Page 30 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Observed Lattice Property Data
edly subject to the special features and limitations that the surface
introduces.

2.1 Observed Lattice Property Data

Geometric The geometric structure of a regular crystal lattice is determined using x-
Structure ray crystallography techniques, by recording the diffraction patterns of x-
ray photons that have passed through the crystal. From such a recorded
pattern (see Figure 2.1 (a)), we are able to determine the reflection planes
formed by the constituent atoms and so reconstruct the relative positions
of the atoms. This data is needed to proceed with a geometric (or, strictly
speaking, group-theoretic) characterization of the crystal lattice’s sym-
metry properties. We may also use an atomic force microscope (AFM) to
map out the force field that is exerted by the constituent atoms on the sur-
face of a crystal. From such contour plots we can reconstruct the crystal
structure and determine the lattice constants. We must be careful, though,
because we may observe special surface configurations in stead of the
actual bulk crystal structure, see Figure 2.1 (b).

Elastic The relationship between stress and strain in the linear region is via the
Properties elastic property tensor, as we shall shortly derive in Section 2.3.1. To
measure the elastic parameters that form the entries of the elastic prop-
erty tensor, it is necessary to form special test samples of exact geometric
shape that, upon mechanical loading, expose the relation between stress
and strain in such a way that the elastic coefficients can be deduced from
the measurement. The correct choice of geometry relies on the knowl-
edge of the crystal’s structure, and hence its symmetries, as we shall see
in Section 2.2.1. The most common way to extract the mechanical prop-
erties of crystalline materials is to measure the direction-dependent
velocity of sound inside the crystal, and by diffracting x-rays through the
crystal (for example by using a synchrotron radiation source).

Semiconductors for Micro and Nanosystem Technology 29