Chemistry Reference
In-Depth Information
Chapter 12
Step-Bunching Instabilities of Vicinal Surfaces
During Growth and Sublimation of Crystals -
the Role of Electromigration of Adatoms
S. Stoyanov
Abstract
This review is devoted to the mechanisms of a rather strange phe-
nomenon - the step configuration at the vicinal surface of a Si crystal depends on the
direction
of the electric current through it. This phenomenon opens an easy way to
manipulate the surface structure and to create a template for production of ordered
arrays of nano-crystals on Si surface. The BCF model is generalized to account for
the surface electromigration and the considerations are focused on the step-bunching
instability induced by the drift of the adatoms. A simplified form of the equations
of step dynamics at a vicinal crystal surface is presented and the results of the linear
stability analysis are given. The non-linear effects in the step dynamics are studied
in the frame of the continuum model equation and the treatment is restricted to
the steady-state shape of the bunches of steps - the self-similarity of the bunch
shape and the relation between the width and the height of the bunch. The scaling
relations for the shape of the bunches opened a pathway for a number of interesting
experiments, which are briefly described.
12.1 Introduction and Historical Overview
In 1989 A. Latyshev and his colleagues in Novosibirsk reported [
1
] rather strange
observations on the distribution of steps at Si surfaces slightly deviated from the
(111) face (such stepped surfaces are called vicinal). Carrying out experiments on
step dynamics in high-temperature sublimation, they heated the Si crystal by passing
direct electric current through it. The unexpected feature, discovered by Latyshev
and co-workers, was that the step configuration at the vicinal surface depends on
the
direction
of the electric current. For instance, in the temperature interval 1250-
1350
◦
C, an electric current with a step-down direction destabilized the initial regular
distribution of the elementary steps at the vicinal crystal surface. In a relatively short
time of heating with step-down current the steps formed bunches, separated by wide
