1.2. CRYSTAL STRUCTURE 13
4Å4Å(2 x 4 unit cell)
(a) (b)
Top layer As atoms
Second layer Ga atoms
Third layer As atomsIDEAL SURFACE RECONSTRUCTED SURFACE
Figure 1.9: The structure (a) of the unreconstructed GaAs (001) arsenic-rich surface. The miss-
ing dimer model (b) for the GaAs (001) (2×4) surface. The As dimers are missing to create a 4
unit periodicity along one direction and a two unit periodicity along the perpendicular direction.
The reconstructed surfaces that occur in nature are generally classified as C(2×8) or C(2×4) etc.,
representing the increased periodicity along the[ ̄110]and [110] respectively. The C(2×4) case
is shown schematically in figure 1.9, for an arsenic stabilized surface (i.e., the top monolayer is
As). The As atoms on the surface form dimers (along[ ̄110]on the surface to strengthen their
bonds. In addition, rows of missing dimers cause a longer range ordering as shown to increase
the periodicity along the [110] direction to cause a C(2×4) unit cell. Similar reconstruction
occurs for Si surfaces as well.
Example 1.1Calculate the planar density of atoms on the (111) surface of GaAs.
As can be seen from figure 1.6, we can form a triangle on the (111) surface. There are
three atoms on the tips of the triangle. These atoms are shared by six other similar
triangles. There are also 3 atoms along the edges of the triangle which are shared by two
adjacent triangles. Thus the number of atoms in the triangle are
3
6+
3
2
=2
Theareaofthetriangleis√
3 a^2 / 2. The density of GaAs atoms on the surface is then
7. 29 × 1014 cm−^2.