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STM Lab 5 Physics 212 5. Scanning Tunneling Microscopy LabSuzanne Amador Kane 3/13/06 (parts of this manual were adapted from the Burleigh Instruments ISTM manual, and the Physics 407 Lab manual from University of Wisconsin)
In this lab, you will learn about the principles behind the operation of the scanning tunneling microscope, the first of many modern “scanning probe microscopies” that have opened up the wonders of surface nanoscale imaging for scientists. You will see how the basic quantum mechanical principles of tunneling are utilized in the operation of this instrument, how tunneling is used to create a surface “topogram” which allows the height of the surfaces of conductors to be imaged at the atomicscale, and how one can use this information to take quantitative measurements on surfaces. You will learn how to operate our Nanosurf EasyScan STM (an instructional STM capable of atomic resolution) and take images of a goldcoated nanoscale grid, the surface of graphite and other samples with nanometerscale features. You will use surface analysis tools to measure the dimensions of the nanogrid (and calibrate your STM) and the bond angles and lengths for graphite. If you have time, you can also use mathematical image processing methods to process the images to reduce noise and to extract useful information. We will review six important topics in this lab to understand how STM works. While we are studying these topics in the context of STM, they all are of great general utility and interest for experimental science:
2) Background on Tunneling and the STMThe quantum mechanical phenomenon of tunneling is described in texts such as Griffiths, Introduction to Quantum Mechanics (section 82, pp. 320325), Eisberg and Resnick Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (pp. 199209) and Modern Physics by Bernstein, Fishbane and Gasiorowicz (pp. 203218). You should reread the relevant sections of your textbook if you are not familiar with them at this point. We first consider the case of a massive particle such as an electron which travels along a onedimensional path from a region with potential energy V=0 to one with potential energy V = V_{o} = constant (this is known as a step potential). (Fig. 1(a)) The electron wave is totally reflected from the interface, yet unlike a classical particle, the electron has a finite probability of being found in the classically forbidden region where E < V_{o}. This is because its wavefunction decays to zero exponentially over a distance determined by V_{o} and E. (Fig. 1(b))
Figure 1. (a) Potential energy function for a step potential and corresponding wavefunction (b). Reproduced from Eisberg and Resnick. Now, consider the case where the potential energy only equals Vo over a distance a, after which it drops back down to V=0. This case, known as a barrier potential, is illustrated in Fig. 2(a). Now, the wavefunction will not in general have decayed to zero when it reaches the other side of the potential energy barrier. : (a) (b) Figure 2. (a) Potential energy function for a barrier potential and corresponding wavefunction (b). Reproduced from Eisberg and Resnick. The net result is that the electron wavefunction has nonzero amplitude with probability amplitude T (for transmission) on the other side of the barrier, with approximate dependence: T exp(  2 k a) Eq.1 where 1/k is a measure of the distance over which the exponentially varying wavefunction decays within the barrier. (Here we have kept only the dominant exponential variation of T; see the recommended texts for a full equation for T.) It is determined by the values of the particles total energy, E, and the potential energy, V(x), within the barrier by: Eq.2 This means that if the electron wavefunction describes a situation in which an electron is incident from the left, it has a probability of either being reflected from the barrier or being transmitted, even though it must pass through a classically forbidden region to do so. It is as though a tennis ball thrown against your dorm room wall suddenly disappears from your room and reappears on the other side! The electrons within an electrical conductor (such as a metal or suitably prepared semiconductor) are in states well described by a free particle wavefunction. As a result, when two conductors are brought very close together yet still separated by an insulating barrier (such as an air gap or layer of insulating oxide), electrons can still flow between them by tunneling. If an electrical circuit is completed between the two conductors, this flow of electrons can be sustained and measured as an electrical current. Just as the transmission coefficient, T, has an exponential dependence on distance, so does the tunneling current depend exponentially upon separation between the two conductors. This is the situation in many common lab settings. If you join two pieces of wires by twisting them together or by sticking them into a breadboard, you often are relying on efficient tunneling across the small gap between them to complete your circuit. This is because you often have thin layers of insulating metal oxides coating the surfaces of copper wires. This is also what happens in STM. There, one conductor is the very sharp tip of a metal such as tungsten or platinum (with a small 10% admixture of iridium to improve its stiffness). These materials are chosen because you can use them to produce STM tips that have very sharp protrusions ending in only one or a few atoms (if you are lucky!) Imagine that you get a tip in which one atoms protrudes beyond the others by a few Angstroms, as shown in Fig. 3 Figure 3. The STM tip (at top) narrows down to a very sharp point at which one (or a very few) atoms protrude by atomic dimensions. The sample to be imaged is shown at the bottom. From Wisconsin ISTM manual. The sample to be imaged is shown at the bottom of Fig. 3. The sample must be approximately flat and itself electrically conducting (or at least a semiconductor). Now the distance, a, between conductors is the tipsample separation between the bottommost tip atom and the atoms most close to it on the sample. Now, assume there is some way to bring the tip and sample to a separation of several Angstroms. The tunneling current between them varies exponentially with tipsample separation, a. This allows us to see why we can get away with assuming that just the one protruding atom contributes to the tunneling current. The tiny extra distance between the sample and the other tip atoms leads to an enormous reduction in their tunneling currents, due to this strong exponential dropoff. As a result, in the discussion to follow, we will assume that the tunneling current arises only from the one protruding atom. There are two ways in which STM tunneling is more complicated than the barrier potential discussed above. First, the potential energies of the electrons in the tip and samples may differ. This corresponds in the simplest case to different workfunctions (like the workfunctions discussed in the photoelectric effect) for the different conductors. Second, in order to keep the tunneling current flowing, one must apply an electrical “bias” voltage between the tip and sample. This results in a bias electric field being applied across the gap between the tip and sample, and this modifies the potential energy function the electron experiences. (Fig. 4) Figure 4 From Wisconsin ISTM manual Instead of a constant, flattopped barrier, a sloping potential energy barrier results, with: V(x) = W – e x, Eq.3 where e = electronic charge, W = work function for one of the metals, x = distance across the gap, and = electric field from the applied bias voltage. To compute the new transmission coefficient, T, which is proportional to the tunneling current, one would compute instead: Eq.4 using the equation above for V(x). This detailed relation still yields a tipsample tunneling current vs. distance that varies approximately exponentially. (Fig. 5) Figure 5. From Wisconsin ISTM manual SUMMARY: We expect our tunneling current from the STM: to be virtually zero for large tipsample separations; to be dominated by tunneling currents from only the bottommost atom for nanometer scale separations; to vary exponentially with tipsample separation; and to depend upon tipsample bias voltage. 