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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 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 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 ELASTICTUNNELING 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!