Scanning Tunneling Microscopy

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Clara Cummings
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1 EMSE Scanning Tunneling Microscopy EMSE-515 F. Ernst 1

2 Scanning Tunneling Microscope: Working Principle 2

3 Scanning Tunneling Microscope: Construction Principle 1 sample 2 sample holder 3 clamps 4 tip 5 tip holder 6 scanner tube 7 approach motor rod 8 motor mount 9 approach mount 10 quartz balls 11 Zener diode 3

Scanning Tunneling Microscope: Construction Principle design of Binnig and Rohrer (1982) vacuum (also operates in gas or liquid) atomically sharp tip piezo-electrostatic manipulator ( louse,

4 Scanning Tunneling Microscope: Construction Principle design of Binnig and Rohrer (1982) vacuum (also operates in gas or liquid) atomically sharp tip piezo-electrostatic manipulator ( louse, crawls) enables motion in two dimensions fine-positioning of the tip: piezoelectric transducers (typically: 1 nm/v) tip specimen distance: < 1 nm (in liquids: smaller than solvent molecule size) 4

5 Electron Tunneling Through an Energy Barrier consider two metals separated by vacuum gap quantum mechanics: electrons can overcome energy barrier! unbiased: no net electron current tunnel barrier E F1 E b1 φ 1 φ 2 w E b2 E F2 5

6 Electron Tunneling Through an Energy Barrier biased (U t : net current from one metal into the other) tunneling current E F1 E b1 E b2 tunneling current E F2 6

Tunneling Current solution of the stationary Schrödinger equation H = E for potential troughs separated by barrier within each trough: oscillatory wave function

7 Tunneling Current solution of the stationary Schrödinger equation H = E for potential troughs separated by barrier within each trough: oscillatory wave function solution within barrier: exponential damping, [z] = [0] Exp[ z] = 1 2m 0 (V E) m 0 : electron mass; V : potential of the barrier; E: energy of the tunneling electrons; 7

8 Wave Function Across a Tunneling Barrier Separating Two Metals [z] = 0 Exp[ z] E F1 tunneling current E F2 0 z 8

9 Tunneling Current as a Function of Barrier Width tunneling current at energy level E: i t [E] i t [E] is proportional to probability density of finding electrons at z = w probability of finding electrons at z = w: [w] 2 therefore i t [E] [w] 2 Exp[ 2 w], = 1 2m 0 (V E) 9

More Realistic Models for the Tunneling Current reality: image charge, image forces real specimen surface is curved results of more realistic modeling:

10 More Realistic Models for the Tunneling Current reality: image charge, image forces real specimen surface is curved results of more realistic modeling: barrier is asymmetric size and shape of the tunneling barrier depend on the barrier width w size and shape of the tunneling barrier depend on the bias voltage U t 10

11 Tunneling Resistance Work Function magnitude of the tunneling current: a few na tunneling resistance: R t := U t /I t Fowler Nordheim relation R t [w] = Exp[Aw ] A constant with unit ev 1 nm 1 ; w width of the tunneling barrier; = 1 2 ( ) e ective work function. 11

12 Interpretation of the Measured Tunneling Current local tunneling barrier of the surface surface topography (but: maxima atoms!) work function for electrons (tip and specimen) electron density electron density of states current voltage characteristics I t [U t ] spectroscopy 12

13 Problems in Practice vibrations hysteresis of piezo transducers thermal drift (di erent materials!) specimen charging electric field tunneling current distinguish real surface topography from local variations of the work function ( STS) 13

14 STM Modes of Operation di erent modes of STM operation provide di erent information about the specimen surface not all modes may be possible for a given specimen (surface roughness) 14

15 STM Constant-Height Mode 15

16 STM Constant-Current Mode 16

Topography constant-current mode operation under constant current feed-back surface topography measured quantity: voltage U z of piezoelectric transducer image:

17 Topography constant-current mode operation under constant current feed-back surface topography measured quantity: voltage U z of piezoelectric transducer image: intensity height z above the surface constant-height mode high scanning speed / smooth surfaces measured quantity: tunneling current It image: intensity tunneling current 17

18 STM Resolution vertical and lateral resolution three-dimensional information atomic resolution is possible, but often STM is used with less resolution: 10 nm to 1 µm quantitative understanding: requires theory describing the tunneling current 18

19 Examples 19

20 STM: Si (111) 7 7 Surface Reconstruction 20

21 Example: Self-Organized Nanowires on Layered Crystals 21

22 Example: Self-Organized Nanowires on Layered Crystals 22

23 STM: Rb Nanowires on TiTe 2 23

24 STM: Rb Nanowires on TiTe 2 24

Scanning Tunneling Microscopy

Scanning Tunneling Microscopy The wavelike properties of electrons allows them to tunnel beyond the regions of a solid into a region of space forbidden for them to exist in. In this region they can be