probing electronic struructure at atomic scale b.g. shin

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 of one element can combine with atoms of

other elements to 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.

Atoms cannot be divided, or created.

It’s wrong.

DALTON’S ATOMIC THEORY OF MATTER

MODERN ATOMIC THEORY OF MATTERAn 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

Typically,

If

The current

2 =

T=I(z)/I(0)=exp(-2Κz)

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 arrangementis 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 OBSERVATIONSSI(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 OBSERVATIONSSI(111)-7×7

P3m1 symmetry

The DAS model

A dimer refers to a molecule composed of two identical subunits or monomers linked together

EXPERIMENTAL OBSERVATIONSSI(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.

As angular momentum states are dominant(or for large R),this model becomes less accurate.

An STM image is a contour of Fermi-level local density of states at the center of curvature of the tip

For metals, it is essentially a charge-density contour.

And atomic corrugations on low-Miller-index metal surfaces are too small to be observed.

SOME EXPERIMENTAL FACTS ABOUT STM

1. The atomic resolution is not always observable. – certain tip-sharpening procedures must be carried out.

2. 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 TIP-SAMPLE 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 MICROSCOPEUsing the interatomic force

AFM - PRINCIPLEBy keeping the force constant, a topographic image of constant force is obtained.

THE BRADEEN THEORYPROVE THE CLUE OF BCS THEORY

V-I GRAPH - TUNNELING JUNCTION

EXPECTATION

BARDEEN THEORYASSUMPTIONS

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

For P_x at centered x_0

For d_xy at centered x_0, y_0

An Intuitive look

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!