Computer study of boron and phosphorus at the Si(100)̶2 ╳ 1 surface

The AM1 semiempirical numerical method combined with the geometry optimization procedure was used to study the energetics of active impurities (B, P) in substitutional positions at the Si(100)- surface. It has been found that phosphorus prefers to be in the first layer (in dimers). Boron has the lowest energy in the second layer. Energy profits, counting from the fourth bulk-like layer, for B and P are 1.33 eV and 0.56 eV, respectively. Comparing of the P-Si and P-P dimers energetics has shown that P-Si dimers are more preferable energetically. Received: 26 March 1998 / Accepted: 9 June 1998     

Visualisation of a supersonic free-jet expansion using laser-induced fluorescence spectroscopy: Application to the measurement of rate constants at ultralow temperatures

2 Σ⁺, v^′=0) by air at 26±4 K. A value of 2.56±0.40×10^-10 molecule^-1 cm³ s^-1 was obtained, a factor of more than four higher than at room temperature, and consistent with attractive forces dominating the quenching of OH(A²Σ⁺). A d etailed computational fluid dynamics (CFD) simulation of the supersonic free-jet expansion was performed, providing a two-dimensional visualisation of temperature and density variations throughout the expansion. The CFD calculations reproduced the salient features of the experimental temperature and density profiles along the centreline. Comparison between experiment and computation has allowed validation of CFD codes. Received: 31 January 1997/Revised version: 24 March 1997     

Imaging and post-processing of laser-induced fluorescence from NO in a diesel engine

Received: 11 July 1996/Revised version: 12 November 1996     

Stability and diffusion of surface clusters

Using kinetic Monte Carlo simulations and a bond-counting ansatz, thermal stability and diffusion of an adatom island on a crystal surface are studied. At low temperatures, the diffusion constant D is found to decrease for a wide range of island sizes like , where is close to one, N being the number of adatoms in the cluster. By heating up the surface, the system undergoes a phase transition above which the island disappears. Characteristics of that transition are discussed. Received 20 January 1999     

A history-dependent stochastic predator-prey model: Chaos and its elimination

A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA) and computer simulations. The MFA results a series of bifurcations in the phase space of mean predator and prey densities, leading to a chaotic phase. Because of emerging correlations between the two species distributions, the interaction rate alters and if it is chosen to be the value which is obtained from the simulation, then the chaotic phase disappears. Received 12 July 1999     

Shearing behavior of polydisperse media

We study the shearing of polydisperse and bidisperse media with a size ratio of 10. Simulations are performed with a two-dimensional shear cell using contact dynamics. With a truncated power law for the polydisperse media we find that they show a stronger dilatancy and greater resistance to shearing than bidisperse mixtures. To model additives used to control viscosity we introduce so-called “point-like particles”. Even changing the kinematic behavior very little, the point-like particles reduce the force necessary to maintain a fixed shearing velocity.     

Comparison of different gettering techniques for Cu–p+ versus polysilicon and oxygen precipitates

We performed measurements of gettering efficiencies for Cu in silicon wafers with competing gettering sites. Epitaxial wafers (p/p+) boron-doped with a polysilicon back side allowed us to compare p+ gettering with polysilicon gettering. We further measured metal distributions in p+/p- epitaxial test wafers, with the p- substrate wafers pretreated for oxygen precipitation to compare p+ gettering with oxygen precipitate gettering. Our test started with a reproducible spin-on contamination in the 10¹² atoms/cm² range, followed by thermal treatment in order to redistribute the metallic impurity. Wafers were then analyzed by a novel wet chemical layer-by-layer etching technique in combination with inductively coupled plasma mass spectrometry. This led to “stratigraphical” concentration profiles of the impurity, with typical detection limits of 5–10×10¹² atoms/cm³. Twenty-five percent of the total Cu contamination in the p/p+/poly wafer was found in the p+ layer, whilst 75% was gettered by the polysilicon. Obviously, polysilicon exhibits a stronger gettering than p+ silicon, but due to the large distance from the front surface, polysilicon was less effective in reducing impurities from the front side of a wafer compared with p+ gettering. An epitaxial layer p+ on top of p- substrates with oxygen precipitates gettered 50% of the total Cu; while the other 50% of the Cu was measured in the p- substrate wafer with oxygen precipitates. Without oxygen precipitates, 100% of the spiked Cu contamination was detected inside the p+ layer. Gettering by oxygen precipitates thus occurs in the same temperature range as that where p+ silicon begins to getter Cu. Received: 3 September 2001 / Accepted: 17 October 2001 / Published online: 27 March 2002     

Modeling of Cu gettering in p- and n-type silicon and in poly-silicon

Based on experimental findings we set up calculations of numerical modeling of gettering efficiencies for Cu in various silicon wafers. Gettering efficiencies for Cu were measured by applying a reproducible spin-on contamination in the 10¹² atoms/cm² range, followed by a thermal treatment to redistribute the metallic impurity. Subsequently, the wafers were analyzed by a novel wet chemical layer-by-layer etching technique in combination with inductively coupled plasma mass spectrometry. We investigated p/p+ and n/n+ epitaxial wafers with different doping levels and different substrate-doping species. We have also investigated gettering efficiencies of phosphorus-diffused p- and n-type wafers. Heavilyboron doped silicon exhibited a gettering efficiency of ∼100%, while gettering by n+ silicon occurred for doping levels >3×10¹⁹ atoms/cm³ only. In another set of experiments we investigated the dependence of the gettering efficiency of p-type wafers with poly-silicon back sides for different cooling rates and Cu spiking levels. A strong dependence on both parameters was found. Cu gettering in p/p+ epitaxial wafers was modeled by calculating the increased solubility of Cu in p+ silicon compared to non-doped silicon taking into account the Fermi-level effect, which stabilizes donors in p+ silicon, and the pairing reaction between Cu and B. Calculated gettering efficiencies were in very good agreement with experimental results. Gettering in n+ silicon was similarly modeled in terms of pairing reactions and the Fermi-level effect. But, for n-type silicon, many experimental uncertainties existed; thus, we applied our expressions to solubility data of Hall and Racette to obtain the unknown parameters. The empirical calculations were in good agreement even with results on n/n+ wafers. For phosphorus-diffused wafers we had to consider an excess vacancy concentration of 1.2–5.5 times the equilibrium concentration to explain the experimental findings by the model. Gettering by poly-silicon back sides was simulated by solving the time-dependent diffusion equation with boundary conditions that take into account different surface reaction rates of silicon point defects. Using this advanced model, the experimentally measured gettering efficiencies were reproduced within the uncertainty of the measurement. Received: 3 September 2001 / Accepted: 4 September 2001 / Published online: 20 December 2001     

The structure of mixed nitrogen-argon clusters

Using realistic pair potentials, we investigate the structures of mixed clusters of argon and nitrogen in order to interpret the experimental electron diffraction patterns reported by the Torchet group. Simulations of small clusters indicate that argon tends to segregate at the center of the clusters. For larger clusters, in the range of 50 to 200 molecules, MC methods have been used to simulate structures that are likely to be generated in the molecular beam. By comparing predicted electron diffraction patterns with those recorded in the experiments, our models allow us to estimate the average size and composition of the mixed clusters for a given set of experimental conditions (nozzle stagnation pressure and Ar partial pressure).     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Dielectrophoresis of nanocolloids: A molecular dynamics study

Dielectrophoresis (DEP), the motion of polarizable particles in non-uniform electric fields, has become an important tool for the transport, separation, and characterization of microparticles in biomedical and nanoelectronics research. In this article we present, to our knowledge, the first molecular dynamics simulations of DEP of nanometer-sized colloidal particles. We introduce a simplified model for a polarizable nanoparticle, consisting of a large charged macroion and oppositely charged microions, in an explicit solvent. The model is then used to study DEP motion of the particle at different combinations of temperature and electric field strength. In accord with linear response theory, the particle drift velocities are shown to be proportional to the DEP force. Analysis of the colloid DEP mobility shows a clear time dependence, demonstrating the variation of friction under non-equilibrium. The time dependence of the mobility further results in an apparent weak variation of the DEP displacements with temperature.     

Influence of sublayer atoms on Si(100) surface reconstructions

Influence of sublayer atoms on Si(100) surface reconstruction has been examined with density functional theory and molecular dynamic simulation. We found that the displacements of sublayer atoms under the buckled dimer affect the motions of their neighboring atoms and thus play an important role in determining the surface reconstructions. The present results reveal the relationship between the surface dimer reconstruction and the motion of the sublayer atoms and provide an account for experimental observations of Si(100) surface reconstructions at very low temperatures.     

Computer simulation study of the Levy flight process

The random walk simulation of a Levy flight shows a linear relation between the mean square displacement 〈r²〉 and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (l_m) affects the diffusion coefficient, even though it remains constant for l_m greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results also imply that the movement of a Levy flight particle is similar to the case in which the particle moves in each time step with an average jump length 〈l〉. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use a time average instead of an ensemble average. The difference between the time average and ensemble average results shows that the Levy distribution may be a non-ergodic distribution.     

Comparison of the ELP and multicanonical methods in simulation of the heptapeptide deltorphin

To investigate the performance of the energy landscape paving (ELP) procedure for peptides, we apply it here to deltorphin, a linear heptapeptide with bulky side chains (H-Tyr¹-D-Met²-Phe³-His⁴-Leu⁵-Met⁶-Asp⁷-NH₂) and compare the results with the Multicanonical method (MUCA) in regard of finding the low-energy structures. Deltorphin is modeled in vacuum by the potential energy function ECEPP. Received 23 July 2002 / Received in final form 18 September 2002 Published online 31 December 2002     

Simulating (electro)hydrodynamic effects in colloidal dispersions: Smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the “Smoothed Profile (SP) method” is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.     

The linkage between macroscopic gettering mechanisms and electronic configuration of 3d-elements in p/p+ epitaxial silicon wafers

We have measured the gettering efficiencies for Cr, Mn, Fe, Co, Ni and Cu in p/p+ epitaxial wafers. The gettering test started with a reproducible spin-on contamination on the front side of the wafers in the 10¹²–10¹⁴ atoms/cm² range, followed by thermal treatment to redistribute the metallic impurities in the wafer. The gettering efficiencies were measured by a novel wet chemical stratigraphic etching technique in combination with inductively-coupled plasma mass spectrometry. The residual bulk metal contamination was also measured by this method. This procedure led to global distributions of the 3d elements on the wafer’s front side, in the bulk of the wafer and on the wafer’s back side. Recovery rates were found to be 34%, 2.3%, 100%, 85%, 100% and 100% for Cr, Mn, Fe, Co, Ni and Cu, respectively. An impurity segregation effect in the wafer bulk was measured for Cu (100%) and Cr (34%), while no detectable segregation-induced gettering mechanisms were detected for the other elements in the applied concentration range. The segregation-induced gettering mechanisms were interpreted from the electronic structure of the metallic impurities. For segregation gettering by increased solubility in p+ silicon, the metallic species must form donors. Only Cu⁺ (3d ¹⁰) and Cr⁺ (3d ⁵) can form singly positively charged species that exhibit a spherical electronic distribution. It is well known from spinell structures that 3d ¹⁰ and, to a smaller extent 3d ⁵, are stable configurations in tetrahedral structures like the silicon lattice. Thus, we link the segregation-induced gettering mechanism in p/p+ epitaxial wafer to the electronic configuration of the 3d elements. Received: 19 January 2001 / Accepted: 31 January 2001 / Published online: 20 June 2001     

Mechanical property of carbon nanotubes with intramolecular junctions: Molecular dynamics simulations

Intramolecular junctions (IMJs) of carbon nanotubes hold a promise of potential applications in nano-electromechanical systems. However, their structure-property relation is still unclear. Using the revised second-generation Tersoff-Brenner potential, molecular dynamics simulations were performed to study the mechanical properties of single-walled to four-walled carbon nanotubes with IMJs under uniaxial tension. The dependence of deformation and failure behaviors of IMJs on the geometric parameters was examined. It was found that the rupture strength of a junction is close to that of its thinner carbon nanotube segment, and the rupture strain and Young's modulus show a significant dependence on its geometry. The simulations also revealed that the damage and rupture of multi-walled carbon nanotube junctions take place first in the innermost layer and then propagate consecutively to the outer layers. This study is helpful for optimal design and safety evaluation of IMJ-based nanoelectronics.     

Studies of nanocluster coalescence at high temperature

Molecular Dynamics simulations and high resolution electron microscope observations were used to determine the mechanism of nanocluster coalescence in detail. In the simulations, the tight-binding second momentum approximation potential was used to describe the interatomic interactions. The calculations not only reproduced the experimentally observed translation and reorientation during the coalescing process, but also made it possible to determine the time scale of each step in the process and to observe details of the process that could not be obtained from the experiment. For high temperature coalescence, a new mechanism differing from classical theory is proposed. Received: 14 October 2002 / Accepted: 16 October 2002 / Published online: 28 March 2003 RID="*" ID="*"Corresponding author. Fax: +52-55/3003-6414, E-mail: ascencio@imp.mx     

Quantitative evaluation about property of thin-film formation

Chemical vapor deposition (CVD) is gradually emphasized as one promising method for nanomaterial formation. Such growth mechanism has been mainly investigated on basis of experiment. Due to large cost of the equipment of experiment and low level of current measurement, the comprehension about authentic effect of formation condition on properties of nanomaterial is limited in qualitative manner. Three quantitative items: flatness of primary deposition, adhesion between cluster and substrate, and degree of epitaxial growth were proposed to evaluate the property of thin film. In this simulation, three different cluster sizes of 203, 653, 1563 atoms with different velocities (0, 10, 100, 1000, 3000 m/s) were deposited on a Cu(0 0 1) substrate whose temperatures were set between 300 and 1000 K. Within one velocity range, not only the speed of epitaxial growth and adhesion between thin film and substrate were enhanced, but also the degree of epitaxy increased and the shape of thin film became more flat with velocity increasing. Moreover, the epitaxial growth became well as the temperature of substrate was raised within a certain range, and the degree of epitaxy of small cluster was larger than larger cluster. The results indicated that the property of thin film could be controlled if the effect of situations of process was made clear.     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002