# Ted EinsteinUniversity of Maryland, College Park | UMD, UMCP, University of Maryland College Park · Department of Physics

Ted Einstein

Ph.D. (1973) U. of Pennsylvania, Physics

## About

288

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## Publications

Publications (288)

We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and w...

Relationships between concentration of unintentionally doped carbon in GaN and its metalorganic vapor phase epitaxy conditions were investigated theoretically. A kinetic-thermodynamic model which considers kinetic behavior of adsorbed atoms on vicinal surface was proposed. Thermodynamic properties of gas species and adsorption energies obtained by...

A scanning tunneling microscopy study of anthraquinone (AQ) on the Au(111) surface shows that the molecules self-assemble into several structures depending on the local surface coverage. At high coverages, a close-packed saturated monolayer is observed, while at low coverages, mobile surface molecules coexist with stable chiral hexamer clusters. At...

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length la. For la=0 the...

We present a kinetic Monte Carlo study of the relaxation dynamics and steady state configurations of 〈110〉 steps on a vicinal (001) simple cubic surface. This system is interesting because 〈110〉 (fully kinked) steps have different elementary excitation energetics and favor step diffusion more than 〈100〉 (nominally straight) steps. In this study we...

We present a kinetic Monte Carlo study of the relaxation dynamics and steady state configurations of 〈110〉 steps on a vicinal (001) simple cubic surface. This system is interesting because 〈110〉 (fully kinked) steps have different elementary excitation energetics and favor step diffusion more than 〈100〉 (nominally straight) steps. In this study we...

We present a kinetic Monte Carlo study of the relaxation dynamics and steady state configurations of 〈110〉 steps on a vicinal (001) simple cubic surface. This system is interesting because 〈110〉 (fully kinked) steps have different elementary excitation energetics and favor step diffusion more than 〈100〉 (nominally straight) steps. In this study we...

In this paper we explore the meandering instability of vicinal steps with a kinetic Monte Carlo simulations (kMC) model including the attractive next-nearest-neighbor (NNN) interactions. kMC simulations show that increase of the NNN interaction strength leads to considerable reduction of the meandering wavelength and to weaker dependence of the wav...

In studies of epitaxial growth, analysis of the distribution of the areas of capture zones (i.e. proximity polygons or Voronoi tessellations with respect to island centers) is often the best way to extract the critical nucleus size i. For non-random nucleation the normalized areas s of these Voronoi cells are well described by the generalized Wigne...

We present a method of analyzing the results of density functional modeling of molecular adsorption in terms of an analogue of molecular orbitals. This approach permits intuitive chemical insight into the adsorption process. Applied to a set of anthracene derivates (anthracene, 9,10-anthraquinone, 9,10-dithioanthracene, and 9,10-diselenonanthracene...

This chapter discusses the equilibrium crystal shape (ECS) from a physical
perspective, beginning with a historical introduction to the Wulff theorem. It
takes advantage of excellent prior reviews, particularly in the late 1980's,
recapping highlights from them. It contains many ideas and experiments
subsequent to those reviews. Alternatives to Wul...

This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning
with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews,
particularly in the late 1980s, recapping highlights from them. It contains many ideas and experiments
subsequent to those reviews. Alternatives to Wulf...

We propose a novel island nucleation and growth model explicitly including
transient (ballistic) mobility of the monomers deposited at rate $F$, assumed
to be in a hot precursor state before thermalizing. In limiting regimes,
corresponding to fast (diffusive) and slow (ballistic) thermalization, the
island density $N$ obeys scaling $N \propto F^\al...

The Burton–Cabrera–Frank (BCF) theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatom...

Spurred by theoretical predictions from Ferrari et al. (Phys Rev E 69:035102(R), 2004), we rederived and extended their result heuristically. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps...

Exposure to oxygen at 300–340 °C results in triangular etch pits with uniform orientation on the surfaces of atomically thin molybdenum disulfide (MoS2), indicating anisotropic etching terminating on lattice planes. The triangular pits grow laterally with oxidation time. The density of pits scarcely depends on oxidation time, temperature, and MoS2...

We have argued that the capture-zone distribution (CZD) in submonolayer
growth can be well described by the generalized Wigner distribution (GWD)
$P(s)=a s^\beta \exp(-b s^2)$, where $s$ is the CZ area divided by its average
value. This approach offers arguably the best method to find the critical
nucleus size $i$, since $\beta \approx i + 2$. Vari...

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical s...

We have carried out a systematic study of the wrinkling instability of
graphene membranes supported on SiO2 substrates with randomly
placed silica nanoparticles. At small nanoparticle density, monolayer
graphene adheres to the substrate and is highly conformal over the
nanoparticles. With increasing nanoparticle density, and decreasing
nanoparticle...

Surface oxidation of MoS2 markedly affects its electronic,
optical, and tribological properties. However, oxidative reactivity of
atomically thin MoS2 has yet to be addressed. Here, we
investigate oxidation of atomic layers of MoS2 using atomic
force microscopy and Raman spectroscopy. MoS2 is mechanically
exfoliated onto SiO2 and oxidized in Ar/O2...

An ``overlayer'' of molecules that breaks the AB symmetry of graphene
can produce (modify) a band gap in single- (bi-) layer graphene.footnotetextM. Li et al., Phys. Rev. B 76, 155438 (2007) Since the
triangular shaped trimesic acid (TMA) molecule forms two familiar
symmetry breaking configurations, we are motivated to model TMA
physisorption on gr...

Ordered molecular superlattices, particularly those made of planar
aromatics with their attendant pi orbitals, have the potential to break
the graphene sublattice degeneracy and create a band gap. Trimesic acid
(TMA) is a promising candidate due to its self-assembly into
symmetry-breaking superlattices nearly commensurate with that of
graphene. We...

While most Monte Carlo simulations assume only nearest-neighbor steps
interact elastically, most analytic frameworks (especially the
generalized Wigner distribution) posit that each step elastically repels
all others. In addition to the elastic repulsions, we allow for possible
surface-state-mediated interactions. We investigate analytically and
nu...

The utility of using the distribution of capture zones (CZD) to
characterize epitaxial growth continues to mount. For non-Poisson
deposition (i.e. when island nucleation is not fully random) the areas
of these Voronoi cells (proximity polygons) can be well described by the
generalized Wigner distribution (GWD), particularly in the central
region ar...

In the many years since it was first proposed, the Burton- Cabrera-Frank
(BCF) model of step-flow has been experimentally established as one of
the cornerstones of surface physics. However, many questions remain
regarding the underlying physical processes and theoretical assumptions
that give rise to the BCF theory. In this work, we formally derive...

Stating that island nucleation is an essential step in the formation of
an epitaxial or supported layer may appear trivially obvious. However,
less trivial is the observation that the size of the critical nucleus
plays a crucial role in that it determines both the island density (and
therefore the size of domains) and the evolution of the island
mo...

The response of the Cu(111) Shockley surface state to an external electrical
field is characterized by combining a density-functional theory calculation for
a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis
is facilitated by a decoupling of the Kohn-Sham states via a rotation in
Hilbert space. We find that the surface st...

Single-layer graphene (SLG) supported on SiO(2) shows anomalously large chemical reactivity compared to thicker graphene, with charge inhomogeneity-induced potential fluctuations or topographic corrugations proposed as the cause. Here we systematically probe the oxidative reactivity of graphene supported on substrates with different surface roughne...

To manipulate the Cu(111) partially-filled Shockley surface state, we
study its response to an external fieldootnotetextKB, TLE, PH;
arXiv 1109:6706 E and physisorbed PAHs and quinone molecules. We use
density-functional theory calculations with periodic-boundary
conditions. The van der Waals density functional version vdW-DF2
accounts for the mole...

We utilize scanning tunneling microscopy to characterize the nucleation,
growth, and morphology of C60 on ultrathin SiO2
grown at room temperature. C60 thin films are deposited in
situ by physical vapor deposition with thicknesses varying from <0.05
to ˜1 ML. Island size and capture zone distributions are examined
for a varied flux rate and substra...

Growing one-dimensional metal structures is an important task in the
investigation of the electronic and magnetic properties of new devices.
We used kinetic Monte-Carlo (kMC) method to simulate the formation of
nanowires of several metallic and non-metallic adatoms on Cu and Pt
vicinal surfaces. We found that mono-atomic chains form on step-edges
d...

Graphene's structure and electronic properties provide a framework for
understanding molecule-substrate interactions and developing techniques
for band gap engineering. Controlled deposition of molecular adsorbates
can create superlattices which break the degeneracy of graphene's
two-atom unit cell, opening a band gap. We simulate scanning tunnelin...

In studying the growth of islands on a surface subjected to a particle
flux, we found it useful to characterize the distribution of the areas
of associated Voronoi (proximity or Wigner-Seitz) cells in terms of the
generalized Wigner surmiseootnotetextAP & TLE, PRL 99 (2007)
226102; PRL 104 (2010) 149602 and the gamma distributions. Here we show
tha...

Chemical reactivity of single layer graphene supported on a substrate is
observed to be enhanced over thicker graphene. Possible mechanisms for
the enhancement are Fermi level fluctuations due to ionized impurities
on the substrate, and structural deformation of graphene induced by
coupling to the substrate geometry. Here, we study the
substrate-de...

Atomically-thin graphene is arguably the thinnest possible mechanical
membrane: graphene's effective thickness (the thickness of an isotropic
continuum slab which would have the same elastic and bending stiffness)
is significantly less than 1 å, indicating that graphene can
distort out-of-plane to conform to sub-nanometer features. Here we study
th...

Submonolayer films of C(60) have been deposited on ultrathin SiO(2) films for the purpose of characterizing the initial stages of nucleation and growth as a function of temperature. Capture zones extracted from the initial film morphology were analyzed using both the gamma and generalized Wigner distributions. The calculated critical nucleus size i...

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set...

DOI:https://doi.org/10.1103/PhysRevB.85.049903

Thin membranes exhibit complex responses to external forces or geometrical
constraints. A familiar example is the wrinkling, exhibited by human skin,
plant leaves, and fabrics, resulting from the relative ease of bending versus
stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest
known membrane, deposited on a silica subs...

Motivated by recent numerical studies of Ag on Pt(111), we derive an expression for the RKKY interaction mediated by surface states, considering the effect of anisotropy in the Fermi edge. Our analysis is based on a stationary phase approximation. The main contribution to the interaction comes from electrons whose Fermi velocity v(F) is parallel to...

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, th...

3-phenyl-propynenitrile (PPN) adsorbs on Cu(111) in a hexagonal network of molecular trimers formed through intermolecular interaction of the cyano group of one molecule with the aromatic ring of its neighbor. Heptamers of trimers coalesce into interlocking pinwheel-shaped structures that, by percolating across islands of the original trimer covera...

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p(n)(XY)(x,y), which represents th...

Anthraquinone self-assembles on Cu(111) into a giant honeycomb network with exactly three molecules on each side. Here we propose that the exceptional degree of order achieved in this system can be explained as a consequence of the confinement of substrate electrons in the pores, with the pore size tailored so that the confined electrons can adopt...

Using Monte Carlo calculations of the two-dimensional (2D) triangular lattice gas model, we demonstrate a mechanism for the spontaneous formation of honeycomb structure of anthraquinone (AQ) molecules on a Cu(111) plane. In our model long-range attractions play an important role, in addition to the long-range repulsions and short-range attractions...

Intermolecular force plays an important role in self-assembly and surface pattern formation. Anthracene and similar unsubstituted arenes attach to a metallic substrate predominantly through van der Waals interaction leading. In this contribution we present images how anthracene on Cu(111) forms a large number of highly ordered patterns that feature...

The challenging endeavor of modulating the morphology of graphene via a patterned substrate to produce a controlled deformation has great potential importance for strain engineering the electronic properties of graphene. An essential step in this direction is to understand the response of graphene to substrate features of known geometry. Here we em...

Using Monte Carlo calculations of the two-dimensional triangular lattice with a 2-component 3-state Potts model, we demonstrate a mechanism for the spontaneous formation of fish-like patterns of anthracene (AC) molecules on Cu(111) by sputtering and annealing, then cooling to ˜ 80 K. The two components are an AC on a hollow site and another on a br...

We show that the behavior of CO adsorbed into the pores of large regular networks on Cu(111) is significantly affected by their nano-scale lateral confinement and that formation of the networks themselves is directed by the Shockley surface state. Saturation coverages of CO are found to exhibit persistent dislocation lines; at lower coverages their...

We discuss the factors that lead to the amazing regular giant honeycomb network formed by quinones on Cu(111). Using a related lattice gas model with many characteristic energies, we can reproduce many experimental features. These models require a long-range attraction, which can be attributed to indirect interactions mediated by the Shockley surfa...

We study the configurational structure of the point island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p^xyn (x,y), which represents the...

Earlier we showed [PRL 99, 226102 (2007)] that the CZD in growth could be well described by P(s)=a s^beta(-bs^2), where s is the CZ area divided by its average value. Painstaking simulations by Amar's [PRE 79, 011602 (2009)] and Evans's [PRL 104, 149601 (2010)] groups showed inadequacies in our mean field Fokker-Planck argument relating beta to the...

For detailed applications of lattice-gas models to surface systems, multisite interactions often play at least as significant
a role as interactions between pairs of adatoms that are separated by a few lattice spacings. We recall that trio (3-adatom,
non-pairwise) interactions do not inevitably create phase boundary asymmetries about half coverage....

DOI:https://doi.org/10.1103/PhysRevLett.106.069903

A unified explanation of the physics underlying all the distinctive features of the growth instabilities observed on Cu vicinals has long eluded theorists. Recently, kinetic Monte Carlo studies showed that codeposition of impurities during growth could account for the key distinctive experimental observations [Hamouda et al., Phys. Rev. B 77, 24543...

In an accompanying article we showed that surface morphologies obtained through codeposition of a small quantity (2%) of impurities with Cu during growth (step-flow mode, theta = 40 ML) significantly depends on the lateral nearest-neighbor binding energy (E-NN) to Cu adatom and the diffusion barrier (E-d) of the impurity atom on Cu(0 0 1). Based on...

We study theoretical aspects of step fluctuations on vicinal surfaces by adding conservative white noise to the Burton-Cabrera-Frank model in one spatial dimension. We consider material deposition from above, as well as entropic and elastic-dipole step repulsions. Two approaches are discussed: (i) the linearization of stochastic equations when fluc...

Experimental advances in recent years make possible quantitative observations of step-edge fluctuations. By applying a capillary-wave analysis to these fluctuations, one can extract characteristic times, from which one learns about the mass-transport mechanisms that underlie the motion as well as the associated kinetic coefficients [1-3]. The latte...

DOI:https://doi.org/10.1103/PhysRevB.82.239903

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical ap...

The diffusion and arrangements of CO adsorbates within nanometer-scale pores on a copper surface are investigated by low-temperature scanning tunneling microscopy. In contrast to extended terraces, confinement stabilizes dislocation lines that expose more than one-fourth of the adsorbate population to potentially more reactive adsorption configurat...

Nanoscale confinement of adsorbed CO molecules in an anthraquinone network on Cu(111) with a pore size of ≈4 nm arranges the CO molecules in a shell structure that coincides with the distribution of substrate confined electronic states. Molecules occupy the states approximately in the sequence of rising electron energy. Despite the sixfold symmetr...

Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films. We show that the FOs at the Pb(111) surface decay as 1/x with the distance x from the surface, different f...

Adsorbing anthracene on a Cu(111) surface results in a wide range of complex and intriguing superstructures spanning a coverage range from 1 per 17 to 1 per 15 substrate atoms. In accompanying first-principles density-functional theory calculations we show the essential role of van der Waals interactions in estimating the variation in anthracene ad...

A Reply to the Comment by Maozhi Li, Yong Han, and J. W. Evans.

Experiments show that benzene condenses into two different structural phases: a compact and a sparse phase, both of approximately hexagonal symmetry. The vdW-DF calculations demonstrate that the denser benzene-overlayer phase, with lattice constant 6.74 ,s due to direct benzene-benzene vdW attraction. The structure of the second, sparser phase, wit...

The previous talk showed that codeposition of impurity atoms during epitaxial growth could be used for nanostructuring of surfaces. Based on their lateral nearest-neighbor binding energies (ENN) to Cu and their diffusion barriers (Ed) on Cu(001), we classify the candidate impurity atoms into four sets. We find that codeposition of impurities from d...

A unified explanation of the physics underlying all the distinctive features of the growth instabilities observed on Cu vicinalsfootnotetextN. Néel H.-J. Ernst., J. Phys.: Condensed Matter 15, S3227 (2003). has long eluded theorists. Recently, kinetic Monte Carlo studies showed that codeposition of impurities during growth could account for all the...

Using Monte Carlo simulations, we computefootnotetextRS, ABH, and TLE, Phys. Rev. B 80 (2009) 153415. the TWDs of surfaces in which steps can touch each other, forming multiple-atomic height steps, but cannot cross (no overhangs), and so inconsistent with the standard mapping to spinless fermions. Our numerical results show that the generalized Wig...

With a recently developed van der Waals density functional (vdW-DF)footnotetextM. Dion et al., Phys. Rev. Lett. 92 (2004) 246401 we study the adsorption of benzene on Cu(111).footnotetextKB, TLE, and PH, Phys. Rev. B 80 (2009) 155431 The vdW-DF inclusion of nonlocal correlations changes the relative stability of 8 high-symmetry binding-position opt...

Using Monte Carlo calculations of the two-di-men-sion-al (2D) lattice gas model, we study the diffusion of CO molecules inside anthraquinone (AQ) hexagons on a Cu(111) plane. We use experimentally-derived CO-CO interactionsfootnotetextK.L. Wong, , L. Bartels, J. Chem.Phys.123, 201102 (2005) and the analytic expression for the long-range surface-sta...