Abstract
The interaction of CH3 and H with amorphous hydrocarbon surfaces plays a central role during plasmadeposition of such films. Recently, this interaction has been explored in particle beamexperiments. A rate equation model has been proposed which explains the experimentalobservations on the basis of elementary surface reactions. This model includes severalparameters which have the meaning of either a reaction cross section or a rateconstant. The predictive power of the model and its applicability to more complexhydrocarbon deposition processes hinges on a reliable determination of the modelparameters. In this paper, we develop a Bayesian analysis of the data. The result of thisanalysis are estimation distributions for each parameter rather than single numbers.We use this in-depth information to draw valuable conclusions about the abilityof the model to describe the surface reactions. We find strong indications for adependence of the reaction cross sections on the particles’ angle of incidence.
Highlights
PII: S1367-2630(03)66661-9 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft distributions of experimental errors on the estimation of distributions of parameters
The calculated growth rate results from a simple rate equation model which partitions the surface of the growing film into three types of surface site: db is the fraction of surface sites which carry a dangling bond, H3 is the coverage of trihydride terminated sites and H refers to cross-linked surface sites
In this paper we have analysed the synergistic interaction of CH3 radicals and atomic hydrogen with the surface of an amorphous hydrocarbon film
Summary
We briefly describe the idea of Bayesian probability theory and its application to data analysis. The first term in the numerator of equation (5) is the likelihood function It represents the probability of measuring the data set D given H , e.g. given specific values for the model parameters. The result of this analysis is the posterior probability on the left-hand side. Equation (5) can be used for the purpose of parameter estimation by displaying it as a function of H : the left-hand side can be viewed as a posterior distribution As such it displays how much belief we can put on each value of the model parameters, given the data D as the outcome of our experiments. In that sense it seems not appropriate to separate the determination of best fit values from the ‘error calculation’
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