Here, we report on GeSn microdisk lasers encapsulated with a SiN x stressor layer to produce tensile strain. A 300 nm GeSn layer with 5.4 at. % Sn, which is an indirect band-gap semiconductor as-grown with a compressive strain of −0.32 %, is transformed via tensile strain engineering into a truly direct band-gap semiconductor. In this approach the low Sn concentration enables improved defect engineering and the tensile strain delivers a low density of states at the valence band edge, which is the light hole band. Continuous wave (cw) as well as pulsed lasing are observed at very low optical pump powers. Lasers with emission wavelength of 2.5 µm have thresholds as low as 0.8 kW cm −2 for ns-pulsed excitation, and 1.1 kW cm −2 under cw excitation. These thresholds are more than two orders of magnitude lower than those previously reported for bulk GeSn lasers, approaching these values obtained for III-V lasers on Si. The present results demonstrate the feasabiliy and are the guideline for monolithically integrated Si-based laser sources on Si photonics platform. arXiv:2001.04927v1 [physics.app-ph] 14 Jan 2020 at an Sn concentration of 8 at. % 3 . The lattice mismatch between Sn-containing alloys and the Ge buffer layer, the typical virtual substrate for their epitaxial growth, generates compressive strain in the grown layer, which counteracts the effect of Sn incorporation, decreasing the directness ∆E L−Γ = E L − E Γ . On the contrary, applying tensile strain will increase the directness. Finding a proper balance between a moderate Sn content to minimize crystal defects and to maintain thermal stability of the GeSn alloy on one hand and making use of tensile strain on the other hand are the keys to bring lasing threshold and operation temperature close to application's requirements. The mainstream research to increase ∆E L−Γ focuses on high Sn content alloys 5, 12 , obtained by epitaxy of thick strain-relaxed GeSn layers. A large directnesss is obtained, leading to higher temperature operation, although at the expense of steadily increasing laser threshold 13 . We have recently theoretically proposed an alternative approach, which is based on two key ingredients: employing moderate Sn content GeSn alloys, and inducing tensile strain in them 14 . This study indicated that, if a given directness is reached via tensile strain rather than by increasing Sn content, the material can provide a higher net gain. The underlying physics originates in the valence band splitting and lifting up of the light hole, LH, band above the heavy hole, HH, band. Its lower density of states (DOS) reduces the carrier density required for transparency, hence reduces the lasing threshold, as will be shown below. GeSn alloys with a moderate Sn content offer a couple of ...

In a recent paper [1] we presented precise lattice QCD results of our European Twisted Mass Collaboration (ETMC). They were obtained by employing two mass-degenerate flavours of twisted mass fermions at maximal twist. In the present paper we give details on our simulations and the computation of physical observables. In particular, we discuss the problem of tuning to maximal twist, the techniques we have used to compute correlators and error estimates. In addition, we provide more information on the algorithm used, the autocorrelation times and scale determination, the evaluation of disconnected contributions and the description of our data by means of chiral perturbation theory formulae.