Interaction of H2 with Si(001)-(2 x 1): solution of the barrier puzzle

Anatomy of a Spin: The Information-Theoretic Structure of Classical Spin Systems

Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system’s observed emergent patterns. Recent developments in information theory, however, suggest quantifying collective organization in a system- and phenomenon-agnostic way: decomposing the system’s thermodynamic entropy density into a localized entropy, that is solely contained in the dynamics at a single location, and a bound entropy, that is stored in space as domains, clusters, excitations, or other emergent structures. As a concrete demonstration, we compute this decomposition and related quantities explicitly for the nearest-neighbor Ising model on the 1D chain, on the Bethe lattice with coordination number k = 3 , and on the 2D square lattice, illustrating its generality and the functional insights it gives near and away from phase transitions. In particular, we consider the roles that different spin motifs play (in cluster bulk, cluster edges, and the like) and how these affect the dependencies between spins.

Cluster properties of the one-dimensional lattice gas: the microscopic meaning of grand potential

Using a concrete example, we demonstrate how the combinatorial approach to a general system of particles, which was introduced in detail in an earlier paper [Fronczak, Phys. Rev. E 86, 041139 (2012)], works and where this approach provides a genuine extension of results obtained through more traditional methods of statistical mechanics. We study the cluster properties of a one-dimensional lattice gas with nearest-neighbor interactions. Three cases (the infinite temperature limit, the range of finite temperatures, and the zero temperature limit) are discussed separately, yielding interesting results and providing alternative proof of known results. In particular, the closed-form expression for the grand partition function in the zero temperature limit is obtained, which results in the nonanalytic behavior of the grand potential, in accordance with the Yang-Lee theory.

Evidence for hydrogen desorption through both interdimer and intradimer paths from Si(100)-(2 x 1)

Despite intensive work there are still controversial issues about desorption and adsorption of hydrogen on Si(100)-(2 x 1). In particular, the relative importance of the various interdimer- and intradimer-desorption paths is not clear. Nanosecond-pulse-laser desorption data have been used to argue that the 4H interdimer path is important, while data from thermal-desorption time-of-flight measurements suggest a large translationally hot contribution which cannot arise from the 4H interdimer path. The observation of a translationally hot desorption fraction at low to medium coverage can be accounted for by including the 2H interdimer path in quantum dynamical calculations. In this paper we investigate this issue further and present evidence that supports the inclusion of the intradimer path. Specifically, our results show that the intradimer and 3H interdimer paths provide the major contributions to the translationally hot fraction in the desorbate. Our conclusions are based on density-functional calculations of hydrogen translational excitation, mean-field analysis of thermal-desorption experiments over a range of ramp rate, and Monte Carlo simulations of nanosecond-pulse-laser experiments.

Desorption dynamics of deuterium molecules from the Si(100)-(3x1) dideuteride surface

We measured polar angle (theta)-resolved time-of-flight spectra of D2 molecules desorbing from the Si(100)-(3x1) dideuteride surface. The desorbing D2 molecules exhibit a considerable translational heating with mean desorption kinetic energies of approximately 0.25 eV, which is mostly independent of the desorption angles for 0 degrees<or=theta<or=30 degrees. The observed desorption dynamics of deuterium was discussed along the principle of detailed balance to predict their adsorption dynamics onto the monohydride Si surface.

Exact cluster size distribution in the one-dimensional Ising model

The exact solution for the cluster size distribution in the one-dimensional Ising model is obtained. In the thermodynamic limit the result is a simple analytical formula which gives the normalized number of clusters of different sizes. The analytical prediction is compared with Monte Carlo simulations and the energy dependence of the distribution is studied.

Coverage dependent desorption dynamics of deuterium on Si(100) surfaces: Interpretation with a diffusion-promoted desorption model

We studied coverage dependence of time-of-flight (TOF) spectra of D2 molecules thermally desorbed from the D/Si(100) surface. The mean translational energies Et of desorbed D2 molecules were found to increase from 0.20+/-0.05 eV to 0.40+/-0.04 eV as the desorption coverage window was decreased from 1.0 ML> or =thetaD> or =0.9 ML to 0.2 ML> or =thetaD> or =0 ML, being consistent with the kinetics switch predicted in the interdimer mechanism. The measured TOF spectra were deconvoluted into 2H, 3H, and 4H components by a curve fitting method along the principle of detailed balance. As a result, it turned out that the desorption kinetics changes from the 4H to the 3H situation at high coverage above thetaD=0.9 ML, while the 2H desorption is dominant for a quite wide coverage region up to thetaD=0.8 ML. A dynamic desorption mechanism by which the desorption is promoted by D-atom diffusion to dangling bonds was proposed.

Spatial fluctuations and anomalous reaction order in a reactive scheme involving a cooperative full desorption

Anomalous reaction rates have been found in the hydrogen desorption of H-terminated surfaces in semiconductor epitaxy, with a reaction order shifting from two to one, or even taking fractional values. We analyze the issue in terms of a cooperative full desorption (CFD) reaction A+A--k3-->S+S , coupled to an adsorption reaction S--k1-->A and an alternative desorption route A--k2-->S . Steady state properties of the three-step reactive scheme are analyzed in a one-dimensional lattice in the absence of diffusion. Microscopic Monte Carlo simulations show anomalous spatial distributions of reactants in the stationary state: depending on the reaction rate constants of the overall scheme, either a local "aggregation" or a local "dispersion" of A -particles is observed. The CFD reaction itself is well described by a fractional order kinetics that takes into account these anomalies and that depends on the kinetic rate constants of the overall adsorption-desorption reaction mechanism. The problem is addressed with an analytical approach for the active neighborhood of a reactant, which provides a closed expression of the reaction order as a function of the kinetic parameters. This approach is in excellent agreement with numerical simulations. Spatial correlations, as well as fluctuation correlations, are also formalized in terms of the kinetic constants. We discuss the results in the context of the hydrogen evolution reaction on silicon surfaces.

Energy density analysis of cluster size dependence of surface-molecule interactions: H2, C2H2, C2H4, and CO adsorption onto Si(100)-(2×1) surface

Adsorption of H2, C2H2, C2H4, and CO onto a Si(100)-(2x1) surface has been treated theoretically using Si(12n - 3)H(8n + 4) (n = 1-4) clusters. The energy density analysis (EDA) proposed by Nakai has been adopted to examine surface-molecule interactions for different cluster sizes. EDA results for the largest model cluster Si45H36 have shown that the adsorption-induced energy density variation in Si atoms decays with distance from the adsorption site. Analysis of this decay, which can be carried out using the EDA technique, is important because it enables verification of the reliability of the model cluster used. In the cases of H2, C2H2, C2H4, and CO adsorption onto the Si(100)-(2x1) surface, it is found that at least a Si21H20 cluster is necessary to treat the surface-molecule interaction with chemical accuracy.

Hydrogen desorption kinetics from the Si(1−x)Gex(100)-(2×1) surface

We study the influence of germanium atoms upon molecular hydrogen desorption energetics using density functional cluster calculations. A three-dimer cluster is used to model the Si((1-x))Ge(x)(100)-(2x1) surface. The relative stabilities of the various monohydride and clean surface configurations are computed. We also compute the energy barriers for desorption from silicon, germanium, and mixed dimers with various neighboring configurations of silicon and germanium atoms. Our results indicate that there are two desorption channels from mixed dimers, one with an energy barrier close to that for desorption from germanium dimers and one with an energy barrier close to that for desorption from silicon dimers. Coupled with the preferential formation of mixed dimers over silicon or germanium dimers on the surface, our results suggest that the low barrier mixed dimer channel plays an important role in hydrogen desorption from silicon-germanium surfaces. A simple kinetics model is used to show that reasonable thermal desorption spectra result from incorporating this channel into the mechanism for hydrogen desorption. Our results help to resolve the discrepancy between the surface germanium coverage found from thermal desorption spectra analysis, and the results of composition measurements using photoemission experiments. We also find from our cluster calculations that germanium dimers exert little influence upon the hydrogen desorption barriers of neighboring silicon or germanium dimers. However, a relatively larger effect upon the desorption barrier is observed in our calculations when germanium atoms are present in the second layer.

Molecular beam investigation of hydrogen dissociation on Si(001) and Si(111) surfaces

The influence of molecular vibrations on the reaction dynamics of H2 on Si(001) as well as isotopic effects have been investigated by means of optical second-harmonic generation and molecular beam techniques. Enhanced dissociation of vibrationally excited H2 on Si(001)2 x 1 has been found corresponding to a reduction of the mean adsorption barrier to 390 meV and 180 meV for nu=1 and nu=2, respectively. The adsorption dynamics of the isotopes H2 and D2 show only small differences in the accessible range of beam energies between 50 meV and 350 meV. They are traced back to different degrees of vibrational excitation and do not point to an important influence of quantum tunneling in crossing the adsorption barrier. The sticking probability of H2 on the 7 x 7-reconstructed Si(111) surface was found to be activated both by H2 kinetic energy and surface temperature in a qualitatively similar fashion as H2/Si(001)2 x 1. Quantitatively, the overall sticking probabilities of H2 on the Si(111) surface are about one order of magnitude lower than on Si(001), the influence of surface temperature is generally stronger.

Quantum Monte Carlo calculations of H2 dissociation on Si(001)

The dissociative adsorption of H2 on the Si(001) surface is theoretically investigated for several reaction pathways using quantum Monte Carlo methods. Our reaction energies and barriers are at large variance with those obtained with commonly used approximate exchange-correlation density functionals. Our results for adsorption support recent experimental findings, while, for desorption, the calculations give barriers in excess of the presently accepted experimental value, pinpointing the role of coverage effects and desorption from steps.

Translational heating of D(2) molecules thermally desorbed from Si(100) and Ge(100) surfaces

The translational energies of D(2) molecules thermally desorbed from the Si(100) and Ge(100) surfaces under a heating rate of 6 K/s have been measured. In contrast to the previous laser desorption study, results show a considerable translational heating; the observed translational temperature is about 3 times higher than the desorption temperature for both surfaces. This fact indicates that energy barriers for adsorption are present even in the desorption pathway. Detailed balance is applicable to the adsorption and desorption dynamics of hydrogen on the Si(100) surface.

Probing high-barrier pathways of surface reactions by scanning tunneling microscopy

The ability of scanning tunneling microscopy to probe the pathways of thermally activated high-barrier surface processes is frequently limited by competing low-barrier processes that can confuse measurement of the true initial and final configuration. We introduce an approach to circumvent this difficulty by driving the surface process with nanosecond laser heating. The method is applied to determine the pathway of recombinative desorption in the H/Si(001) system. The observed configuration of dangling bonds after laser heating reveals that the desorbed hydrogen molecules are not formed on single dimers, but rather from neighboring silicon dimers via an interdimer reaction pathway.

Stereochemistry on Si(001): angular dependence of H2 dissociation

The angular dependence of the dissociative adsorption of molecular hydrogen at terrace and step sites of vicinal single-domain Si(001) surfaces was investigated by means of molecular beam techniques and optical second-harmonic generation. A strongly anisotropic behavior was observed for terrace adsorption with polar distributions of cos3theta and cos12theta parallel and perpendicular to the dimer, respectively. The D(B)-steps show enhanced reactivity under glancing incidence in the upwards direction. The results are traced back to the directionality of the covalent surface bonds.

Real-space study of the pathway for dissociative adsorption of H2 on Si(001)

Dissociative adsorption of molecular hydrogen on clean Si(001) surfaces has been investigated by means of scanning tunneling microscopy. The dissociated hydrogen atoms are found to occupy Si atoms of adjacent dimers. In addition to this interdimer configuration associated with the adsorption of isolated hydrogen molecules, pairs of adjacent doubly occupied dimers are readily formed. They arise from the enhanced reactivity of partially occupied dimers following the initial H2 adsorption step. The results are considered in light of recent adsorption and desorption measurements.

Role of interdimer interactions in NH3 dissociation on si(100)-(2x1)

The dissociation of NH3 on Si(100)-(2x1) is investigated by a combination of infrared absorption spectroscopy and density functional cluster calculations, revealing that this reaction is governed by a complex set of interdimer interactions involving both bare and adsorbate-covered Si dimers. We propose that such adsorbate-induced changes in the electronic structure of neighboring dimers may have general implications for controlling the two-dimensional ordering of reactions on the dimerized Si(100) surface.

Dimer preparation that mimics the transition state for the adsorption of H2 on the Si(100)-2 x 1 surface

A chemically induced dimer configuration was prepared on the silicon (Si) (100) surface and was characterized by scanning tunneling microscopy (STM) and spectroscopy (STS). These prepared dimers, which are essentially untilted and differ both electronically and structurally from the dynamically tilting dimers normally found on this surface, are more reactive than normal dimers. For molecular hydrogen (H2) adsorption, the enhancement is about 10(9) at room temperature. There is no appreciable barrier for the H2 reaction at prepared sites, indicating the prepared configuration closely approximates the actual dimer structure in the transition state. This previously unknown ability to prepare specific surface configurations has important implications for understanding and controlling reaction dynamics on semiconductor surfaces.