A thin interface asymptotic for a phase-field model of epitaxial growth with different adatom diffusivities

Here we extend a phase-field model for epitaxial step-flow growth originally derived by Liu and Metiu to capture the case of different adatom diffusivities at neighboring terraces as well as an arbitrary Ehrlich-Schwoebel (ES) barrier. Our extended model approach bridges the atomic to continuum scale in the sense that it takes into account atomic attachment kinetics in full detail and likewise allows to simulate long range transport processes above the surface efficiently. To verify the model we present a matched asymptotic analysis of the derived model equations, which shows that in a special limit the presented model can be related to the Burton-Cabrera-Frank (BCF) model with different kinds of attachment coefficients at either side of a step edge. We demonstrate the capability of our approach by presenting numerical simulations with an Ehrlich-Schwoebel (ES) barrier, which reproduce the well-known step meandering instability. Thereby we show how mathematical analysis helps to specify and validate a phase-field model and thus contributes to the further development of this modeling approach at the nano- to microscale.     

A model for vibration transmission of light-heavy structures

The vibration transmission of light-heavy structures is investigated in this paper. The light-heavy structure consists of a thin beam and a mass block. Based on numerical simulations with the finite element method and experiments, the block's effect on the thin beam is defined. A theoretical model for this beam-block structure is successfully developed, which is validated and agrees very well with the numerical and experimental models. Two kinds of transfer functions of velocities between any two points on the beam-block structure are studied experimentally and theoretically. The theoretical transfer functions agree well with the experimental results. There are peaks and valleys in the transfer functions, where the peaks occur at the anti-resonant frequencies of the second point and the valleys at the anti-resonant frequencies of the first point. Away from these peaks and valleys the magnitude of the transfer functions are about 0 dB for two points on the beam, and about 20 dB in our experiments for a point on the beam and another point on the block (close to the theoretical prediction of 18 dB determined by the mass ratio of the beam and the block). With these transfer functions, new techniques might be developed for indirect measurement of the vibration of the thin beam by measuring the vibration of the block.     

Strain induced adatom correlations

A Born–Green–Yvon type model for adatom density correlations is combined with a model for adatom interactions mediated by the strain in elastic anisotropic substrates. The resulting nonlinear integral equation is solved numerically for coverages from zero to a limit given by stability constraints. W, Nb, Ta and Au surfaces are taken as examples to show the effects of different elastic anisotropy regions.Results of the calculation are shown by appropriate plots and discussed. A mapping to superstructures is tried. Corresponding adatom configurations from Monte Carlo simulations are shown.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

Friedel oscillations around an adatom

Friedel oscillations around an adatom on a metal surface are studied analytically and numerically. Non-linear response and a general surface model potential are used. Parallel to the surface the amplitude of the oscillations goes as r^?5 but any other direction into the metal as r^?3.     

A faulted matrix model for the spiral growth of polytype structures

A faulted matrix model for the spiral growth of polytype structures is proposed and takes into account the presence of stacking faults in the basic structure. The most probable structures theoretically deduced from such a model are shown to be in excellent agreement with those actually observed in PbI₂.     

Theoretical investigation of structures and energetics of sodium adatom and its dimer on graphene: DFT study

Extensive ab initio calculations have been performed to study the energetics of a sodium (Na) atom and its dimer adsorbed on graphene using the SIESTA package Soler et al. (2002) [1] which works within a DFT(density functional theory)–GGA (generalized gradient approximation) pseudopotential framework. The adsorption energy, geometry, charge transfer, ionization potential and density of states (DOS), partial density states (PDOS) of adatom/dimer-graphene system have been calculated. After considering various sites for adsorption of Na on graphene, the center of a hexagonal ring of carbon atoms is found to be the preferred site of adsorption while the Na₂ dimer prefers to rest parallel to the graphene sheet. We find insignificant energy differences among adsorption configurations involving different possible sites in parallel orientation, which implies high mobility of the dimer on the graphene sheet. We also notice only a slight distortion of the graphene sheet perpendicular to its plane upon adatom adsorption. However, some lateral displacements seen are more perceptible.     

Self-consistent model of nanowire growth and crystal structure with regard to the adatom diffusion

A self-consistent model of growth and structure of semiconductor nanowires is proposed. The crystal phase of group III–V semiconductor nanowires is studied. The critical radius of the transition from the hexagonal wurtzite (WZ) structure to the cubic structure of zinc blende (ZB) type is calculated as a function of parameters of the system of materials and the gaseous medium supersaturation. The model presented here is applicable to both gas-phase and molecular beam epitaxies and allows one to calculate the probability of formation of the WZ and ZB phases under various deposition conditions.     

Estimation of the solitary adatom charge

The Harrison method of bonding orbitals and the model of surface molecules are used to calculate the charge of a solitary adatom. The values of the charge are compared with those obtained earlier from the dependence of the work function of an adsorption system on the adatom concentration.     

Electron density oscillations around an adatom

An analytical asymptotic expression for the induced electron density oscillations around an adatom is derived. Four different regions can be distinguished: preasymtotic, bulk asymptotic (R^?3 decay of the amplitude of the oscillations), transition (no simple inverse power law) and far asymptotic (R^?5 decay parallel to the surface, R^?3 into the metal) regions.     

Submonolayer island growth with adatom exchange

Submonolayer epitaxy is studied with two simple theoretical models where adatom exchange with a surface atom yields a stable nucleus for island growth. The results are relevant to systems where surface layer inclusions are formed by alloying and where buried islands are formed in the presence of surfactants. Rate equations and Monte Carlo simulations are used to study the evolution of the island size distributions. The rate equations reproduce all of the qualitative features found in both the simulations and in recent experiments when the coverage-dependent rate of adatom capture by islands is calculated self-consistently.     

Quantum size effects in adatom island decay

The decay of hexagonal Ag adatom islands on top of larger Ag adatom islands on a Ag(111) surface is followed by a fast-scanning tunneling microscope. Islands do not always show the expected increase in decay rate with decreasing island size. Rather, distinct quantum size effects are observed where the decay rate decreases significantly for islands with diameters of 6, 9.3, 12.6, and 15.6 nm. We show that electron confinement of the surface state electrons is responsible for this enhancement of the detachment barrier for adatoms from the island edge.     

Crystal-glass phase transitions in the adatom layers

Phase transitions in the two-dimensional crystalline films adsorbed onto an imperfect substrate (with impurities and defects) are analyzed. It is shown that the phase transition from the commensurate long-range-order (LRO) crystal to the glass state occurs with increase of impurity concentration. The orientational correlation function is shown to tend algebraically to zero at large distances in the glass state. The influence of defects on the phase transition from the LRO-commensurate crystal to the disordered state at the definite temperature T_m is considered.     

A data-efficient self-supervised deep learning model for design and characterization of nanophotonic structures

With its tremendous success in many machine learning and pattern recognition tasks, deep learning, as one type of data-driven models, has also led to many breakthroughs in other disciplines including physics, chemistry and material science. Nevertheless,the supremacy of deep learning over conventional optimization approaches heavily depends on the huge amount of data collected in advance to train the model, which is a common bottleneck of such a data-driven technique. In this work, we present a comprehensive deep learning model for the design and characterization of nanophotonic structures, where a self-supervised learning mechanism is introduced to alleviate the burden of data acquisition. Taking reflective metasurfaces as an example, we demonstrate that the self-supervised deep learning model can effectively utilize randomly generated unlabeled data during training, with the total test loss and prediction accuracy improved by about 15% compared with the fully supervised counterpart.The proposed self-supervised learning scheme provides an efficient solution for deep learning models in some physics-related tasks where labeled data are limited or expensive to collect.     

Quantum size effect on adatom surface diffusion

Using scanning tunneling microscopy, we demonstrate that the nucleation density of Fe islands on the surface of nanoscale Pb films oscillates with the film thickness, providing a direct manifestation of the quantum size effect on surface diffusion. The Fe adatom diffusion barriers were derived to be 204+/-5 and 187+/-5 meV on a 21 and 26 monolayer (ML) Pb film, respectively, by matching the kinetic Monte Carlo simulations to the experimental island densities. The effect is further illustrated by the growth of Fe islands on wedged Pb films, where the Fe island density is consistently higher on the odd-layer films than on the even-layer films in the thickness range of 11 to 15 ML.