IMAGING TECHNIQUES IN CONDENSED MATTER PHYSICS SCANNING TUNNELING AND ATOMIC FORCE MICROSCOPES

Transcription

1 1 IMAGING TECHNIQUES IN CONDENSED MATTER PHYSICS SCANNING TUNNELING AND ATOMIC FORCE MICROSCOPES

2 2 WHY THIS TOPIC? STM and AFM images are ubiquitous in condensed matter physics. It is important to understand how to interpret them. I have some experience working with STM s myself. Also, STMs and AFMs are designed to produce pictures and.. Who doesn t like pretty pictures?? IMB STM Image gallery: Crommie et al. (1) and (2)

3 3 CONTENTS 1. Physical setup of an STM 2. Basic theory of operation 3. An example 4. How the STM achieves such high resolution 5. How to move around individual atoms 6. Briefly, Atomic Force Microscopy

4 4 APPARATUS Author s drawing, based on (4)

5 5 WHAT IT LOOKS LIKE Argonne National Laboratory(12)

6 6 QUANTUM TUNNELING Julian Chen Introduction to Scanning Tunneling Microscopy (4)

7 7 FINITE, SQUARE POTENTIAL WELL In the classically allowed regions, the quantum-mechanical wave-function of a particle is, where ψ z = ψ 0 e ±ikz 2m(E U) k = ħ In the classically forbidden regions the wave-function is, where ψ z κ = κ z = ψ 0 e 2m(U E) ħ Nanoscience instruments (5)

8 8 FOR THE ELECTRON For electrons, the amplitude of the wave-function in the tip is about an order of magnitude smaller if the tip is 0.1 nm away from the sample. Set φ metal surface s work function Transmission coefficient is then, I inside the tip T I on the surface where, κ = 2mφ ħ For a gold surface, κ = 2 ( ) ev (5.4 ev) ( )nm/s ev s = e 2κz =11.9 nm 1 The transmission coefficient is, T = e nm 1 z

9 9 OF COURSE, FOR THE LION Transmission coefficient, Work function, T = e 2κz φ = Energy required to take down a fence energy available to a lion = ~1kg of TNT ~4 MJ Decay factor, [most ridiculous calculation ever presented] κ = kg (~106 J) ~10 38 J s For z=1cm T = e m ~ Web (6)

10 10 HEY, YOU PROMISED PICTURES... Wait! Watch this cool video first =CIVMFlg0qVo

11 11 7X7 RECONSTRUCTION OF SI(111) Binning et al. (7)

12 12 MODERN VIEW OF SI(111) RECONSTRUCTION Myslivecek et al. (8)

13 13 THEORETICAL VIEW (9)

14 14 HOW TO GET ATOMIC RESOLUTION? Distance to sample surface, Δz = Δx2 2R The current is then, I Δx = I 0 exp ( 2κ Δx2 ) 2R Typically, κ 10nm 1, for R = 1nm the current drops by an order of magnitude for Δx = 0.3nm In theory, this would be the resolution limit of an STM because of the limitations in measuring current, but STM s often achieve.2nm resolution. Drawing based on (4)

15 15 HOW TO GET ATOMIC RESOLUTION? Chen (10) Achieving.2 nm scale resolution depends on getting the atom on the tip in a particular quantum state with advantageous geometrical properties for tunneling. There is no set procedure to obtain this state other than repeatedly crashing the tip into the sample and sending electrical pulses through it until the desired resolution appears. SpongeBob SquarePants

16 16 HOW DO MAKE THESE KIND OF PICTURES? IMB STM Image gallery: Crommie et al. (1) and (2)

17 17 USING THE TIP TO PICK UP INDIVIDUAL ATOMS Chen (4)

18 18 DIFFERENT MOLECULAR ORBITALS Repp et al. (13)

19 19 NON-CONTACT ATOMIC FORCE MICROSCOPE Chen (4)

20 FIRST ATOMIC RESOLUTION FOR AFM 20 Giessibl (11)

21 21 KEY DIFFERENCES STM s require Ultra High Vacuum (UHV), less than 10 8 mbar, to operate in while AFM s can operate at ambient pressure or even submerged. STM s tend to scan faster and give higher resolution, but they only work with conducting surfaces while AFM s work on any surface, and, today, their resolution rivals the STM.

22 22 WHAT TO TAKE FROM THIS PRESENTATION You can explain this to your friends! IMB STM Image gallery: Crommie et al. (1) and (2)

23 23 REFERENCES 1) M.F. Crommie, C.P. Lutz, D.M. Eigler. Confinement of electrons to quantum corrals on a metal surface. Science 262, (1993). 2) STM rounds up electron waves at the QM corral. Physics Today 46 (11), (1993). 3) 4) Julian Chen. Oxford Science Publications. Introduction to Scanning Tunneling Microscopy. Second Edition (2008) 5) 6) 7) G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel. 7 7 reconstruction on Si(111) resolved in real space. Phys. Rev. Lett. 50, (1983). 8) J. Myslivecek, A. Strozeska, J. Steffl, P. Sobotik, I. Ostadal, and B. Voigtlander. Structure of the adatom electron band of the Si(111)-7 7 surface. Phys. Rev. B 73, (R) (2006). 9) 10) C. J. Chen. Microscopic view of scanning tunneling microscopy. J. Vac. Sci. Technol. A 9, (1991). 11) F. J. Giessibl. Atomic resolution of silicon (111)-7 7 surface by atomic force microscopy. Science 267, (1995). 12) 13) J. Repp and G. Meyer. Molecules on insulating films: STM imaging of individual molecule orbitals. Phys. Rev. Lett. 94, (2005).