Growth mode modelling

No ab initio molecular dynamic method, such as the Car-Parrinello (1985) approach, has yet been applied to metal-oxide interfaces to determine the growth modes, because it would require too much memory and computation time. Several molecular dynamic approaches, making use of empirical potentials, have derived trends in the wetting, the growth and the nucleation modes of clusters on surfaces (e.g. Harding, 1992). 

To conclude, one is very far from having a thorough picture of the first stages of formation of a metal-oxide interface. Except in very few cases, one ignores the nature of the adsorption sites and the number of interfacial bonds. For large size clusters, there is no clear criterion for 

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A critical part of the calculations is to calculate the tie-line at the interface corresponding to local equilibrium, and Enomoto (1992) used the central atoms model to predict the thermodynamic properties of a and 7. Some assumptions were made concerning the growth mode and the calculation of this tie-line is dependent on whether growth occurred under the following alternative conditions ... 

A model describing the relationship between the performance and the process variables allows the prediction of process results and the optimization of process variables for a specific application. However, the interactions among deposition chemistry, transport processes, and growth modes are complex and, consequently, poorly understood. Therefore, CVD process development has progressed through extensive one-parameter-at-a-time experimentation and empirical design rules. 

Rate Expressions. A major difficulty in CVD reactor modeling is the choice of appropriate rate expressions, Rp for the gas-phase-species balance and the surface boundary conditions. As described previously (see Nucleation and Growth Modes), most of CVD chemical kinetics is unknown. Therefore, rate parameters may have to be estimated from experimental growth data as part of the reactor-modeling effort. 

It appears from the above that microcosm and/or mesocosm tests are limited by the constraints of experimentation, in that usually only a limited number of recovery scenarios can be investigated. Consequently, modeling approaches may provide an alternative tool for investigating likely recovery rates under a range of conditions. Generic models, like the logistic growth mode (for example, see Barnthouse 2004) and life history and individual-based (meta)population models, which also may be spatially explicit, provide mathematical frameworks that offer the opportunity to explore the recovery potential of individual populations. For an overview of these life history and individual-based models, see Bartell et al. (2003) and Pastorok et al. (2003). 

Values of a, p, and z are suitable quantities for the comparison of experimental data and theoretical models. Therefore, the preceding summary of the dynamic scaling approach provides a way for determining the dominant mechanism for the rough surface growth mode, irrespective of vdiether the development of the rough surface results from the accumulation or the dissolution of the solid phase. 

The difficulty facing the reviewer is the almost complete incompatibility between direct kinetic measurements and electronic/compositional studies of metal deposits. Kinetic results have been used to construct models of the surface metal phase with varying degrees of geometric complexity and/or thin film growth mode, but in all cases the metal is assumed a priori to be on top of the semiconductor and to desorb from it in some classical way. Unfortunately, direct measurement of the interface chemistry... 

Fig. 3.16 Comparison of the growth of a Fe and b Gd on W(110) in the submonolayer coverage regime. For both metals the coverage is about 0.25 MF. The scan range for both images is 70 nm X 70 nm. Below the STM images structure models are shown to highlight the difference in the growth mode. Reprinted with permission from [38]. Copyright (1999) by the American Physical Society...

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