The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform
Ellen D. Williams - One of the best experts on this subject based on the ideXlab platform.
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Persistence and survival in Equilibrium Step fluctuations
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: M. Constantin, Chandan Dasgupta, S. Das Sarma, Daniel B. Dougherty, Ellen D. WilliamsAbstract:Results of analytic and numerical investigations of first-passage properties of Equilibrium fluctuations of monatomic Steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations, are considered. Results of experiments in which dynamical scanning tunnelling microscopy is used to evaluate these first-passage properties for Steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.
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Infinite family of persistence exponents for interface fluctuations.
Physical review letters, 2003Co-Authors: M. Constantin, Chandan Dasgupta, S. Das Sarma, Daniel B. Dougherty, Oleksandr Bondarchuk, Ellen D. WilliamsAbstract:We show experimentally and theoretically that the persistence of large deviations in Equilibrium Step fluctuations is characterized by an infinite family of independent exponents. These exponents are obtained by carefully analyzing dynamical experimental images of Al/Si(111) and Ag(111) Equilibrium Steps fluctuating at high (970 K) and low (320 K) temperatures, respectively, and by quantitatively interpreting our observations on the basis of the corresponding coarse-grained discrete and continuum theoretical models for thermal surface Step fluctuations under attachment/detachment ("high-temperature") and edge-diffusion limited kinetics ("low-temperature"), respectively.
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Dynamics of Step fluctuations on a chemically heterogeneous surface of Al/Si(111)-(√3×√3)
Physical Review B, 2002Co-Authors: Igor Lyubinetsky, Daniel B. Dougherty, Theodore L. Einstein, Ellen D. WilliamsAbstract:The analysis of the dynamics of Equilibrium Step fluctuations has been extended to a chemically heterogeneous surface. The multicomponent reconstructed Al/Si~111!-~)3)! surface has been studied using variabletemperature scanning tunneling microscopy at elevated temperatures. The temporal correlation functions for both single Steps and Step arrays follow a t1/2 dependence over the entire temperature range ~770–1020 K!, consistent with a rate limiting mechanism of random attachment and detachment of atoms at Step edges. The alternative mechanism, diffusion from Step-to-Step, is shown to be inconsistent with more detailed analytic approximations to the correlation function for the measured Step-Step separation. An activation energy of 1.9 eV and the major kinetic parameters that govern surface mass transport and Step equilibration processes have been determined.
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Nanostructure evolution and electromigration on silicon: Experimental application of length-scaling predictions
Solid State Communications, 1998Co-Authors: Ellen D. WilliamsAbstract:As the size-scale of practical devices shrinks into the sub-micron regime, the atomic characteristics of the component materials are increasingly likely to manifest themselves in the fabrication, properties and stability of the devices. Predicting and controlling this behavior is a challenging problem in statistical mechanics, which can be approached via a length-scaling approach called the continuum Step model. The successful application of this model to developing and analyzing experiments on surface mass transport on Si will be presented. The relationship between Equilibrium Step fluctuations and large scale mass transport on Si surfaces has demonstrated in quantitative measurements on the formation and decay of metastable structures. The use of this approach to determine the physical mechanisms underlying the spontaneous formation of metastable structures under a driving force induces by bulk electrical current, e.g. a surface electromigration effect, will be reviewed.
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Measurement of the anisotropy ratio during current-induced Step bunching
Surface Science, 1995Co-Authors: Ellen D. Williams, Yunong Yang, Daniel Kandel, John D. WeeksAbstract:Abstract Instabilities in Step structure induced by direct-current heating have been measured using STM on Si(111) surfaces with an Equilibrium Step separation of approximately 1500 A. The two-dimensional structure of kinetically formed Step bunches and associated “crossing arrays” of single-height Steps shows qualitatively good agreement with predictions of a generalized theory of Step-flow instability. Quantitative analysis of the structures is consistent with the theory. The result provides the first experimental determination of an effective anisotropy ratio governing kinetic Step bunching. The measured value of this anisotropy ratio is 0.20 ± 0.03.
Bene Poelsema - One of the best experts on this subject based on the ideXlab platform.
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Comment on “Step dynamics and Equilibrium structure of monoatomic Steps on Si(100)-2×1”
Physical Review B, 1997Co-Authors: Henricus J.w. Zandvliet, Wulf Wulfhekel, B.l.m. Hendriksen, Bene PoelsemaAbstract:In contrast to a recent claim by Sanchez and Aldao [Phys. Rev. B 54, R11 058 (1996)] that the relaxation dynamics of attachment processes influences the Equilibrium Step structure we argue that the Step structure in thermodynamic Equilibrium is only governed by the configurational free energy regardless of the exact details of the relaxation dynamics.
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comment on Step dynamics and Equilibrium structure of monoatomic Steps on si 100 2 1
Physical Review B, 1997Co-Authors: Henricus J.w. Zandvliet, Wulf Wulfhekel, B.l.m. Hendriksen, Bene PoelsemaAbstract:In contrast to a recent claim by Sanchez and Aldao [Phys. Rev. B 54, R11 058 (1996)] that the relaxation dynamics of attachment processes influences the Equilibrium Step structure we argue that the Step structure in thermodynamic Equilibrium is only governed by the configurational free energy regardless of the exact details of the relaxation dynamics.
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Fluctuations of monatomic Steps on Si(001).
Physical review. B Condensed matter, 1995Co-Authors: Henricus J.w. Zandvliet, Bene Poelsema, H.b. ElswijkAbstract:The motion of monatomic Steps on Si(001) is studied on an atomic scale at elevated temperatures with scanning tunneling microscopy. The kinks in the Step edges move in units of two dimers along the monatomic A-type Step edge and perpendicular to the monatomic B-type Step edge. The overall time dependencies of the Equilibrium Step fluctuations of A- and B-type Step edges were found to be both proportional to t0.6±0.1. The fluctuations of long kinks in the B-type Step edge are, however, much larger and exhibit initially a linear t dependence, i.e., one-dimensional random-walk behavior. Both time dependencies can be understood in terms of the Langevin equation.
S. Das Sarma - One of the best experts on this subject based on the ideXlab platform.
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Persistence and survival in Equilibrium Step fluctuations
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: M. Constantin, Chandan Dasgupta, S. Das Sarma, Daniel B. Dougherty, Ellen D. WilliamsAbstract:Results of analytic and numerical investigations of first-passage properties of Equilibrium fluctuations of monatomic Steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations, are considered. Results of experiments in which dynamical scanning tunnelling microscopy is used to evaluate these first-passage properties for Steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.
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Generalized survival in Equilibrium Step fluctuations.
Physical Review E, 2004Co-Authors: Magdalena Constantin, S. Das SarmaAbstract:We investigate the dynamics of a generalized survival probability $S(t,R)$ defined with respect to an arbitrary reference level $R$ (rather than the average) in Equilibrium Step fluctuations. The exponential decay at large time scales of the generalized survival probability is numerically analyzed. $S(t,R)$ is shown to exhibit simple scaling behavior as a function of system size $L$, sampling time $\ensuremath{\delta}t$, and the reference level $R$. The generalized survival time scale ${\ensuremath{\tau}}_{s}(R)$ associated with $S(t,R)$ is shown to decay exponentially as a function of $R$.
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Generalized survival in Equilibrium Step fluctuations.
Physical review. E Statistical nonlinear and soft matter physics, 2004Co-Authors: Magdalena Constantin, S. Das SarmaAbstract:We investigate the dynamics of a generalized survival probability S(t,R) defined with respect to an arbitrary reference level R (rather than the average) in Equilibrium Step fluctuations. The exponential decay at large time scales of the generalized survival probability is numerically analyzed. S(t,R) is shown to exhibit simple scaling behavior as a function of system size L, sampling time deltat, and the reference level R. The generalized survival time scale tau(s) (R) associated with S(t,R) is shown to decay exponentially as a function of R.
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Survival in Equilibrium Step fluctuations.
Physical Review E, 2004Co-Authors: Chandan Dasgupta, Magdalena Constantin, S. Das Sarma, Satya N. MajumdarAbstract:We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability S(t) in Equilibrium Step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. S(t) is shown to exhibit a simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical scanning tunneling microscopy data on Step fluctuations on Al/Si(111) and Ag(111) surfaces.
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Survival in Equilibrium Step fluctuations
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2004Co-Authors: Chandan Dasgupta, Magdalena Constantin, S. Das Sarma, Satya N. MajumdarAbstract:We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in Equilibrium Step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. $S(t)$ is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on Step fluctuations on Al/Si(111) and Ag(111) surfaces.
Henricus J.w. Zandvliet - One of the best experts on this subject based on the ideXlab platform.
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Comment on “Step dynamics and Equilibrium structure of monoatomic Steps on Si(100)-2×1”
Physical Review B, 1997Co-Authors: Henricus J.w. Zandvliet, Wulf Wulfhekel, B.l.m. Hendriksen, Bene PoelsemaAbstract:In contrast to a recent claim by Sanchez and Aldao [Phys. Rev. B 54, R11 058 (1996)] that the relaxation dynamics of attachment processes influences the Equilibrium Step structure we argue that the Step structure in thermodynamic Equilibrium is only governed by the configurational free energy regardless of the exact details of the relaxation dynamics.
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comment on Step dynamics and Equilibrium structure of monoatomic Steps on si 100 2 1
Physical Review B, 1997Co-Authors: Henricus J.w. Zandvliet, Wulf Wulfhekel, B.l.m. Hendriksen, Bene PoelsemaAbstract:In contrast to a recent claim by Sanchez and Aldao [Phys. Rev. B 54, R11 058 (1996)] that the relaxation dynamics of attachment processes influences the Equilibrium Step structure we argue that the Step structure in thermodynamic Equilibrium is only governed by the configurational free energy regardless of the exact details of the relaxation dynamics.
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Fluctuations of monatomic Steps on Si(001).
Physical review. B Condensed matter, 1995Co-Authors: Henricus J.w. Zandvliet, Bene Poelsema, H.b. ElswijkAbstract:The motion of monatomic Steps on Si(001) is studied on an atomic scale at elevated temperatures with scanning tunneling microscopy. The kinks in the Step edges move in units of two dimers along the monatomic A-type Step edge and perpendicular to the monatomic B-type Step edge. The overall time dependencies of the Equilibrium Step fluctuations of A- and B-type Step edges were found to be both proportional to t0.6±0.1. The fluctuations of long kinks in the B-type Step edge are, however, much larger and exhibit initially a linear t dependence, i.e., one-dimensional random-walk behavior. Both time dependencies can be understood in terms of the Langevin equation.
Chandan Dasgupta - One of the best experts on this subject based on the ideXlab platform.
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Persistence and survival in Equilibrium Step fluctuations
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: M. Constantin, Chandan Dasgupta, S. Das Sarma, Daniel B. Dougherty, Ellen D. WilliamsAbstract:Results of analytic and numerical investigations of first-passage properties of Equilibrium fluctuations of monatomic Steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations, are considered. Results of experiments in which dynamical scanning tunnelling microscopy is used to evaluate these first-passage properties for Steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.
-
Survival in Equilibrium Step fluctuations.
Physical Review E, 2004Co-Authors: Chandan Dasgupta, Magdalena Constantin, S. Das Sarma, Satya N. MajumdarAbstract:We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability S(t) in Equilibrium Step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. S(t) is shown to exhibit a simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical scanning tunneling microscopy data on Step fluctuations on Al/Si(111) and Ag(111) surfaces.
-
Survival in Equilibrium Step fluctuations
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2004Co-Authors: Chandan Dasgupta, Magdalena Constantin, S. Das Sarma, Satya N. MajumdarAbstract:We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability $S(t)$ in Equilibrium Step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. $S(t)$ is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on Step fluctuations on Al/Si(111) and Ag(111) surfaces.
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Infinite family of persistence exponents for interface fluctuations.
Physical review letters, 2003Co-Authors: M. Constantin, Chandan Dasgupta, S. Das Sarma, Daniel B. Dougherty, Oleksandr Bondarchuk, Ellen D. WilliamsAbstract:We show experimentally and theoretically that the persistence of large deviations in Equilibrium Step fluctuations is characterized by an infinite family of independent exponents. These exponents are obtained by carefully analyzing dynamical experimental images of Al/Si(111) and Ag(111) Equilibrium Steps fluctuating at high (970 K) and low (320 K) temperatures, respectively, and by quantitatively interpreting our observations on the basis of the corresponding coarse-grained discrete and continuum theoretical models for thermal surface Step fluctuations under attachment/detachment ("high-temperature") and edge-diffusion limited kinetics ("low-temperature"), respectively.