The interpretation of STM images in light of Tersoff and Hamann tunneling model

Transcription

1 The interpretation of STM images in light of Tersoff and Hamann tunneling model The STM image represents contour maps of constant surface LDOS at E F, evaluated at the center of the curvature of the tip. Higher wavefunctions (l,..) gave minor corrections, thus a good model for single atom tip.

2 Modifications of the simple model Effect of finite bias on tip (zero voltage wave functions): eu Iα nt ( ± eu ± E) ns ( E, ro ) de 0 U-Applied bias between tip and sample, n t (eu±e)-tip density of states at an energy E under bias U, n s (E,r o )-sample density of states at an energy E at the center of curvature of tip. (E f is taken =0)

3 Modifications of the simple model W and platinum-iridium are the most widely used for tip material, the density of states at E f is dominated by d states.

4 CCT Imaging with different tip atoms The 2x2 nm image of Au (111) changes during imaging probably due to change of effective orbital of the tip end

5 Comparison with theory Theoretical corrugation amplitude for s and d z 2 tip state on Al (111) Conclusion the orbital at the end of the tip determines the spatial resolution in STM

6 Constant current of Na tip over Na, S, and He adatoms Negative tip displacement for He: the closed valence shell of He produces a local decrease in density of states near EF; Reduced tunneling current => negative tip displacement in CCT. Bumps or holes in CCT may not correspond to presence or absence of atoms!

7 Common Tip Models a) Spherical potential well (continuum): Predicted resolution: 2 A o ( R+s) 1/2 Based on experimental results this model was not accurate enough b) Cluster of atoms or multiatom tip

8 Common Tips Models c) Single atom interacting tip d) Adsorbed atom on a metal electrode (Jellium model - free-electron metal substrate))

9 STM Working Modes Constant height vs constant current imaging

10 Constant Current Imaging (CCI)

11 STM Instrumentation Pohl, D. W. IBM J. Res. Dev. 30, 417 (1986), Kuk and silverman, Rev. Sci. Instrum. 60, 165 (1989) 1. Mechanical Construction 2. Electronics 3. Data Acquisition

12 Vibration Isolation To obtain vertical resolution of 0.01Å, a tip-sample stability of ~ Å is required Typical floor vibration ~ µm, Hz, Vibration Isolation

13 Damping low frequency (<20 Hz, building) tension wires or springs (resonance frequency ~1-5 Hz), air table (resonance frequency ~ 1 Hz). Medium frequency ( Hz,motors, acoustic noise) mounting on heavy plates. External vibration isolation system+rigid STM design can reduce external vibrations by a factor of ( Interference filter ).

14 STM design An example for an approach mechanism

15 STM Positioning Devices - Tripod Three dimensional movement of tip and sample Tip movement -piezoelectric drives. Sample-piezoelectric, magnetic (magnet inside a coil), mechanical.

16 STM Scanners - Piezoelectric bars h V l l = d31 l h V

17 Tube Scanners

18 Design Considerations: Tube scanner: higher sensitivity due to thin walls, symmetrical vs. asymmetrical voltage. Single tube scanner: higher resonance frequency scan rate, stability voltage signals to produce a scan. Large piezoresponse. STM Scanners (cont.) Low cross-talk between x,y and z piezodrives. Low nonlinearity, hysteresis, creep, and thermal drift. Sample-Tip Approach Mechanisms: Step size has to be smaller then the total range of z piezodrive; Step resolution of 50 Å,and dynamic range of cm is reuired! Inchworm (electrostrictive actuator), motion not limited in distance. (כינה) Inchworm = louse Two dimensional

19 Approach mechanism - Inchworm

20 STM Electronics (general)

21 STM Electronics (cont.) Careful design for low currents nad stable feedback circuits. Sample and hold amplifier local I-V characteristics Computer: 4-5 DAC s, 2 ADC s, real-time plane fit etc.

22 Tip preparation and characterization Atomic resolution: single atom termination, For atomic structures: macroscopic shape of little importance Large scale structure: macroscopic tip shape is important 1Å difference 1 order of magnitude in tunneling current.

23 Important factors: Chemical composition of tip Oxide layer (jump to contact) For atomic resolution - type of atom (tip material does not dictate atom at the tip!) Higher resolution has been obtained by tunneling into or from d-orbitals (W). Tip material: hard+low workfunction, UHV-W, Mo, Ir Air-Pt, Au (soft) Pt-Ir. Tip preparation: Electrolytic etching (drop-off technique) Cutting (with scissors) Tip preparation