Étude de la formation et de l'évolution de nanostructures par méthodes Monte Carlo

Cette thèse, composée de quatre articles scientifiques, porte sur les méthodes numériques atomistiques et leur application à des systèmes semi-conducteurs nanostructurés. Nous introduisons les méthodes accélérées conçues pour traiter les événements activés, faisant un survol des développements du domaine. Suit notre premier article, qui traite en détail de la technique d'activation-relaxation cinétique (ART-cinétique), un algorithme Monte Carlo cinétique hors-réseau autodidacte basé sur la technique de l'activation-relaxation nouveau (ARTn), dont le développement ouvre la voie au traitement exact des interactions élastiques tout en permettant la simulation de matériaux sur des plages de temps pouvant atteindre la seconde. Ce développement algorithmique, combiné à des données expérimentales récentes, ouvre la voie au second article. On y explique le relâchement de chaleur par le silicium cristallin suite à son implantation ionique avec des ions de Si à 3 keV. Grâce à nos simulations par ART-cinétique et l'analyse de données obtenues par nanocalorimétrie, nous montrons que la relaxation est décrite par un nouveau modèle en deux temps: "réinitialiser et relaxer" ("Replenish-and-Relax"). Ce modèle, assez général, peut potentiellement expliquer la relaxation dans d'autres matériaux désordonnés. Par la suite, nous poussons l'analyse plus loin. Le troisième article offre une analyse poussée des mécanismes atomistiques responsables de la relaxation lors du recuit. Nous montrons que les interactions élastiques entre des défauts ponctuels et des petits complexes de défauts contrôlent la relaxation, en net contraste avec la littérature qui postule que des "poches amorphes" jouent ce rôle. Nous étudions aussi certains sous-aspects de la croissance de boîtes quantiques de Ge sur Si (001). En effet, après une courte mise en contexte et une introduction méthodologique supplémentaire, le quatrième article décrit la structure de la couche de mouillage lors du dépôt de Ge sur Si (001) à l'aide d'une implémentation QM/MM du code BigDFT-ART. Nous caractérisons la structure de la reconstruction 2xN de la surface et abaissons le seuil de la température nécessaire pour la diffusion du Ge en sous-couche prédit théoriquement par plus de 100 K.This thesis consists of four scientific articles concerning atomistic numerical methods and their use to simulate semi-conducting systems where nanometer-scale structures play a crucial role. We introduce accelerated methods designed to study systems driven by activated events. Afterwards, our first article presents, in depth, the kinetic Activation-Relaxation Technique (kART), an off-lattice, self-learning kinetic Monte Carlo algorithm based on the Activation-Relaxation Technique nouveau (ARTn). This method permits the exact treatment of elastic effects in materials over time-scales reaching one second. This algorithmic development, combined to recent empirical data, forms the basis of our second article. We explain the origin of heat release by self-implanted crystalline silicon in nanocalorimetry experiments after 3 keV ion bombardment, with the help of kART simulations. We show that the structural relaxation is described by a two-step "Replenish-and-Relax" model. This model is quite general and can potentially explain relaxation in other disordered materials. In the next chapter, i.e. the third article, we push the analysis further and give a complete atomistic description of the mechanisms responsible for structural relaxation during the anneal. We show that punctual defects and small defects complexes control the relaxation, in net contrast with the literature that identify "amorphous pockets" as the drivers of relaxation. Finally, we study some aspects related to the growth of Ge quantum dots on Si (001). After short chapters explaining the scientific context of this work and methodological details, our fourth article concerns the wetting layer formed by Ge deposition on Si (001), using a QM/MM implementation of the bigDFT-ART code. We characterize the 2xN surface reconstruction atomistic structure and decrease the minimum temperature at which deep Ge intermixing is predicted by ab initio calculations by more than 100 K

Understanding long-time vacancy aggregation in iron: a kinetic activation-relaxation technique study

Vacancy diffusion and clustering processes in body-centered-cubic (bcc) Fe are studied using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities. For monovacancies and divacancies, k-ART recovers previously published results while clustering in a 50-vacancy simulation box agrees with experimental estimates. Applying k-ART to the study of clustering pathways for systems containing from one to six vacancies, we find a rich set of diffusion mechanisms. In particular, we show that the path followed to reach a hexavacancy cluster influences greatly the associated mean-square displacement. Aggregation in a 50-vacancy box also shows a notable dispersion in relaxation time associated with effective barriers varying from 0.84 to 1.1 eV depending on the exact pathway selected. We isolate the effects of long-range elastic interactions between defects by comparing to simulations where those effects are deliberately suppressed. This allows us to demonstrate that in bcc Fe, suppressing long-range interactions mainly influences kinetics in the first 0.3 ms, slowing down quick energy release cascades seen more frequently in full simulations, whereas long-term behavior and final state are not significantly affected.Comment: 11 pages, 12 figures. Updated to post-review manuscrip

Strain effect and intermixing at the Si surface: A hybrid quantum and molecular mechanics study

We investigate Ge mixing at the Si(001) surface and characterize the $2\times N$ Si(001) reconstruction by means of hybrid quantum and molecular mechanics calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to correctly take into account long range deformation induced by reconstruted and defective surfaces. We focus in particular on the dimer vacancy line (DVL) and its interaction with Ge adatoms. We first show that calculated formation energies for these defects are highly dependent on the choice of chemical potential and that the latter must be chosen carefully. Characterizing the effect of the DVL on the deformation field, we also find that the DVL favors Ge segregation in the fourth layer close to the DVL. Using the activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex diffusion path permits the substitution of the Ge atom in the fourth layer, with barriers compatible with mixing observed at intermediate temperature.Comment: 11 pages, 7 figures, 3 table

A unified moment tensor potential for silicon, oxygen, and silica

Si and its oxides have been extensively explored in theoretical research due to their technological and industrial importance. Simultaneously describing interatomic interactions within both Si and SiO$_2$ without the use of \textit{ab initio} methods is considered challenging, given the charge transfers involved. Herein, this challenge is overcome by developing a unified machine learning interatomic potentials describing the Si/ SiO$_2$/ O system, based on the moment tensor potential (MTP) framework. This MTP is trained using a comprehensive database generated using density functional theory simulations, encompassing a wide range of crystal structures, point defects, extended defects, and disordered structure. Extensive testing of the MTP is performed, indicating it can describe static and dynamic features of very diverse Si, O, and SiO$_2$ atomic structures with a degree of fidelity approaching that of DF

Diffusion of point defects in crystalline silicon using the kinetic activation-relaxation technique method

We study point-defect diffusion in crystalline silicon using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities based on the activation-relaxation technique (ART nouveau), coupled to the standard Stillinger-Weber potential. We focus more particularly on the evolution of crystalline cells with one to four vacancies and one to four interstitials in order to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics. We show formation energies, activation barriers for the ground state of all eight systems, and migration barriers for those systems that diffuse. Additionally, we characterize diffusion paths and special configurations such as dumbbell complex, di-interstitial (IV-pair+2I) superdiffuser, tetrahedral vacancy complex, and more. This study points to an unsuspected dynamical richness even for this apparently simple system that can only be uncovered by exhaustive and systematic approaches such as the kinetic activation-relaxation technique

Accelerating Training of MLIPs Through Small-Cell Training

While machine-learned interatomic potentials have become a mainstay for modeling materials, designing training sets that lead to robust potentials is challenging. Automated methods, such as active learning and on-the-fly learning, construct reliable training sets, but these processes can be resource-intensive. Current training approaches often use density functional theory (DFT) calculations that have the same cell size as the simulations that the potential is explicitly trained to model. Here, we demonstrate an easy-to-implement small-cell training protocol and use it to model the Zr-H system. This training leads to a potential that accurately predicts known stable Zr-H phases and reproduces the α-β pure zirconium phase transition in molecular dynamics simulations. Compared to traditional active learning, small-cell training decreased the training time of the α-β zirconium phase transition by approximately 20 times. The potential describes the phase transition with a degree of accuracy similar to that of the large-cell training method

Kinetic Activation Relaxation Technique

We present a detailed description of the kinetic Activation-Relaxation Technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe and structural relaxation in a-Si (amorphous silicon).Comment: 13 pages, 11 figures. Final version as published, Figs. 6 and 7 exchanged, minor typographical and stylistic correction

The Activation-Relaxation Technique : ART nouveau and kinetic ART

The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method

Thermodynamics, kinetics, and mechanics of cesium sorption in cement paste: A multiscale assessment

Cesium-137 is a common radioactive byproduct found in nuclear spent fuel. Given its 30 year half life, its interactions with potential storage materials—such as cement paste—is of crucial importance. In this paper, simulations are used to establish the interaction of calcium silicate hydrates (C-S-H)—the main binding phase of cement paste—with Cs at the nano- and mesoscale. Different C-S-H compositions are explored, including a range of Ca/Si ratios from 1.0 to 2.0. These calculations are based on a set of 150 atomistic models, which qualitatively and quantitatively reproduce a number of experimentally measured features of C-S-H—within limits intrinsic to the approximations imposed by classical molecular dynamics and the steps followed when building the models. A procedure where hydrated Ca[superscript 2+] ions are swapped for Cs[superscript 1+] ions shows that Cs adsorption in the C-S-H interlayer is preferred to Cs adsorption at the nanopore surface when Cs concentrations are lower than 0.19 Mol/kg. Interlayer sorption decreases as the Ca/Si ratio increases. The activation relaxation technique nouveau is used to access timescales out of the reach of traditional molecular dynamics (MD). It indicates that characteristic diffusion time for Cs[superscript 1+] in the C-S-H interlayer is on the order of a few hours. Cs uptake in the interlayer has little impact on the elastic response of C-S-H. It leads to swelling of the C-S-H grains, but mesoscale calculations that access length scales out of the range of MD indicate that this leads to practically negligible expansive pressures for Cs concentrations relevant to nuclear waste repositories