Session A5: Surfaces: Structure, Transitions and Morphological Evolution

The Relaxation of Vicinal (001) with ZigZag [110] Steps

This talk presents a kinetic Monte Carlo study of the relaxation dynamics of $\left[110\right]$ steps on a vicinal $\left(001\right)$ simple cubic surface. This system is interesting because $\left[110\right]$ steps have different elementary excitation energetics and favor step diffusion more than close-packed $\left[100\right]$ steps. In this talk we show how this leads to relaxation dynamics showing greater fluctuations on a shorter time scale for $\left[110\right]$ steps as well as 2-bond breaking processes being rate determining in contrast to 3-bond breaking processes for $\left[100\right]$ steps. The existence of a steady state is shown via the convergence of terrace width distributions at times much longer than the relaxation time. In this time regime excellent fits to the modified generalized Wigner distribution (as well as to the Berry-Robnik model when steps can overlap) were obtained. Also, step-position correlation function data show diffusion-limited increase for small distances along the step as well as greater average step displacement for zigzag steps compared to straight steps for somewhat longer distances along the step. Work supported by NSF-MRSEC Grant DMR 05-20471 as well as a DOE-CMCSN Grant.   

Embedded Atom Method Potential for Ni-Cu Alloys and Its Applications for Ni, Cu growth on Cu(111)

We developed a semi-empirical, many-body type model potential to investigate static and dynamic properties of Ni-Cu alloys. The formalism is based on the embedded atom method with improved optimization techniques. The Ni-Cu alloy potential was determined by fitting to data on lattice parameters, cohesive energies for L1$_{0}$, L1$_{1}$, L1$_{2}$, and L1$_{3}$ phases, together with vacancy formation energies, bulk modulus and elastic properties for L1$_{2}$, L1$_{3}$ phases. Our preliminary calculations for energy barriers for the diffusing Ni and Cu atoms on Cu(111) based on the nudged elastic band method are found to be consistent with the available experimental and other theoretical results. Our ultimate goal is to describe the varying characteristics in growing islands of pure Cu, Ni atoms and mixed Ni-Cu combinations on Cu(111) [S. Pons et al., Surf. Sci., \textbf{511}, 449, (2002)].   

Computational diffusion model of reconstructed regions in Ag/Si epitaxial growth

The thermal decay of Ag islands, grown epitaxially in a Stranski-Krastanov mode on Si(001) and Si(111) surfaces, has been studied experimentally with photoemission electron microscopy (PEEM). In a range of elevated temperatures the islands decay mainly by dissociation of Ag atoms from island edges, rather than by direct desorption into the gas phase. On the surrounding surface, the Ag atoms are subject to thermally-activated diffusion and desorption. The Ag surface concentration decreases with distance from the island edges. Where the local concentration is above a critical value, coverage-dependent reconstructed overlayers form surrounding the islands. The spread of the overlayers, relative to the position of the decaying island, depends on competition between diffusion and desorption. Previous quasi-static models [1] have shown that the observed reconstructed regions are related to the atomistic parameters describing surface diffusion, and have been applied to extract diffusion coefficients from the experimental data. Here we present results from a dynamic diffusion model that captures many of the qualitative and quantitative time- and temperature-dependent phenomena observed in the experiments. \\[4pt] [1] K.R. Roos et. al. PRL 100, 016103 (2008); D. Wall et. al. NJP 12 (2010) 103019   

Plasma-assisted molecular beam epitaxy growth of ZnSnN$_{2}$

The Zn-IV-nitrides are a promising series of ``earth abundant element'' semiconductors with a predicted band gap range of 0.6 eV to 5.4 eV, which, like the (Al,Ga,In)N family, spans the entire visible solar spectrum. Considering this alternative family has a number of advantages, including the avoidance of indium, the price of which has varied almost an order of magnitude over the past decade, and surface electron accumulation which is present in the In-rich alloys. Not all members of this family have yet been synthesized, in particular ZnSnN$_{2}$, the most important member for PV with its predicted band gap of approximately 2 eV. We have successfully grown a series of these films using plasma-assisted molecular beam epitaxy using elemental Zn and Sn sources. In this report, we discuss the relationship between process parameters and microstructure, as well as stoichiometry as determined by Rutherford backscattering spectrometry. Additionally, we provide preliminary estimates for its bandgap energy based on photoluminescence and optical absorption.   

Transition between two patterns on an Au-deposited Si(111) surface

Two distinct patterns have been observed by depositing sub-monolayer Au onto a Si(111)-(7$\times $7) surface with a small miscut angle. Upon depositing Au at 600\r{ }C, we find that a stripe of (5$\times $2) reconstruction forms at the upper step edge in every terrace. For 700\r{ }C deposition, one entire terrace out of several terraces transforms into the (5$\times $2) reconstruction while the other terraces are totally unaffected by the Au deposition. The relative population between the (5$\times $2) and the (7$\times $7) terrace is governed by the amount of deposited Au. After annealing at a temperature above 700\r{ }C the striped (5$\times $2) pattern transforms into the (5$\times $2)-terrace pattern. The similarity between this ?coarsening? of (5$\times $2) reconstruction and the Ostwald ripening of clusters is striking and will be discussed. One application using the (5$\times $2) pattern as a template to grow nanostructure in designated regions will be demonstrated.   

Unusual Island Formations of Iridium on Ge(111) Studied by STM

We have used scanning tunneling microscopy (STM) to characterize the growth of iridium onto Ge(111). Iridium was deposited onto the Ge(111) c(2x8) surface at different coverages less than 1ML, and the samples were annealed to temperatures between 550K and 750K. A new form of growth was observed, consisting of pathways connecting larger iridium islands. As the annealing temperature increased, the iridium growth first formed unusual shapes with finger-like protrusions. Next, these shapes broke apart into smaller islands, which ultimately formed into larger islands at higher temperatures. High resolution images have been obtained, which allow insight into the atomic arrangements.   

Thickness-dependent Adatom-Adatom Binding Energy on Pb(111): The Effect of Quantum Size Effect on Critical Nucleus

We perform first-principles calculations to investigate adatom-adatom binding energies on Pb(111) as a function of film thickness. An odd-even thickness-dependent oscillation is found in the adatom-adatom binding energies, in analogy to the similar behavior in adatom surface binding energies and diffusion barriers found previously. We will discuss these results in relation to the thickness-dependent island nucleation density and compactness, as observed in recent experiments.   

De-wetting of thin films: Analytic theory of cluster coarsening dynamics

Long range de-wetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multi-layer islands) and pits, observed in thin films of soft materials (polymers), as well as in thin films of liquid and solid metals. These long range de-wetting interactions introduce a distinct long lasting early-time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle), and by effective coarsening exponents that depend on cluster size. In this study, we develop an analytic theory capable to calculate these effective size-dependent coarsening exponents characterizing the cluster growth in the early-time cross-over regime. Such a pronounced cross-over behavior has been indeed seen in experiments; however its physical origin has remained elusive to this date. Our results attribute these observed phenomena to ubiquitous long range de-wetting interactions acting across thin films.   

Surface morphological stabilization of crystalline solids under the simultaneous action of electric, thermal, and mechanical fields

We report a detailed analysis of the morphological stability of planar surfaces of electrically and thermally conducting stressed crystalline elastic solids under the simultaneous action of an electric field, an imposed temperature gradient, and uniaxial tension. Our analysis is based on linear stability theory and self-consistent dynamical numerical simulation according to a fully nonlinear model that accounts for curvature- and stress-driven surface diffusion, surface electromigration and thermomigration, as well as surface diffusional anisotropy. Our self-consistent dynamical simulations combine a front tracking method for monitoring surface morphological evolution with Galerkin boundary-integral computations of the displacement and temperature fields and the electrostatic potential. We determine the surface morphological stability domain boundaries and the critical values of the applied electric-field strength and temperature gradient required to stabilize the planar surface morphology. We explore the synergistic or competing effects on the surface morphological response of the simultaneously applied thermal and electric fields, aiming at optimization of the electric-field strength and temperature gradient requirements for planar surface stabilization.   

Electromigration-driven morphological evolution of monolayer-thick epitaxial islands on substrates

Electromigration-driven dynamics, with and without the simultaneous action of elastic strain, can lead to pattern formation of surface morphological features that may have significant impact on nanofabrication. An important example is epitaxial islands on substrates; for heteroepitaxial islands, misfit strain is induced due to lattice mismatch with the substrate. We develop a fully nonlinear model for the driven morphological evolution of monolayer-thick coherently strained islands on crystalline elastic substrates with diffusional mass transport limited to the island circumference. We carry out self-consistent dynamical simulations of such island dynamics, combining front tracking methods with solutions to the corresponding electrostatic and elastostatic boundary-value problems. We develop a universal scaling theory that explains the simulation results for the dependence of the island migration speed on the island size, electric field, and epitaxial system parameters for isolated, morphologically stable islands. We investigate systematically thermal, elastic, and size effects on the migration and morphological evolution of heteroepitaxial islands. We also find and characterize a variety of stable asymptotic states in the driven dynamical response of such heteroepitaxial islands.   

Electromigration-driven surface morphological stabilization of coherently strained thin films on elastically deformable substrates

We study the surface morphological stability of a coherently strained thin film grown epitaxially on a substrate and subjected to an external electric field; both infinitely thick and finite-thickness elastic substrates are examined. Due to its lattice mismatch with the substrate material, the film may undergo a Stranski-Krastanow (SK) instability, resulting in formation of islands on the film surface. To examine the morphological stability of the epitaxial film's planar surface state, we conduct a linear stability analysis based on a three-dimensional model of driven surface morphological evolution. We also consider the use of thin compliant substrates, which partly accommodate elastically the lattice-mismatch strain. We find that, regardless of the substrate type, the simultaneous action of a properly applied and sufficiently strong electric field is necessary to stabilize the planar morphology; in such cases, surface electromigration can inhibit SK-type instabilities and control the onset of island formation on the film surface. Our analysis shows that the critical electric-field strength required to stabilize the planar morphology of a thin film on a compliant substrate can be reduced by up to two orders of magnitude compared to that for a conventional thick substrate.   

Quantum Monte Carlo Study of Surface Energy

The accuracy of Density Functional Theory (DFT) is based on the exchange-correlation approximation used and needs to be checked by highly accurate quantum many-body approaches. We have performed calculations of the surface energies using the state-of-the-art diffusion quantum Monte Carlo (QMC) method to examine the accuracy of LDA and GGA (PBE) functionals in the study of surface energy. The systems studied include NaCl(100), MgO(100), CaO(100), TiO$_{2}$(110), Si(100)-(2x2), C(100)-(2x2), and Ge(100)-(2x2) surfaces. Our results indicate that (i) the surface energy by DMC is always larger than the surface energy by LDA; and (ii) the surface energy by LDA is always larger than the surface energy by GGA. For the surface energies of NaCl(100) and MgO(100), the DMC results reproduce the experimental measured values accurately. To conclude, when compared the surface energies obtained by DFT and DMC, the results predicted by DFT using either LDA or GGA functional are underestimated.   

Reconstructions of the GaN(10$\bar{1}$$\bar{1}$) surfaces: Density functional theory calculations

GaN has been extensively studied for its potential applicability in optoelectronics as well as in spintronics. The functional performance in such applications depends on the surface characteristics of thin films. Thin films of GaN are typically grown along the polar [0001] direction, but their light-emission efficiency is reduced due to the electron-hole separation. A strategy to remedy such an undesired effect is to grow films along nonpolar or semipolar directions. In this presentation, we will address the reconstructions of the Ga-terminated semipolar (10$\bar{1}$$\bar{1}$) surface. We performed the density functional theory calculations using the generalized gradient approximation, the projector augmented wave potentials, and the repeated slabs. From the calculated energetics of various reconstructions, we found that there exist a few structural motifs of GaN(10$\bar{1}$$\bar{1}$). They are short Ga chains and Ga vacancies. For instance, a 4 $\times$ 2 reconstruction with a Ga tetramer and surface Ga vacancies is stable in the N-rich condition, which is significantly different from the previous results [Akiyama \emph{et al}, Jpn. J. Appl. Phys. 48, 100201 (2009)]. Our results would provide a comprehensive understanding on the Ga-terminated semipolar surfaces.   

Cross-sectional scanning tunneling microscopy at GaN (10-10)

Group-III nitrides are the materials of choice for optoelectronic devices in the green to ultraviolet wavelength range. Recently, the question arose, whether the growth of GaN based devices could be improved by switching from polar surfaces to the non-polar ones. For non-polar GaN surfaces only little is known about the exact energetic positions of surface states, and thus their possible influence on the Fermi level. Furthermore, GaN still suffers from high dislocation densities, far above that of zincblende type III-V semiconductor crystals, which are detrimental for optoelectronic applications of GaN. Therefore we investigated the GaN(10-10) cleavage surface by cross-sectional scanning tunneling microscopy nd spectroscopy. We were able to identify the energetic positions of the intrinsic surface states and the Fermi level. We found that both, the filled N-derived and empty Ga-derived dangling bond states are outside the fundamental band gap, the latter one being 0.1--0.2~eV above the conduction band minimum. The observed band gap is 3.4$\pm$0.2~eV, in agreement with the nominal value from the bulk. The observed Fermi level pinning of about 1.0~eV below the conduction band edge is attributed to a high defect density at the surface, but not to intrinsic surface states.   

Geometrical and Electronic structures of Planar and Buckled Silicene on Ag(111)

Silicene grown on the Ag(111) surface was investigated by scanning tunneling microscopy / spectroscopy (STM / STS). Two atomic arrangements of honeycomb lattice, planar and buckled, were found. The planar silicene is consisted of Si atoms in the same height while the buckled one shows slightly twisted structure in the vertical direction. Compared to the planar silicene, the lateral distance between two neighboring atoms in the buckled silicene is reduced with about 7{\%}. Assuming that there is no change in the length of Si-Si bond, the angle between the Si-Si bond and the axis normal to the surface is 110 degrees, which is close to the bond angle of 109 degrees in the sp$^{3}$ hybridization. This might suggest that the Si-Si bonding in the buckled silicene is formed mainly by sp$^{3}$ hybridization rather than sp$^{2}$ However, our STS observations certainly showed a Dirac cone feature at the Fermi level for both types of silicene. Thus, we conclude that the electronic configuration of buckled silicene partially remains in sp$^{2}$ hybridization and the charge carriers still behave as the massless Dirac fermions.