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Electronic structure (properties)
single atom multiple atoms solid
atomic orbitals molecular orbitals band
For core-level they are still atomic-like, bands have k-dependence and
may have s, p, d, f… or mixed (hybrid) character depending on origin.
Bands
Bands may be separated by band-gaps of energy Eg. Depending upon number
of electrons and DOS, band may be filled, partially filled or empty. Top
(partially-)filled band called valence band. Bottom empty band called
conduction band.
Work function
Ev
Energy require to move electron from EF to EV at the surface called
Workfunction (for semiconductors and insulators from the most
loosely bound electrons inside the solid). Normally in the order of
electron volts.
Work function
Work function affects thermionic emission, the contact potential
between two solids, filed emission, and the bonding of absorbate atoms
to a surface. Work function mainly depends on the depth W of the
attractive potential for the conduction electrons inside the solid (bulk
property).
Surface contributions to
W (work function f):
Image potential
Surface double layer
(surface contamination,
crystallographic surface
orientation).
The attractive force for –e outside the metal:
e2/4pe0(2d)2
Surface double layer
The surface atoms unbalanced
distortion of the electron
clouds  increased electron
density between the cores
compared with the bulk  A
double layer with either net
positive or net negative charge
at the outside.
Electric double layer
Influence on work function in
the order of a few tenth of
electronvolt.
Distortion of charge at the surface
Charge distribution near the surface
Charge distribution
near surface of a
Jellium model.
Orientation of surface  Density of atoms
 Charge density work function
Experimental results
Methods for measurement?
Step density effects
Monolayer Xe absorption effect
Electronic surface states
The electronic states exists only at surface
Semi-Infinite Chain in the Nearly-Free Electron
Model for Surface States
In this model in the bulk
there is potential with
cosine function: V(z) =
2 Vb cos (2pz/a)
There is equation to
solve:
(-h2/2m d2/dz2 +
V(z)) f(z) = E f(z)
For the bulk we have
solution like in the Fig. b
Semi-Infinite Chain in the Nearly-Free Electron
Model for Surface States
With real wave vector k: the matching
(both f and df/dz) of the wave function
inside the solids and the exponentially
decaying electron wave function at the
vacuum side gives one solution for the
surface, eg. Bloch waves inside the
solid with exponentially decaying tails
on the vacuum side.
With complex wave vector k: we have
waves on both side exponentially decay.
The matching of both side allows only
one energy values for a wave vector,
this energy is in the forbidden bulk
energy gap.
The
solution
with
imaginary k have energy
eigenvalues falls inside
the energy gap!
Surface States of a 3D crystal
In 3d each k will give its
own E(k||), therefore we
have
“bands”
(with
different k together).
However, for surface
state, there is no k
dependence, there is only
single line.
In-plane is still bloch waves!!
The surface states can propagate with bulk states can mix
with them, these surface states therefore propagate deep into
bulk with large amplitude at the surface: surface resonance.
Electronic states: 1D  2D  3D
K||
k
One an atom have only a state in the Brillouin zone, with increasing
number of atoms in 1D case, there will be one band level. For the surface
with increasing atom layers K|| experience single band level to bands and
K from 1 state to one band level.
Intrinsic Surface states
Exists on clean and well-ordered surface and have 2D translational
symmetry parallel the surface.
Those can be described by nearly-free electron model are called
Shockley States. they have complex wave vectors with amplitude
exponentially decaying into the solid.
Those can be described by tight-bonding approximation are called
Tamm states. These are due to missing bonding partners and have
less overlap of wave
function. The splitting and
shift of the energy levels is
smaller than in the bulk.
Basically every orbital
involved
in
chemical
bonding gives one surface
state level.
Higher-lying
state
conduction-band like and
therefore acceptor-type.
In reality,
Intrinsic Surface states
states can
Lower-lying state valence-band like and therefore donor-type. For be built
conduction band type surface states, the charge character:
of both
Neutral (empty)  negative (with electron)
type of
For valence band type surface states, the charge character:
bands.
Positive (empty)  neutral (with electron)
In the extreme case, the bonds are broken and the remaining lobes of
the orbital stick out from the surface called dangling bonds, the surface
states then called dangling-bonds states.
If the surface-induced modification of the chemical bonds are among
the topmost several layers, these surface states are back bond states.
Extrinsic Surface states
The surface states due to the defects (missing atoms, line defects) or
adsorbed atoms have no 2D translational symmetry parallel the
surface. They are localized where the defects or adsorbed atoms exist
and the bonding geometry for the surrounding atoms changed.
Surface States for metal
1. s-/p-like states
Simple metal Al, Na, Mg, etc have bulk bands derived from sp- electrons, which are free electron like. The nearly free
electron model for surface states is suitable for such systems.
These surface states lies in the gap of bulk bands and have also
parabolic dispersion.
Surface States for metal
2. d-like states
Transition metal have d
bands, which are very
localized and therefore with
much less dispersion than sp
band. The d bands cross and
hybridize with sp bands and
lead to new gaps where the
surface state can exist.
They lies closely to the high
lying bulk states and have
also different dispersion (not
parabolic).
Layer-resolved Local Density of States (LDOS)
d electrons localized + Surface atoms with
fewer neighbours (more free atom like) 
different surface layer DOS (sharper)
Surface core-level shift
In order to keep the
charge neutrality (the
same Fermi energy
level), for those with
d bands less than half
filled (< 5), the core
level have negative
shift (higher binding
energy) and for those
more than half filled
have positive shift.
Image-potential Surface States
There
are
surely
unoccupied
(empty)
surface states above
the Fermi energy,
among them there are
Image-potential
Surface States, which
are
due
to
the
approaching electron
captured by the image
potential which can
falls into the bulk
bands gap and behave
similar like bulk-band
derived surface states.
Image-potential Surface
States
The energy of the trapped electron have a
eigen value of such states en,
therefore the total energy of the
image-potential surface states:
E(k||) = h2k||2/2m* -en + ef
These states therefore have parabolic
dispersion and less sensitive to
contamination. They are with fixed
energy to vacuum level (change
kinetic energy as f change).
For bulk band derived surface states:
a. sensitive to contamination.
b. within gap of the bulk bands.
c. dispersion only on k||
Also for Image-potential ones
Surface states on semiconductor
Each dangling
bond orbital will
result
in
a
surface state for
nonreconstructed
surface,
however, most
semiconductor
do
have
reconstruction
and
makes
situation
complicated!!!
Surface states on semiconductor
Reconstruction on
the surface is
intimately
connected with the
dispersion
of
surface states. The
study
of
the
surface states, on
the other hand, can
help to construct
and verify surface
structure models.
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