We use analytic formulae obtained from a simple model of crystal growth by molecular{beam epitaxy to determine step{edge barriers to interlayer transport. The method is based on information about the surface morphology at the onset of nucleation on top of rst{layer islands in the submonolayer coverage regime of homoepitaxial growth. The formulae are tested using kinetic Monte Carlo simulations of a solid{on{solid model and applied to estimate step{edge barriers from scanning{tunneling microscopy data on initial stages of Fe(001), Pt(111), and Ag (111) Nearly thirty years ago, it was found in eld{ion{ microscopy experiments that interlayer transport on some metal surfaces is suppressed by additional activation barriers to hopping over step edges, 1 and such barriers were recently shown to be present on a semiconductor surface as well. 2 The consequences of this Ehrlich{Schwoebel (ES) barrier for growth on vicinal 3;4 and singular 5 surfaces have been theoretically investigated. In particular, study of the e ects of the ES barrier for growth on a singular surface led to new insights into homoepitaxial growth modes 6 as well as into kinetic roughening of growing surfaces. 2 The ES barrier has emerged as a material parameter of an importance comparable to the surface di usion barrier. It is, however, very di cult to determine this quantity experimentally.Very recently, Meyer et al. 7 proposed (amongst other suggestions) a method of determining the ES barrier based on the surface morphology at the onset of nucleation on top of rst{layer islands as seen by scanning tunneling microscopy (STM). In this paper, we provide a more consistent analytical treatment of this problem and derive a formula di erent from the one proposed by Meyer et al.. This formula and its modi cations are tested using kinetic Monte Carlo (KMC) simulations and applied to STM data for Fe/Fe(001), Ag/Ag(111), and Pt/Pt(111) homoepitaxy.We consider a model of the initial stages of homoepitaxy similar to the one proposed by Lewis and Anderson 8 with circular{shaped islands regularly distributed over a perfect singular surface (Fig. 1). Growth is initiated by a ux of atoms incoming to the surface. The adatom density on the surface increases until it reaches a critical value c at a time t=0 when islands of radius r 0 =1 separated by a distance 2L are formed. (Notice that all lengths are given in units of the lattice constant and are accordingly dimensionless.) We assume that the interisland free{adatom density is then well approximated by its steady{state form with weakly time{dependent coefcients (quasi{static approximation 9 ). We will consider relaxing the assumption of an instantaneous steady state later. Each island has an e ective catchment area of radius L with free{adatom ux equal to zero at a distance r=L. Based on these assumptions, the adatom density on the substrate immediately following nucleation is the solution of the di usion equation Dr 2 + F =0 (1) with boundary conditions (cf. Ref. 9, Section 7.4) d =dr r=R(t) = (R(t)) (and thus als...
The exact solution for a forced, undamped quantum harmonic oscillator is obtained by S-matrix techniques. The force F(t) is assumed to vanish at t = ±∞. The only restriction is that the Fourier transform of F(t) must exist. The transition probabilities are obtained in closed form in terms of Laguerre polynomials. The mean energy transfer to the oscillator is found to be independent of the initial state and is in agreement with the classical result for an oscillator originally at rest. This problem provides a good example of field theoretical procedures in an elementary context. Therefore, all field theoretical concepts are carefully defined and explained as they are introduced in order that the discussion may be self-contained.
Thirteen moment equations for a binary mixture of Maxwell molecules are used to discuss the way in which a disparate-mass gas approaches equilibrium, the way in which a normal description may or may not emerge, and the usefulness and applicability of a number of existing treatments of two-temperature disparate-mass gases and associated temperature-difference relaxation equations. Corrections to some of the predictions in the literature are also found necessary.
Onedimensional Brownian motion near an absorbing boundary: Solution to the steady state Fokker-Planck equation J. Chem. Phys. 79, 2302 (1983); 10.1063/1.446034 Comment on ''Steady, onedimensional Brownian motion with an absorbing boundary''
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