PY5020 Nanoscience Scanning probe microscopy

Transcription

1 PY500 Nanoscience Scanning probe microscopy

2 Outline Scanning tunnelling microscopy (STM) - Quantum tunnelling - STM tool - Main modes of STM

3 Contact probes V bias Use the point probes to measure the local I-V curves at different locations on the surface.

4 Schematic of a tunnelling gap with a square barrier Φ is the work function; ~ 5 ev for metals E f is the Fermi energy

5 Schrödinger equation can be solved for each area square barrier U(z) 0 U(z) V U(z) 0 0 d Ψ U(z) Ψ EΨ m dz Schrödinger equation: Solutions for different areas: ikz ikz Ψ e Ae Ψ Be Ce Ψ De 1 3 me m( V E) me k 0 k z z ik(z-d )

6 Probability current density through the barrier Transmitted current: Incident current: Transition Probability:

7 Potential is complicated by potential wells at atom locations

8 Similar approach is applied as in the square barrier problem Search for wave functions satisfying: Probability of finding an electron at a distance z into the barrier:

9 Apply positive bias ΔV to the substrate to make current flow eδv I E F E Ψ ev n (0) d Local density of states (LDOS) is defined as: 1 E N electrons / unit ( z, E) Ψ (z) E n energy interval At a distance z at energy E e n volume

10 I is linear with voltage for small ΔV Since = Current I through the tunnel barrier: Comparing these equations: Or in simple form

11 Scanning electron microscope We can raster x and y while measure z, i.e. have a 3D microscope

12 Topography scan

13 Controling the tunnelling gap A

14 Ultra high vacuum

15 STM images 7x7 reconstraction on Si(111) Takayanagi K et. al. Surf. Sci V P HOPG honey comb structure Courtesy of Alexander Chaika

16 Scanning tunnelling spectroscopy (STS) I f 4 e (E) tip (E) substrate (E) f ( E ) f ( E ev ) ( E ) ( E ev ) T(, V ) d F is the Fermi-Dirac distribution function F is the local density of states of tip (LDOS) is the LDOS of substrate tip F substrate F T(, V ) is the e transmission probability at energy ε and applied voltage V

17 Fermi-Dirac distribution function T=5 K T=1000 K T=5000 K E-E f Varies between 1 and 0. Tells probability of occupation of a certain election state as a function of energy with respect to a Fermi level.

18 Assumptions of STS 0 ) ( ) ( 4 ev F substrate F tip d ev E T E e d V T ev E E ev E f E f e I F substrate F tip F F ), ( ) ( ) ( ) ( ) ( 4 ) ( ev E const V I F substrate V At room temperature kt = 5 mev For V>~kT/e, f(e) can be well approximated by a step function LDOS of tip does not change significantly with E

19 Current Imaging Tunnelling Spectroscopy (CITS) Acquire a topography image and measure I-V curve at each point

20 Apparent tunnel barrier height

21 What is the force on lead atom on the tip F kz

22 Cantilever can be used to measure fine deflections STM Tip F

23

24 The force on the tip atom Atoms interact via the close and long range forces that are electrostatic in nature Lead atom of the tip interacts with the lead atom on the substrate (atomic interactions short range atomic bond). Groups of atoms on the tip and substrate interact collectively via the WanderVaals forces (long range of the order of nm) What spring constant of a cantilever should be? F kz k is the spring constant ~ H z m 10 kg k m 1N / m

25 Tip-sample forces Surface ~ 0.5 nm Set point d

26 The method of choice today A B C D Normal force A+B = Up C+D=Down Measure the difference Magnitude of voltage tells by how much the tip moved Polarity of the voltage gives Up or Down Lateral force A+C=Left B+D=Right Adv. Mater. (009) 1,

27 Photodiode How to maintain constant height Ref. Voltage (set point)

28 The Lennard-Jones potential - Captions dispersion and Pauli repulsive interactions - U* is depth of potential; at r = σ U(r) goes to zero 6 1 * * * 4 ) ( r r r r U r U σ σ

29 Electrostatic interatomic and intermolecular forces - Ion-ion U ( r) Q1Q 4 r 0 Charge-dipole Dipole-dipole U ( r) p 1 p Qp cos( ) U ( r) 4 r 0 cos( 1)cos( ) sin( 1)sin( )cos( ) 3 4 r 0 Angle averaged dipole-dipole (Keesom) U ( r) p1 p 3(4 ) k 0 B Tr 6 Angle averaged dipole induced Polarisation (Debye) U ( r) p1 0 p (4 ) r Dispersion interatomic Intermolecular interaction (London) U ( r) 3 ( ) r 6 I1I I I 1

30 Van der Waals forces Van der Waals is a sum of forces which interaction potential varies as 1/r 6 : Orientation or Keesom force: thermally angle averaged dipole-dipole interaction between two atoms or molecules Debye force: thermally angle averaged dipole-induced dipole interaction London or Dispersion force: dispersion force between acting between molecules and atoms irrespective of their polarisation U ( r) U ( r) U ( r) U ( r) Keesom Debue London p p (40) kbtr ( 40) r p p 3 ( ) r 6 I1I I I 1 C 6 r

31 From interaction to tip-sample interaction simple theory

32 From interaction to tip-sample interaction simple theory

33 Surface surface interactions

34 Derjaguin approximation By measuring the lift off force of tip from the substrate it is possible to correlate the tip sample force to the values of surface energy. From the previous slides: F( d) W W planesphere d plane plane ( d) C R 6d C 1d tip By comparing these equation, the Derjaguin approximation: F( d) sphere plane RtipW ( d) plane plane

35 From F-z to F-d curves

36 Cantilever can be used to measure fine deflections l F b h I bh 1 3

37 Cantilever equilibrium position δ δ

38 F-d to F-z conversion δ =

39 Chemically resolved AFM