Diffusion in Potential Fields: Time-Dependent Capture on
Radial and Rectangular Substrates
J.A. Venables and P. Yang, Materials Research Soc. 859E (2005) JJ9.2.1-6
In rate equation models of nucleation and growth on surfaces, it has often been
assumed that the energy surface of the substrate is flat, that diffusion is isotropic,
and that capture numbers can be calculated in the diffusion-controlled limit. We lift
these restrictions analytically, and illustrate the results using a hybrid discrete
FFT method of solving for the 2D time-dependent diffusion field of ad-particles, which
has been implemented in Matlab 6.5. A general substrate energy surface is included
by transformation of the field. The method can work with any boundary conditions,
but is particularly clear for periodic boundary conditions, such as might be
appropriate following nucleation on a regular (rectangular) array of defects. The
method is instructive for visualizing potential and diffusion fields, and for
demonstrating the time-dependence of capture numbers in the initial stages of
deposition and annealing.
Latest version of this document: 22nd February 2010.