Computation of three dimensional dendrites with finite elements
Journal of Computational Physics
Journal of Computational Physics
A level set method for thin film epitaxial growth
Journal of Computational Physics
Numerical simulation of grain-boundary grooving by level set method
Journal of Computational Physics
IBM Journal of Research and Development - Q-Coder adaptive binary arithmetic coder
An integral equation method for epitaxial step-flow growth simulations
Journal of Computational Physics
The influence of electric fields on nanostructures-Simulation and control
Mathematics and Computers in Simulation
AMDiS - adaptive multidimensional simulations: adaptive finite elements for complex domains
ACMOS'05 Proceedings of the 7th WSEAS international conference on Automatic control, modeling and simulation
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
An adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth. Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height; boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional "surface" diffusion. The problem is solved using two independent meshes: a two-dimensional mesh for the adatom diffusion and a one-dimensional mesh for the boundary evolution. The diffusion equation is discretized by the first-order implicit scheme in time and the linear finite element method in space. A technique of extension is used to avoid the complexity in the spatial discretization near boundaries. All the elements are marked, and the marking is updated in each time step, to trace the terrace height. The evolution of the terrace boundaries includes both the mean curvature flow and the surface diffusion. Its governing equation is solved by a semi-implicit front-tracking method using parametric finite elements. Simple adaptive techniques are employed in solving the adatom diffusion as well as the boundary motion problem. Numerical tests on pure geometrical motion, mass balance, and the stability of a growing circular island demonstrate that the method is stable, efficient, and accurate enough to simulate the growing of epitaxial islands over a sufficiently long time period.