Universality class of discrete solid-on-solid limited mobility nonequilibrium growth models for kinetic surface roughening

Abstract

We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.

Renormalization of stochastic lattice models: Epitaxial surfaces

“…For high enough temperatures activated surface diffusion delays this instability, but eventually the surface becomes unstable even if surface diffusion strongly dominates over WV relaxation processes at atomistic scales. Indeed, our results provide an analytic justification for the conclusion reached by KMC simulations [44][45][46] that a given relaxation mechanism can lead to qualitatively different surface morphologies depending on the dimensionality of the substrate (i.e. nonuniversal behavior) and the length and time scales considered.…”

“…Indeed, it is well known [10,57] that even for relatively small system sizes KMC simulations of the EW model show scaling behavior consistent with Eq. (45). Moreover, the 1D EW equation has been derived previously [89] as an asymptotic description of the 1D EW model.…”

“…A more accurate multiscale analysis of the EW model therefore necessitates the inclusion of the term ν 6 ∇ 6 u in the calculation of the RG trajectories from the initial conditions in Table I [53]. As discussed (21), (45), and (56) for the EW model on substrates of dimension d obtained with the representative choice δ = 0.01. We have set a ⊥ = a = τ0 = 1 and we have D2 = 0 for d = 1 and d = 2.…”

“…Moreover, experiments and computer simulations only access transient regimes of morphological evolution, whereas universality, which is often invoked [10,11] to justify a particular continuum equation for a given experimental setup, is appropriate only in the limit of infinitely large length and time scales. Indeed, the difficulties encountered with the description of recent computer simulations [45][46][47] and experiments [30][31][32][33][48][49][50] of homoepitaxial growth in terms of the standard equations of surface growth show that this program remains problematic. This is exacerbated by the fact that, from a technological perspective [29][30][31][32][33], the initial, rather than the asymptotic behavior of homoepitaxial surfaces, is of primary interest.…”

Persistence and first-passage properties in nonequilibrium systems

“…The exponents in this case are known only numerically in one and two dimensions [277]. For example in d = 1, α ≈ 1, β ≈ 1/3 and z ≈ 3 [277][278][279].…”