Electron Counting Model Research Articles

Parameter-Free and Electron Counting Satisfied Material Representation for Machine Learning Potential Energy and Force Fields.

We proposed a parameter-free volume element representation that satisfies the electron counting model and obtains accurate machine learning potential energy and direct force fitting of randomly perturbed hexagonal BN. Our method preserves permutational, translational, and rotational invariance and can be extended to three-dimensional systems, verified by a system of bulk Si. As a result, we obtained 0.57 meV/atom potential energy root mean squared error (RMSE) and 59 meV/Å force RMSE for perturbed bulk BN systems and 0.43 meV/atom potential energy RMSE and 36 meV/Å force RMSE for perturbed Si systems. In addition, an unbiased perturbation-based data set construction scheme is introduced and a continuous population distribution is obtained with a training data set of 4500, which is about 1 order of magnitude smaller than standard methods based on first-principles molecular dynamics simulations and saves a large amount of computing resources. General validity of our model is verified by structure optimization, molecular dynamics simulations, and extrapolations.

Abnormal stability of hydrogenic defects and magnetism near the HSrCoO2.5(0 0 1) surface

For conventional semiconductors, defect usually occurs on the surfaces to satisfy electron counting model, relax stress, and induce reconstructions. However, it is highly complex for BM-SrCoO2.5 (BM-SCO) and HSrCoO2.5 (HSCO) thin films because of oxygen vacancy channels (OVCs) in the bulk that can be considered as internal surfaces in addition to the most stable (001) surface. Therefore, it is unclear which surface provides the most preferred sites for H related defects to form. In addition, these defects may play significant roles in the phase transformation and magnetism tuning in the ionic liquid gating. To answer this question, we investigated the stability of the surfaces, H vacancies, and interstitials in HSCO using density functional theory. Unlike the general stability of H related defects in conventional semiconductors, the H vacancy prefers sites near the external surface or OVCs, while the H interstitial prefers sites of oxygen on a layer that contains six-fold coordinated Co in bulk because of the significant energy penalty by surface-induced local distortions and the crystal field splitting of Co atoms, exhibiting a weak ferromagnetism. These findings enrich the general understanding of complex surface phenomena of defect formation and provide an explanation of the good reversibility during phase transformation.

A brief review of reconstructions and electronic structures of MoS2 zigzag edges

Transition metal dichalcogenides, mainly focusing on MoS2, have attracted intensive studies in terms of their electronic and optical properties. Their lower-dimensional counterparts, such as nanoribbons and nanoclusters, gradually draw more research attention because of their potential applications in various electronic and spintronic devices. The edge states are essential to determine the intriguing electronic and magnetic properties of the nanocrystals. In this review, we mainly focus on the zigzag edges in the MoS2 system because they are more common in experiments. We first review the physical properties of the unreconstructed edges and then introduce the principles of edge reconstructions, the electron counting model (ECM). Then, based on the ECM, intrinsic edge reconstructions with different periodicities are discussed. The literature we reviewed suggests that the conductivities and magnetism of the edge states are highly related to the periodicities of the edges. Finally, the effects of the edge passivation with extrinsic atoms are reviewed. Edge passivation plays an important role in tuning the electronic and magnetic properties of the edge states and determining the morphology during the crystal growth. Furthermore, MoS2 zigzag edges could be an ideal platform to investigate the interplay between the edge states with different periodicities and magnetic dopants in the future.

Switchable electronic and enhanced magnetic properties of CrI3 edges.

Owing to its novel electronic and magnetic properties, two-dimensional CrI3 has great potential in the application of spintronic devices. However, as an inevitable line defect, the properties of the edges of CrI3 remain elusive. Here, via first-principles calculations with spin-orbit coupling, we investigated the thermodynamic stabilities, electronic and magnetic properties of thirteen CrI3 edges with different structures. We showed that zigzag edges are more stable than armchair edges, and a CrI3 nanoribbon can be either metallic or insulating depending on its chemical growth conditions. The edge stability and associated electronic properties can be understood in terms of the octahedron ligand field and electron counting model. In most cases, both the magnetic moment and Curie temperature can be enhanced by edges, which are in startle contrast to the surfaces of three-dimensional ferromagnetic materials, where a magnetic dead layer is often observed.

III-V colloidal nanocrystals: control of covalent surfaces.

Colloidal quantum dots (QDs) are nanosized semiconductors whose electronic features are dictated by the quantum confinement effect. The optical, electrical, and chemical properties of QDs are influenced by their dimensions and surface landscape. The surface of II–VI and IV–VI QDs has been extensively explored; however, in-depth investigations on the surface of III–V QDs are still lagging behind. This Perspective discusses the current understanding of the surface of III–V QDs, outlines deep trap states presented by surface defects, and suggests strategies to overcome challenges associated with deep traps. Lastly, we discuss a route to create well-defined facets in III–V QDs by providing a platform for surface studies and a recently reported approach in atomistic understanding of covalent III–V QD surfaces using the electron counting model with fractional dangling bonds.

Towards understanding the special stability of SrCoO2.5 and HSrCoO2.5

Reversible hydrogen incorporation was recently attested [N. Lu, $\textit{et al.}$, Nature $\textbf{546}$, 124 (2017)] in ${\text{SrCo}\text{O}_{2.5}}$, the brownmillerite phase (BM) of strontium cobalt oxide (SCO), opening new avenues in catalysis and energy applications. However, existing theoretical studies of BM-SCO are insufficient, and that of ${\text{HSrCo}\text{O}_{2.5}}$, the newly-reported hydrogenated SCO (H-SCO), is especially scarce. In this work, we demonstrate how the electron-counting model (ECM) can be used in understanding the phases, particularly in explaining the stability of the oxygen-vacancy channels (OVCs), and in examining the Co valance problem. Using density-functional theoretical (DFT) methods, we analyze the crystalline, electronic, and magnetic structures of BM- and H-SCO. Based on our structure search, we discovered stable phases with large bandgaps (> 1 eV) for both BM-SCO and H-SCO, agreeing better with experiments on the electronic structures. Our calculations also indicate limited charge transfer from H to O that may explain the special stability of the H-SCO phase and the reversibility of H incorporation observed in experiments. In contrary to the initial study, our calculation also suggests intrinsic antiferromagnetism (AFM) of H-SCO, showing how the measured ferromagnetism (FM) has possible roots in hole doping.

Tuning hydrogen adsorption on pure and doped ZnO (0001¯) surfaces by a simple electron counting model

Hydrogen (H) adsorption strengths on oxygen-terminated (0001¯) surfaces of pure and doped wurtzite ZnO are investigated under varying H surface coverage conditions. Consistent with the prediction of the classical electron counting rules, a 12 monolayer (ML) of adsorbed H changes the electronic structure of pure ZnO (0001¯) surface from metallic to semiconductor state by saturating unpaired electrons of surface oxygen atoms. This closed-shell electron configuration of the ZnO (0001¯) surface significantly reduces the adsorption strengths of subsequent H atoms, making the dissociative adsorption of a H2 molecule endothermic. We apply a simple electron counting model to predict and tune the coverage-dependent H adsorption strengths on general polar semiconductor surfaces. This model is confirmed by our investigations of H adsorption on (0001¯) surfaces of ZnO with a series of dopant elements (Na, Mg, Al, Ti, Fe, Sn, etc.). It can also be applied to H adsorption on other similar polar semiconductors, such as ZnO (0001¯) containing O vacancies, wurtzite GaN (0001¯), and zincblende ZnS (1¯1¯1¯) surfaces.

Metal–Insulator Transition of Ge–Sb–Te Superlattice: An Electron Counting Model Study

Ge–Sb–Te superlattice (GST-SL) is a newly emerging electronic material for nonvolatile phase-change memory with ultralow energy cost. However, its switching mechanism is still unclear with intensive debates. In this work, by first-principles calculations and an electron counting model study, we study the possible mechanism of phase change and the accompanying property transition of GST-SL. GST-SL are separated into individual layers by van der Waals gaps. We demonstrate that both the global chemical stoichiometry of the material and the local chemical stoichiometry of individual layer block are required to have an insulating band gap according to an electron counting model analysis. The electrical property can be adjusted by changing the local stoichiometry, such as producing defects around van der Waals gaps. Inspired by a previous experiment, we propose that a stacking-fault motion can spontaneously alter the band gap and results in a metal–insulator transition. This transition may provide a significant change of carrier concentration and indicate an ultralow energy-consumption process with a low energy barrier. The present investigations reveal a picture of electrical transition in GST-SL and may guide us to improve its device performances.

Multivalency-Induced Band Gap Opening at MoS2 Edges

Zigzag edges of monolayer MoS2 and other transition-metal (TM) dichalcogenides are experimentally shown to exhibit strong photoluminescence. Atomic models that have been proposed for these edges, however, are all metallic. Here, we address this puzzle by using first-principles calculations. We found that a more generic electron counting model (ECM) can be developed, which, when coupled with the ability of TM atoms at edges to change their valency from 4+ to 5+, can quantitatively account for the band gap opening at the zigzag edges. Due to the ECM, a 3× periodicity along the zigzag edge is necessary to open the band gap. Moreover, consistent with experiment, oxygen adsorption is shown to open even larger band gaps than intrinsic edges.

Structures and stabilities of CBHz (z ≤ 8) and CxB3-xHz (x = 1, 2, z ≤ 14): prediction of novel organo-boron radicals

Hydrogenated boron-carbon clusters, i.e. organo-borons, have received considerable attention both theoretically and experimentally. Herein, using a topology searching strategy, we systematically explore the structures and stabilities of small organo-borons with CBHz (z ≤ 8) and CxB3-xHz (x = 1, 2,z≤ 14) stoichiometry, with particular interests in the intrinsic stabilities of the organo-boron radicals. At the CCSD(T)/aug-cc-pVQZ//B3LYP/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVTZ levels, the stabilities of these global minimum organo-boron species were evaluated by considering dissociation pathways and the binding energy per atom. Aside from the five already studied radicals (CBH2, CBH4, C2BH2, C2BH4 and CB2H3), we predict six novel radicals, i.e. CBH6, C2BH6, C2BH8, CB2H, CB2H5 and CB2H7, which could be detected under suitable circumstances. However, observation of the highly hydrogenated CB2H9 radical is much less likely due to its minute stability towards H-extrusion. The computationally determined stable/meta-stable maximum hydrogenation numbers for CB, C2B and CB2 (6, 8 and 8, respectively) are in excellent agreement with a simple electron-counting model for CxBy chains. The newly predicted organo-boron radicals await future laboratory verification.

Step energy and step interactions on the reconstructed GaAs(001) surface

Using ab initio total energy calculations we have studied the relation between the step atomic configuration and its properties (step energy, donor/acceptor behavior, and step interaction) on a ${\ensuremath{\beta}}_{2}(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructed GaAs (001) surface. The results have been tested against the widely used elastic dipole model for the step energy and step interaction considered valid for stress-free surfaces. We have found that acceptor-behaving steps have an attractive interaction and donor-behaving steps have a repulsive interaction in contrast with the elastic dipole model which predicts always a repulsive interaction between like-oriented steps. To account for the attractive interaction we consider the electrostatic dipole interaction having the ${L}^{\ensuremath{-}2}$ scaling with the step distance $L$ and therefore compatible with the standard elastic model. Using a model charge distribution with localized point charges at the step based on the electron counting model we show that the electrostatic step interaction can indeed be generally attractive and of the same order of magnitude of the negative elastic dipole interaction. Our results show however that the usually employed dipole model is unable to account for the repulsive/attractive step interaction between donorlike/acceptorlike steps. Therefore, the ab initio results suggest an important electronic contribution to the step interaction, at least at the short step distances accessible to the first-principles study. Our results explain qualitatively many experimental observations and provide an explanation to the step bunching phenomenon on GaAs(001) induced by doping or by critical growth conditions as due to the stabilization of attractively interacting step structures. These ideas would lead to the development of a bottom-up surface step engineering.

Origin of symmetric STM images for the asymmetric atomic configuration on GaAs(001)–c(4 × 4)α surfaces

The empty-state scanning tunneling microscopy (STM) images of GaAs-c(4×4)α show symmetric features at positive biases, contrary to the naive prediction based on electron counting model. In this paper, we report that STM simulations based on first-principles electronic structure calculations successfully demonstrate symmetric images consistent with the STM observations. Furthermore, simple analysis has revealed that the origin of the symmetric images is the combined local electron density of multiple orbitals, and is essentially different from those on GaAs–c(4×4)β surfaces.

Ge quantum dots encapsulated by AlAs grown by molecular beam epitaxy on GaAs without extended defects

We demonstrate nearly spherical, strain-free, self-assembled Ge quantum dots (QDs) fully encapsulated by AlAs, grown on (100) GaAs by molecular beam epitaxy. The QDs were formed without a wetting layer using a high temperature, in situ anneal. Subsequent AlAs overgrowth was free from anti-phase domains and threading dislocations in cross section transmission electron microscopy. The straddling band alignment for Ge in AlAs promises strong and tunable confinement for both electrons and holes. The reflection high-energy electron diffraction pattern changed from 2 × 3 to 2 × 5 with anneal, which can be explained by surface reconstructions based on the electron-counting model.

Atomic and electronic structure of GaP/Si(111), GaP/Si(110), and GaP/Si(113) interfaces and superlattices studied by density functional theory

The atomic structure of GaP(111)/Si(111), GaP(110)/Si(110), and GaP(113)/Si(113) heterointerfaces was studied by ab initio calculations employing the density functional theory (DFT). Relative formation energies were computed for the interface layers allowing for atomic intermixing. The application of the electron-counting model, a construction principle used for surface reconstructions, to the case of the GaP(111)/Si(111) interfaces leads to electronic compensation at the heterovalent interfaces and to a reduction of the interface formation energy. The specific equilibrium (111) interface reconstruction can be tuned by changing the chemical potential. In particular, the GaP(111)A/Si(111) interface was found to be abrupt and uncompensated under P-rich conditions, whereas it is compensated under Ga-rich conditions. The GaP(111)B/Si(111) interface was found to be compensated. Contrary to the (111) interfaces, stoichiometric abrupt interfaces were found to be the most energetically favorable for the GaP(110)/Si(110) and the GaP(113)/Si(113) interfaces. These interfaces do not reconstruct. Although both interfaces are compensated, the GaP(113)/Si(113) superlattice exhibits a polarization field, in contrast to the (110) superlattice.

Phase diagram of graphene nanoribbons and band-gap bifurcation of Dirac fermions under quantum confinement

A $p$-$T$ phase diagram of graphene nanoribbons (GNRs) terminated by hydrogen atoms is established based on first-principles calculations, where the stable phase at standard conditions (25 \ifmmode^\circ\else\textdegree\fi{}C and 1 bar) is found to be a zigzag GNR (zzGNR). The stability of this new GNR is understood based on an electron-counting model, which predicts semiconducting nonmagnetic zzGNRs. Quantum confinement of Dirac fermions in the stable zzGNRs is found to be qualitatively different from that in ordinary semiconductors. Bifurcation of the band gap is predicted to take place, leading to the formation of polymorphs with distinct band gaps but equal thermodynamic stability. A tight-binding model analysis reveals the role of edge symmetry on the band-gap bifurcation.

Atomic and electronic structure of S-terminated GaAs(001) surface

We have reported, from ab initio calculations, on the changes in the electronic and structural properties due to S adsorption on the GaAs(001) surface. In our investigation, we have considered the experimentally observed (2×6) reconstruction for S coverages of n/12 monolayers (MLs), with n=2, 4, 5, 6, 8, and 10. Electronic energy levels and density of states for all the six coverages of S have been discussed. Using the chemical potential argument our calculations suggest that the reconstruction with S coverage of 10/12 ML (the Tsukamoto model) represents the most energetically preferable structure for S/GaAs(001). However, while this adsorption geometry is consistent with the electron counting model, it does not passivate the GaAs(001) surface electronically. The most effective reduction in the density of states in bulk band gap region is obtained for the coverage of 0.5 ML with five mixed As–S dimers, though this geometry is inconsistent with the electron counting model for chemical passivation of the surface.

Bismuth-stabilizedc(2×6)reconstruction on a InSb(100) substrate: Violation of the electron counting model

By means of scanning tunneling microscopy/spectroscopy (STM/STS), photoelectron spectroscopy, and first-principles calculations, we have studied the bismuth (Bi) adsorbate-stabilized InSb(100) substrate surface which shows a $c(2\ifmmode\times\else\texttimes\fi{}6)$ low-energy electron diffraction pattern [thus labeled $\text{Bi}/\text{InSb}(100)c(2\ifmmode\times\else\texttimes\fi{}6)$ surface] and which includes areas with metallic STS curves as well as areas with semiconducting STS curves. The first-principles phase diagram of the Bi/InSb(100) surface demonstrates the presence of the Bi-stabilized metallic $c(2\ifmmode\times\else\texttimes\fi{}6)$ reconstruction and semiconducting $(4\ifmmode\times\else\texttimes\fi{}3)$ reconstruction depending on the chemical potentials, in good agreement with STS results. The existence of the metallic $c(2\ifmmode\times\else\texttimes\fi{}6)$ phase, which does not obey the electron counting model, is attributed to the partial prohibition of the relaxation in the direction perpendicular to dimer rows in the competing reconstructions and the peculiar stability of the Bi-stabilized dimer rows. Based on (i) first-principles phase diagram, (ii) STS results, and (iii) comparison of the measured and calculated STM and photoemission data, we show that the measured $\text{Bi}/\text{InSb}(100)c(2\ifmmode\times\else\texttimes\fi{}6)$ surface includes metallic areas with the stable $c(2\ifmmode\times\else\texttimes\fi{}6)$ atomic structure and semiconducting areas with the stable $(4\ifmmode\times\else\texttimes\fi{}3)$ atomic structure.

Car–Parrinello simulation of initial growth stage of gallium nitride on carbon nanotubes

Car–Parrinello molecular dynamics (CPMD) simulations based on the density functional theory (DFT) were conducted to determine the initial growth process of gallium nitride on exterior wall of single-walled carbon nanotubes (SWCNTs). The theoretical results revealed that the nitrogen-adsorbed surface is more easily formed on the pristine surface of SWCNTs than on the gallium-adsorbed surface. The results also demonstrated that the growth of gallium nitride on metallic SWCNTs is more stable than that on semiconducting ones. The gallium nitride construction structures on both (10, 0) and (5, 5) SWCNTs come to satisfy the electron counting model. Our theoretical approach provides an atomic-scale insight into the regions of the initial growth processes of gallium nitride on single-wall carbon nanotubes.

Bi- and Au-Induced Reconstructions on GaAs(001)-2 ×4 Surface

Submonolayer Bi and Au adsorptions on the GaAs(001)-2 × 4 surface are investigated by scanning tunnelling microscopy, low energy electron diffraction and first-principles calculations. The 1 × 4 and 3 × 4 reconstructed surface induced by Bi and Au, respectively, are revealed and their structural models are proposed based on experiments and first-principles calculations. Moreover, the validity of the recently proposed generalized electron counting (GEC) model [Phys. Rev. Lett. 97 (2006) 126103] is examined in detail by using the two surfaces. The GEC model perfectly explains the structural features, such as the characteristic short double-line structure in the Bi-1 × 4 surface and the 3× arrangement of four-atom Au clusters.

Structural and electronic properties of Bi-adsorbate-stabilized reconstructions on the InP(100) andGaAsxN1−x(100)surfaces

Bismuth (Bi) adsorbate-stabilized reconstructions on the InP(100) and $\mathrm{Ga}{\mathrm{As}}_{x}{\mathrm{N}}_{1\ensuremath{-}x}(100)$ surfaces have been studied by scanning tunneling microscopy (STM) and spectroscopy (STS), x-ray photoelectron spectroscopy, and low-energy electron diffraction. With decreasing coverage, Bi is found to stabilize the $(2\ifmmode\times\else\texttimes\fi{}1)$, $(2\ifmmode\times\else\texttimes\fi{}8)$, and $(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructions on the InP(100) surface and the $(2\ifmmode\times\else\texttimes\fi{}1)$ and $(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructions on the $\mathrm{Ga}{\mathrm{As}}_{x}{\mathrm{N}}_{1\ensuremath{-}x}(100)$. STM results show that both the $\mathrm{Bi}∕\mathrm{In}\mathrm{P}(100)(2\ifmmode\times\else\texttimes\fi{}4)$ and $\mathrm{Bi}∕\mathrm{Ga}{\mathrm{As}}_{x}{\mathrm{N}}_{1\ensuremath{-}x}(100)(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructions can be described with the $\ensuremath{\alpha}2$-like structural model. The current-voltage curves measured by STS show the $\mathrm{Bi}∕\mathrm{In}\mathrm{P}(100)(2\ifmmode\times\else\texttimes\fi{}1)$ and $\mathrm{Bi}∕\mathrm{Ga}{\mathrm{As}}_{x}{\mathrm{N}}_{1\ensuremath{-}x}(100)(2\ifmmode\times\else\texttimes\fi{}1)$ structures, which do not obey the electron counting model, to be semiconducting and metallic, respectively. Combining our experimental findings, we propose atomic models for the $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstructions. An issue why Bi stabilizes unusual $(2\ifmmode\times\else\texttimes\fi{}1)$ structures is discussed.