Rate equations model for layer epitaxial growth kinetics

Quantitative modeling ofin situx-ray reflectivity during organic molecule thin film growth

“…[40]. More recently, Trofimov et al [42][43][44][45][46] , developed a new variant of this class of models, specifically for the purpose of linking atomistic kinetics to morphology in thin, multilayer films.…”

“…Models by Kariotis et al 41 , Trofimov et al [42][43][44][45][46] , and Koponen 37,38 draw explicitly on nucleation theory 47 , and include additional equations to Eq. 6 representing the adatom and island densities on each layer.…”

“…The last model employed for our comparison is a simplified version of an atomistic, rate-equation model developed by Trofimov et al [42][43][44][45][46] . Unlike the layer-wise models just described, this model includes three rate equations for each layer, describing the rates of change of the adatom density, island density, and coverage.…”

“…A clear advantage of this model is the ability to directly connect morphology, including in-plane parameters such as the nucleation density, evolves as a function of layer number, and as a function of real, physical parameters such as D/J, the ratio of adatom diffusivity to the incident flux. For example, it is found that, even for homoepitaxy, the saturation island density decreases as a function of layer number during LBL growth 44 . This phenomena has recently been directly observed in SrTiO 3 homoepitaxy using pulsed laser deposition 51 .…”

“…Examination of Ref. [44] shows that all of the atomistic physics is contained in the evaluation of the critical coverage for each layer θ n,cr . Defining this as a fit parameter, we have:…”