Download 1.5 Introduction to Surface Electronics

Lecture Notes by John A. Venables. Latest version 28 January 2003
© Arizona Board of Regents for Arizona State University and John A. Venables
1.5 Introduction to Surface Electronics
Refs: Prutton, Chap 4; Zangwill, Chap. 4; Lüth, Chap 6; More specialist review articles,
such as J.E. Inglesfield, in D.A. King and D.P. Woodruff (eds) The Chemical Physics of Solid
Surfaces and Heterogeneous Catalysis, vol 1, especially sects 1, 2.1 and 2.2. There are many such
articles, and various specialist books. Here we are concerned only to define and understand a few
terms, which will be used in a general context; the discussion is at a similar level of detail to my
book, section 1.5. A detailed study of electronic effects can be done later. The terms we will need
include the following. I will draw the corresponding diagrams on the board and discuss them:
a) Work Function, 
This is the energy, typically a few eV, required to
move an electron from the Fermi Level, EF, to the
vacuum level, E0. The work function depends on
the crystal face {hkl} and rough surfaces typically
have lower , as discussed later in section A1.
b) Electron Affinity,  and Ionisation Potential  .
Both of these would be the same for a metal, and equal to ,
but for a semiconductor or insulator, they are different. The
electron affinity is the difference between the vacuum level
E0, and the bottom of the Conduction Band EC. The ionisation
potential is E0 - EV, where EV is the top of the Valence Band.
These terms are not specific to surfaces: they are also used for
atoms and molecules generally, as the energy level that a) the
next electron goes into, and b) the last electron comes from.
c) Surface States and related ideas
A surface state is a state localized at the surface, which decays
exponentially into the bulk, but which may travel along the
surface. The wave function is typically of the form
  u(r)exp (-i k|z|) exp (i k// r),
where, for a state in the band gap, k is complex, leading to
decay away from the surface on both sides.
Such a state is called a resonance if it overlaps with a bulk band, as then it may have an
increased amplitude at the surface, but evolves continuously into a bulk state. A surface
plasmon is a collective excitation located at the surface, with frequency typically p/2.
d) Surface Brillouin Zone
A surface state takes the form of a Bloch wave in the 2dimensions of the surface, in which there can be energy
dispersion as a function of the k// vector. For electrons
crossing the surface barrier, k// is conserved, k is not. The
k// conservation is to within a 2D reciprocal lattice
vector, i.e.  G//. This is the theoretical basis of (electron
and other) diffraction from surfaces.
e) Band Bending, due to Surface States
In a semiconductor, the bands can be bent near the surface due to
surface states. Under zero bias, the Fermi level has to be ‘level’,
and this level typically goes through the surface states which lie in
the band gap. Thus you can convince yourself that a p-type
semiconductor has bands, which are bent downwards as you
approach the surface. This leads to a reduction in the electron
affinity. Some materials (eg Cs/p-type GaAs) can even be
activated to negative electron affinity, and such materials form a
potent source of electrons, which can also be spin-polarized as a
result of the band structure.
f) The Image Force
You will recall from elementary electrostatics that a charge outside a conducting plane has a field
on it equivalent to that produced by a fictitious ‘image charge’. The corresponding potential felt
by the electron, V(z) = -e/4z. For a dielectric, with permitivity , there is also a (reduced)
potential V(z) = -(e/4z) (-1)/(+1). It is often useful to think of metals as the limit  , and
vacuum as   1. The diagram showing the lines of electric field from an incident electron in the
dielectric case is on the cover of Lüth’s book, and is described in section 4.6.2 (3rd edition, page
165). (Note added 13 May '02) In this section, I have been too sloppy in the formulae and have used oldfashioned c.g.s units without thinking. In MKS (S.I.) units, these formulae should be multiplied by the
constant K = 1/(40). Thanks to Richard Forbes and Michael Isaacson for spotting this, and to Yong
Jiang for working through the related problem 1.6 on the first assignment in Spring 2002.
g) Screening
The above description emphasizes the importance of screening, in general, and also in connection
with surfaces. We can also notice the very different length scales involved in screening, from
atomic dimensions in metals, (2kF)-1, increasing through narrow and wide band gap
semiconductors to insulators, and vacuum; there is no screening (at our type of energies!), unless
many ions and electrons are present (i.e. a plasma). In general, nature tries very hard to remove
long-range (electric and magnetic) fields, which contribute unwanted macroscopic energies. We
will come back to this point, which runs throughout the physics of defects; in this sense, the
surface is simply another defect with a planar geometry.