STM Lab 5-15 Physics 212
5. Scanning Tunneling Microscopy Lab
Suzanne 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)
1) Introduction
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 atomic-scale, 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 gold-coated nanoscale grid, the surface of graphite and other samples with nanometer-scale 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:
1) How quantum mechanical tunneling works in STM
2) How to control very small displacements using piezoelectric transducers
3) How to use feedback to control tunneling currents
4) How to vibrationally isolate sensitive systems
5) How to collect data electronically
6) How to image process STM data to extract useful information
2) Background on Tunneling and the STM
The quantum mechanical phenomenon of tunneling is described in texts such as Griffiths, Introduction to Quantum Mechanics (section 8-2, pp. 320-325), Eisberg and Resnick Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (pp. 199-209) and Modern Physics by Bernstein, Fishbane and Gasiorowicz (pp. 203-218). 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 one-dimensional path from a region with potential energy V=0 to one with potential energy V = Vo = 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 < Vo. This is because its wavefunction decays to zero exponentially over a distance determined by Vo and E. (Fig. 1(b))
(a) (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 tip-sample separation between the bottom-most 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 tip-sample 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 drop-off. 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, flat-topped barrier, a sloping potential energy barrier results, with:
V(x) = W – e e x, Eq.3
where e = electronic charge, W = work function for one of the metals, x = distance across the gap, and e = 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 tip-sample 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 tip-sample separations; to be dominated by tunneling currents from only the bottom-most atom for nanometer scale separations; to vary exponentially with tip-sample separation; and to depend upon tip-sample bias voltage.
3) STM Operation
The EasyScan STM works in one of two modes for imaging the surfaces of samples. You can see how these work in a good video at the website: http://www.iap.tuwien.ac.at/www/surface/STM_Gallery/stm_schematic.html The easiest to understand is Constant Height mode. (Also, see the EasyScan Manual page 30. Note that your laboratory notebook contains two EasyScan manuals: one for the instrument and one for the software. Unless we specify the software manual, you should assume that references to the manual refer to the main instrument manual.) In this mode, one simply scans the tip in the plane of the sample, left and right, while holding the height of the tip constant. The tip’s motions are controlled by a cylinder of piezoelectric material. Such materials have the properties that they respond to an applied voltage by changing their dimensions. One polarity of voltage results in a shortening of the piezoelectric, while the opposite polarity induces an expansion. By varying the voltage on a piezoelectric, displacements at the sub-Angstrom range can be achieved reproducibly. The position of the STM tip can thus be finely controlled both in the plane of the sample (the x-y plane) and in the z-direction.
The tip-sample spacing varies as the tip is scanned horizontally over the sample, because the surface has atomic-level peaks and valleys due to its atomic structure, and so the tunneling current also varies. So, if one measures the tunneling current It as a function of in-plane location (x,y), one can “map out” the topography with atomic precision; high current corresponds to a raised area of the sample. The act of repeatedly scanning x and y back-and-forth to yield an image is also called rastering. (Fig. 6(c)). This yields a map of (x,y,It) from which an image of the sample’s surface can be made. Since one cannot plot in three dimensions, two methods are used to create such surface plots. Either colors (or shades of gray) are used to indicate current (a scale bar is conventionally printed by the side of the image to indicate correspondences between currents and shadings) or a computer reconstruction of the surface is generated and the image is viewed from an angle to indicate its 3D structure. (Fig. 6)
(a) (b)
(c)
Figure 6 Different methods of represent STM measurements. (a) Burleigh instruments image of the surface of graphite, in which gray-scale (shades of gray) are used to indicate height within the plane; (b) IBM image of a “quantum corral” (ring of atoms binding a surface electron) in which computer 3D reconstructions are used to indicate surface structure. (c) Cartoon of how rastering works to accumulate images, and how the information collected is used to make up images of the sort shown in (a) and (b). (IBM STM Gallery http://www.almaden.ibm.com/vis/stm/gallery.html)
Current mode/constant height mode is a good method for imaging atomic scale structure and you will use it to image the surface of graphite at atomic resolution. However, if you try to use constant height mode to image structures with bumps large compared to the tip-sample spacing, you will hit your tip on the sample and damage it! You can avoid this problem by imaging instead in Constant Current mode. (See the EasyScan Manual page 30.) In this mode, feedback is used to fix the current at a constant target value (called the Reference Current) as the piezoelectric is used to scan the tip back-and-forth in-plane. If the sample surface is higher at one point than another, the tunneling current goes up. The feedback circuit responds by retracting the tip so the tunneling current is restored to the reference value. If the sample surface is lower at one point, the tunneling current decreases, and the feedback circuit and uses the piezos to lower the tip until the tunneling current returns to the reference value. In this mode, the position of the tip (rather than tunneling current) is recorded to yield the map of the surfaces’ topography as (x,y, tip z). This interplay between measurement (of tunneling current) and regulated control (of tip height, which regulates the tunneling current) is an instance of negative feedback. It’s negative feedback because a greater tunneling current results in a tip displacement that reduces the tunneling current. In other words, the motion of the tip always opposes the change measured in the tunneling current.
As a practical matter, you will begin imaging by using Constant Current mode, then—if you wish to see atomic scale details—switch over to Constant Height mode after you have found a flat region to safely scan this way.
Understanding the Easy Scan STM Controller Electronics
The EasyScan STM is controlled by a computer attached to a controller box that allows you to set and monitor the tunneling current, bias voltage, scan range and feedback controls. While these controls are described in the manual, which follows this introduction, it will help if you have an overview first. All of this is controlled in software only (no external knobs to turn!) within the Easy Scan program. You should have an icon for this program on your lab setup. First, be sure you have the EasyScan power supply turned OFF. This is so you can use the software in simulation mode to understand how it works. When you double-click on the EasyScan icon on your desktop to start the program, it will say that it cannot find the controller box, and ask if you wish to run in simulation mode. Answer “Yes”, and proceed.