Interfacial Studies in Semiconductor Heterostructures by X-Ray Diffraction Techniques

X-ray radiation is a non-destructive probe well suited to assess structural perfection of semiconductor material. Three techniques are used to study the interfacial roughness, period fluctuations and annealing-induced interdiffusion in various superlattice structures. Reflectivity of long period Si/Si1-xGex multiple quantum wells reveals an asymmetry oriented along the direction of miscut in the interface roughness with the Si1-xGex to Si interfaces being about twice as rough (0.5 versus 0.3 nm) as the Si to Si1-xGex interfaces. For Si-Si0.65Ge0.35 multiple quantum wells, diffuse scattering is minimal for a growth temperature of 550°C and increases substantially at very low (250°C) or high (750°C) growth temperatures. In (SimGen)p short period superlattices, the X-ray reflectivity data are consistent with interfacial mixing over about two monolayers and thickness fluctuations of about 5% vertically in the structures. For superlattices grown on vicinal surfaces, the roughness spectrum is correlated with the surface miscut orientation. Double-crystal X-ray diffraction using symmetrical and asymmetrical reflections has been used to study epitaxial lattice distortion and strain relaxation in InGaAs/GaAs heterostructures grown on (100) on-orientation and 2° off (100) GaAs surfaces. It is shown that thick InGaAs films retain an appreciable fraction of their initial strain and that their crystal lattice is triclinically distorted. The magnitude of the deformation is larger when growth is carried out on a vicinal surface

Measurement of the extent of strain relief in InGaAs layers grown under tensile strain on InP(100) substrates

International audienceHigh resolution x‐ray diffraction has been used to investigate the structural properties of InxGa1−xAs epitaxial layers grown under tension on InP(100) substrates. The nominal indium composition (x=0.42) corresponds to a small lattice mismatch and a two dimensional growth mode. We have also included for comparison two samples grown under compression covering the mostly strained and the mostly relaxed regimes. Our results show that the residual strain and the asymmetry in strain relaxation along 〈011〉 directions are always larger for layers under tension. This can be explained by the difference in dislocation glide velocity induced by a different indium content, by the dissociation of perfect dislocations and partially by the difference in thermal expansion coefficients between substrate and epilayer. The larger asymmetry in strain relaxation for tensile strain layers is interpreted by the existence of microcracks aligned in the [011] direction

Alloying effects on the critical layer thickness in InxGa1−xAs/InP heterostructures analyzed by Raman scattering

International audienceRaman scattering has been used to estimate the critical layer thickness and to analyze the alloying effect on strain relaxation in InxGa1−xAs layers grown by molecular beam epitaxy on InP [001]-oriented substrate, for x ranging from 0.0 to 1.0. Measurements of longitudinal optical GaAs-like phonon frequency and Raman linewidth showed that the indium/gallium ratio contents greatly influences the strain relaxation. A comparison between Raman and x-ray diffraction measurements of relaxation ratios as a function of layer thickness is presented. The results can be explained in terms of the combined effect of strain and chemical and structural disorder

A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266

We report the discovery and characterisation of a super-Earth and a sub-Neptune transiting the bright ($K=8.8$), quiet, and nearby (37 pc) M3V dwarf TOI-1266. We validate the planetary nature of TOI-1266 b and c using four sectors of TESS photometry and data from the newly-commissioned 1-m SAINT-EX telescope located in San Pedro M\'artir (Mexico). We also include additional ground-based follow-up photometry as well as high-resolution spectroscopy and high-angular imaging observations. The inner, larger planet has a radius of $R=2.37_{-0.12}^{+0.16}$ R$_{\oplus}$ and an orbital period of 10.9 days. The outer, smaller planet has a radius of $R=1.56_{-0.13}^{+0.15}$ R$_{\oplus}$ on an 18.8-day orbit. The data are found to be consistent with circular, co-planar and stable orbits that are weakly influenced by the 2:1 mean motion resonance. Our TTV analysis of the combined dataset enables model-independent constraints on the masses and eccentricities of the planets. We find planetary masses of $M_\mathrm{p}$ = $13.5_{-9.0}^{+11.0}$ $\mathrm{M_{\oplus}}$ ($<36.8$ $\mathrm{M_{\oplus}}$ at 2-$\sigma$) for TOI-1266 b and $2.2_{-1.5}^{+2.0}$ $\mathrm{M_{\oplus}}$ ($<5.7$ $\mathrm{M_{\oplus}}$ at 2-$\sigma$) for TOI-1266 c. We find small but non-zero orbital eccentricities of $0.09_{-0.05}^{+0.06}$ ($<0.21$ at 2-$\sigma$) for TOI-1266 b and $0.04\pm0.03$ ($<0.10$ at 2-$\sigma$) for TOI-1266 c. The equilibrium temperatures of both planets are of $413\pm20$ K and $344\pm16$ K, respectively, assuming a null Bond albedo and uniform heat redistribution from the day-side to the night-side hemisphere. The host brightness and negligible activity combined with the planetary system architecture and favourable planet-to-star radii ratios makes TOI-1266 an exquisite system for a detailed characterisation

A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266

We report the discovery and characterisation of a super-Earth and a sub-Neptune transiting the bright (K = 8.8), quiet, and nearby (37 pc) M3V dwarf TOI-1266. We validate the planetary nature of TOI-1266 b and c using four sectors of TESS photometry and data from the newly-commissioned 1-m SAINT-EX telescope located in San Pedro Mártir (México). We also include additional ground-based follow-up photometry as well as high-resolution spectroscopy and high-angular imaging observations. The inner, larger planet has a radius of R = 2.37_(−0.12)^(+0.16) R_⊕ and an orbital period of 10.9 days. The outer, smaller planet has a radius of R = 1.56_(−0.13)^(+0.15) R_⊕ on an 18.8-day orbit. The data are found to be consistent with circular, co-planar and stable orbits that are weakly influenced by the 2:1 mean motion resonance. Our TTV analysis of the combined dataset enables model-independent constraints on the masses and eccentricities of the planets. We find planetary masses of M_p = 13.5_(−9.0)^(+11.0) M_⊕ (<36.8 M_⊕ at 2-σ) for TOI-1266 b and 2.2_(−1.5)^(+2.0) M_⊕ (<5.7 M_⊕ at 2-σ) for TOI-1266 c. We find small but non-zero orbital eccentricities of 0.09_(−0.05)^(+0.06) (<0.21 at 2-σ) for TOI-1266 b and 0.04 ± 0.03 (< 0.10 at 2-σ) for TOI-1266 c. The equilibrium temperatures of both planets are of 413 ± 20 and 344 ± 16 K, respectively, assuming a null Bond albedo and uniform heat redistribution from the day-side to the night-side hemisphere. The host brightness and negligible activity combined with the planetary system architecture and favourable planet-to-star radii ratios makes TOI-1266 an exquisite system for a detailed characterisation

BOLZANO VERSUS KANT: MATHEMATICS AS A SCIENTIA UNIVERSALIS

Abstract. The paper will discuss some changes in Bolzano’s definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano’s works will be distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes will be interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence ot the overcome of Kant’s terminology, and of the radicalization of Bolzano’s anti-Kantianism. It will be argued that Bolzano’s evolution can be understood as a coherent move, if one compares the criticism expressed in the Beyträge on the notion of quantity with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is based on the discovery that two unknown texts mentioned by Bolzano can be identified with works by von Spaun and Vieth respectively. Bolzano’s evolution will be interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano’s unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, it will be argued that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and it will be suggested that the question of ideal elements in mathematics, which has been interpreted as a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. 1