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Transcript of The Scanning Tunneling Microscope - teachers... · PDF file 2009-08-21 ·...

  • Is it possible to see atoms?

    1

    The Scanning Tunneling Microscope

    Survey 1 4.1 The Working Principle of The Scanning Tunneling Microscope 2 4.2 The Setup of The Scanning Tunneling Microscope easyScan 7 4.3 The Sample Surface 9 4.4 Problems and Solutions 12

    Survey The Scanning Tunneling Microscope (STM) was developed in the early 80's at the IBM research laboratory in Rüschlikon, Switzerland, by Gerd Binnig and Heinrich Rohrer. For their revolutionary innovation Binnig and Rohrer were awarded the Nobel prize in Physics in 1986 (see Nobel prize lecture by G. Binnig, a review article, and noteworthy publications in the STM folder). Selected books are on reserve in the Physics library for this course, including: “Scanning Tunneling Microscopy I & II“, edited by H.-J. Güntherodt and R. Wiesendanser (QC173 .4 S94 S35 and S352); “Scanning Tunneling Microscopy and Spectroscopy – Theory, Technology, and Applications”, edited by D.A. Bonnell (QH212 S35 S365). In the STM a small sharp conducting tip is scanned across the sample’s surface; the separation is so close (approximately 1 nm) that a quantum mechanical tunneling current can flow. With the help of that current the tip-surface distance can be controlled very precisely. In this way an enormous resolution is achieved so that the atomic arrangement of metallic surfaces can be probed. Related kinds of microscopic techniques soon followed, such as the atomic force microscope (AFM). Its microscopic tip can even be used as a working tool to manipulate single atoms and move them around on the sample surface. Nowadays, all these techniques have become essential diagnostic tools in current research (key word: nanotechnology).

  • Is it possible to see atoms?

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    4.1 The Working Principle of The Scanning Tunneling Microscope

    With the scanning tunneling microscope a small metal tip is brought very close to the sample surface, normally within about 1 nm, i.e. several atomic layers. The small gap between the tip and sample is a classicaly forbidden region for electrons. However, quantum mechanics tells us that there is a finite probability that electrons can tunnel through this gap. If tip and surface are put under a small voltage UT , a tunneling current IT flows (see figure 4.1). This current is strongly dependent on the distance between the tip and the structures on the surface. The surface can be scanned with the tip keeping either the height of the tip or the tunneling current constant. The tunneling current or the feedback parameters are detected. If the surface is scanned in parallel lines, similar to reading a book written in braille, then a three dimensional picture of the surface is generated.

    Sample

    Scanning Device

    Feedback Loop

    ITIT

    UT

    Uz Ux

    Uy

    Ux Uy

    Figure 4.1: The principle of the scanning tunneling microscope The principle of the STM is easy to understand, but before an actual STM can be constructed, the physics of the STM must be understood and many technological problems must be solved. At first we will have a closer look at the physical principles. The technical realization will be described later.

  • Is it possible to see atoms?

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    The Tunneling Effect with the Tunneling Microscope

    Tunneling Electrons

    Sample, e.g. Graphite

    Atoms

    Metaltip Voltage Source

    Feedback Loop

    + UT

    Tunneling Current IT

    Figure 4.2: Simplified picture of the tunneling process with a tunneling microscope Figure 4.2 shows schematically the tip, the sample surface and the gap inbetween. In the current loop between sample and tip the magnitude of the current is constantly measured (approximately a picoampere). With the STM only electrically conductive materials can be examined. Actively involved in the imaging is only the very end of the metal tip nearest the sample. The smaller the structures to be observed, the sharper the tip has to be. Fortunately, it is quite easy to produce sharp tips. To get a spacial resolution better than the diameter of an atom, one single atom should be at the end of the tip. Very often such an atom comes from the surface itself. It is being removed from the surface by high electric fields and sticks to the tip. The conduction electrons of a metal are able to move almost freely inside the metal. However, they are unable to leave it because of the attractive force of the positively charged cores. For the electrons to be able to leave the sample, work must be done - the so called work function Φ. In a red-hot metal the thermal energy is sufficient to free the electrons, as first observed experimentally by Edison. However, at room temperature, according to the laws of classical physics, insufficient energy is available and electrons should remain in the metal. Quantum physics makes a different prediction.

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    The Tunneling Condition Using the energy-time uncertainty relation ΔEΔt ≥ h, one can derive the „tunnel condition“ d2(EBarr) ≤ 2h2/m , where d is the width of the potential barrier, EBarr the height of the energy barrier, and m the electron mass. Let’s now test whether the tunnel condition is satisfied for the STM. The width of the potential barrier corresponds to the distance d between the tip and the sample, i. e. about 10-9 m. Its height EBarr is given by the work function and amounts a few eV, i. e. about 10-18 J. From the left side of the tunnel condition one has: d ! EBarr " 10

    #9 m ! 10

    #8 J "10

    #18 J ! s ! kg

    #1/ 2 From the right side:

    h ! 2 m " 7 !10

    #34 J ! s ! 2 !10

    30 kg

    #1 "10

    #18 J ! s ! kg

    #1/ 2

    This rough estimate shows that we can understand electron tunneling in the STM merely by considering the uncertainty principle. The Tunneling Current Electrons may not only tunnel from the tip to the sample but also in the opposite direction. Figure 4.3 demonstrates this fact: in the energy diagram below, where it assumed that tip and sample have identical work functions, the effect of an applied voltage U is that the electrons on one side of the barrier have more energy than on the other side. The former electrons are now free to move to the other side as an electrical current. The slope of the potential is drawn with a slanting potential barrier.

    Sample Tip UTip = 0

    Position

    Energy

    UTip < 0

    UTip > 0

    Tunneling to the Sample

    Tunneling to the Tip

    Figure 4.3: Depending on the direction of the voltage, the electrons tunnel to the sample or to the tip

  • Is it possible to see atoms?

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    Quantum physics allows a quantitative estimate of the tunneling current and its dependence on the distance d between the sample and the tip: I

    T = c

    1 !U

    T !e

    " c 2

    #!d The tunneling current decreases exponentially with the distance. The constant c1 depends on the electron densities inside both the sample and the tip. The exponent contains another constant, c2 , and the work function of the metals Φ. If the tip and the sample have different work functions, the mean value should be used here. Typical working parameters are: IT = 10-9 A, UT = 100 mV, Φ = 5 eV and d = 10-9 m. If you take a closer look at the relation for the tunneling current, perhaps you see the following. The tunneling microscope does not simply measure the height of the structures on the sample surface, but also gives information gives information on the electron densities of the tip and sample at the measuring position. You will use this fact when trying to interpret the scanning picture for the graphite sample or the rings in the scan on the title page where 48 iron atoms form a „quantum corral“ on a copper surface. With the STM you can not only see atoms but also the ring-shaped maxima of the electron density inside: a standing wave of the probability density of the electrons! The above idea of bound electrons with a given energy is an oversimplified picture. In reality there are electrons of different energies up to a maximal energy, the Fermi energy, inside a metal. The number of electrons with a given energy may change rapidly with the energy, as indicated in figure 4.4. In a metal only electrons up to a given energy Emax are present (in the figure only in the hatched regions). If electrons with a given energy want to tunnel to the other metal, only as may electrons can do so as the energy distribution of that metal allows (unhatched region of the energy distribution). In the graphic the tunneling process of the electrons at a given energy is shown with arrows.

    U FSample

    !Tip

    Emax,Sample

    Emax,Tip

    Electron Density

    Tip Gap Sample Energy

    Figur 4.4: The tunneling current depends on the frequency distribution of the electrons inside a metal

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    If there is a particularly large number of electrons at a given energy present and there are a large number of unoccupied states with this energy in the other metal, the tunneling current will be particularly large. The constant c1 in the relation for the tunneling current, therefore, depends on the energy distribution of the electrons. If you change the external voltage, you may gain information on the energy distribution of the electrons inside the sample. It is possib