PROBING ELECTRONIC STRURUCTURE AT ATOMIC SCALE

1. PROBING ELECTRONIC STRURUCTURE AT ATOMIC SCALE B.G. Shin

2. 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.

3. DALTON’S ATOMIC THEORY OF MATTER

4. 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.

5. ON BINNIG’S 1978 LABORATORY NOTE BOOK T=I(z)/I(0)=exp(-2Κz) Typically, If The current 2 =

6. 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. HighVacuum environment is required!

7. 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.

8. THE STRUCTURE OF SI(111)-7×7 RESOLVED IN REAL SPACE

9. 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

11. P6MM WITH A GLIDE LINE

12. P3M1 WITH A MIRROR LINE

13. EXPERIMENTAL OBSERVATIONSSI(111)-7×7 • The LEED pattern exhibits p6mm symmetry and show that the unit cell ofthis 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 -> 19dangling bonds are at different energy levels.

14. EXPERIMENTAL OBSERVATIONSSI(111)-7×7 P3m1 symmetry A dimer refers to a molecule composed of two identical subunits or monomers linked together The DAS model

15. EXPERIMENTAL OBSERVATIONSSI(111)-7×7

16. LOW MILLER INDEX PLANES

17. 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.

18. TERSOFF-HAMANN MODEL For metals, it is essentially a charge-density contour. And atomic corrugations on low-Miller-index metal surfaces are too small to be observed. 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

19. SOME EXPERIMENTAL FACTS ABOUT STM • 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.

20. 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.

21. DEPENDENCE OF CORRUGATION ON TIP-SAMPLE DISTANCE

22. CORRUGATION REVERSAL DURING A SCAN Au(111)

23. TUNGSTEIN TIP Near the Fermi level, the density of sates of tungsten is dominated by various d-states.

24. SHARPENING PROCEDURE

25. THE ATOMIC FORCE MICROSCOPE Using the interatomic force

26. AFM - PRINCIPLE By keeping the force constant, a topographic image of constant force is obtained.

27. THE BRADEEN THEORYPROVE THE CLUE OF BCS THEORY

28. V-I GRAPH - TUNNELING JUNCTION

29. EXPECTATION

30. 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.

31. BARDEEN THEORY IN 1-D

32. TIME PERTURBATION

33. THE ORIGIN OF ELASTIC-TUNNELING CONDITION

34. TUNNELING MATRIX Symmetric form implies the reciprocity principle

35. BARDEEN THEORY IN 3-D

36. THE RECIPROCITY PRINCIPLE

37. TOTAL CURRENT For kT is much smaller than energy resolution

38. DERIVATIVE RULE An Intuitive look For P_x at centered x_0 For d_xy at centered x_0, y_0

40. 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!