Shape-independent scaling of excitonic confinement in realistic quantum wires

The scaling of exciton binding energy in semiconductor quantum wires is investigated theoretically through a non-variational, fully three-dimensional approach for a wide set of realistic state-of-the-art structures. We find that in the strong confinement limit the same potential-to-kinetic energy ratio holds for quite different wire cross-sections and compositions. As a consequence, a universal (shape- and composition-independent) parameter can be identified that governs the scaling of the binding energy with size. Previous indications that the shape of the wire cross-section may have important effects on exciton binding are discussed in the light of the present results.Comment: To appear in Phys. Rev. Lett. (12 pages + 2 figures in postscript

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Thermal ionization of excitons in V-shaped quantum wires

The exciton-to-free-carrier transition in GaAs and In_xGa_{1-x}As V-shaped quantum wires is revealed by means of temperature-dependent magnetoluminescence experiments. The experimental results are in excellent agreement with the diamagnetic shift obtained from a solution of the full two-dimensional Schrödinger equation for electrons and holes including magnetic-field and excitonic effects. In the GaAs wires, the exciton-to-free-carrier transition is found to occur at temperature consistent with the exciton binding energies. In the In_xGa_{1-x}As wires the diamagnetic shift of the luminescence is found to be free-carrier-like, independent of temperature, due to the weakening of the exciton binding energy induced by the internal piezoelectric field

Radiometric characterization of type-II InAs/GaSb superlattice (t2sl) midwave infrared photodetectors and focal plane arrays

In recent years, Type-II InAs/GaSb superlattice (T2SL) has emerged as a new material technology suitable for high performance infrared (IR) detectors operating from Near InfraRed (NIR, 2-3μm) to Very Long Wavelength InfraRed (LWIR, λ > 15μm) wavelength domains. To compare their performances with well-established IR technologies such as MCT, InSb or QWIP cooled detectors, specific electrical and radiometric characterizations are needed: dark current, spectral response, quantum efficiency, temporal and spatial noises, stability… In this paper, we first present quantum efficiency measurements performed on T2SL MWIR (3-5μm) photodiodes and on one focal plane array (320x256 pixels with 30μm pitch, realized in the scope of a french collaboration ). Different T2SL structures (InAs-rich versus GaSb-rich) with the same cutoff wavelength (λc= 5μm at 80K) were studied. Results are analysed in term of carrier diffusion length in order to define the optimum thickness and type of doping of the absorbing zone. We then focus on the stability over time of a commercial T2SL FPA (320x256 pixels with 30μm pitch), measuring the commonly used residual fixed pattern noise (RFPN) figure of merit. Results are excellent, with a very stable behaviour over more than 3 weeks, and less than 10 flickering pixels, possibly giving access to long-term stability of IR absolute calibration

Low dimensionality semiconductors: modelling of excitons viavia a fractional-dimensional space

An interaction space with a fractionnal dimension is used to calculate in a simple way the binding energies of excitons confined in quantum wells, superlattices and quantum well wires. A very simple formulation provides this energy versus the non-integer dimensionality of the physical environment of the electron-hole pair. The problem then comes to determining the dimensionality $\alpha$. We show that the latter can be expressed from the characteristics of the microstructure. $\alpha$ continuously varies from 3 (bulk material) to 2 for quantum wells and superlattices, and from 3 to 1 for quantum well wires. Quite a fair agreement is obtained with other theoretical calculations and experimental data, and this model coherently describes both three-dimensional limiting cases for quantum wells ($L_{\rm w}\rightarrow 0$ and $L_{\rm w}\rightarrow \infty$) and the whole range of periods of the superlattice. Such a simple model presents a great interest for spectroscopists though it does not aim to compete with accurate but often tedious variational calculations.Nous utilisons un espace des interactions doté d'une dimension fractionnaire pour calculer simplement l'énergie de liaison des excitons confinés dans les puits quantiques, superréseaux et fils quantiques. Une formulation très simple donne cette énergie en fonction de la dimensionalité non-entière de l'environnement physique de la paire électron-trou. Le problème revient alors à déterminer cette dimensionalité $\alpha$, dont nous montrons qu'une expression peut être déduite des caractéristiques de la microstructure. $\alpha$ varie continûment de 3 (matériau massif) à 2 pour un puits quantique ou un superréseau, et de 3 à 1 pour un fil quantique, selon le confinement du mouvement des porteurs. Les comparaisons avec d'autres calculs théoriques et données expérimentales sont toujours très convenables, et cette théorie décrit d'une façon cohérente les limites tridimensionnelles du puits quantique ($L_{\rm w}\rightarrow 0$ et $L_{\rm w}\rightarrow \infty$) et toute la gamme des périodes du superréseau. Un tel modèle, qui ne vise pas à concurrencer les calculs variationnels très précis mais souvent complexes, présente, de par sa souplesse, un grand intérêt pour les spectroscopistes

New laser and detector structures for mid-infrared

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