Scanning Tunneling Microscopy Wei-Bin Su, Institute of Physics, Academia Sinica
Tunneling effect Classical physics Field emission 1000 ~ 10000 V E V metal-vacuum-metal tunneling metal metal Quantum physics < 10 V < 10 Å
Scanning Tunneling Microscopy (STM) Si(111)7 7 scanner feedback bias <10Å sample metal tip tunneling current preamp Pt(100)-R0.7 0
Principle of scanning tunneling microscopy T(s)~exp(-2κs) ; κ=(2mφ/ħ 2 ) 1/2 ; φ=(φ t + φ s )/2 κ~ 1 Å -1 the current decays about e 7.4 times when s increases by 1 Å Cu(111) surface 0.02 Å I 0 ev ρs (E F -ev+ε) ρ T (E F +ε)d ε ρ T is constant di/dv ρ s (E F -ev)
Scanning Tunneling Spectroscopy (STS) (feedback off) I-V spectroscopy (feedback on) Z-V spectroscopy I Z V V ev I 0 ρ s (E F -ev+ε) ρ T (E F +ε)d ε ρ T is constant di/dv ρ s (E F -ev) scanning sample
Structure of STM
Tube Scanner -y Metal free area Piezoelectric ceramic PZT [Pb(Zr,Ti)O 3 ] (piezo)
Motor for coarse approach V t Reverse direction V t
Electronic Control 1. Auto approach 2. Data acquisition V z (x,y) The contrast of STM image is the variation of voltage applied to z-electrode of tube scanner.
Vibration Isolation The tip-sample distance must be kept constant within 0.01Å to get good atomic resolution. Therefore it is absolutely necessary to reduce inner vibrations and to isolate the system from external vibrations. Environmental vibrations are caused by: Vibration of the building 15-20 Hz Running people 2-4 Hz Vacuum pumps Sound ω 0 = k/m Damping Factor α m k Q = ω 0 /2α Vibration damping can be done by Suspension with springs (including additional eddy current dampers) Pneumatic systems magnets and copper plates
Pneumatic systems
Tip The tip is the trickiest part in the STM experiment. It needs a small curvature to resolve coarse structures. For atomic resolution a minitip with a one atomic end is necessary. Tips typically are made out of tungsten, platinum or a Pt-Ir wire. A sharp tip can be produced by: Cutting and grinding Electrochemical etching Most often the tip is covered with an oxide layer and contaminations from the etchant and is also not sharp enough. Thus other treatments to the tip, like annealing or field evaporation are necessary. It is also possible to do tip-sharpening during tunneling. Sudden rise of the bias voltage to about -7V (at the sample) for 2-4 scan lines. By this treatment some W atoms may walk to the tip apex due to the nonuniform electric field and form a nanotip. Controlled collision on Si surface. The tip may pick up a Si-cluster which forms a monoatomic apex with a p z like dangling bond.
Environment for STM : Air, Liquid, Ultra high vacuum (UHV) Working temperature of STM : RT, HT (high to 1200 K), LT (low to 0.3 K) Atomic scale resolution Si(111)7 7 Pt(100)-R0.7 0 For obtaining order arrangement of atom, UHV is necessary.
UHV chamber UHV RT STM Defects of UHV RT STM: Thermal effect reduces the energy resolution in scanning tunneling spectroscopy Physical phenomena appearing at low temperature cannot be observed. Thermal drift (relative movement of tip and sample) Development of LT-STM
Improvement of Energy resolution by reducing temperature S.H. Pan et al., Nature 411, 920 (2001). Superconducting gap
Atomic Manipulation Low temperature can reduce the relative movement between tip and sample, facilitating atomic manipulation.
Home made LT UHV STM Homemade STM UHV-compatible LHe Cryostat STM Lowest temperature ~ 5 K
Applications of scanning tunneling microscopy Surface reconstruction FCC(100) FCC(111)
22 3 Reconstruction of Au(111) surface FCC HCP FCC (ABC) (ABA)
Reconstruction on Pt(100) Pt(100)-R0.7 0 Close packed lattice (0.965 A) / square lattice (A) A=lattice constant
Surface Diffusion Einstein Equation : D=<x 2 >/2αγ D: diffusion coefficient, <x 2 > : mean square displacement of atom α=1 for one dimensional diffusion α=2 for two dimensional diffusion (<x 2 >+ <y 2 >) γ: time interval <x 2 > can be related to the number of jumps N According to random walk theory <x 2 >=Nd 2 d: mean jump distance Γ Is defined as the number of atom jumps per time interval =N/γ D=d 2 Γ/2 Γ=ν 0 exp(-e d /kt) ν 0 is vibration frequency, E d is activation energy D=D 0 exp(-e d /kt)=<x 2 >/2αγ D 0 is the diffusivity=ν 0 d 2 /2 ln (<x 2 >/2αγ)=ln(D 0 )-E d /kt ln(<x 2 >/2αγ) Arrhenius plot 1/T
Surface Diffusion Site Hopping of Single Chemisorbed O 2 Molecule on Si(111)7 7 350 0 C Phys. Rev. Lett. 78, 4797 (1997)
Nucleation and Epitaxial Growth Fe/Fe(100) E d : activation energy E i : binding energy of critical size i Phys. Rev. B 49, 8522 (1994)
Critical size i i=0 i=1 i=2 i=3 monomer dimer trimer tetramer Scaling theory Ns = θs -2 f i (s/s) Ns : island density at size s θ : coverage S : average island size Ns S 2 / θ = f i (s/s) f i (s/s) is an universal Scaling function at critical size i J. G. Amar and F. Family Phys. Rev. Lett. 74, 2066 (1995)
Epitaxial Growth Mode Volmer-Weber Frank-van-der-Merwe Stranski-Krastonov (VW) (FM) (SK) γ s : surface free energy of substrate γ a : surface free energy of adsorbate γ* : interfacial free energy
Pb/Si(111) at RT Stranski-Krastanov growth mode 3D islands Growth nm 10 8 6 4 2 0 400 800 1200 nm Substrate Layer + Island (SK) Growth
The Growth of 2D Pb islands on Si(111)7 7 surfaces at Low Temperature T=208K, θ = 3.2 ML Pb Topography 3D image of topography 2 ML wetting layer 100 nm Phys. Rev. Lett. 86, 5116 (2001)
R a tio 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2.72 ML 3.52 ML 4.32 ML 1 2 3 4 5 6 7 8 9 10 11 12 13 14 I s l a n d t h i c knes(layer) i n t e r l a y e r s p acing=2. 85 Å i n t h e [ 1 1 1 ]direction
Quantum Size Effect-Driven Epitaxial Growth λ = de Broglie wavelength of electron L>> λ L λ M Substrate k z L M L Substrate k z = nπ/l k z Fermi sphere k y k F n=5 n=4 Fermi disc n=3 n=2 n=1 k y k x k x Phys. Rev. Lett. 80, 5381 (1998)
189K 198K 207K 216K 225K 254K N ~ exp[(ie d +E i )/(i+2)k B T] Phys. Rev. B 65, 245401 (2002) E d : the activation for diffusion E i : the binding energy for the critical size i
Arrhenius Plot : Island density vs. 1/Temperature 10 11 Island density (cm -2 ) 10 10 10 9 4.4 4.6 4.8 5.0 5.2 5.4 1000/Temperature (K -1 ) The nucleation and the quantum size effect are two independent factors in the formation of an island, the former results in the creation of an island and the latter determines the thickness of the created island.
2.72 ML 3.52 ML Average island area (nm 2 ) 1400 1200 1000 800 600 400 2 3 4 5 6 Coverage(ML) 2D Growth driven by the quantum size effect 4.32 ML (500 500 nm 2 )
(a) (a) (a) 2.3 ML, 170 K (a) 1 2 cluster1 cluster2 9.1Å 15.9Å (Å) 2.0 16 1.6 12 1.2 0.8 8 0.4 4 0.00 (b) +0.02ML -0.4 (Å) 16 20.5Å 11.3Å 12 8 4 (Å) 15 5 0 10 20 30 40 (nm) (c) +0.02ML 0 (Å) 20 16 Phys. Rev. B 68, 033405 (2003) 20.4Å 11.3Å 12 8 4 0 0 5 10 15 20 (nm)
Height (nm) 2.565 2.280 1.995 1.710 1.425 1.140 0.855 0.570 0.285 1.995 1.710 1.425 1.140 0.855 0.570 0.285 2.280 1.995 1.710 1.425 1.140 0.855 0.570 0.285 (a) 0.000 0 2 4 6 8 10 12 14 16 18 20 22 24 2.565 0.000 0 2 4 6 8 10 12 14 16 18 20 22 24 Diameter (nm) 2.565 2.280 1.995 1.710 1.425 1.140 0.855 0.570 0.285 1.995 1.710 1.425 1.140 0.855 0.570 0.285 (d) 6-layer 0.000 0.000 0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 24 2.565 2.565 (e) 2.280 2.280 (b) (c) cluster 4-layer 5-layer 7-layer 0.000 0 2 4 6 8 10 12 14 16 18 20 22 24 Transition Probability (f) 2D growth 3D-to-2D growth transition 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 6 7 8 9 0.0 Thickness(layer) Growth transition induced by the quantum size effect Independent transition pathway: N-layer thickness island is transformed from N-layer height cluster Identical cluster can be of different electronic structure (quantum size effect). Phys. Rev. B 71, 073304 (2005)
Self-Assembly Ni cluster on reconstructed Au(111) Phys. Rev. Lett. 66, 1721 (1991).
Self-organized growth of nanostructure arrays on strain-relief patterns Fe islands/cu/pt(111) Ag island/ag/pt(111) Nature 394, 451 (1998)
Ce atomic superlattice on Ag(111) at 3.9 K dimer 3.9 K 4.8 K lattice disappear at 10 K Lattice constant=32 Å Ce: Cerium ( 鈰 ), 稀土族, 原子序 :58 32 Å Ce superlattice is created by standing wave formed around Ce atoms. Phys. Rev. Lett. 92, 016101 (2004).
Quantum Confinement Effect quantum-well states standing-wave state tip metal film substrate STM gap sample
Visualization of quantum confinement effect with STM & STS STM Quantum corral by Eigler et al. in IBM 2D electron gas on Cu(111) STS Pb/Cu(111) 7 6 5 4 3 2 1 0 quantum-well state standing-wave state in STM gap 0 2 4 6 8 10 Sample bias STM gap standing-wave state quantum-well state
Application of standing-wave state in STM gap on work function measurement of thin metallic film dz/dv (Å/V) dz/dv (Å/V) (a) 7 6 5 4 Au(111) Ag 3 2 1 0 1 2 3 4 5 0 6 7 8 9 10 12 9 6 3 (c) (d) 1-layer Ag Au(111) (b) 0 Ag 1 2 0 1 2 3 4 5 6 7 8 9 10 Sample bias (V) Cu(111) 1-layer Ag Cu(111) 1 2 3 4 5 Energy shift (ev) Phys. Rev. Lett. 99, 216103 (2007) -0.6-0.5-0.4-0.3-0.2-0.1 0.0 E vac1 E vac2 (e) Energy Ag/Au Ag/Cu 0 1 2 3 4 5 Order E F φ 1 φ 2-0.47 ev -0.3 ev E vac standing-wave states sample Superposition of image potential and applied potential Constant Energy Shift = Work Function Difference z z
Photoemission (-0.33 ev) Standing-wave states (-0.3 ev) dz/dv (Å/V) 10 8 6 4 2 0 1 2 3 1-layer Ag Cu(111) 0 1 2 3 4 5 6 7 8 9 10 Sample bias (V) Energy shift (ev) 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 Order Wallauer et al., Surf. Sci 331, 731 (1995) Both techniques are consistent. Precision can be better than 20 mev.
Influence of image potential effect on empty quantum well states Pb island/cu(111) (a) (b) di/dv dz/dv dz/dv (arb. unit) 3π/2d (c) (d) 0.5 1.0 1.5 2.0 2.5 (N) 16 14 10 6 4 2 (N) 13 11 9 7 5 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Sample bias (V) Sample bias (V) 31 26 27 28 29 30 27 28 23 24 25 26 19 20 21 17 18 11 12 13 14 10 8 9 6 5 7 26 23 24 25 21 22 22 20 21 23 18 19 18 19 16 17 15 14 15 12 13 11 12 9 10 8 6 7 even odd 2k(N+1)d=2nπ Energy separation (ev) 1.2 1.0 0.8 0.6 0.4 13-layer Cal. Exp. quantum-well states E= ħ 2 (2n+1)π 2 /2m*(N+1) 2 d 2 (c) 20 21 22 23 24 25 Quantum number cannot be explained by simple square well Shrinking behavior Phys. Rev. Lett. 102, 196102 (2009)
Manifestation of image potential effect through Empty Quantum Well States E F Image potential Energy separation (ev) 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 13-layer Exp. Cal. (only square well) Cal. (including image potential) 21 22 23 24 25 Quantum number For simple square well: 2k(N+1)d=2nπ Including phase φ B contributed from image potential 2k(N+1)d+φ B =2nπ E V =4.6 ev above E F ħ 2 k 2 /2m*=E+E F m*=1.14 m 0 E: energy of quantum well state E V : vacuum level
Pb band structure along Γ-L direction: detect with quantum-well states 2k(N+1)d+φ B =2nπ 6 5 Energy (ev) 5 4 3 2 Energy (ev) 4 3 2 1 Yang et al. ab initio from Ref. [1] 1 0.85 0.90 0.95 1.00 1.05 1.10 1.15 k perpendicular (a0-1 ) Phys. Rev. Lett. 106, 249602 (2011) 0 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 k perpendicuar ( A O -1 ) k F =1.6 Å -1 angle-resolved photoemission spectroscopy, k F =1.598 Å 1 (bulk)