Introduction to the Scanning Tunneling Microscope

Transcription

1 Introduction to the Scanning Tunneling Microscope A.C. Perrella M.J. Plisch Center for Nanoscale Systems Cornell University, Ithaca NY Measurement I. Theory of Operation The scanning tunneling microscope (STM) is based on a quantum mechanical phenomenon known as tunneling. In tunneling, a particle, in this case an electron, can jump from one location to another without spending any time in between. An example of tunneling can be seen in Figure. If a particle is incident upon a barrier in the classical picture it will simply bounce off, just like throwing a ball at a wall. In quantum mechanics, that same particle is not guaranteed to bounce back (reflect) but rather has some probability of doing so which is written as R. If the particle doesn t reflect, then it will transmit, or tunnel through the barrier with some probability T. R and T are related by: R+T = This means the particle either reflects or is transmitted. The probability of transmission, or tunneling, is T e -βw Where β is a constant that depends on the energy of the particle and the barrier, and w is the width of the barrier. This exponential dependence on distance is what makes the STM such a sensitive instrument for exploring surfaces. In a STM, electrons are allowed to be in either the tip or the sample. The space between the two can be viewed as the barrier. If the distance between the two is small enough, electrons will tunnel from one to Potential Energy R e - e - Position Classical e - e - T Quantum Figure.- A particle incident on a barrier. In the classical world it only bounces off. In quantum mechanics it can be transmitted with probability T, or reflected with probability R. the other. If there is no voltage applied to either the tip or the sample, electrons will tunnel back and forth with equal probability and no current will be measured. However if a voltage (typically 0. to V) is applied to either the tip or the sample, electrons will prefer to tunnel from the lower voltage to the higher one. This flow of electrons is measured as the tunnel current and will be used to measure the distance between the tip

2 tip Sample V x,y,z piezo scanner I ~na tunnel pre-amplifier 0 8 gain Figure 2. Simple STM schematic. Electrons tunneling between the tip and the sample flow through the feedback circuit. The computer adjusts the Z piezo to keep the tunnel current constant. and the sample. Figure 2 shows a simple schematic of the STM circuit. In this example the sample is at 0V while the tip is at -V. In this configuration, electrons tunnel from the tip to the sample. The flow of electrons is measured as a current by the STM pre-amplifier and fed into the computer. Operation of the STM is done in constant current feedback mode. Here the tunnel current, and thus the distance between the tip and the sample, is kept constant by the computer as the tip scans back and forth. If the tip scans across the surface and encounters a high point, the computer will send a signal to the scan head to retract the tip in order to keep the tunnel current constant. The scan head assembly in Figure 2 is typical for all STMs. Piezo electronic ceramics can be compressed or stretched by applying modest voltages to the material. There is a voltage signal that controls ±X, ±Y, and ±Z. This means that the topographic image that one sees in the STM software is a recording of the change in Z voltage required to keep the tunnel current constant as a function of X and Y. II. Measuring Graphite with Atomic Resolution One of the triumphs of the STM was the direct imaging of atomic structure. The sensitivity of piezo electrics and exponential dependence of the tunneling phenomenon on distance make atomic resolution commonplace in modern laboratories. Graphite is a particularly good sample to look at for this type of structure because it cleaves in sheets. Thus a single atomic sheet can span hundreds of nanometers. In this section the goal will be to obtain an image of the graphite surface with atomic resolution that we will analyze later. Follow the instructions in the Nanosurf STM system manual for obtaining atomic resolution images of graphite (pg. 7). It may take some time to obtain a high quality, defect free image. Even if the tip is sharp and the area is flat, thermal and electrical drift may take some time to fade away. Thermal drift is due to temperature fluctuations in the tip or sample. As things warm up, they expand, as they cool down they shrink. While it may not seem like much to the naked eye, the STM is sensitive to very small changes in distance. Electrical drift is due to a change in the wires and op-amps. As current flows

3 through the devices in the circuit, equilibrium will eventually be obtained. Again, these are small effects, but this is a sensitive instrument. Drift is usually pretty easy to see. A relatively clean image will appear to grow or shrink as the scan direction changes. Eventually, when all of the drift has died down, these images should not depend on scan direction. Page 28 of the manual shows some examples of the kinds of experimental artifacts you may encounter. Work on obtaining as clear an image as you can. An example of a successful image is shown in figure 2.9Å 3. Here it may not be clear as to what the pattern is, but a definite pattern (i.e. regular structure) is visible. We will go over processing the image later. If you obtain an image like the one shown in figure 3 make sure you follow the instructions on page 27 in order to save your data. Figure 3 Successful atomic resolution of graphite Filename(s) of graphite images: Once a good image is obtained using the parameters outlined in the NanoSurf manual, adjust the scan parameters and try answering the questions below. The constant β is proportional to V where V is the tip voltage. That means in order to keep a constant tunnel current, the tip must get closer to the sample when the voltage decreases. What advantage would there be to having the tip closer? What about having it further away? Try testing your predictions by adjusting the tip voltage. Does the magnitude of the tip voltage make a difference? What about the sign of the tip voltage? What other scan parameter could one adjust which would also move the tip closer or further away? If you change this parameter does it have the same effect as changing the voltage?

4 III. Scanning Steps in Gold If you have time, follow the instructions for scanning the gold sample that start on page 34. For this sample you will find that the interesting features are not on the atomic scale, but rather on the 50 to 250 nm scale. Scans of this size should reveal the growth pattern of gold on the silicon substrate. Typically samples like this are made by evaporating metals on polished substrates, usually silicon. However, the atoms rarely stack up as a perfect single crystal when grown this way. The result is what is known as a polycrystalline film. In a polycrystalline film atoms still stack with an ordered structure, but the crystal orientation can vary either a little or a lot over the entire film. In the case of Gold on Silicon, the metal film grows by forming islands on the substrate. As more metal is deposited, the Au atoms strike the surface and move around until they attach to the edge of the island. As the islands widen, new ones form on top of them and the film gets thicker. This formation can be seen in both figure 4 and on page 34 of the manual. Because this sample is exposed to atmosphere, the surface can become contaminated. Try to avoid sections of the sample where foreign matter appears to be stuck to the surface. As with the graphite sample, save your images for analysis. 0nm Figure 4 - Gold steps. The green line crosses a single atomic step. Filename(s) of gold images:

5 Processing and Analysis I. Fourier Transforms and Filtering A major part of experimental analysis is extracting the important information from the raw data. Figure 3 shows the periodic structure of a graphite surface. However there are other features in the image, like noise and scan lines, which are not important to studying the sample. These are typical artifacts in STM images and can be removed so the real data is more easily seen and measured. Begin by opening the program WsXM. Open one of the graphite images that you saved. You may need to change the file type menu to all Figure 5. Launch FFT files in order to see the *.ezd file which contains your data. The file will load and you will need to minimize the directory browser in order to see your data. Press the Fast Fourier Transform (FFT) button to activate the FFT dialog box (See Figure 5). The Fast Fourier transform is a mathematical process that transforms data into a series of sine waves, each with a different frequency and amplitude. See appendix A at the end of the lesson for a slightly more detailed explanation of Fourier transforms. When the dialog box opens, press filter. You may have to change the Zoom to 4 in order to see the features. The FFT of figure 3 is shown below in figure 6. The bright points in the upper right hand image indicate that there are features in the real image that occur with a specific period. This is not surprising since you can see with your naked eye the fact that the graphite structure has a period. What we will do is effectively filter every other signal by passing only the signals with the frequency Figure 6. FFT dialog box

6 represented by the bright points. To do this use press the Filter button to generate the image in the lower right of figure 6. Select the frequencies by holding the left mouse button over the center of the bright spot and dragging a small box around it. Do this with any signal that appears in the image. In figure 6, a passband is selected for two separate signals. Activate the passband by right clicking the lower right hand image. You should see the image appear like the one in figure 7. Here the atomic lattice should appear with greater clarity than it did in figure 3. This processed image can now be more easily analyzed than the raw image. Line profiles are one of the more 2.9Å commonly used analysis tools in topographic measurements. These profiles produce plots of height vs. distance along a section of the image. To get to the line profile tool, select profile from the process menu. This will allow you Figure 7 Filtered image of graphite surface. to draw a line across the image. As you draw the line, a plot like the one shown in figure 8 should form. You can use this to accurately measure the mean distance between atoms along one of the crystal axis, as well as observe the apparent height of each carbon atom. Page 33 of the manual as a description of the graphite surface and what the bright and dark features of the image represent. Use the line profile tool to measure the atomic spacing along different directions. How many different spacing values can you measure? What are these values? Z[Å] X[Å] Figure 8. Profile along blue line in figure 7. Can you detect a difference in the height between the atoms with nearest neighbors in the lattice below, and those without?

7 What is the apparent height difference? Since drift can effect these values, if you have time and the data, compare the spacing values for images that have two different scan directions. Is there a difference in the lattice spacing? Can you think of a way to correct for drift effects with your two images? Describe how the correct lattice could be calculated. II. Step Edges in Gold If you have time, open a captured image of the Au mesas. Using the line profile tool you should be able to measure the height of a single atomic step. Measure 0-20 steps and record their values. What is the mean atomic step height? Does it look like any of your atomic step height measurements is actually an integer number of a single atomic step height?

8 III. How much is too much? Figure 9. The Quantum Corral In this exercise we have demonstrated the usefulness of image processing. However at what point is there too much processing? When does the final image look more like artwork than real data? This is something scientists debate continuously, but here is an example of a highly processed image. Figure 9 shows the famous quantum corral from IBM. The image displays not only a ring of atoms with incredible clarity, but also quantum mechanical wave function effects inside the corral. Most people see this image without thinking of how it was obtained. Certainly a very good STM was used to manipulate and measure the atoms in this image, but exactly how much processing is involved? Figure 0 shows the progression from raw data to the final image. You can decide for yourself how much processing is too much. Raw Data Figure 0 Processing of the Quantum Corral Final Image

9 Appendix A Fourier Transforms A complete explanation of the Fourier transform (FT) is beyond the scope of this exercise. Most good math, physics and engineering text books have a description of the actual equations involved. A short list of places on the web to investigate is given below for those who are interested. However a basic description of the FT can be useful in understanding what the data processing is actual doing. The idea behind the FT is that any signal can be written as the sum of sine waves, with each frequency sine wave having its own amplitude. The FT signal is the amplitude corresponding to each frequency. For example: Signal Plot of signal Fourier Transform y = sin(x) y = sin(2x) y = sin(3x) + 2sin(x) Signal Strength Signal Strength Signal Strength frequency 2 3 frequency 2 3 frequency In WsXM, the software goes through the image and breaks it into sine waves (in the case of a spatial image the frequency has units of /length) and maps the amplitude of each sine component. Features with regular spacing will appear much brighter than those without regular spacing. You can choose to pass only those signals with a specific frequency thus removing any unwanted or random signal. Additional information on Fourier transforms