Diffusion of Ge below the Si(100) surface: theory and experiment

Moving closer to experimental level materials property prediction using AI

While experiments and DFT-computations have been the primary means for understanding the chemical and physical properties of crystalline materials, experiments are expensive and DFT-computations are time-consuming and have significant discrepancies against experiments. Currently, predictive modeling based on DFT-computations have provided a rapid screening method for materials candidates for further DFT-computations and experiments; however, such models inherit the large discrepancies from the DFT-based training data. Here, we demonstrate how AI can be leveraged together with DFT to compute materials properties more accurately than DFT itself by focusing on the critical materials science task of predicting “formation energy of a material given its structure and composition”. On an experimental hold-out test set containing 137 entries, AI can predict formation energy from materials structure and composition with a mean absolute error (MAE) of 0.064 eV/atom; comparing this against DFT-computations, we find that AI can significantly outperform DFT computations for the same task (discrepancies of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>0.076$$\end{document}>0.076 eV/atom) for the first time.

Adatom-Driven Oxygen Intermixing during the Deposition of Oxide Thin Films by Molecular Beam Epitaxy

Thin film deposition from the vapor phase is a complex process involving adatom adsorption, movement, and incorporation into the growing film. Here, we present quantitative experimental data that reveals anion intermixing over long length scales during the deposition of epitaxial Fe₂O₃ and Cr₂O₃ films and heterostructures by oxygen-plasma-assisted molecular beam epitaxy. We track this diffusion by incorporating well-defined tracer layers containing ¹⁸O and/or ⁵⁷Fe and measure their redistribution on the nanometer scale with atom probe tomography. Molecular dynamics simulations suggest potential intermixing events, which are then examined via nudged elastic band calculations. We reveal that adatoms on the film surface act to "pull up" subsurface O and Fe. Subsequent ring-like rotation mechanisms involving both adatom and subsurface anions then facilitate their mixing. In addition to film deposition, these intermixing mechanisms may be operant during other surface-mediated processes such as heterogeneous catalysis and corrosion.

Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning

The current predictive modeling techniques applied to Density Functional Theory (DFT) computations have helped accelerate the process of materials discovery by providing significantly faster methods to scan materials candidates, thereby reducing the search space for future DFT computations and experiments. However, in addition to prediction error against DFT-computed properties, such predictive models also inherit the DFT-computation discrepancies against experimentally measured properties. To address this challenge, we demonstrate that using deep transfer learning, existing large DFT-computational data sets (such as the Open Quantum Materials Database (OQMD)) can be leveraged together with other smaller DFT-computed data sets as well as available experimental observations to build robust prediction models. We build a highly accurate model for predicting formation energy of materials from their compositions; using an experimental data set of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1,963$$\end{document}1,963 observations, the proposed approach yields a mean absolute error (MAE) of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.06$$\end{document}0.06 eV/atom, which is significantly better than existing machine learning (ML) prediction modeling based on DFT computations and is comparable to the MAE of DFT-computation itself.

Machine-learning approaches based on DFT computations can greatly enhance materials discovery. Here the authors leverage existing large DFT-computational data sets and experimental observations by deep transfer learning to predict the formation energy of materials from their elemental compositions with high accuracy.

ElemNet: Deep Learning the Chemistry of Materials From Only Elemental Composition

Conventional machine learning approaches for predicting material properties from elemental compositions have emphasized the importance of leveraging domain knowledge when designing model inputs. Here, we demonstrate that by using a deep learning approach, we can bypass such manual feature engineering requiring domain knowledge and achieve much better results, even with only a few thousand training samples. We present the design and implementation of a deep neural network model referred to as ElemNet; it automatically captures the physical and chemical interactions and similarities between different elements using artificial intelligence which allows it to predict the materials properties with better accuracy and speed. The speed and best-in-class accuracy of ElemNet enable us to perform a fast and robust screening for new material candidates in a huge combinatorial space; where we predict hundreds of thousands of chemical systems that could contain yet-undiscovered compounds.

An efficient algorithm for finding the minimum energy path for cation migration in ionic materials

The Nudged Elastic Band (NEB) is an established method for finding minimum-energy paths and energy barriers of ion migration in materials, but has been hampered in its general application by its significant computational expense when coupled with density functional theory (DFT) calculations. Typically, an NEB calculation is initialized from a linear interpolation of successive intermediate structures (also known as images) between known initial and final states. However, the linear interpolation introduces two problems: (1) slow convergence of the calculation, particularly in cases where the final path exhibits notable curvature; (2) divergence of the NEB calculations if any intermediate image comes too close to a non-diffusing species, causing instabilities in the ensuing calculation. In this work, we propose a new scheme to accelerate NEB calculations through an improved path initialization and associated energy estimation workflow. We demonstrate that for cation migration in an ionic framework, initializing the diffusion path as the minimum energy path through a static potential built upon the DFT charge density reproduces the true NEB path within a 0.2 Å deviation and yields up to a 25% improvement in typical NEB runtimes. Furthermore, we find that the locally relaxed energy barrier derived from this initialization yields a good approximation of the NEB barrier, with errors within 20 meV of the true NEB value, while reducing computational expense by up to a factor of 5. Finally, and of critical importance for the automation of migration path calculations in high-throughput studies, we find that the new approach significantly enhances the stability of the calculation by avoiding unphysical image initialization. Our algorithm promises to enable efficient calculations of diffusion pathways, resolving a long-standing obstacle to the computational screening of intercalation compounds for Li-ion and multivalent batteries.

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.

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.

Formation of Co/Ge intermixing layers after Co deposition on Ge(111)2 × 1 surfaces

The formation of a novel surface reconstruction upon Co deposition on freshly cleaved Ge(111)2 × 1 surfaces is studied by means of scanning tunneling microscopy (STM) at 4.5 K. Previously we demonstrated that at this low substrate temperature the deposited Co atoms remain immobile after they become embedded underneath the Ge(111)2 × 1 surface. We now demonstrate that at higher substrate temperatures the embedded Co atoms are able to diffuse below the surface in a direction parallel to the upper π-bonded chain rows. This one-dimensional temperature-induced mobility results in subsurface accumulation of Co atoms at atomic steps, at domain boundaries and on atomically flat Ge terraces at, e.g., vacancies or adatoms, where reconstructed Co/Ge intermixing layers are formed. Voltage dependent STM images reveal that the Co related surface reconstruction locally exhibits an ordered atomic structure with the same inter-atomic distance as that of the initial 2 × 1 reconstructed pure Ge(111) surface. On the other hand, the presence of the Co results in a doubling of the periodicity along the [21[overline]1[overline]] direction in the STM images, which can be related to the modified electronic properties of the π-bonded chains.

Anomalous smoothing preceding island formation during growth on patterned substrates

We show that on suitably pit-patterned Si(001), deposition of just a few atomic layers of Ge can trigger a far larger flow of Si into the pits. This surprising effect results in anomalous smoothing of the substrate preceding island formation in the pits. We show that the effect naturally arises in continuum simulations of growth, and we identify its physical origin in the composition dependence of the surface diffusivity. Our interpretation suggests that anomalous smoothing is likely to also occur in other technologically relevant heteroepitaxial systems.

Nonequilibrium composition profiles of alloy quantum dots and their correlation with the growth mode

Equilibrium composition profiles (CPs) of epitaxial alloy quantum dots (QDs) are well established theoretically. However nonequilibrium CPs may occur experimentally. Using an atomistic-strain-model Monte Carlo simulation method, we demonstrate a striking correlation between the nonequilibrium CPs of QDs and the kinetic growth mode: the layer-by-layer growth (LG) and faceted growth (FG) form a core-shell structure having the triangle core of the unstrained and V-shaped core of the strained component, respectively, and both are distinctly different from the equilibrium CP. Comparing simulations with experiments, we infer that the InGaAs dots on GaAs grow by FG, while GeSi dots on Si grow first by LG followed by FG. Our findings suggest a possible method for controlling the CPs of QDs by selecting the growth mode.

Alloying mechanisms for epitaxial nanocrystals

The different mechanisms involved in the alloying of epitaxial nanocrystals are reported in this Letter. Intermixing during growth, surface diffusion, and intraisland diffusion were investigated by varying the growth conditions and annealing environments during chemical vapor deposition. The relative importance of each mechanism was evaluated in determining a particular composition profile for dome-shaped Ge:Si (001) islands. For samples grown at a faster rate, intermixing during growth was reduced. Si surface diffusion dominates during H2 annealing, whereas Ge surface diffusion and intraisland diffusion prevail during annealing in a PH3 environment.

Identification of Ge/Si intermixing processes at the Bi/Ge/Si(111) surface

The chemical contrast between Si and Ge obtained by scanning tunneling microscopy on Bi-covered Si(111) surfaces is used as a tool to identify two vertical Ge/Si intermixing processes. During annealing of an initially pure Ge monolayer on Si, the intermixing is confined to the first two layers approaching a 50% Ge concentration in each layer. During epitaxial growth, a growth front induced intermixing process acting at step edges is observed. Because of the open atomic structure at the step edges, relative to the terraces, a lower activation barrier for intermixing at the step edge, compared to the terrace, is observed.

Origin of apparent critical thickness for island formation in heteroepitaxy

We find that a continuum model of heteroepitaxy exhibits a sharp crossover with increasing coverage, from planar growth to island formation. The "critical thickness" at which this Stranski-Krastanov transition occurs depends sensitively on misfit strain, with a dependence strikingly similar to that seen experimentally. The initial planar growth occurs because of intermixing of deposited material with the substrate. While the transition is strictly kinetic in nature, it depends only weakly on growth rate. The role of surface segregation is also discussed.

Critical role of surface steps in the alloying of Ge on Si(001)

Using low-energy electron microscopy, we show that intermixing of Ge on Si(001) during growth is enhanced on stepped surfaces and is hindered on terraces where step flow does not occur. On large terraces we have identified a dramatic and unanticipated structural rearrangement that facilitates intermixing: Pairs of steps spontaneously form and migrate over the surface, leaving alloyed regions in their wake. The driving force for step formation is the entropy gain associated with the enhanced intermixing of Ge.

A flexible nudged elastic band program for optimization of minimum energy pathways using ab initio electronic structure methods

A driver program for carrying out nudged elastic band optimizations of minimum energy reaction pathways is described. This approach allows for the determination of minimum energy pathways using only energies and gradient information. The driver code has been interfaced with the GAUSSIAN 98 program. Applications to two isomerization reactions and to a cluster model for H(2) desorption from the Si(100)-2 x 1 surface are presented.

Theoretical studies of atomic-scale processes relevant to crystal growth

The study of adsorption, diffusion, island formation, and interlayer transport of atoms on a growing surface has been an active field in the past decade, because of both experimental and theoretical advances. Experiments can give detailed images of patterns formed on growing surfaces. An important challenge to the theoretical studies is the identification of dynamical processes controlling the pattern formation and overall surface morphology. This can be achieved by accurate modeling of the atomic interactions, a thorough search for active atomic-scale processes, and simulation of the growth on the experimental timescale to allow for detailed comparison with the experimental measurements. An overview of some of the theoretical methodology used in these studies and results obtained for one of the most extensively studied systems, Pt(111), is given here. A remarkable richness of phenomena has emerged from these studies, where apparently small effects can shift the balance between competing molecular processes and thereby change the morphology of a growing surface. The article concludes with a discussion of possible future directions in this research area.