Surface Formation Energy Research Articles

Temperature dependence of surface stress across an order-disorder transition:p(1×2)O/W(110)

Strain relaxations of a $p(1\ifmmode\times\else\texttimes\fi{}2)$ ordered oxygen layer on W(110) are measured as a function of temperature across the disordering transition using low-energy electron diffraction. The measured strains approach values of 0.027 in the $[1\overline{1}0]$ and $\ensuremath{-}0.053$ in the [001] direction. On the basis of the measured strain relaxations, we give quantitative information on temperature-dependent surface stress using the results of ab initio calculations. From the surface formation energy for different strains, determined by first-principles calculations, we estimate that surface stress changes from $\ensuremath{-}1.1$ for the ordered phase to $\ensuremath{-}0.2\text{ }\text{N}/\text{m}$ for the disordered one along $[1\overline{1}0]$, and from 5.1 to 3.4 N/m along [001]. Moreover, our observation that the strains scale inversely with domain size confirms that the strain relaxation takes place at the domain boundaries.

Formation energies of low-indexed surfaces of tin dioxide terminated by nonmetals

The surface formation energies of four low-indexed surfaces, including (001), (100), (110) and (011), of tin dioxide (SnO(2)) terminated by nonmetals (H, N, O, F, Cl, Br, and I) have been studied with the frameworks of density functional theory. A strong dependence of relative surface stabilities on surface atoms has been presented based on the calculations. Several instructions, in particular the selection of specific precursors and morphology controlling agents, have been further illustrated as a guideline for experimentalists. (C) 2010 Elsevier Ltd. All rights reserved.

The self-consistent charge density functional tight binding study on wurtzite nanowire

We present a first-principle study on the atomic and electronic structure of II–VI wurtzite ZnO unsaturated nanowire and examine the dependence of surface stress on nanowire lateral size and shapes (hexagonal, triangular and tube-like) with diameter up to 31 Å. We investigate the unsaturated dangling bond state in the region of bandgap with varying the wire’s diameter. We also calculated the surface formation energy and find that it decrease with increasing the wire diameter and a greater stability (lower surface formation energy) comes with hexagonal wires. Young’s modulus calculation and various tensile tests have been applied to show the mechanical properties. The electronics properties of these wires (e.g. band structure, Density of State, charge transfer via Mulliken population analysis) also exhibit wire’s diameter dependence behaviors.

Surface Reconstructions on GaN and InN Semipolar (2021) Surfaces

The reconstructions on semipolar GaN(2021) and InN(2021) surfaces are investigated on the basis of first-principles total-energy calculations. The surface formation energy clarifies that there are several reconstructions depending on the growth conditions. For GaN, the surface where topmost N atoms are desorbed is stable under N-rich conditions, whereas a metallic reconstruction with a Ga adlayer is stabilized under Ga-rich conditions. For InN, in contrast, the surface with an In adlayer is favorable regardless of the growth conditions. We also provide immediate access to the atomic structures of semipolar (2021) surfaces under realistic growth conditions using surface phase diagrams.

Surface Reconstructions on GaN and InN Semipolar (112̄2) Surfaces

The reconstructions on semipolar GaN(112̄2) and InN(112̄2) surfaces are systematically investigated on the basis of first-principles total-energy calculations. The surface formation energy clarifies that there are several reconstructions depending on the growth conditions: The surface with a Ga adatom is stable under N-rich conditions, whereas metallic reconstructions are favorable under Ga-rich (In-rich) conditions. The accumulation of electrons on the InN(112̄2) surface is also predicted from the analysis of its band structures. Furthermore, we provide immediate access to the atomic structures of semipolar surfaces under realistic growth conditions using surface phase diagrams.

Reconstructions of GaN and InN Semipolar (1011) Surfaces

We report a systematic and comprehensive investigation of reconstructions of semipolar GaN(1011) and InN(1011) surfaces by first-principles total-energy calculations. The surface formation energy indicates that there are several reconstructions depending on the growth conditions: The 1×2 surface consisting of a single Ga–Ga dimer and Ga vacancies is stable under N-rich conditions, whereas metallic reconstructions are favorable under Ga-rich (In-rich) conditions. We also characterize atomic structures of semipolar surfaces under realistic growth conditions using surface phase diagrams. For InN, the analysis of density of states predicts charge accumulations on semipolar surfaces.

Diffusion and formation energies of adatoms and vacancies on magnesium surfaces

This paper reports classical molecular statics calculations of magnesium {0 0 0 1}, {11¯01}, {11¯00}A, {112¯0} and {11¯00}B surfaces, specifically formation energies of defects (adatoms and surface vacancies) and flat surfaces and diffusion energy barriers of the defects. The formation energies show that the {11¯01} surface is thermodynamically more favorable than {11¯00}A, {11¯20} and {11¯00}B surfaces; in contrast, literature reports have often ignored the {11¯01} surface. The diffusion energy barriers of both adatoms and surface vacancies show strong diffusion anisotropy on {11¯01}, {11¯00}A, {112¯0} and {11¯00}B surfaces. Based on this anisotropy, the ratio of diffusion distances (of either adatoms or surface vacancies) along two orthogonal directions on {11¯01} is 37–55 at room temperature. Using the results of formation energies and diffusion energy barriers we develop a more complete understanding of surface orientations in Mg nanoblades synthesized by physical vapor deposition [F. Tang, T. Parker, H.-F. Li, G.-C. Wang, T.-M. Lu, J. Nanosci. Nanotechnol. 7 (2007) 3239]. In contrast to previous reports, we postulate that the side surfaces of Mg nanoblades are {11¯01} because (a) they have the second lowest surface formation energy and (b) the ratio of diffusion distances on them agrees with the experimental value of approximately 50.

Boron and indium incorporation in GaP(0 0 1) surfaces by vapour deposition: Density-functional supercell calculations of the surface stability

Using surface supercells and the density-functional method, surface formation energies are calculated for probable GaP(0 0 1) reconstructions without and with indium or/and boron substitutions. Obtained surface stability diagrams provide surface compositions and surface structures in dependence on the growth conditions: indium atoms are built into the c(4 × 4) patterns under strongly P-rich conditions and into the β2(2 × 4) reconstruction under less P-rich conditions. Under In-rich and non-P-rich conditions, initial structures of metallic InGa phases are formed in the (2 × 4) mixed-dimer reconstruction. In the c(4 × 4) and (2 × 4) mixed-dimer patterns the full range of In:Ga content is accessible by variation of the In:Ga ratio in the gas phase. Boron can be built into the c(4 × 4) patterns of the GaP(0 0 1) surface in form of isolated atoms or nearest-neighbours under strongly P-rich and moderately to strongly B-rich conditions. The boron incorporation is strongly enhanced at the surface in respect to theoretical predictions for the bulk, what explains the larger content found experimentally. Assuming P-rich conditions, which are suitable for the growth of the ternary alloys, the obtained surface stability diagram for the quaternary (BInGa)P shows that nearly the full range of In:Ga content is accessible. However, the boron content in the alloy is restricted as found analogously for (BGa)P and is independent of the indium content. The expected increase of the boron content in presence of indium cannot be confirmed. Contrary to the analogous GaAs systems, boron atoms do not substitute phosphor atoms (antisite position) in GaP, (InGa)P, (BGa)P, and (BInGa)P.

Effect of In-Adlayer on AlN (0001) and (000−1) Polar Surfaces

On the basis of the first-principles total-energy calculations within the density-functional theory, the surface formation energies and the charge density differences of AlN (0001) and (000−1) polar surfaces with an In-, Al-, or N-adlayer have been studied. The results show that In presents surfactant effect on AlN (0001) but does not behave as such on AlN (000−1), which is the same as the case of GaN. The surfactant effect of In is attributable to the much weaker In−Al bond than the Al−N bond on the Al-polar AlN surface and the bigger average diffusion coefficient for Al atoms on the Al-polar AlN surface with In-adlayer according to the calculated charge density differences and diffusion barriers, respectively.

Geometries and Electronic Structures for the Adsorption of Li on Si(001) Surface with Different Coverages

Using density functional theory, based on the pseudo-potential plane wave basis set, the geometries and electronic structures of Li/Si(001) systems with different Li atom coverages were investigated systematically. The effect of Li adsorption on surface properties was also investigated. Our results indicated that Li atoms preferred to adsorb on high symmetry sites between adjacent Si-Si dimers and that the smallest average adsorption energy was predicted for the 0.75 monolayer (ML) coverage. By analyzing the band structures, the Si(001) surface varied from semiconductor to conductor, then to semiconductor again with increasing Li coverage. The bandgap of the Si(001) surface increased obviously at 1.00 ML coverage because of the significant destruction of surface Si-Si dimers after Li adsorption. Since electrons obviously transferred from the Li atom to the substrate, the work function of the surface decreased and oscillated with an increase in coverage. Furthermore, according to the calculated surface formation energy, the phase corresponding to 0.75 ML coverage should be difficult to observe.

Adsorption of Al on the Si(0 0 1) surface

The first-principles calculations have been presented to study the adsorption of aluminum (Al) on the Si(0 0 1)(2×1) surface. We have investigated the optimized geometries and electronic structures of the adatom–substrate system. The adsorption energy of the system has been calculated. The most stable adsorption sites were consequently determined to be HH site and T3+T4. It is shown that the Si–Si dimer is asymmetric on the reconstructed bare surface and become symmetric upon Al adsorption. In addition, the bond length of Si–Si was found to be considerably elongated in the adsorption system. It is found that the work function change obtained in our work is different from other previous results on the adsorption of alkali metals on the Si(0 0 1) surface. In order to investigate the relative stability of phases at different coverages, the surface formation energy of the adsorption system was calculated. To shed light on the nature of the Al–Si bond and the character of silicon surface, the density of states (DOS) and difference charge density of the system were evaluated.

Density functional theory calculations of the surface structure of the inverse spinel zincorthotitanate

We present an examination of many different surface terminations ofZn2TiO4(ZTO) obtained by density functional theory calculations. We have examined a total of 41 surfaceterminations generated from the {001}, {011}, and {111} families of surfaces. Termination of theanisotropic bulk structure of ZTO can produce asymmetric corrugated surfaces that possiblyinclude surface termination artifacts. We have addressed this issue with surface ‘smoothing’via atomic transposition of individual atoms across the slab. This procedure reduces theenergy penalty associated with large geometric corrugations in the surface layer,particularly in the case of ZTO(111) surfaces. The interface with the lowest energy wasfound to be a termination of the ZTO(010) surface having a surface formation energy of1.09 J m−2. A moderately higher energy surface termination was found for the ZTO(110)surface. This ZTO(110) surface has a surface formation energy approximately0.1 J m−2 higher than that of the lowest energy ZTO(010) surface.

First-principles study of the structures and energetics of stoichiometric brookiteTiO2surfaces

First-principles density functional theory calculations at the generalized gradient approximation level are performed to investigate the structures and energetics of ten stoichiometric $1\ifmmode\times\else\texttimes\fi{}1$ low-index surfaces of brookite, the rarest and least understood of the natural polymorphs of titanium dioxide $(\mathrm{Ti}{\mathrm{O}}_{2})$. For each surface, different possible terminations are considered, and their structural relaxations are analyzed. As a general trend, undercoordinated surface Ti atoms are found to relax inward so as to form $\mathrm{Ti}{\mathrm{O}}_{x}$ polyhedra with O atoms at the vertices, analogous to the $\mathrm{Ti}{\mathrm{O}}_{6}$ octahedra of the bulk structure. For some surfaces, very large relaxations, involving several subsurface layers, are found to occur. From the computed surface formation energies, the relative stabilities of the different terminations are determined and found to be mainly related to the concentration of exposed coordinatively unsaturated metal (Ti) atoms. The equilibrium crystal shape of brookite $\mathrm{Ti}{\mathrm{O}}_{2}$ is also determined, and the relative fraction of each exposed surface is estimated.

Modelling Damage Progression by a Statistical Energy-Balance Algorithm

In this contribution some characteristics and predictive capabilities are discussed of a recently introduced model for damage progression and energy release, in view of modelling Acoustic Emission. The specimen is discretized in a network of connected springs, similar to a Fibre Bundle Model approach, with the spring intrinsic strengths statistically distributed according to a Weibull distribution. Rigorous energy balance considerations allow the determination of the dissipated energy due to crack surface formation and kinetic energy propagation. Based on results of simulations, the macroscopic behaviour emerging from different choices at “mesoscopic” level is discussed, in particular the relevance of model parameters such as the distribution of spring cross sections, Weibull modulus values, and discretization parameters in determining results like stressstrain curves and energy scaling versus time or specimen size.

Bond-order potential for silicon

The tight-binding description of covalent bonding is used to propose a four-level, bond-order potential for elemental silicon. The potential addresses both the $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ bonding and the valence of this $sp$-valent element. The interatomic potential is parametrized using ab initio and experimental data for the diamond cubic, simple cubic, face-centered-cubic, and body-centered-cubic phases of silicon. The bond-order potential for silicon is assessed by comparing the predicted values with other estimates of the cohesive energy, atomic volume, and bulk modulus for the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Sn}$, bc8, st12, and 46 clathrate structures. The potential predicts a melting temperature of $1650\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in good agreement with the experimental value of $1687\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The energetics of various high-symmetry point defect structures and the structure and energetics of small silicon clusters are investigated. The potential also provides a robust description of surface reconstructions; it notably predicts with high fidelity the surface formation energy of the (111) $7\ifmmode\times\else\texttimes\fi{}7$ dimer adatom stacking fault configuration.

Performance on molecules, surfaces, and solids of the Wu-Cohen GGA exchange-correlation energy functional

We present the results of Kohn-Sham calculations on molecules, surfaces, and solids which were obtained using a recently proposed exchange-correlation energy functional [Z. Wu and R. E. Cohen, Phys. Rev. B 73, 235116 (2006)]. The Wu-Cohen (WC) functional, like the well-known PBE functional [J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], is of the generalized gradient approximation form and was derived from the homogeneous electron gas and mathematical relations obeyed by the exact functional. The results on molecular systems show that among the functionals we tested, PBE remains superior for the energetics of covalent and noncovalent bonds. While this is not too surprising for noncovalent bonds due to the very good performance of PBE, unfortunately this holds also for covalent bonds, where PBE is a functional of rather poor quality. Calculations on transition-metal surfaces show that WC improves over local-density approximation (LDA) and PBE for the surface formation energy of $3d$ elements, while LDA is the best for heavier elements. In most cases, the lattice constant of solids as determined by the WC functional is in between the LDA and PBE results and on average closer to experiment. We show for each group of compounds which functional performs best and provide trends. In the particular case of lattice constants whose values are determined by weak interactions (e.g., the interlayer distance in graphite), the LDA functional is more accurate than the generalized gradient approximation functionals.

There is plenty of room for new structures at the bottom

The atomic structure of a surface is its most fundamental physical property since it defines the actual system under study, in the first place. Most other physical quantities sensitively depend on the surface structure. For all surfaces currently under investigation, the atomic configuration is by far not as precisely known as the respective bulk atomic structure, resulting, e.g., from X-ray structure determination. Therefore, each and every investigation of any surface property – no matter how sophisticated it may be – also adds to our understanding of its particular atomic structure at the same time. As a consequence, the history of investigations of innumerable surface properties is a history of surface structure determinations, as well. For most surfaces various experimental as well as theoretical studies have been carried out to arrive at convincing surface structure models complying with Charlie Duke’s claim that ‘‘one method is never enough’’. In theory, the optimal structure of clean stoichiometric surfaces is determined by minimizing the total energy of a surface system within the framework of quantum mechanics, which currently is done mainly with density functional theory employing either the local density approximation or some variant of the generalized gradient approximation. Since it is nowadays possible to prepare surfaces by epitaxial growth rather than by cleaving, nonstoichiometric surfaces need to be considered, as well. To do so, one usually refers to ab initio thermodynamics. In such cases a comparison of grand canonical potentials of structures with different stoichiometry or different adatom coverages yielding surface formation energies is a very powerful means to arrive theoretically at optimal surface structures. As suggested by Qian et al. [1] as well as by Northrup and Froyen [2], the formation energy of a binary semiconductor compound AB can be formulated in terms of the gas-phase chemical potential of only one of the two constituents, e.g., lA. The formation energy can then be studied from the A-rich to the B-rich regime just by monitoring the value of lA within its accessible range determined by the heat of formation of the AB bulk compound. There are many examples for which joint experimental and theoretical efforts have converged to generally accepted reconstruction models, to date. To name only a few, the famous Si(111)-(7 · 7), the Si(001)-(2 · 1) or the SiC(001)(3 · 2) surface shall be mentioned, which reconstruct according to the Takayanagy dimer-adatom-stacking-fault (DAS) model [3], the asymmetric dimer model (ADM) [4–8] or the two-adlayer asymmetric-dimer model (TAADM) [9–11], respectively. But there are many other semiconductor surfaces for which either the efforts have not yet lead to generally accepted models or not all possible reconstructions have been worked out, to date. The Letter of Segev and Van de Walle in this issue [12] adds a particularly nice facet to the last class of surface systems. It addresses the reconstruction of polar and nonpolar surfaces of InN and GaN which are wide-band-gap semiconductors whose hexagonal surfaces are currently moving into the focus of interest because of their paramount technological potential for advanced microelectronic and optoelectronic devices. Their specific electronic properties are the very basis of their technological importance. A most quantitative description of their surface atomic and electronic structure is highly desirable, therefore. Now it turns out, that the clean stoichiometric hexagonal surfaces of InN and GaN do not represent

Boron and indium substitution in GaAs(0 0 1) surfaces: Density-functional supercell calculations of the surface stability

Using the density-functional method and surface supercells the surface formation energies are calculated for the most stable GaAs(0 0 1) surface reconstructions without and with up to four indium or/and boron substitutions. Optimal conditions for the growth of the alloys are derived from calculated surface stability diagrams. The incorporation of indium into GaAs without phase separation is possible under strong As-rich conditions and medium to In-rich conditions. Less As-rich conditions can lead to the formation of an InAs phase. Ga-rich conditions give an InGa phase. Isovalent boron incorporation into GaAs without phase separation is possible under strong arsenic and reduced boron exposure. A BAs phase can be formed under more B-rich conditions. More Ga-rich conditions lead to the boron substitution in arsenic positions. The formed boron dimers can be a starting point for the formation of a boron phase. A true antisite boron substitution is less probable. Using the suitable growth conditions obtained for the ternary alloys it is energetically more favourable to incorporate both indium and boron (formation of BInGaAs) than to incorporate only one of the two elements (In or B). The antisite boron incorporation is not favoured in combination with isovalent boron or indium.

Magnetic Properties and Electronic Structure of Cr-Diffused SiC

In this presentation, the magnetic properties and electronic structure of Cr incorporated SiC(100) surface, including the surface formation energy and the surface electronic structure, was extensively investigated using ab initio calculations. the surfaces of p(2times1) and c(4times2)-AUDD were employed to simulate the Si-terminated SiC(100) surface, and the c(2times2) was prepared to calculate the C-terminated surface. The total magnetic moment and the magnetization energy were obtained by the spin-polarized calculation for one Cr atom in the SiC(100) surface supercell. Due to the surface effect of SiC(100), the total magnetic moment of SiC(100):Cr-p(2times1) was found to be increased. The origin of the surface magnetism will be discussed in terms of the density of states and the wave function characteristics around the Fermi level.

Effect of strain on atomic ordering and action of surfactants in ternary alloy thin films

Effect of surfactant $(\mathrm{Sb})$ on ordering in alloy thin films of $(\mathrm{In},\mathrm{Ga})\mathrm{P}$ and $(\mathrm{In},\mathrm{Ga})\mathrm{As}$, lattice mismatched with the substrate, is studied using ab initio total energy calculations based on the density functional theory. Anion-terminated thin films of $(\mathrm{In},\mathrm{Ga})\mathrm{As}$ on the $\mathrm{GaAs}\phantom{\rule{0.2em}{0ex}}[001]$ substrate and $(\mathrm{In},\mathrm{Ga})\mathrm{P}$ on the $\mathrm{GaP}\phantom{\rule{0.2em}{0ex}}[001]$ substrate are assumed in the ordered $\mathrm{CuPt}\text{\ensuremath{-}}\mathrm{B}$ geometry, with the $\ensuremath{\beta}2(2\ifmmode\times\else\texttimes\fi{}4)$-reconstructed surface. The results are compared with the previous calculations on the same alloy layers but lattice matched with the substrate. Consequences of strain (due to lattice mismatch) on the ordering in these films, bare and covered with surfactant, are discussed in relation with surface and interface geometries and in terms of the surface formation and interchange energies.