Evolution of optical constants and electronic structure of disordered Si_1-xGe_xalloys

Abstract

The energy shifts of optical interband transition edges, E'0, E1, E1+Δ1 and E2, of relaxed Si1-xGex alloys grown epitaxially on Si(001) substrates by molecular beam epitaxy have been studied as a function of Ge composition using their complex dielectric functions measured by spectroscopic ellipsometry at room temperature. The interband transition edges were resolved by a line shape fitting on the numerical second derivative spectra of the dielectric functions. The E'0, E1, E1+Δ1 and E2(Σ) edges are found to shift to lower energies with increasing Ge composition while the E2(X) edge shifts to higher energies. Also it is found for E1 and E1+Δ1 energies that downward bowing exists and for Δ1 energy that upward bowing exists. These behaviours of the transition edges are understood by comparing the band structure of Si with that of Ge and interpreted as due to the effect of the random potential originated by alloying disorder.

Electronic band-edge structure, effective masses, and optical absorption of Si1-xGe x using an extended FPLAPW/VCA/LDA+U computational method

“…Our calculations also show that the Si energy band gap along the ΓL-line is fairly constant in k-space, which should result in strong absorption at this energy. In our earlier LDA calculations [17], we did not obtain any sharp absorption peak, even if one can see a small tendency to a broad peak for Ge rich alloys associated with transitions along the ΓL-line, and excitation effects was discussed since Bahng et al [16] assumed excitonic line shape for fitting this sharp low-energy absorption peak. Still with the FPLAPW/LDA+U SIC approach these peaks are not as pronounced as in the ellipsometry spectra, however, the present FPLAPW/LDA+U SIC approach show much stronger absorption peaks in accordance with the measurements.…”

“…2(a), we show the spectroscopic ellipsometry measurement of the imaginary part ε 2 (ω) the dielectric function performed by Bahng et al [16]. The calculated LDA+U SIC dielectric function is shown in Fig.…”

“…16, depends strongly on composition. This peak was interpreted as interband transitions along the ΓL-line.…”

Electronic and Optical Properties of SiGe alloys within first-principles schemes

“…2 for Si(50%) Ge(50%) show a relatively good comparison between DFT-LDA-RPA and GW-BSE data, aside from the first peak region below 3eV. In comparison with experiments [18], at the optical onset the GW-BSE curve shows good agreement with data obtained at x = 0.4, 0.6 concentrations, while the DFT-LDA-RPA curve suffers of evident mismatch [1]. This point suggests the need of correct inclusion of high-order effects in the Si-Ge alloys optical functions to correctly reproduce their behaviors in the whole energy range.…”

Micro-combinatorial sampling of the optical properties of hydrogenated amorphous $$\hbox {Si}_{1-x}\,\hbox {Ge}_{{x}}$$ for the entire range of compositions towards a database for optoelectronics

“…In terms of the Si and Ge concentration ratio, besides reports dealing with the concentration dependent properties of c-Si 1−x Ge x 25,30,43,69 , there are also numerous studies that focus on amorphous compounds 40,50,[66][67][68][69][70][71][72][73][74] . Comprehensive parameterizations for both the photon energies and compositions were presented for crystalline materials, in many cases supported by density of states calculations 75 , also pointing out the Vegard's lawlike behavior 69 . In this study we further strictly focus on the amorphous cases.…”