Accurate generation of stochastic dynamics based on multi-model generative adversarial networks.

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques.

Stress-Induced Acceleration and Ordering in Solid-State Dewetting.

We report on the influence of elastic strain on solid-state dewetting. Using continuum modeling, we first study the consequences of elastic stress on the pinching of the film away from the triple line during dewetting. We find that elastic stress in the solid film decreases both the time and the distance at which the film pinches in such a way that the dewetting front is accelerated. In addition, the spatial organization of islands emerging from the dewetting process is affected by strain. As an example, we demonstrate that ordered arrays of quantum dots can be achieved from solid-state dewetting of a square island in the presence of elastic stress.

A self-ordered, body-centered tetragonal superlattice of SiGe nanodot growth by reduced pressure CVD.

Self-ordered three-dimensional body-centered tetragonal (BCT) SiGe nanodot structures are fabricated by depositing SiGe/Si superlattice layer stacks using reduced pressure chemical vapor deposition. For high enough Ge content in the island (>30%) and deposition temperature of the Si spacer layers (T > 700 °C), we observe the formation of an ordered array with islands arranged in staggered position in adjacent layers. The in plane periodicity of the islands can be selected by a suitable choice of the annealing temperature before the Si spacer layer growth and of the SiGe dot volume, while only a weak influence of the Ge concentration is observed. Phase-field simulations are used to clarify the driving force determining the observed BCT ordering, shedding light on the competition between heteroepitaxial strain and surface-energy minimization in the presence of a non-negligible surface roughness.

InAs/GaAs Sharply Defined Axial Heterostructures in Self-Assisted Nanowires.

We present the fabrication of axial InAs/GaAs nanowire heterostructures on silicon with atomically sharp interfaces by molecular beam epitaxy. Our method exploits the crystallization at low temperature, by As supply, of In droplets deposited on the top of GaAs NWs grown by the self-assisted (self-catalyzed) mode. Extensive characterization based on transmission electron microscopy sets an upper limit for the InAs/GaAs interface thickness within few bilayers (≤1.5 nm). A detailed study of elastic/plastic strain relaxation at the interface is also presented, highlighting the role of nanowire lateral free surfaces.

Machine learning potential for interacting dislocations in the presence of free surfaces.

Computing the total energy of a system of N interacting dislocations in the presence of arbitrary free surfaces is a difficult task, requiring Finite Element (FE) numerical calculations. Worst, high accuracy requires very fine meshes in the proximity of each dislocation core. Here we show that FE calculations can be conveniently replaced by a Machine Learning (ML) approach. After formulating the elastic problem in terms of one and two-body terms only, we use Sobolev training to obtain consistent information on both energy and forces, fitted using a feed-forward neural network (NN) architecture. As an example, we apply the proposed methodology to corrugated, heteroepitaxial semiconductor films, searching for the minimum-energy dislocation distributions by using Monte Carlo. Importantly, the presence of an interaction cutoff allows for the application of the method to systems of different sizes without the need to repeat training. Millions of energy evaluations are performed, a task which would have been impossible by brute-force FE calculations. Finally, we show how forces can be exploited in running 2D ML-based dislocation dynamics simulations.

Atomic-scale insights on the formation of ordered arrays of edge dislocations in Ge/Si(001) films via molecular dynamics simulations.

Heteroepitaxial films of Ge on Si(001) are receiving wide attention due to several possible applications in micro- and opto-electronics. Understanding the dynamic behavior of linear defects, such as dislocations, is key. They are unavoidably present in such systems due to the lattice mismatch between the two materials, and can directly influence devices performances. It has been experimentally demonstrated more than fifteen years ago that a suitable choice of the growth parameters allows for the formation of a nicely ordered net of [Formula: see text] dislocations at the Ge/Si interface, improving the overall film quality and strain relaxation uniformity. Atomic-scale details on the set of mechanisms leading to such an outcome are however still missing. Here we present a set of classical molecular dynamics simulations shedding light on the full set of microscopic processes driving to the experimentally observed array of linear defects. This includes simple gliding of [Formula: see text] dislocations and vacancy-promoted climbing and gliding. The importance of the particular experimental conditions, involving a low-temperature stage followed by an increase in temperature, is highlighted.

Strained MOSFETs on ordered SiGe dots.

The potential of strained DOTFET technology is demonstrated. This technology uses a SiGe island as a stressor for a Si capping layer, into which the transistor channel is integrated. The structure information of fabricated samples is extracted from atomic force microscopy (AFM) measurements. Strain on the upper surface of a 30 nm thick Si layer is in the range of 0.7%, as supported by finite element calculations. The Ge content in the SiGe island is 30% on average, showing an increase towards the top of the island. Based on the extracted structure information, three-dimensional strain profiles are calculated and device simulations are performed. Up to 15% enhancement of the NMOS saturation current is predicted.

Faceting of Si and Ge crystals grown on deeply patterned Si substrates in the kinetic regime: phase-field modelling and experiments.

The development of three-dimensional architectures in semiconductor technology is paving the way to new device concepts for various applications, from quantum computing to single photon avalanche detectors. In most cases, such structures are achievable only under far-from-equilibrium growth conditions. Controlling the shape and morphology of the growing structures, to meet the strict requirements for an application, is far more complex than in close-to-equilibrium cases. The development of predictive simulation tools can be essential to guide the experiments. A versatile phase-field model for kinetic crystal growth is presented and applied to the prototypical case of Ge/Si vertical microcrystals grown on deeply patterned Si substrates. These structures, under development for innovative optoelectronic applications, are characterized by a complex three-dimensional set of facets essentially driven by facet competition. First, the parameters describing the kinetics on the surface of Si and Ge are fitted on a small set of experimental results. To this goal, Si vertical microcrystals have been grown, while for Ge the fitting parameters have been obtained from data from the literature. Once calibrated, the predictive capabilities of the model are demonstrated and exploited for investigating new pattern geometries and crystal morphologies, offering a guideline for the design of new 3D heterostructures. The reported methodology is intended to be a general approach for investigating faceted growth under far-from-equilibrium conditions.

Prismatic Ge-rich inclusions in the hexagonal SiGe shell of GaP-Si-SiGe nanowires by controlled faceting.

Formation of Ge-rich prismatic inclusions in the hexagonal SiGe shell of GaP-Si-SiGe nanowires is reported and discussed in relation to a growth model that explains their origin. An accurate TEM/EDX analysis shows that such prisms develop right on top of any {112[combining macron]0} facet present on the inner GaP-Si surface, with the base matching the whole facet extension, as large as tens of nanometers, and extending within the SiGe shell up to a thickness of comparable size. An enrichment in Ge by around 5% is recognized within such regions. A phase-field growth model, tackling both the morphological and compositional evolution of the SiGe shell during growth, is exploited to assess the mechanism behind the prism formation. A kinetic segregation process, stemming from the difference in surface mobility between Ge (faster) and Si (slower), is shown to take place, in combination with the evolution of the SiGe shell morphology. Actually, the latter moves from the one templated by the underlying GaP-Si core, including both {101[combining macron]0} and {112[combining macron]0} facets, to the more energetically convenient hexagon, bounded by {101[combining macron]0} facets only. Simulations are shown to accurately reproduce the experimental observations for both regular and asymmetric nanowires. It is then discussed how a careful control of the GaP core faceting, as well as a proper modulation of the shell growth rate, allows for direct control of the appearance and size of the Ge-rich prisms. This tunability paves the way for a possible exploitation of these lower-gap regions for advanced designs of band-gap-engineering.

Reentrant Behavior of the Density vs. Temperature of Indium Islands on GaAs(111)A.

We show that the density of indium islands on GaAs(111)A substrates have a non-monotonic, reentrant behavior as a function of the indium deposition temperature. The expected increase in the density with decreasing temperature, indeed, is observed only down to 160 ∘C, where the indium islands undertake the expected liquid-to-solid phase transition. Further decreasing the temperature causes a sizable reduction of the island density. An additional reentrant increasing behavior is observed below 80 ∘C. We attribute the above complex behavior to the liquid-solid phase transition and to the complex island-island interaction which takes place between crystalline islands in the presence of strain. Indium solid islands grown at temperatures below 160 ∘C have a face-centered cubic crystal structure.

Self-Assembly of Nanovoids in Si Microcrystals Epitaxially Grown on Deeply Patterned Substrates.

We present an experimental and theoretical analysis of the formation of nanovoids within Si microcrystals epitaxially grown on Si patterned substrates. The growth conditions leading to the nucleation of nanovoids have been highlighted, and the roles played by the deposition rate, substrate temperature, and substrate pattern geometry are identified. By combining various scanning and transmission electron microscopy techniques, it has been possible to link the appearance pits of a few hundred nanometer width at the microcrystal surface with the formation of nanovoids within the crystal volume. A phase-field model, including surface diffusion and the flux of incoming material with shadowing effects, reproduces the qualitative features of the nanovoid formation thereby opening new perspectives for the bottom-up fabrication of 3D semiconductors microstructures.

Kinetic Control of Morphology and Composition in Ge/GeSn Core/Shell Nanowires.

The growth of Sn-rich group-IV semiconductors at the nanoscale can enrich the understanding of the fundamental properties of metastable GeSn alloys. Here, we demonstrate the effect of the growth conditions on the morphology and composition of Ge/GeSn core/shell nanowires by correlating the experimental observations with a theoretical interpretation based on a multiscale approach. We show that the cross-sectional morphology of Ge/GeSn core/shell nanowires changes from hexagonal to dodecagonal upon increasing the supply of the Sn precursor. This transformation strongly influences the Sn distribution as a higher Sn content is measured under the {112} growth front. Ab initio DFT calculations provide an atomic-scale explanation by showing that Sn incorporation is favored at the {112} surfaces, where the Ge bonds are tensile-strained. A phase-field continuum model was developed to reproduce the morphological transformation and the Sn distribution within the wire, shedding light on the complex growth mechanism and unveiling the relation between segregation and faceting. The tunability of the photoluminescence emission with the change in composition and morphology of the GeSn shell highlights the potential of the core/shell nanowire system for optoelectronic devices operating at mid-infrared wavelengths.

Structure and Stability of Partial Dislocation Complexes in 3C-SiC by Molecular Dynamics Simulations.

In this work, the structure and stability of partial dislocation (PD) complexes terminating double and triple stacking faults in 3C-SiC are studied by molecular dynamics simulations. The stability of PD complexes is demonstrated to depend primarily on the mutual orientations of the Burgers vectors of constituent partial dislocations. The existence of stable complexes consisting of two and three partial dislocations is established. In particular, two types of stable double (or extrinsic) dislocation complexes are revealed formed by two 30° partial dislocations with different orientations of Burgers vectors, or 30° and 90° partial dislocations. Stable triple PD complexes consist of two 30° partial dislocations with different orientations of their Burgers vectors and one 90° partial dislocation, and have a total Burgers vector that is equal to zero. Results of the simulations agree with experimental observations of the stable PD complexes forming incoherent boundaries of twin regions and polytype inclusions in 3C-SiC films.

Growth and Coalescence of 3C-SiC on Si(111) Micro-Pillars by a Phase-Field Approach.

3C-SiC is a promising material for low-voltage power electronic devices but its growth is still challenging. Heteroepitaxy of 3C-SiC on Si micrometer-sized pillars is regarded as a viable method to achieve high crystalline quality, minimizing the effects of lattice and thermal expansion mismatch. Three-dimensional micro-crystals with sharply-faceted profiles are obtained, eventually touching with each other to form a continuous layer, suspended on the underlying pillars. By comparing experimental data and simulation results obtained by a phase-field growth model, here we demonstrate that the evolution of the crystal morphology occurs in a kinetic regime, dominated by the different incorporation times on the crystal facets. These microscopic parameters, effective to characterize the out-of-equilibrium growth process, are estimated by a best-fitting procedure, matching simulation profiles to the experimental one at different deposition stages. Then, simulations are exploited to inspect the role of a different pillar geometry and template effects are recognized. Finally, coalescence of closely spaced crystals ordered into an hexagonal array is investigated. Two possible alignments of the pattern are compared and the most convenient arrangement is evaluated.

Morphological Evolution of Pit-Patterned Si(001) Substrates Driven by Surface-Energy Reduction.

Lateral ordering of heteroepitaxial islands can be conveniently achieved by suitable pit-patterning of the substrate prior to deposition. Controlling shape, orientation, and size of the pits is not trivial as, being metastable, they can significantly evolve during deposition/annealing. In this paper, we exploit a continuum model to explore the typical metastable pit morphologies that can be expected on Si(001), depending on the initial depth/shape. Evolution is predicted using a surface-diffusion model, formulated in a phase-field framework, and tackling surface-energy anisotropy. Results are shown to nicely reproduce typical metastable shapes reported in the literature. Moreover, long time scale evolutions of pit profiles with different depths are found to follow a similar kinetic pathway. The model is also exploited to treat the case of heteroepitaxial growth involving two materials characterized by different facets in their equilibrium Wulff's shape. This can lead to significant changes in morphologies, such as a rotation of the pit during deposition as evidenced in Ge/Si experiments.

Reduced-Pressure Chemical Vapor Deposition Growth of Isolated Ge Crystals and Suspended Layers on Micrometric Si Pillars.

In this work, we demonstrate the growth of Ge crystals and suspended continuous layers on Si(001) substrates deeply patterned in high aspect-ratio pillars. The material deposition was carried out in a commercial reduced-pressure chemical vapor deposition reactor, thus extending the "vertical-heteroepitaxy" technique developed by using the peculiar low-energy plasma-enhanced chemical vapor deposition reactor, to widely available epitaxial tools. The growth process was thoroughly analyzed, from the formation of small initial seeds to the final coalescence into a continuous suspended layer, by means of scanning and transmission electron microscopy, X-ray diffraction, and µ-Raman spectroscopy. The preoxidation of the Si pillar sidewalls and the addition of hydrochloric gas in the reactants proved to be key to achieve highly selective Ge growth on the pillars top only, which, in turn, is needed to promote the formation of a continuous Ge layer. Thanks to continuum growth models, we were able to single out the different roles played by thermodynamics and kinetics in the deposition dynamics. We believe that our findings will open the way to the low-cost realization of tens of micrometers thick heteroepitaxial layer (e.g., Ge, SiC, and GaAs) on Si having high crystal quality.

Highly Mismatched, Dislocation-Free SiGe/Si Heterostructures.

Defect-free mismatched heterostructures on Si substrates are produced by an innovative strategy. The strain relaxation is engineered to occur elastically rather than plastically by combining suitable substrate patterning and vertical crystal growth with compositional grading. Its validity is proven both experimentally and theoretically for the pivotal case of SiGe/Si(001).

Photodetection in Hybrid Single-Layer Graphene/Fully Coherent Germanium Island Nanostructures Selectively Grown on Silicon Nanotip Patterns.

Dislocation networks are one of the most principle sources deteriorating the performances of devices based on lattice-mismatched heteroepitaxial systems. We demonstrate here a technique enabling fully coherent germanium (Ge) islands selectively grown on nanotip-patterned Si(001) substrates. The silicon (Si)-tip-patterned substrate, fabricated by complementary metal oxide semiconductor compatible nanotechnology, features ∼50-nm-wide Si areas emerging from a SiO2 matrix and arranged in an ordered lattice. Molecular beam epitaxy growths result in Ge nanoislands with high selectivity and having homogeneous shape and size. The ∼850 °C growth temperature required for ensuring selective growth has been shown to lead to the formation of Ge islands of high crystalline quality without extensive Si intermixing (with 91 atom % Ge). Nanotip-patterned wafers result in geometric, kinetic-diffusion-barrier intermixing hindrance, confining the major intermixing to the pedestal region of Ge islands, where kinetic diffusion barriers are, however, high. Theoretical calculations suggest that the thin Si/Ge layer at the interface plays, nevertheless, a significant role in realizing our fully coherent Ge nanoislands free from extended defects especially dislocations. Single-layer graphene/Ge/Si-tip Schottky junctions were fabricated, and thanks to the absence of extended defects in Ge islands, they demonstrate high-performance photodetection characteristics with responsivity of ∼45 mA W(-1) and an Ion/Ioff ratio of ∼10(3).

Engineered Coalescence by Annealing 3D Ge Microstructures into High-Quality Suspended Layers on Si.

The move from dimensional to functional scaling in microelectronics has led to renewed interest toward integration of Ge on Si. In this work, simulation-driven experiments leading to high-quality suspended Ge films on Si pillars are reported. Starting from an array of micrometric Ge crystals, the film is obtained by exploiting their temperature-driven coalescence across nanometric gaps. The merging process is simulated by means of a suitable surface-diffusion model within a phase-field approach. The successful comparison between experimental and simulated data demonstrates that the morphological evolution is driven purely by the lowering of surface-curvature gradients. This allows for fine control over the final morphology to be attained. At fixed annealing time and temperature, perfectly merged films are obtained from Ge crystals grown at low temperature (450 °C), whereas some void regions still persist for crystals grown at higher temperature (500 °C) due to their different initial morphology. The latter condition, however, looks very promising for possible applications. Indeed, scanning tunneling electron microscopy and high-resolution transmission electron microscopy analyses show that, at least during the first stages of merging, the developing film is free from threading dislocations. The present findings, thus, introduce a promising path to integrate Ge layers on Si with a low dislocation density.