Transcript Probing Electronic Sturucture at Atomic Scale

PROBING ELECTRONIC
STRURUCTURE AT ATOMIC
SCALE
B.G. Shin
DALTON’S ATOMIC THEORY OF MATTER
Elements are made of tiny particles called atoms.
 All atoms of a given element are identical.
 The atoms of a given element are different from those
of any other element.
Atoms cannot be
 Atoms of one element can combine with atoms of other
or created.
elements todivided,
form compounds.
A given compound
always has the same relative numbers of types of
atoms.
 Atoms cannot be created, divided into smaller particles,
nor destroyed in the chemical process. A chemical
reaction simply changes the way atoms are grouped
together.

It’s wrong.
DALTON’S ATOMIC THEORY OF MATTER
MODERN ATOMIC THEORY OF MATTER
An atom consists of a number of electrons in a series of
stationary states surrounding an extremely small,
positively charged nucleus.
ON BINNIG’S 1978
LABORATORY NOTE BOOK
T=I(z)/I(0)=exp(-2Κz)
Typically,
If
The current
2
=
LOW ENERGY ELECTRON DIFFRACTION
LEED is surface sensitive
Low energy electrons interact strongly with matter:
electron mean free path λe is small.
Only e- scattered from near surface can leave the
surface, surface sensitive.
High Vacuum environment is required!
LOW ENERGY ELECTRON DIFFRACTION

The observation of a LEED pattern does not
guarantee that the whole surface is ordered!
Red spot : add atom
But, in experiment,
Just a spot.
The details of the
arrangement
is ambiguous.
THE STRUCTURE OF SI(111)-7×7
RESOLVED IN REAL SPACE
THE SYMBOLS FOR PLANE GROUPS
(THE HERMANN-MAUGUIN SYMBOL)
p : primitive
 c : centered
 Numbers : 1,2,3,4,6 : axial symmetry
 m : a symmetry under a mirror reflection
 g : a symmetry with respect to a glide line, that is,
one-half of the unit vector translation followed by
a mirror reflection

P6MM WITH A GLIDE LINE
P3M1 WITH A MIRROR LINE
EXPERIMENTAL OBSERVATIONS
SI(111)-7×7
The LEED pattern exhibits p6mm symmetry and
show that the unit cell of this reconstructed
surface is constituted of 49 silicon atoms on the
original Si(111) surface.
 But STM shows that there are 12 adatoms and
one large hole in each unit cell.
 12 Dangling bonds at the adatoms, 6 at the rest
atom, and 1 at the center atom deep in the corner
hole -> 19 dangling bonds are at different energy
levels.

EXPERIMENTAL OBSERVATIONS
SI(111)-7×7
P3m1 symmetry
A dimer refers to
a molecule
composed of two
identical subunits
or monomers
linked together
The DAS model
EXPERIMENTAL OBSERVATIONS
SI(111)-7×7
LOW MILLER INDEX PLANES
ATOMIC RESOLUTION OF CLEAN METAL
The observed corrugations amplitudes were one
to two orders of magnitudes greater than the
predictions of the Tersoff-Hamann model.
 The reported atomic resolution on Au(111)
surface, with a corrugation amplitude 30 pm, was
a pleasnt surprise at that time.

TERSOFF-HAMANN MODEL
Except for the s-wave tip wavefunction,
all other tip wavefunctions are neglected.
For metals, it is essentially a
charge-density
contour.
As angular
momentum states are dominant
(or for large R),
And atomic corrugations
on lowthis model becomes less accurate.
Miller-index metal surfaces are
too small to be observed.
An STM image is a contour of Fermi-level local density
of states at the center of curvature of the tip
SOME EXPERIMENTAL FACTS
ABOUT STM
1.
2.
The atomic resolution is not
always observable. – certain
tip-sharpening procedures must
be carried out.
During the scanning, the image
often shows spontaneous
changes, and the atomic
resolution could appear or
disappear unexpectedly.
SOME EXPERIMENTAL FACTS
ABOUT STM
3. In many cases, the atomic corrugation is
inverted. – a spontaneous tip restructuring
4. The atomic corrugation has an almost
exponential dependence on the tip-smaple
ditance. The Highest atomic corrugations are
always observed at very short tip-sample
distance.
DEPENDENCE OF CORRUGATION ON TIPSAMPLE DISTANCE
CORRUGATION REVERSAL DURING A SCAN
Au(111)
TUNGSTEIN TIP
Near the Fermi level, the density of sates of tungsten
is dominated by various d-states.
SHARPENING PROCEDURE
THE ATOMIC FORCE MICROSCOPE
Using the interatomic force
AFM - PRINCIPLE
By keeping the force constant,
a topographic image of constant force is obtained.
THE BRADEEN THEORY
PROVE THE CLUE OF BCS THEORY
V-I GRAPH - TUNNELING JUNCTION
EXPECTATION
BARDEEN THEORY
ASSUMPTIONS
Tunneling is weak enough that the first –order
approximation is valid.
 Tip and sample states are nearly orthogonal.

The electron-electron interaction can be ignored.
 Occupation probabilities for the tip and sample
are independent of each other, and do not change,
despite the tunneling
 The tip and sample are each in electrochemical
equlibrium.

BARDEEN THEORY IN 1-D
TIME PERTURBATION
THE ORIGIN OF ELASTIC-TUNNELING
CONDITION
TUNNELING MATRIX
Symmetric form implies the reciprocity principle
BARDEEN THEORY IN 3-D
THE RECIPROCITY PRINCIPLE
TOTAL CURRENT
For kT is much smaller than energy resolution
DERIVATIVE RULE
An Intuitive look
For P_x at centered x_0
For d_xy at centered x_0, y_0
PHASE EFFECT
The tunneling matrix element for a p_z tip state is
proportional to the z derivative of the sample wave function
at the center of the apex atom.
Variation of the wave function is highlighted!