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We explore the morphological stability during the growth of strained multilayer structures in a dynamical model which describes the coupling of elastic fields, wetting effect, and deposition process. We quantitatively show the significant influence of the wetting effect on the stability properties, in particular for short-period multilayers. Our results are qualitatively similar to recent experimental observations in AlAs/InAs/InP(001) system. We also give predictions for strain-balanced multilayers., Comment: 4 pages, 2 figures

We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system recursively in terms of that of the old states of the buried layers. In turn, we use the result for the elastic state to derive the morphological evolution equation of surface profile to first order of perturbations, with the solution explicitly expressed by the growth conditions and material parameters of all the deposited layers. We apply these results to two kinds of multilayer structures. One is the alternating tensile/compressive multilayer structure, for which we determine the effective stability properties, including the effect of varying surface mobility in different layers, its interplay with the global misfit of the multilayer film, and the influence of asymmetric structure of compressive and tensile layers on the system stability. The nature of the asymmetry properties found in stability diagrams is in agreement with experimental observations. The other multilayer structure that we study is one composed of stacked strained/spacer layers. We also calculate the kinetic critical thickness for the onset of morphological instability and obtain its reduction and saturation as number of deposited layers increases, which is consistent with recent experimental results. Compared to the single-layer film growth, the behavior of kinetic critical thickness shows deviations for upper strained layers., Comment: 27 pages, 11 figures; Phys. Rev. B, in press

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations., Comment: 26 pages, 13 eps figures

A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early nonequilibrium processes of surface evolution, and calculate the stability conditions and diagrams for different cases of material parameters. There are two key considerations in our treatment: the coupling between top free surface of the film and the bulk phase underneath, and the dependence of both Young's and shear elastic moduli on local composition. The combination and interplay of different elastic effects caused by lattice misfit between film and substrate (misfit strain), composition dependence of film lattice parameter (compositional strain) and of film elastic constants lead to complicated and rich stability results, in particular the joint stability or instability for morphological and compositional profiles, the asymmetry between tensile and compressive layers, as well as the possible stabilization and suppression of surface decomposition even below the effective critical temperature. We also compare our results with the observations of some postdeposition annealing experiments., Comment: 14 pages, 6 eps figures

A Bus Route Model (BRM) can be defined on a one-dimensional lattice, where buses are represented by "particles" that are driven forward from one site to the next with each site representing a bus stop. We replace the random sequential updating rules in an earlier BRM by parallel updating rules. In order to elucidate the connection between the BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg (NaSch) model, we propose two alternative extensions of the NaSch model with space-/time-dependent hopping rates. Approximating the BRMPU as a generalization of the NaSch model, we calculate analytically the steady-state distribution of the {\it time headways} (TH) which are defined as the time intervals between the departures (or arrivals) of two successive particles (i.e., buses) recorded by a detector placed at a fixed site (i.e., bus stop) on the model route. We compare these TH distributions with the corresponding results of our computer simulations of the BRMPU, as well as with the data from the simulation of the two extended NaSch models. We also investigate interesting kinetic properties exhibited by the BRMPU during its time evolution from random initial states towards its steady-states., Comment: Accepted for publication in EPJB

We show how the interface curvature autocorrelation function (ICAF) and associated structure factor (ICSF), of relevance in non-equilibrium pattern-formation problems where sharp interfaces are present, provide new and interesting information on domain structure, as yet not visible via the order-parameter structure factor (OPSF). This is done by discussing numerical simulations of model A (non-conserved relaxational phase-ordering kinetics) in two-dimensional systems. The ICAF is Gaussian over short distances and exhibits dynamical scaling and $t^{1/2}$ power-law growth. We use it to show what the typical length-scale in the model A dynamics corresponds to physically and how it can be obtained uniquely, rather than simply within a multiplicative constant. Experimental methods to measure the ICAF and/or ICSF are still needed at this point., Comment: A slightly revised version of the original is given here which is now published in Eur. Phys. J. B 9, 719-724 (1999)

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the domain interfaces. The dynamics is shown to depend strongly on the local Gaussian curvature of the surface, and can be fundamentally different from that in flat systems: dynamical scaling breaks down despite the persistence of the dominant interfacial undulation mode; growth laws are slower than $t^{1/2}$ and even logarithmic; a new very-late-stage regime appears characterized by extremely slow interface motion; finally, the zero-temperature fixed point no longer exists, leading to metastable states. Criteria for the existence of the latter are derived and discussed in the context of more complex systems., Comment: Submitted to Physical Review Letters on Mar 13, 1998. Withdrawn July 1998. Submitted full version to J. Stat. Phys. July 21, 1998, which is now published in J. Stat. Phys. 95, 949-979 (1999)

We obtain bounds on the decay exponent lambda of the autocorrelation function in phase ordering dynamics. For non-conserved order parameter, we recover the Fisher and Huse inequality, lambda > = d/2. If the order parameter is conserved we also find lambda >= d/2 if the initial time t1 = 0. However, for t1 in the scaling regime, we obtain lambda >= d/2 + 2 for d >= 2 and lambda >= 3/2 for d=1. For the one-dimensional scalar case, this, in conjunction with previous results, implies that lambda is different for t1 = 0 and t1 >> 1. In 2-dimensions, our extensive numerical simulations for a conserved scalar order parameter show that lambda approx 3 for t1=0 and lambda approx 4 for t1 >> 1. These results contradict a recent conjecture that conservation of order parameter requires lambda = d. Quenches to and from the critical point are also discussed. (uuencoded PostScript file with figures appended at end)., Comment: 11 pages

We combine random walks, growth and decay, and convection, in a Monte Carlo simulation to model 1D interface dynamics with fluctuations. The continuum limit corresponds to the deterministic Fisher equation with convection. We find qualitatively the same type of asymmetry, as well as velocity difference, for interface profiles moving in opposite directions. However a transition apparent in the mean-field (continuum) limit is not found in the Monte Carlo simulation., Comment: 2.5 pages (texed) with 4 postscript figures, TeX 3.14t3

A laser focussed onto a semiconductor film can create a disordered lamellae pattern of coexisting molten-solid regions. We present a continuum model based on the higher reflectivity of the molten regions. For large latent heat, this model becomes equivalent to a model of block copolymers. The characteristic wavenumber of the lamellae is that marginally stable to slow variations in the orientation (the zig-zag instability) and is obtained via systematic expansions from two limits. The lamellae can also be unstable to the zig-zag instability and Eckhaus instability simultaneously. This instability is a signal of dynamic steady states. We numerically study the behaviour after a quench. The lamellar size agrees with the analytic results and experiments. For shallow quenches, locally parallel stripes slowly straighten in time. For deep quenches, a disordered lamellae forms. We construct the director field and determine the orientational correlation length. Near onset the correlation is fixed by the system size. Far from onset the correlation length saturates at a finite value. We study the transition to the time-dependent asymptotic states with decreasing latent heat. postScript figures available on request, Comment: 44 pages, revtex 3.0

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough., Comment: 5 pages, PostScript format