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Closing the gap between experiments and simulations in the investigation of high-pressure silicon phase transitions calls for advanced, new-generation modeling approaches. By exploiting massive parallelization, we here provide molecular dynamics (MD) simulations of Si nanoindentation based on the Gaussian Approximation Potential (GAP). Results are analyzed by exploiting a customized Neural Network Phase Recognition (NN-PR) approach, helping to shed light on the phase transitions occurring during the simulations. Our results show that GAP provides a realistic description of silicon phase transitions. With the support of NN-PR method, the formation mechanism and stability of high-pressure phases are comprehensively studied. Additionally, we also show how simulations based on the less demanding and widely-used Tersoff potential are still useful to investigate the role played by the indenter tip modeling. However, high-pressure phases obtained with GAP are more consistent with observations made in nanoindentation experiments, removing a spurious phase that is shown by Tersoff simulations. This behavior is explained on the base of relative phase stability with comparison with Density Functional Theory (DFT) calculations. This work provides insight into the application of state-of-the-art Machine Learning (ML) methods on nanoindentation simulations, enabling further understanding of the phase transition mechanisms in silicon.

Predicted topological crystalline insulators such as Pb1−xSnxTe are an interesting candidate for applications in quantum technology, as they can host spin-polarized surface states. Moreover, in the nanowire geometry, a quasi-1D system can be realized with potential applications exploiting Majorana fermions. Herein, the selective area growth of Pb1−xSnxTe islands and nanowires over the full range of x is demonstrated, and their in-depth growth dynamics and faceting are analyzed. By transmission electron microscopy, the single-crystalline and defect-free nature of the grown material and the homogeneous, controllable Pb/Sn ratio in the nanowires is confirmed. With support of phase-field growth simulations, it is shown that the crystal faceting mainly follows the driving force of surface energy minimization, favoring the lowest energy {200} surfaces. A kinetic enhancement of adatom incorporation on {110} facets is recognized to limit their extension with respect to {200} and {111} facets. After inspecting all possible in-plane orientations, we identify the <110> directions as the optimal candidate for the growth of high-quality and perfectly straight Pb1−xSnxTe nanowires, enabling the design of complex networks due to their threefold symmetry. This work opens the way to systematic transport investigation of the carrier density in Pb1−xSnxTe nanowires and can facilitate further optimization of the Pb1−xSnxTe system.

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 90 ∘ 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 60 ∘ 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.

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.

Both the typical timescale and sizes involved in epitaxial growth are a major challenge when attempting to simulate the process at the atomic scale. Therefore, continuum approaches have been developed allowing one to match experimental conditions. Despite yielding only an average description of the system behavior, continuum models can tackle several realistic aspects of growth such as preferential exposure of crystalline facets, strain relaxation, and out of equilibrium morphologies [1]. Examples of all such complexity will be given by analyzing our results on several diverse systems such as films, pillars, islands, and nanowires. While working at the continuum level allows for a significant reduction of the computational costs, there is still the need of further speeding up simulations, particularly when use of finite element methods is required at every timestep. We shall show that a convenient convolutional, recurrent neural network approach [2] can tackle the problem of predicting structural evolution by surface diffusion, after being trained on a phase-field generated dataset. While showing good accuracy, the ML approach guarantees very significant speed ups. Exciting perspectives, also in terms of extending machine-learning approaches beyond deterministic models, are discussed. References [1] Albani, M et al., “Faceting of Si and Ge crystals grown on deeply patterned Si substrates in the kinetic regime: phase-field modelling and experiments”, Sci. Rep. 11, 18825 (2021). [2] Lanzoni, D et al., “Morphological evolution via surface diffusion learned by convolutional, recurrent neural networks: Extrapolation and prediction uncertainty”, Phys. Rev. Mat. 6, 103801 (2022).

Atomistic simulations of growth at typical experimental conditions face some critical challenges due to both the extremely long time-scales and the large (often even when dealing with nanostructures!) size scales involved. Continuum approaches, while yielding only an average description of the system behavior, can help closing the aforementioned scale gap, as we shall show by discussing several examples [see, e.g., Ref. 1]. However, especially when dealing with anisotropic systems and/or in the presence of stress fields, continuum models can also be computationally demanding. The fast development of Machine Learning (ML) approaches in the last few years influenced all scientific fields and did not spare modeling of phenomena relevant to crystal growth. If on one hand attention was largely focused on the development of a new generation of accurate but relatively cheap interatomic potentials, techniques such as convolutional, recurrent neural networks have been exploited by us and other groups to speed up continuum simulations. We shall show, by mainly focusing on surface-diffusion-driven deterministic evolution [2], that reliable predictions are possible on extended time scales and that uncertainty can be conveniently quantified. Interestingly, ML models are not limited to deterministic dynamics. Very recently, indeed, we showed that generative adversarial networks can be exploited to learn stochastic processes [3]. Overall, it is evident that a new generation of ML-based methods for investigating growth is presently under development, opening exciting perspectives in terms of process control and efficient choice of the growth parameters.

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.

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.

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 {1120} 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 {1010} and {1120} facets, to the more energetically convenient hexagon, bounded by {1010} 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.

The growth of multi-layer germanium-tin (GeSn) quantum wells offers an intriguing pathway towards the integration of lasers in a CMOS platform. An important step in growing high quality quantum well interfaces is the formation of an initial wetting layer. However, key atomic-scale details of this process have not previously been discussed. We use scanning tunneling microscopy combined with density functional theory to study the deposition of Sn on Ge(1 0 0) at room temperature over a coverage range of 0.01 to 1.24 monolayers. We demonstrate the formation of a sub-2% Ge content GeSn wetting layer from three atomic-scale characteristic ad-dimer structural components, and show that small quantities of Sn incorporate into the Ge surface forming two atomic configurations. The ratio of the ad-dimer structures changes with increasing Sn coverage, indicating a change in growth kinetics. At sub-monolayer coverage, the least densely packing ad-dimer structure is most abundant. As the layer closes, forming a two-dimensional wetting layer, the more densely packing ad-dimer structure become dominant. These results demonstrate the capability to form an atomically smooth wetting layer at room temperature, and provide critical atomic-scale insights for the optimization of growth processes of GeSn multi-quantum-wells to meet the quality requirements of optical GeSn-based devices.

The metastable hexagonal-diamond phase of Si and Ge (and of SiGe alloys) displays superior optical properties with respect to the cubic-diamond one. Based on first-principle calculations we show that the surface energy of the typical facets exposed in Si and Ge nanowires is lower in the hexagonal-diamond phase than in the cubic one. By exploiting a synergic approach based also on a recent state-of-the-art interatomic potential and on a simple geometrical model, we investigate the relative stability of nanowires in the two phases up to few tens of nm in radius, highlighting the surface-related driving force and discussing its relevance in recent experiments. We also explore the stability of Si and Ge core-shell nanowires with hexagonal cores (made of GaP for Si nanowires, of GaAs for Ge nanowires). In this case, the stability of the hexagonal shell over the cubic one is also favored by the energy cost associated with the interface linking the two phases. Interestingly, our calculations indicate a critical radius of the hexagonal shell much lower than the one reported in recent experiments, indicating the presence of a large kinetic barrier allowing for the enlargement of the wire in a metastable phase.

Graded layers are widely exploited in semiconductor epitaxy as they typically display lower threading dislocation density with respect to constant-composition layers. However, strain relaxation occurs via a rather complex distribution of misfit dislocations. Here we exploit a suitable computational approach to investigate dislocation distributions minimizing the elastic energy in overcritical constant-composition and graded layers. Predictions are made for SiGe/Si systems, but the methodology, based on the exact (albeit in two dimensions and within linear elasticity theory) solution of the stress field associated with a periodic distribution of defects, is general. Results are critically compared with experiments, when possible, and with a previous mean-field model. A progressive transition from one-dimensional to two-dimensional distributions of defects when continuous linear grading is approached is clearly observed. Interestingly, analysis of the low-energy distribution of dislocations reveals close analogies with typical pile-ups as produced by dislocation multiplication.

3C-SiC epitaxially grown on Si displays a large wealth of extended defects. In particular, single, double and triple stacking faults (SFs) are observed to coexist in several experiments. Overabundance of defects has so far limited the exploitation of 3C-SiC/Si for power electronics, in spite of its several ideal properties (mainly in terms of the wide gap, high breakdown fields and thermal properties) and the possibility of direct integration in the Si technology. Here we use a multiscale approach, based on both classical molecular dynamics (MD) simulations and first-principles calculations, for the in-depth investigation of the origin, nature and properties of most common 3C-SiC/Si(001) extended defects. Our MD simulations reveal a natural path for the formation of partial dislocation complexes terminating both double and triple SFs. The MD results are used as an input for superior DFT calculations, allowing us to better determine the core structure and to investigate electronic properties. It turns out that the partial dislocation complexes terminating double and triple SFs are responsible for the introduction of electronic states significantly filling the band gap. On the other hand, individual partial dislocations terminating single SFs only induce states very close to the gap edge. We conclude that partial dislocation complexes, in particular the most abundant triple ones, are killer defects in terms of favoring leakage currents. Suggestions coming from theory/simulations for devising a strategy to lower their occurrence are discussed.

Strain relaxed Si 1 - x Ge x buffer layers on Si(001) can be used as virtual substrates for the growth of both strained Si and strained SiGe, which are suitable materials for sub-7 nm CMOS devices due to their enhanced carrier mobility. For industrial applications, the threading dislocation density (TDD) has to be as low as possible. However, a reduction of the TDD is limited by the balance between dislocation glide and nucleation as well as dislocation blocking. The relaxation mechanism of low strain Si 0.98 Ge 0.02 layers on commercial substrates is compared to substrates with a predeposited SiGe backside layer, which provides threading dislocations at the edge of the wafer. It is shown that by the exploitation of this reservoir, the critical thickness for plastic relaxation is reduced and the formation of misfit dislocation bundles can be prevented. Instead, upon reaching the critical thickness, these preexisting dislocations simultaneously glide unhindered from the edge of the wafer toward the center. The resulting dislocation network is free of thick dislocation bundles that cause pileups, and the TDD can be reduced by one order of magnitude.

The threading dislocation density (TDD) in plastically relaxed Ge/Si(001) heteroepitaxial films is commonly observed to decrease progressively with their thickness due to mutual annihilation. However, there exists a saturation limit, known as the geometrical limit, beyond which a further decrease of the TDD in the Ge film is hindered. Here, we show that such a limit can be overcome in SiGe/Ge/Si heterostructures thanks to the beneficial role of the second interface. Indeed, we show that Si0.06Ge0.94/Ge/Si(001) films display a TDD remarkably lower than the saturation limit of Ge/Si(001). Such a result is interpreted with the help of dislocation dynamics simulations. The reduction of TDD is attributed to the enhanced mobility acquired by preexisting threading dislocations after bending at the new interface to release the strain in the upper layer. Importantly, we demonstrate that the low TDD achieved in Si0.06Ge0.94/Ge/Si layers is preserved also when a second, relaxed Ge layer is subsequently deposited. This makes the present reverse-grading technique of direct interest also for achieving a low TDD in pure-Ge films.

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.

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.

Compositional segregation is commonly observed during the growth of III-V alloys in core-shell nanowires. Nanometer-thin stripes, enriched in one of the alloy components, are observed along the six <1 1 2> directions perpendicular to the [1 1 1]-wire axis, departing from the core to the outer shell edges in between the {1 1 0} faceted sidewalls. While it has been well established that the phenomenon occurs because of the different mobility of the alloy components, the actual mechanisms by which it happens are yet unclear. A phase-field model, coupling deposition and surface diffusion dynamics, is here developed to inspect the simultaneous evolution of the shell morphology and composition during growth. Both surface energy anisotropy and orientation-dependent growth rates are taken into account to identify their different role. Simulations reveal that the observed segregation is mainly triggered by the enhanced growth rate at the facet edges, while surface anisotropy keeps the stripes thin. Polarity effects are also included to differentiate the behavior between <1 1 2>A and <1 1 2>B orientations, so to reproduce the experimental observation of a 3-fold symmetry.

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.

We use a convolutional, recurrent neural network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only relatively simple, isolated shapes. After proper data augmentation, training and validation, the model is shown to correctly predict also the evolution of previously unobserved morphologies and to have learned the correct scaling of the evolution time with size. Importantly, we quantify prediction uncertainties based on a bootstrap-aggregation procedure. The latter proved to be fundamental in pointing out high uncertainties when applying the model to more complex initial conditions (e.g., leading to the splitting of high aspect-ratio individual structures). The automatic smart augmentation of the training set and design of a hybrid simulation method are discussed.

Understanding and controlling the morphology of crystals growing from prepatterned shapes, as in selective-area epitaxy, is fundamental for the development of novel device architectures. Here, an in-depth analysis of the faceted growth of ring-shaped crystal structures is presented. This is a prototypical case for assessing the role of thermodynamic and kinetic driving forces, as they induce different faceting between the outer convex region and the inner concave one. The well-established concepts of equilibrium crystal shape, set by surface energy minimization, and its kinetic counterpart, determined by orientation-dependent growth rates, provide a qualitative indication of the outcome of growth experiments. However, they are insufficient to capture the whole evolution pathway. A phase-field growth model including deposition, incorporation, and surface diffusion dynamics is considered, and extensive two- and three-dimensional simulations are performed. A continuum transition in the crystal morphology is recognized by varying the magnitude of the anisotropic surface energy vs the incorporation times. The in-depth analysis of a realistic case, mimicking experiments in the literature, highlights the prominent role of kinetics and of material redistribution from the outer to the inner perimeter of the ring. Finally, the templating effect of the initial pattern is investigated by considering polygonal profiles with different orientations, showing their effect on the facet formation and evolution.

Triggered by experimental observations of nanometer-sized Ni precipitate motion in a La2O3 matrix, the migration and morphological evolution by interface diffusion of an initially circular two-dimensional precipitate located near the free surface of its matrix is numerically investigated by means of phase-field simulations. Considering isotropic interface and elastic energies, it is found that the precipitate migrates towards the free surface, suitably adapting its shape during the motion. The case of two precipitates located near the free surface is also considered as well as the problem of an evolving precipitate near a squared corner of the matrix free surfaces. [Figure not available: see fulltext.].

Silicon-germanium and pure germanium are appealing for the microelectronic industry because of their full compatibility with silicon technology combined with several attractive properties, including high saturation velocity, high carrier mobility, and adjustable bandgap. Epitaxial deposition of Ge (or SiGe) on Si is unavoidably accompanied, at least for thick enough films, by nucleation of dislocations. Reducing the density of linear defects threading through the film and reaching the free surface, i.e. the typical active device region, is one of the main present goals of the wide industrial and academic community devoted to the integration of different materials on Si. Threading dislocations, indeed, can be detrimental in terms of device performances. A profound understanding of the microscopic mechanisms determining the typical arrays of dislocations can surely help in devising strategies for controlling the evolution of the defects. Molecular Dynamics (MD) is a valid tool that can be used to shed light on dislocation dynamics. Indeed, several works appeared in the Literature, analyzing dislocation gliding in semiconductor thin films [1, 2]. In non-standard conditions, at high enough temperatures and/or in the presence of a sufficient density of point defects, however, dislocations can move also via climbing. At variance with gliding, climbing does not involve the movement of the defect along the typical glide planes. Here we present a set of classical MD simulations, made using the LAMMPS code [3], based on the Tersoff potential [4], aimed at understanding the atomic-scale mechanisms leading to climbing towards the Si/Ge interface of typical dislocations in a Ge/Si(001). To observe climbing we have devised the following original procedure. Straight dislocation are conveniently inserted in a simulation cell including a Ge film over a Si substrate. At a certain rate, individual vacancies are created in the cell and evolved for a certain time at a high-temperature T