** 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

results

on epitaxial growth of Cu on Cu(001) in the submonolayer

regime

(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

conditions.

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.