An Introduction to the Theory of Crystalline Elemental Solids and ...

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a much richer variety of reconstructions than metal surfaces do, which is certainly the
case. Fortunately, however, much of the qualitative insight into semiconductor surfaces
has been condensed into a series of general principles, first laid down by Duke [105, 106]
and discussed at length in several other places [104, 107]. A discussion of the relevant
principles [108] along with a few examples is sufficient to provide a flavor for how some
of the most-common elemental semiconductor surfaces behave.
The first principle which we discuss here is often described as the basic or guiding
principle of semiconductor surfaces and it states that “the surface structure observed will
be the lowest free energy structure kinetically accessible under the preparation conditions”.
This, rather obvious statement, is true of any surface. However, it is especially pertinent
to semiconductors since which surface is observed is known to depend sensitively on
cleavage, annealing, and growth conditions.
Stemming from the guiding principle are a series of other principles. Of relevance to the
present discussion on elemental semiconductors is one that states that “...the surface
atomic geometry is determined primarily by a rehybridization-induced lowering of the
surface state bands associated with surface bonds or (filled) anion dangling bond states”.
Put another way this principle simply implies that a surface tends to minimize the number
of dangling bonds by formation of new bonds and/or rehybridization. The concept of the
“dangling” bond is absolutely key to understanding semiconductor surface reconstructions.
In an elemental semiconductor, covalent bonds between neighboring atoms contain
two spin paired electrons in, for example, an sp 3 hybrid orbital. When a surface is created
at least one such bond per surface atom is cut, leaving some sp 3 hybrid orbitals to stick
out of the surface. These orbitals are called dangling bonds and they contain less than
two spin paired electrons. Dangling bonds are unstable and reactive and so the above
principle is simply stating that real surfaces will relax or reconstruct to reduce the number
of dangling bonds they possess and, in so doing, minimize the total energy of the system.
Dangling bond states are surface-localized orbitals that reside at an energy between
the valence and conduction bands. Thus these are surface states. Naturally, dangling
bonds on neighboring atoms interact and so the dangling bond levels get broadened into
bands. As an example we show in Fig. 11 the computed surface band structure of the
unreconstructed (100), (110), and (111) surfaces of Si. These are the prototype dangling
bond systems; with the dangling bonds clearly seen in the fundamental gap in each system.
The other principle relevant to elemental semiconductors is one that states that “...surfaces
can lower their energies by atomic relaxations leading to semiconducting (as opposed
to metallic) surface state eigenvalue spectra”. Basically this principle implies that a
semiconductor surface tends to be insulating or semiconducting but not metallic. In
general, if there is a single dangling bond per surface atom or when two or more dangling
bond bands overlap then the surface is metallic. Otherwise the surface is semiconducting.
All three bulk-truncated surfaces of the diamond lattice shown in Fig. 8 are metallic and
thus liable to reconstruct.
Let’s now consider how the (001) and (111) surfaces of the diamond lattice behave.
First, the (001) surface. This surface, in particular the (001) surface of Si, has been
examined in detail at least as much as any other solid surface; often being described
as the backbone of the semiconductor industry. The Si(001) surface undergoes a large
number of reconstructions, notably to p(2×1), p(2×2), and c(4×2) phases. We discuss