Diffusion and Growth on Metal Surfaces (1993-Present)

Publication Numbers: 14,15,16,17,18,21,22,27,30,37,38,40.

The study of thin film growth in molecular beam epitaxy
provides an excellent
laboratory for the study of statistical physics far from
thermal equilibrium in two and three dimensions.
Scanning tunneling microscopy (STM) now provides
essential real space
information down to the atomic scale.
The important theoretical and computational challenges are
to understand the diffusion, nucleation and growth processes
at the atomic scale and from them to predict the
morphologies which emerge at much larger scales.
This effort requires a combination of tools including:
(a) Atomic calculation of energy barriers for hopping and attempt frequencies;
(b) Efficient techniques for the simulation
of the time evolution of the surface morphology;
(c) Visualization
tools for exploring the morphology at different scales.

We have made an important contribution to this effort by
introducing a model that provides a complete and quantitative
description of self-diffusion on different FCC(001) metal substrates
(such as Cu, Ag, Au, Ni, etc) on a common footing with only a few
parameters [38].
These parameters can be obtained from experiments, ab-initio
or semi-empirical calculations.

To demonstrate the approach we studied self diffusion on Cu(001)
using barriers obtained from semi-empirical potentials.
We then performed a quantitative comparison between experimental
on epitaxial growth of Cu on Cu(001) in the submonolayer
(obtained by Wendelken et al.)
and our Monte Carlo simulations.
In these experiments the separation between nucleating islands
on the surface is measured as a function of the incoming flux
and the substrate temperature.
We obtained a good quantitative agreement for the island
separation, the activation energies for the dominant processes
and the dynamical exponents that characterize the growth.

We are currently using this approach
to study electromigration effects
on metal surfaces [40].
Electromigration, at high densities of electric
current causes biased diffusion of atoms which may cause
damage in microelectronic circuits. As the size of these
circuits is reduced, it becomes more essential to understand
and control this phenomenon.
So far we have focused on the analysis of the drift velocity
of surface features such as islands and voids, and its dependence
on the current density and temperature.
In the coming year we will examine the collective behavior of
large ensembles of islands and voids, under electromigration

Future Plans: We plan to study collective effects and
growth instabilities in multilayer growth. We will focus on the
development of a theoretical framework which will be able to
predict under given physical conditions, what would be the
resulting mode of growth.
The understanding of inter-terrace diffusion
at the atomic scale is crucial for this purpose.
The growth instability which gives rise to three dimensional
growth is driven by nucleation of islands on top of islands.
This process is
strongly affected by the Schwoebel barrier for adatom hopping
down a step. However, the Schwoebel barrier strongly depends
on the structure of the growing islands, thus coupling between
the submonolayer and multilayer processes at a broad range of
length and time scales.