Ab Initio-Based Bond Order Potential to Investigate Low Thermal Conductivity of Stanene Nanostructures

First-principles study of the effect of S-atom doping on the optoelectronic properties of stanene

CONTEXT

Based on the first principles, the influence of S-atom doping on the electronic and optical properties of stanene is comprehensively examined in this work. The results show that pure stanene is a quasi-metal with zero bandgap. After doping with an S atom, opening the bandgap of pure stanene becomes possible and the state of the stanene is converted from quasi-metal to semiconductor. Analysis of the density of states reveals that the density of states of all doped systems is primarily made of the p-orbital of the Sn. The overlap population analysis showed that charge transfer occurs between S and Sn atoms under different doping concentrations. The charge transfer increases with increasing doping concentration. The charge transfer reaches a maximum at a doping concentration of 9.38%. The increase in doping concentration causes blue-shifting of the absorption and reflection peaks of the doped system as compared to those of pure stanene. It is expected that these studies can provide theoretical guidance for the practical application of stanene in optoelectronic devices.

METHODS

All simulations are undertaken with the Cambridge Sequential Total Energy Package (CASTEP) (Wei et al. Physica B: Condensed Matter 545:99, 2018; Bafekry et al. Phys Chem Chem Phys, 2021; Zala et al. Appl Surf Sci, 2022; Bafekry et al. Nanotechnology, 2021; Bafekry et al. Phys Chem Chem Phys, 2021; Bafekry et al. J Phys: Condens Matter, 2021), which is based on density functional theory (DFT). For the exchange correlation, the generalized gradient approximation (GGA) is implemented with the Perdew-Burke-Ernzerhof (PBE) functional Perdew et al. Phys Rev B Condens Matter 48:4978, 1993. Using the Monkhorst-Pack technique, a specific K-point sample of the Brillouin zone was carried out Monkhorst and Pack Phys Rev B 13:5188, 1976. After the convergence tests, the K-point grid was set to 3 × 3 × 1. The plane-wave truncation energy was set to 400 eV. The residual stress for all atoms was 0.03 eV/Å. The energy convergence criterion was 1.0 × 10-5 eV. To prevent recurring interactions between the layers, a vacuum layer with a thickness of 20 Å was established in the Z-direction.

Thermal Transport in 2D Materials

In recent decades, two-dimensional materials (2D) such as graphene, black and blue phosphorenes, transition metal dichalcogenides (e.g., WS₂ and MoS₂), and h-BN have received illustrious consideration due to their promising properties. Increasingly, nanomaterial thermal properties have become a topic of research. Since nanodevices have to constantly be further miniaturized, thermal dissipation at the nanoscale has become one of the key issues in the nanotechnology field. Different techniques have been developed to measure the thermal conductivity of nanomaterials. A brief review of 2D material developments, thermal conductivity concepts, simulation methods, and recent research in heat conduction measurements is presented. Finally, recent research progress is summarized in this article.

Data-Driven Materials Innovation and Applications

Owing to the rapid developments to improve the accuracy and efficiency of both experimental and computational investigative methodologies, the massive amounts of data generated have led the field of materials science into the fourth paradigm of data-driven scientific research. This transition requires the development of authoritative and up-to-date frameworks for data-driven approaches for material innovation. A critical discussion on the current advances in the data-driven discovery of materials with a focus on frameworks, machine-learning algorithms, material-specific databases, descriptors, and targeted applications in the field of inorganic materials is presented. Frameworks for rationalizing data-driven material innovation are described, and a critical review of essential subdisciplines is presented, including: i) advanced data-intensive strategies and machine-learning algorithms; ii) material databases and related tools and platforms for data generation and management; iii) commonly used molecular descriptors used in data-driven processes. Furthermore, an in-depth discussion on the broad applications of material innovation, such as energy conversion and storage, environmental decontamination, flexible electronics, optoelectronics, superconductors, metallic glasses, and magnetic materials, is provided. Finally, how these subdisciplines (with insights into the synergy of materials science, computational tools, and mathematics) support data-driven paradigms is outlined, and the opportunities and challenges in data-driven material innovation are highlighted.

Stability of Strained Stanene Compared to That of Graphene

Stanene, composed of tin atoms, is a member of 2D-Xenes, two-dimensional single element materials. The properties of the stanene can be changed and improved by applying deformation, and it is important to know the range of in-plane deformation that the stanene can withstand. Using the Tersoff interatomic potential for calculation of phonon frequencies, the range of stability of planar stanene under uniform in-plane deformation is analyzed and compared with the known data for graphene. Unlike atomically flat graphene, stanene has a certain thickness (buckling height). It is shown that as the tensile strain increases, the thickness of the buckled stanene decreases, and when a certain tensile strain is reached, the stanene becomes absolutely flat, like graphene. Postcritical behaviour of stanene depends on the type of applied strain: critical tensile strain leads to breaking of interatomic bonds and critical in-plane compressive strain leads to rippling of stanene. It is demonstrated that application of shear strain reduces the range of stability of stanene. The existence of two energetically equivalent states of stanene is shown, and consequently, the possibility of the formation of domains separated by domain walls in the stanene is predicted.

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene

We introduce a multi-reward reinforcement learning (RL) approach to train a flexible bond-order potential (BOP) for 2D phosphorene based on ab initio training data sets. Our approach is based on a continuous action space Monte Carlo tree search algorithm that is general and scalable and presents an efficient multiobjective optimization scheme for high-dimensional materials design problems. As a proof-of-concept, we deploy this scheme to parametrize multiple structural and dynamical properties of 2D phosphorene polymorphs. Our RL-trained BOP model adequately captures the structure, energetics, transformation barriers, equation of state, elastic constants, and phonon dispersions of various 2D P polymorphs. We use this model to probe the impact of temperature and strain rate on the phase transition from black (α-P) to blue phosphorene (β-P) through molecular dynamics simulations. A decrease in critical strain for this phase transition with increase in temperature is observed, and the underlying atomistic mechanisms are discussed.

Bonding, structure, and mechanical stability of 2D materials: the predictive power of the periodic table

This tutorial review describes the ongoing effort to convert main-group elements of the periodic table and their combinations into stable 2D materials, which is sometimes called modern 'alchemy'. Theory is successfully approaching this goal, whereas experimental verification is lagging far behind in the synergistic interplay between theory and experiment. The data collected here gives a clear picture of the bonding, structure, and mechanical performance of the main-group elements and their binary compounds. This ranges from group II elements, with two valence electrons, to group VI elements with six valence electrons, which form not only 1D structures but also, owing to their variable oxidation states, low-symmetry 2D networks. Outside of these main groups reviewed here, predominantly ionic bonding may be observed, for example in group II-VII compounds. Besides high-symmetry graphene with its shortest and strongest bonds and outstanding mechanical properties, low-symmetry 2D structures such as various borophene and tellurene phases with intriguing properties are receiving increasing attention. The comprehensive discussion of data also includes bonding and structure of few-layer assemblies, because the electronic properties, e.g., the band gap, of these heterostructures vary with interlayer layer separation and interaction energy. The available data allows the identification of general relationships between bonding, structure, and mechanical stability. This enables the extraction of periodic trends and fundamental rules governing the 2D world, which help to clear up deviating results and to estimate unknown properties. For example, the observed change of the bond length by a factor of two alters the cohesive energy by a factor of four and the extremely sensitive Young's modulus and ultimate strength by more than a factor of 60. Since the stiffness and strength decrease with increasing atom size on going down the columns of the periodic table, it is important to look for suitable allotropes of elements and binaries in the upper rows of the periodic table when mechanical stability and robustness are issues. On the other hand, the heavy compounds are of particular interest because of their low-symmetry structures with exotic electronic properties.

Bandgap prediction of two-dimensional materials using machine learning

The bandgap of two-dimensional (2D) materials plays an important role in their applications to various devices. For instance, the gapless nature of graphene limits the use of this material to semiconductor device applications, whereas the indirect bandgap of molybdenum disulfide is suitable for electrical and photo-device applications. Therefore, predicting the bandgap rapidly and accurately for a given 2D material structure has great scientific significance in the manufacturing of semiconductor devices. Compared to the extremely high computation cost of conventional first-principles calculations, machine learning (ML) based on statistics may be a promising alternative to predicting bandgaps. Although ML algorithms have been used to predict the properties of materials, they have rarely been used to predict the properties of 2D materials. In this study, we apply four ML algorithms to predict the bandgaps of 2D materials based on the computational 2D materials database (C2DB). Gradient boosted decision trees and random forests are more effective in predicting bandgaps of 2D materials with an R2 >90% and root-mean-square error (RMSE) of ~0.24 eV and 0.27 eV, respectively. By contrast, support vector regression and multi-layer perceptron show that R2 is >70% with RMSE of ~0.41 eV and 0.43 eV, respectively. Finally, when the bandgap calculated without spin-orbit coupling (SOC) is used as a feature, the RMSEs of the four ML models decrease greatly to 0.09 eV, 0.10 eV, 0.17 eV, and 0.12 eV, respectively. The R2 of all the models is >94%. These results show that the properties of 2D materials can be rapidly obtained by ML prediction with high precision.

Defect dynamics in two-dimensional black phosphorus under argon ion irradiation

Fundamental understanding of the atomic-scale mechanisms underlying production, accumulation, and temporal evolution of defects in phosphorene during noble-gas ion irradiation is crucial to design efficient defect engineering routes to fabricate next-generation materials for energy technologies. Here, we employed classical molecular dynamics (CMD) simulations using a reactive force field to unravel the effect of defect dynamics on the structural changes in a monolayer of phosphorene induced by argon-ion irradiation, and its subsequent relaxation during post-radiation annealing treatment. Analysis of our CMD trajectories using unsupervised machine learning methods showed that radiation fluence strongly influences the types of defect that form, their dynamics, and their relaxation mechanisms during subsequent annealing. Low ion fluences yielded a largely crystalline sheet featuring isolated small voids (up to 2 nm), Stone-Wales defects, and mono-/di-vacancies; while large nanopores (∼10 nm) can form beyond a critical fluence of ∼10¹⁴ ions per cm². During post-radiation annealing, we found two distinct relaxation mechanisms, depending on the fluence level. The isolated small voids (1-2 nm) formed at low ion-fluences heal via local re-arrangement of rings, which is facilitated by a cooperative mechanism involving a series of atomic motions that include thermal rippling, bond formation, bond rotation, angle bending and dihedral twisting. On the other hand, damaged structures obtained at high fluences exhibit pronounced coalescence of nanopores mediated by 3D networks of P-centered tetrahedra. These findings provide new perspectives to use ion beams to precisely control the concentration and distribution of specific defect types in phosphorene for emerging applications in electronics, batteries, sensing, and neuromorphic computing.

Phonon thermal conductivity of the stanene/hBN van der Waals heterostructure

We use classical non-equilibrium molecular dynamics (NEMD) simulations to investigate the phonon thermal conductivity (PTC) of hexagonal boron nitride (hBN) supported stanene. At first, we examine the length dependent PTCs of bare stanene and hBN, and the stanene/hBN heterostructure and realize the dominance of the hBN layer to dictate the PTC in the heterostructure system. Afterward, we assess the length-independent bulk PTCs of these materials. The bulk PTCs at room temperature are found as ∼15.20 W m-1 K-1, ∼550 W m-1 K-1, and ∼232 W m-1 K-1 for bare stanene and hBN, and stanene/hBN, respectively. Moreover, our simulations reveal that bare stanene exhibits a substantially lower PTC compared to bare hBN, and the predicted PTC of stanene/hBN lies between those of stand-alone stanene and hBN. We also found that the PTC obtained for the stanene/hBN system from NEMD simulations nicely agrees with the theoretical formula developed to predict the PTC of heterostructures of two distinct materials. Temperature studies suggest that the PTC of the stanene/hBN heterostructure system follows a decreasing trend with increasing temperature. Additionally, corresponding phonon density of states (PDOS) and phonon dispersion data are provided to comprehensively understand the phonon properties of bare stanene and hBN, and stanene/hBN. Overall, this NEMD study would offer a deep understating towards the PTC of the stanene/hBN heterostructure and would widen the scope of its successful operations in future nanoelectronic, spintronic, and thermoelectric devices.

Characterization of the mechanical properties of van der Waals heterostructures of stanene adsorbed on graphene, hexagonal boron-nitride and silicon carbide

Stanene has revealed a new horizon in the field of quantum condensed matter and energy conversion devices but its significantly lower tensile strength limits its further applications and effective operation in these nanodevices. Van der Waals heterostructures have given substantial flexibility to integrate different two-dimensional (2D) layered materials over the past few years and have proven highly functional with exceptional features, appealing applications, and innovative physics. Considerable efforts have been made for the preparation, thorough understanding, and applications of van der Waals heterostructures in the fields of electronics and optoelectronics. In this paper, we have executed Molecular Dynamics (MD) simulations to predict the tensile strength of van der Waals heterostructures of stanene (Sn) adsorbed on graphene (Gr), hexagonal boron nitride (hBN), and silicon carbide (SiC) (Sn/Gr, Sn/hBN, and Sn/SiC, respectively) subjected to both armchair and zigzag directional loading at different strain rates for the first time, which has enticing applications in electronic, optoelectronic, energy storage and bio-engineered devices. Among all the van der Waals heterostructures, the Sn/SiC heterostructure exhibits the lowest tensile strength and tensile strain. Furthermore, it has been found that zigzag directional loading could endure more tensile strain before fracture. Besides, it has been disclosed that though the rule of mixtures may accurately reproduce the Young's modulus of these heterostructures, it has limitations to predict the tensile strength. Fracture analysis suggests that for the Sn/hBN heterostructure the fracture initiates from the stanene layer while for the Sn/Gr and Sn/SiC heterostructures the fracture initiates from the Gr and SiC layer, respectively, for both armchair and zigzag directional loading. Overall, this study would aid in the design and efficient operation of Sn/Gr, Sn/hBN, and Sn/SiC heterostructures when subjected to mechanical force.

Lateral and flexural thermal transport in stanene/2D-SiC van der Waals heterostructure

Thermal management is one of the key challenges in nanoelectronic and optoelectronic devices. The development of a van der Waals heterostructure (vdWH) using the vertical positioning of different two-dimensional (2D) materials has recently appeared as a promising way of attaining desirable electrical, optical, and thermal properties. Here, we explore the lateral and flexural thermal conductivity of stanene/2D-SiC vdWH utilizing the reverse non-equilibrium molecular dynamics simulation and transient pump-probe technique. The effects of length, area, coupling strength and temperature on the thermal transport are studied systematically. The projected lateral thermal conductivity of a stanene/2D-SiC hetero-bilayer is found to be 66.67 [Formula: see text], which is greater than stanene, silicene, germanene, MoSe₂ and even higher than some hetero-bilayers, including MoS₂/MoSe₂ and stanene/silicene. The lateral thermal conductivity increases as the length increases, while it tends to decrease with increasing temperature. The computed flexural interfacial thermal resistance between stanene and 2D-SiC is 3.0622 [Formula: see text] [Formula: see text] K.m² W^-1, which is close to other 2D hetero-bilayers. The interfacial resistance between stanene and 2D-SiC is reduced by 70.49% and 50.118% as the temperature increases from 100 K to 600 K and the coupling factor increases from [Formula: see text] to [Formula: see text], respectively. In addition, various phonon modes are evaluated to disclose the fundamental mechanisms of thermal transport in the lateral and flexural direction of the hetero-bilayer. These results are important in order to understand the heat transport phenomena of stanene/2D-SiC vdWH, which could be useful for enhancing their promising applications.

Undulated silicene and germanene freestanding layers: why not?

Silicene and germanene freestanding layers are usually described as a honeycomb lattice formed by two hexagonal sub-lattices presenting a height difference, namely the layer buckling. In this work, first-principles calculations show that silicene and germanene can be rippled at 0 K with various wavelengths, without any compressive strain of the layer. For germanene, the height difference between two Ge atoms from the same sub-lattice can be as high as 4.7 [Formula: see text] for an undulation length of 81 [Formula: see text]. The deformations are related to slight (lower than 1.7°) bond angle modifications, and the energy cost is remarkably low, lying between 0.1 and 0.8 meV per atom. These undulations modify the electronic structure, opening a gap of 15 meV.

Machine learning for interatomic potential models

The use of supervised machine learning to develop fast and accurate interatomic potential models is transforming molecular and materials research by greatly accelerating atomic-scale simulations with little loss of accuracy. Three years ago, Jörg Behler published a perspective in this journal providing an overview of some of the leading methods in this field. In this perspective, we provide an updated discussion of recent developments, emerging trends, and promising areas for future research in this field. We include in this discussion an overview of three emerging approaches to developing machine-learned interatomic potential models that have not been extensively discussed in existing reviews: moment tensor potentials, message-passing networks, and symbolic regression.

Machine-Learning Analysis to Predict the Exciton Valley Polarization Landscape of 2D Semiconductors

We demonstrate the applicability of employing machine-learning-based analysis to predict the low-temperature exciton valley polarization landscape of monolayer tungsten diselenide (1L-WSe₂) using position-dependent information extracted from its photoluminescence (PL) spectra at room temperature. We performed low- and room-temperature polarization-resolved PL mapping and used the obtained experimental data to create regression models for the prediction using the Random Forest machine-learning algorithm. The local information extracted from the room-temperature PL spectra and the low-temperature exciton valley polarization was used as the input and output data for the machine-learning process, respectively. The spatial distribution of the exciton valley polarization in a 1L-WSe₂ sample that was not used for the learning of the decision trees was successfully predicted. Furthermore, we numerically obtained the degree of importance for each input variable and demonstrated that this parameter provides helpful information for examining the physics that shape the spatially heterogeneous valley polarization landscape of 1L-WSe₂.

Machine learning a bond order potential model to study thermal transport in WSe2 nanostructures

Nanostructures of transition metal di-chalcogenides (TMDCs) exhibit exotic thermal, chemical and electronic properties, enabling diverse applications from thermoelectrics and catalysis to nanoelectronics. The thermal properties of these nanoscale TMDCs are of particular interest for thermoelectric applications. Thermal transport studies on nanotubes and nanoribbons remain intractable to first principles calculations whereas existing classical molecular models treat the two chalcogen layers in a monolayer with different atom types; this imposes serious limitations in studying multi-layered TMDCs and dynamical phenomena such as nucleation and growth. Here, we overcome these limitations using machine learning (ML) and introduce a bond order potential (BOP) trained against first principles training data to capture the structure, dynamics, and thermal transport properties of a model TMDC such as WSe2. The training is performed using a hierarchical objective genetic algorithm workflow to accurately describe the energetics, as well as thermal and mechanical properties of a free-standing sheet. As a representative case study, we perform molecular dynamics simulations using the ML-BOP model to study the structure and temperature-dependent thermal conductivity of WSe2 tubes and ribbons of different chiralities. We observe slightly higher thermal conductivities along the armchair direction than zigzag for WSe2 monolayers but the opposite effect for nanotubes, especially of smaller diameters. We trace the origin of these differences to the anisotropy in thermal transport and the restricted momentum selection rules for phonon-phonon Umpklapp scattering. The developed ML-BOP model is of broad interest and will facilitate studies on nucleation and growth of low dimensional WSe2 structures as well as their transport properties for thermoelectric and thermal management applications.

Strain in a single wrinkle on an MoS2 flake for in-plane realignment of band structure for enhanced photo-response

Since 2D transition metal dichalcogenides (TMDs) exhibit strain-tunable bandgaps, locally confining strain can allow lateral manipulation of their band structure, in-plane carrier transport and optical transitions. Herein, we show that a single wrinkle (width = 10 nm-10 μm) on an MoS2 flake can induce confined uniaxial strain to reduce the local bandgap (40-60 meV per % deformation), producing a microscopic exciton funnel with an enhancement in photocurrent over flat MoS2 devices. This study also shows that wrinkles can spatially reconfigure the distribution of dopants and enhance the light absorption in the MoS2 layer via Fabry-Perot interference in its nanocavity. In the field-effect transistor studies on the MoS2 flat-wrinkle-flat device-structure, a higher carrier mobility and an improvement in the on/off ratio were exhibited in the devices with a single wrinkle. This phenomenon is attributed to the built-in potential induced by the bandgap reduction at the wrinkle site and the change in doping of the suspended wrinkle. The wrinkle-induced tunability of the local bandgap and manipulation of the spatial transport barriers, and the enhanced light absorption can enable development of next-generation electronic and optoelectronic devices guided by in-plane deformation of 2D nanomaterials.

Three-dimensional X-ray diffraction imaging of dislocations in polycrystalline metals under tensile loading

The nucleation and propagation of dislocations is an ubiquitous process that accompanies the plastic deformation of materials. Consequently, following the first visualization of dislocations over 50 years ago with the advent of the first transmission electron microscopes, significant effort has been invested in tailoring material response through defect engineering and control. To accomplish this more effectively, the ability to identify and characterize defect structure and strain following external stimulus is vital. Here, using X-ray Bragg coherent diffraction imaging, we describe the first direct 3D X-ray imaging of the strain field surrounding a line defect within a grain of free-standing nanocrystalline material following tensile loading. By integrating the observed 3D structure into an atomistic model, we show that the measured strain field corresponds to a screw dislocation.

Identifying atomic defects during deformation is crucial to understand material response but remains challenging in three dimensions. Here, the authors couple X-ray Bragg coherent diffraction imaging and atomistic simulations to correlate a strain field to a screw dislocation in a single copper grain.

Defect Dynamics in 2-D MoS2 Probed by Using Machine Learning, Atomistic Simulations, and High-Resolution Microscopy

Structural defects govern various physical, chemical, and optoelectronic properties of two-dimensional transition-metal dichalcogenides (TMDs). A fundamental understanding of the spatial distribution and dynamics of defects in these low-dimensional systems is critical for advances in nanotechnology. However, such understanding has remained elusive primarily due to the inaccessibility of (a) necessary time scales via standard atomistic simulations and (b) required spatiotemporal resolution in experiments. Here, we take advantage of supervised machine learning, in situ high-resolution transmission electron microscopy (HRTEM) and molecular dynamics (MD) simulations to overcome these limitations. We combine genetic algorithms (GA) with MD to investigate the extended structure of point defects, their dynamical evolution, and their role in inducing the phase transition between the semiconducting (2H) and metallic (1T) phase in monolayer MoS₂. GA-based structural optimization is used to identify the long-range structure of randomly distributed point defects (sulfur vacancies) for various defect densities. Regardless of the density, we find that organization of sulfur vacancies into extended lines is the most energetically favorable. HRTEM validates these findings and suggests a phase transformation from the 2H-to-1T phase that is localized near these extended defects when exposed to high electron beam doses. MD simulations elucidate the molecular mechanism driving the onset of the 2H to 1T transformation and indicate that finite amounts of 1T phase can be retained by increasing the defect concentration and temperature. This work significantly advances the current understanding of defect structure/evolution and structural transitions in 2D TMDs, which is crucial for designing nanoscale devices with desired functionality.

Thermal transport characterization of stanene/silicene heterobilayer and stanene bilayer nanostructures

Recently, stanene and silicene based nanostructures with low thermal conductivity have incited noteworthy interest due to their prospect in thermoelectrics. Aiming at the possibility of extracting lower thermal conductivity, in this study, we have proposed and modeled stanene/silicene heterobilayer nanoribbons, a new heterostructure and subsequently characterized their thermal transport by using an equilibrium molecular dynamics simulation. In addition, the thermal transport in bilayer stanene is also studied and compared. We have computed the thermal conductivity of the stanene/silicene and bilayer stanene nanostructures to characterize their thermal transport phenomena. The studied nanostructures show good thermal stability within the temperature range of 100-600 K. The room temperature thermal conductivities of pristine 10 nm × 3 nm stanene/silicene hetero-bilayer and stanene bilayer are estimated to be 3.63 ± 0.27 W m^-1 K^-1 and 1.31 ± 0.34 W m^-1 K^-1, respectively, which are smaller than that of silicene, graphene and some other 2D monolayers as well as heterobilayers such as stanene/graphene and silicene/graphene. In the temperature range of 100-600 K, the thermal conductivity of our studied bilayer nanoribbons decreases with an increase in the temperature. Furthermore, we have investigated the dependence of our estimated thermal conductivity on the size of the considered nanoribbons. The thermal conductivities of both the nanoribbons are found to increase with an increase in the width of the structure. The thermal conductivity shows a similar increasing trend with the increase in the ribbon length, as well. Our results suggest that, the low thermal conductivity of our studied bilayer structures can be further decreased by nanostructuring. The significantly low thermal conductivity of the stanene/silicene heterobilayer and stanene bilayer nanoribbons realized in our study would provide a good insight and encouragement into their appealing prospect in the thermoelectric applications.

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene and hBN) and multiplanar (such as stanene and MoS₂) configurations. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently, a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for different classes of nanostructures (graphene, hBN, stanene and MoS₂) and nano-heterostructures (graphene-hBN, graphene-MoS₂, graphene-stanene and stanene-MoS₂), which are categorized on the basis of fundamental structural configurations. The numerical values of shear modulus are compared with the results from the scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of a wide range of nanostructures and nanoheterostructures.

Three-Dimensional Integrated X-ray Diffraction Imaging of a Native Strain in Multi-Layered WSe2

Emerging two-dimensional (2-D) materials such as transition-metal dichalcogenides show great promise as viable alternatives for semiconductor and optoelectronic devices that progress beyond silicon. Performance variability, reliability, and stochasticity in the measured transport properties represent some of the major challenges in such devices. Native strain arising from interfacial effects due to the presence of a substrate is believed to be a major contributing factor. A full three-dimensional (3-D) mapping of such native nanoscopic strain over micron length scales is highly desirable for gaining a fundamental understanding of interfacial effects but has largely remained elusive. Here, we employ coherent X-ray diffraction imaging to directly image and visualize in 3-D the native strain along the (002) direction in a typical multilayered (∼100-350 layers) 2-D dichalcogenide material (WSe₂) on silicon substrate. We observe significant localized strains of ∼0.2% along the out-of-plane direction. Experimentally informed continuum models built from X-ray reconstructions trace the origin of these strains to localized nonuniform contact with the substrate (accentuated by nanometer scale asperities, i.e., surface roughness or contaminants); the mechanically exfoliated stresses and strains are localized to the contact region with the maximum strain near surface asperities being more or less independent of the number of layers. Machine-learned multimillion atomistic models show that the strain effects gain in prominence as we approach a few- to single-monolayer limit. First-principles calculations show a significant band gap shift of up to 125 meV per percent of strain. Finally, we measure the performance of multiple WSe₂ transistors fabricated on the same flake; a significant variability in threshold voltage and the "off" current setting is observed among the various devices, which is attributed in part to substrate-induced localized strain. Our integrated approach has broad implications for the direct imaging and quantification of interfacial effects in devices based on layered materials or heterostructures.

Thermal transport characterization of carbon and silicon doped stanene nanoribbon: an equilibrium molecular dynamics study

Equilibrium molecular dynamics simulation has been carried out for the thermal transport characterization of nanometer sized carbon and silicon doped stanene nanoribbon (STNR). The thermal conduction properties of doped stanene nanostructures are yet to be explored and hence in this study, we have investigated the impact of carbon and silicon doping concentrations as well as doping patterns namely single doping, double doping and edge doping on the thermal conductivity of nanometer sized zigzag STNR. The room temperature thermal conductivities of 15 nm × 4 nm doped zigzag STNR at 2% carbon and silicon doping concentration are computed to be 9.31 ± 0.33 W m⁻¹ K⁻¹ and 7.57 ± 0.48 W m⁻¹ K⁻¹, respectively whereas the thermal conductivity for the pristine STNR of the same dimension is calculated as 1.204 ± 0.21 W m⁻¹ K⁻¹. We find that the thermal conductivity of both carbon and silicon doped STNR increases with the increasing doping concentration for both carbon and silicon doping. The magnitude of increase in STNR thermal conductivity due to carbon doping has been found to be greater than that of silicon doping. Different doping patterns manifest different degrees of change in doped STNR thermal conductivity. Double doping pattern for both carbon and silicon doping induces the largest extent of enhancement in doped STNR thermal conductivity followed by single doping pattern and edge doping pattern respectively. The temperature and width dependence of doped STNR thermal conductivity has also been studied. For a particular doping concentration, the thermal conductivity of both carbon and silicon doped STNR shows a monotonic decaying trend at elevated temperatures while an opposite pattern is observed for width variation i.e. thermal conductivity increases with the increase in ribbon width. Such comprehensive study on doped stanene would encourage further investigation on the proper optimization of thermal transport characteristics of stanene nanostructures and provide deep insight in realizing the potential application of doped STNR in thermoelectric as well as thermal management of stanene based nanoelectronic devices.

Tunable thermal transport of doped stanene nanoribbon considering the impact of doping concentration, doping pattern, temperature and nanoribbon width.

Machine learnt bond order potential to model metal-organic (Co-C) heterostructures

A fundamental understanding of the inter-relationships between structure, morphology, atomic scale dynamics, chemistry, and physical properties of mixed metallic-covalent systems is essential to design novel functional materials for applications in flexible nano-electronics, energy storage and catalysis. To achieve such knowledge, it is imperative to develop robust and computationally efficient atomistic models that describe atomic interactions accurately within a single framework. Here, we present a unified Tersoff-Brenner type bond order potential (BOP) for a Co-C system, trained against lattice parameters, cohesive energies, equation of state, and elastic constants of different crystalline phases of cobalt as well as orthorhombic Co₂C derived from density functional theory (DFT) calculations. The independent BOP parameters are determined using a combination of supervised machine learning (genetic algorithms) and local minimization via the simplex method. Our newly developed BOP accurately describes the structural, thermodynamic, mechanical, and surface properties of both the elemental components as well as the carbide phases, in excellent accordance with DFT calculations and experiments. Using our machine-learnt BOP potential, we performed large-scale molecular dynamics simulations to investigate the effect of metal/carbon concentration on the structure and mechanical properties of porous architectures obtained via self-assembly of cobalt nanoparticles and fullerene molecules. Such porous structures have implications in flexible electronics, where materials with high electrical conductivity and low elastic stiffness are desired. Using unsupervised machine learning (clustering), we identify the pore structure, pore-distribution, and metallic conduction pathways in self-assembled structures at different C/Co ratios. We find that as the C/Co ratio increases, the connectivity between the Co nanoparticles becomes limited, likely resulting in low electrical conductivity; on the other hand, such C-rich hybrid structures are highly flexible (i.e., low stiffness). The BOP model developed in this work is a valuable tool to investigate atomic scale processes, structure-property relationships, and temperature/pressure response of Co-C systems, as well as design organic-inorganic hybrid structures with a desired set of properties.

Machine Learning Force Field Parameters from Ab Initio Data

Machine learning (ML) techniques with the genetic algorithm (GA) have been applied to determine a polarizable force field parameters using only ab initio data from quantum mechanics (QM) calculations of molecular clusters at the MP2/6-31G(d,p), DFMP2(fc)/jul-cc-pVDZ, and DFMP2(fc)/jul-cc-pVTZ levels to predict experimental condensed phase properties (i.e., density and heat of vaporization). The performance of this ML/GA approach is demonstrated on 4943 dimer electrostatic potentials and 1250 cluster interaction energies for methanol. Excellent agreement between the training data set from QM calculations and the optimized force field model was achieved. The results were further improved by introducing an offset factor during the machine learning process to compensate for the discrepancy between the QM calculated energy and the energy reproduced by optimized force field, while maintaining the local "shape" of the QM energy surface. Throughout the machine learning process, experimental observables were not involved in the objective function, but were only used for model validation. The best model, optimized from the QM data at the DFMP2(fc)/jul-cc-pVTZ level, appears to perform even better than the original AMOEBA force field (amoeba09.prm), which was optimized empirically to match liquid properties. The present effort shows the possibility of using machine learning techniques to develop descriptive polarizable force field using only QM data. The ML/GA strategy to optimize force fields parameters described here could easily be extended to other molecular systems.

Silicene growth through island migration and coalescence

We perform massively-parallel classical molecular dynamics (MD) simulations to study the long timescale monolayer silicene growth on an Ir (111) surface. We observe an intricate multi-stage growth process driven by atomic and cluster migration on the surface. Initial growth involves formation of sub-nanometer clusters via adatom surface diffusion. Subsequently, these clusters rearrange spontaneously with each additional Si atom, forming clusters containing 4-7 member rings. Growth of each cluster through adatom adhesion is accompanied by the formation of larger islands through cluster migration and coalescence. Coalescence of smaller, more mobile islands into larger clusters is aided by the internal rearrangement of rings within each cluster. This flexibility, both of clusters and their constituent atoms, allows the impinging clusters to reorient after first contact and form a more perfect union. We also report on the effect of temperature and flux on the growth process and the final nanostructure. Our study provides atomistic insights into the early stage growth mechanisms of silicene which can be significant for controlled synthesis of its 2D monolayers.

The conflicting role of buckled structure in phonon transport of 2D group-IV and group-V materials

Controlling heat transport through material design is one important step toward thermal management in 2D materials. To control heat transport, a comprehensive understanding of how structure influences heat transport is required. It has been argued that a buckled structure is able to suppress heat transport by increasing the flexural phonon scattering. Using a first principles approach, we calculate the lattice thermal conductivity of 2D mono-elemental materials with a buckled structure. Somewhat counterintuitively, we find that although 2D group-V materials have a larger mass and higher buckling height than their group-IV counterparts, the calculated κ of blue phosphorene (106.6 W mK^-1) is nearly four times higher than that of silicene (28.3 W mK^-1), while arsenene (37.8 W mK^-1) is more than fifteen times higher than germanene (2.4 W mK^-1). We report for the first time that a buckled structure has three conflicting effects: (i) increasing the Debye temperature by increasing the overlap of the p_z orbitals, (ii) suppressing the acoustic-optical scattering by forming an acoustic-optical gap, and (iii) increasing the flexural phonon scattering. The former two, corresponding to the harmonic phonon part, tend to enhance κ, while the last one, corresponding to the anharmonic part, suppresses it. This relationship between the buckled structure and phonon behaviour provides insight into how to control heat transport in 2D materials.

Ultrafast Three-Dimensional X-ray Imaging of Deformation Modes in ZnO Nanocrystals

Imaging the dynamical response of materials following ultrafast excitation can reveal energy transduction mechanisms and their dissipation pathways, as well as material stability under conditions far from equilibrium. Such dynamical behavior is challenging to characterize, especially operando at nanoscopic spatiotemporal scales. In this letter, we use X-ray coherent diffractive imaging to show that ultrafast laser excitation of a ZnO nanocrystal induces a rich set of deformation dynamics including characteristic "hard" or inhomogeneous and "soft" or homogeneous modes at different time scales, corresponding respectively to the propagation of acoustic phonons and resonant oscillation of the crystal. By integrating the 3D nanocrystal structure obtained from the ultrafast X-ray measurements with a continuum thermo-electro-mechanical finite element model, we elucidate the deformation mechanisms following laser excitation, in particular, a torsional mode that generates a 50% greater electric potential gradient than that resulting from the flexural mode. Understanding of the time-dependence of these mechanisms on ultrafast scales has significant implications for development of new materials for nanoscale power generation.

Characterization of thermal and mechanical properties of stanene nanoribbons: a molecular dynamics study

Thermal and mechanical properties of stanene nanoribbons have been characterized to aid the design of stanene based thermoelectrics and nanoelectronic devices.

Thermal transport in graphene/stanene hetero-bilayer nanostructures with vacancies: an equilibrium molecular dynamics study

Thermal transport in defected graphene/stanene hetero-bilayer nanostructures has been investigated to encourage the optimal design of thermal and nanoelectronic devices.

Lateral and flexural phonon thermal transport in graphene and stanene bilayers

The predicted in-plane thermal conductivity of the graphene/stanene hetero-bilayer is 311.1 W m⁻¹ K⁻¹, higher than most 2D materials such as phosphorene, hexagonal boron nitride, MoS₂ and MoSe₂.