Light-Hole Gate-Defined Spin-Orbit Qubit

The selective confinement of light-holes (LHs) is demonstrated by introducing a low-dimensional system consisting of highly tensile-strained Ge quantum well enabling the design of an ultrafast gate-defined spin qubit under the electric dipole spin resonance. The qubit size-dependent $g$-factor and dipole moment are mapped, and the parameters inducing their modulation are discussed. It is found that the LH qubit dipole moment is 2 to 3 orders of magnitude higher than that of the canonical heavy-hole qubit. This behavior originates from the significant spin splitting resulting from the combined action of large cubic and linear Rashba spin-orbit interactions that are peculiar to LHs. The qubit relaxation rate is also affected by the strong spin-orbit interaction and follows typically a $B^7$ behavior. The proposed all-group IV, direct bandgap LH qubit provides an effective platform for a scalable qubit-optical photon interface sought-after for long-range entanglement distribution and quantum networks

Mid-infrared emission and absorption in strained and relaxed direct bandgap GeSn semiconductors

By independently engineering strain and composition, this work demonstrates and investigates direct band gap emission in the mid-infrared range from GeSn layers grown on silicon. We extend the room-temperature emission wavelength above ~4.0 {\mu}m upon post-growth strain relaxation in layers with uniform Sn content of 17 at.%. The fundamental mechanisms governing the optical emission are discussed based on temperature-dependent photoluminescence, absorption measurements, and theoretical simulations. Regardless of strain and composition, these analyses confirm that single-peak emission is always observed in the probed temperature range of 4-300 K, ruling out defect- and impurity-related emission. Moreover, carrier losses into thermally-activated non-radiative recombination channels are found to be greatly minimized as a result of strain relaxation. Absorption measurements validate the direct band gap absorption in strained and relaxed samples at energies closely matching photoluminescence data. These results highlight the strong potential of GeSn semiconductors as versatile building blocks for scalable, compact, and silicon-compatible mid-infrared photonics and quantum opto-electronics

On the moments of the aggregate discounted claims with a general dependence

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Évaluation et allocation du risque dans le cadre de modèles avancés en actuariat

Dans cette thèse, on s’intéresse à l’évaluation et l’allocation du risque dans le cadre de modèles avancés en actuariat. Dans le premier chapitre, on présente le contexte général de la thèse et on introduit les différents outils et modèles utilisés dans les autres chapitres. Dans le deuxième chapitre, on s’intéresse à un portefeuille d’assurance dont les composantes sont dépendantes. Ces composantes sont distribuées selon une loi mélange d’Erlang multivariée définie à l’aide de la copule Farlie-Gumbel-Morgenstern (FGM). On évalue le risque global de ce portefeuille ainsi que l’allocation du capital. En utilisant certaines propriétés de la copule FGM et la famille de distributions mélange d’Erlang, on obtient des formules explicites de la covariance entre les risques et de la Tail-Value-at-Risk du risque global. On détermine aussi la contribution de chacun des risques au risque global à l’aide de la régle d’allocation de capital basée sur la Tail-Value-at-Risk et celle basée sur la covariance. Dans le troisième chapitre, on évalue le risque pour un portefeuille sur plusieurs périodes en utilisant le modèle de Sparre Andersen. Pour cette fin, on étudie la distribution de la somme escomptée des ladder heights sur un horizon de temps fini ou infini. En particulier, on trouve une expression ferme des moments de cette distribution dans le cas du modèle classique Poisson-composé et le modèle de Sparre Andersen avec des montants de sinistres distribués selon une loi exponentielle. L’élaboration d’une expression exacte de ces moments nous permet d’approximer la distribution de la somme escomptée des ladder heights par une distribution mélange d’Erlang. Pour établir cette approximation, nous utilisons une méthode basée sur les moments. À l’aide de cette approximation, on calcule les mesures de risque VaR et TVaR associées à la somme escomptée des ladder heights. Dans le quatrième chapitre de cette thèse, on étudie la quantification des risques liés aux investissements. On élabore un modèle d’investissement qui est constitué de quatre modules dans le cas de deux économies : l’économie canadienne et l’économie américaine. On applique ce modèle dans le cadre de la quantification et l’allocation des risques. Pour cette fin, on génère des scénarios en utilisant notre modèle d’investissement puis on détermine une allocation du risque à l’aide de la règle d’allocation TVaR. Cette technique est très flexible ce qui nous permet de donner une quantification à la fois du risque d’investissement, risque d’inflation et le risque du taux de change.In this thesis, we are interested in risk evaluation and risk allocation blems using advanced actuarial models. First, we investigate risk aggregation and capital allocation problems for a portfolio of possibly dependent risks whose multivariate distribution is defined with the Farlie-Gumbel-Morgenstern copula and with mixed Erlang distributions for the marginals. In such a context, we first show that the aggregate claim amount has a mixed Erlang distribution. Based on a top-down approach, closed-form expressions for the contribution of each risk are derived using the TVaR and covariance rules. These findings are illustrated with numerical examples. Then, we propose to investigate the distribution of the discounted sum of ascending ladder heights over finite- or infinite-time intervals within the Sparre Andersen risk model. In particular, the moments of the discounted sum of ascending ladder heights over a finite- and an infinite-time intervals are derived in both the classical compound Poisson risk model and the Sparre Andersen risk model with exponential claims. The application of a particular Gerber-Shiu functional is central to the derivation of these results, as is the mixed Erlang distributional assumption. Finally, we define VaR and TVaR risk measures in terms of the discounted sum of ascending ladder heights. We use a moment-matching method to approximate the distribution of the discounted sum of ascending ladder heights allowing the computation of the VaR and TVaR risk measures. In the last chapter, we present a stochastic investment model (SIM) for international investors. We assume that investors are allowed to hold assets in two different economies. This SIM includes four components: interest rates, stocks, inflation and exchange rate models. First, we give a full description of the model and we detail the parameter estimation. The model is estimated using a state-space formulation and an extended Kalman filter. Based on scenarios generated from this SIM, we study the risk allocation to different background risks: asset, inflation and exchange rate risks. The risk allocation is based on the TVaR-based rule

Mid-Infrared Optical Spin Injection and Coherent Control

The optical injection of charge and spin currents are investigated in Ge$_{1-x}$Sn$_{x}$ semiconductors as a function of Sn content. These emerging silicon-compatible materials enable the modulation of these processes across the entire mid-infrared range. Under the independent particle approximation, the one- and two-photon interband absorption processes are elucidated, and the evolution of the coherent control is discussed for three different polarization configurations. To evaluate the contribution of high-energy transitions, a full-zone 30-band k$\cdot$p is employed in the calculations. It was found that, besides the anticipated narrowing of the direct gap and the associated shift of the absorption to longer wavelengths, incorporating Sn in Ge also increases the one-photon degree of spin polarization (DSP) at the $E_1$ resonance. Moreover, as the Sn content increases, the magnitude of the response tensors near the band edge exhibits an exponential enhancement. This behavior can be attributed to the Sn incorporation-induced decrease in the carrier effective masses. This trend appears to hold also at the $E_1$ resonance for pure spin current injection, at least at low Sn compositions. The two-photon DSP at the band edge exceeds the value in Ge to reach 60 % at a Sn content above 14 %. These results demonstrate that Ge$_{1-x}$Sn$_{x}$ semiconductors can be exploited to achieve the quantum coherent manipulation in the molecular fingerprint region relevant to quantum sensing.Comment: 8 pages, 9 figures, with a Supporting Material fil

Combined Iodine- and Sulfur-based Treatments for an Effective Passivation of GeSn Surface

GeSn alloys are metastable semiconductors that have been proposed as building blocks for silicon-integrated short-wave and mid-wave infrared photonic and sensing platforms. Exploiting these semiconductors requires, however, the control of their epitaxy and their surface chemistry to reduce non-radiative recombination that hinders the efficiency of optoelectronic devices. Herein, we demonstrate that a combined sulfur- and iodine-based treatments yields effective passivation of Ge and Ge0.9Sn0.1 surfaces. X-ray photoemission spectroscopy and in situ spectroscopic ellipsometry measurements were used to investigate the dynamics of surface stability and track the reoxidation mechanisms. Our analysis shows that the largest reduction in oxide after HI treatment, while HF+(NH4)2S results in a lower re-oxidation rate. A combined HI+(NH4)2S treatment preserves the lowest oxide ratio <10 % up to 1 hour of air exposure, while less than half of the initial oxide coverage is reached after 4 hours. These results highlight the potential of S- and I-based treatments in stabilizing the GeSn surface chemistry thus enabling a passivation method that is compatible with materials and device processing

3-D Atomic Mapping of Interfacial Roughness and its Spatial Correlation Length in sub-10 nm Superlattices

The interfacial abruptness and uniformity in heterostructures are critical to control their electronic and optical properties. With this perspective, this work demonstrates the 3-D atomistic-level mapping of the roughness and uniformity of buried epitaxial interfaces in Si/SiGe superlattices with a layer thickness in the 1.5-7.5 nm range. Herein, 3-D atom-by-atom maps were acquired and processed to generate iso-concentration surfaces highlighting local fluctuations in content at each interface. These generated surfaces were subsequently utilized to map the interfacial roughness and its spatial correlation length. The analysis revealed that the root mean squared roughness of the buried interfaces in the investigated superlattices is sensitive to the growth temperature with a value varying from about 0.2 nm (+/- 13%) to about 0.3 nm (+/- 11.5%) in the temperature range of 500-650 Celsius. The estimated horizontal correlation lengths were found to be 8.1 nm (+/- 5.8%) at 650 Celsius and 10.1 nm (+/- 6.2%) at 500 Celsius. Additionally, reducing the growth temperature was found to improve the interfacial abruptness, with 30 % smaller interfacial width is obtained at 500 Celsius. This behavior is attributed to the thermally activated atomic exchange at the surface during the heteroepitaxy. Finally, by testing different optical models with increasing levels of interfacial complexity, it is demonstrated that the observed atomic-level roughening at the interface must be accounted for to accurately describe the optical response of Si/SiGe heterostructures.Comment: 17 A4 pages of main manuscript, 2 table, 5 figures, 20 A4 pages of supplementary informatio

Excitonic Aharonov-Bohm Effect in Isotopically Pure 70Ge/Si Type-II Quantum Dots

We report on a magneto-photoluminescence study of isotopically pure 70Ge/Si self-assembled type-II quantum dots. Oscillatory behaviors attributed to the Aharonov-Bohm effect are simultaneously observed for the emission energy and intensity of excitons subject to an increasing magnetic field. When the magnetic flux penetrates through the ring-like trajectory of an electron moving around each quantum dot, the ground state of an exciton experiences a change in its angular momentum. Our results provide the experimental evidence for the phase coherence of a localized electron wave function in group-IV Ge/Si self-assembled quantum structures.Comment: 4 pages, 4 figure

Decoupling the effects of composition and strain on the vibrational modes of GeSn

We report on the behavior of Ge-Ge, Ge-Sn, Sn-Sn like and disorder-activated vibrational modes in GeSn semiconductors investigated using Raman scattering spectroscopy. By using an excitation wavelength close to E1 gap, all modes are clearly resolved and their evolution as a function of strain and Sn content is established. In order to decouple the individual contribution of content and strain, the analysis was conducted on series of pseudomorphic and relaxed epitaxial layers with a Sn content in the 5-17at.% range. All vibrational modes were found to display the same qualitative behavior as a function of content and strain, viz. a linear downshift as the Sn content increases or the compressive strain relaxes. Simultaneously, Ge-Sn and Ge-Ge peaks broaden, and the latter becomes increasingly asymmetric. This asymmetry, coupled with the peak position, is exploited in an empirical method to accurately quantify the Sn composition and lattice strain from Raman spectra