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The Scanning Tunneling Microscope

Roger A. Freedman and Paul K. Hansma
Department of Physics, University of California, Santa Barbara

The basic idea of quantum mechanics, that particles have properties of waves and vice versa, is among the strangest found anywhere in science. Because of this strangeness, and because quantum mechanics mostly deals with the very small, it might seem to have little practical application. As we will show in this essay, however, one of the basic phenomena of quantum mechanics -- the tunneling of a particle -- is at the heart of a very practical device that is one of the most powerful microscopes ever built. This device, the scanning tunneling microscope or STM, enables physicists to make highly detailed images of surfaces with resolution comparable to the size of a single atom. Such images promise to revolutionize our understanding of structures and processes on the atomic scale.

Before discussing how the STM works, we first look at a sample of what the STM can do. An image made by a scanning tunneling microscope of the surface of a piece of gold is shown in Figure 1. You can easily see that the surface is not uniformly flat, but is a series of terraces separated by steps that are only one atom high. Gentle corrugations can be seen in the terraces, caused by subtle rearrangements of the gold atoms.

What makes the STM so remarkable is the fineness of the detail that can be seen in images such as Figure 1. The resolution in this image -- that is, the size of the smallest detail that can be discerned -- is about 2Å(22 x 10-10) m. For an ordinary microscope, the resolution is limited by the wavelength of the waves used to make the image. Thus an optical microscope has a resolution of no better than 2000 Å, about half the wavelength of visible light, and so could never show the detail displayed in Figure 1. Electron microscopes can have a resolution of Å by using electron waves of wavelength Å or shorter. From the de Broglie formula l = h/p, the electron momentum p required to give this wavelength is 3100 eV/c, corresponding to an electron speed v = p/m = 1.8 x 106 m/s. Electrons traveling at this high speed would penetrate into the interior of the piece of gold in Figure 1, and so would give no information about individual surface atoms.

The image in Figure 1 was made by Gerd Binnig, Heinrich Rohrer, and collaborators at the IBM Research Laboratory in Zurich, Switzerland. Binnig and Rohrer invented the STM and shared the 1986 Nobel Prize in Physics for their work. Such is the importance of this device that unlike most Nobel Prizes, which come decades after the original work, Binnig and Rohrer received their Nobel Prize just six years after their first experiments with an STM.

One design for an STM is shown in Figure 2. The basic idea behind its operation is very simple, as shown in Figure 3. A conducting probe with a very sharp tip is brought near the surface to be studied. Because it is attracted to the positive ions in the surface, an electron in the surface has a lower total energy than would an electron in the empty space between surface and tip. The same thing is true for an electron in the tip. In classical Newtonian mechanics, electrons could not move between the surface and tip because they would lack the energy to escape either material. But because the electrons obey quantum mechanics, they can "tunnel" across the barrier of empty space between the surface and the tip. Let us explore the operation of the STM in terms of the discussion of tunneling in Section 41.9.

For an electron in the apparatus of Figures 2 and 3, a plot of the energy as a function of position would look like Figure 4. The horizontal coordinate in this figure represents electron position. Now L is to be interpreted as the distance between the surface and the tip, so that coordinates less than 0 refer to positions inside the surface material and coordinates greater than L refer to positions inside the tip. The barrier height U = qÆ is the potential energy difference between an electron outside the material and an electron in the material where Æ is the work function of the material. That is, an electron in the surface or tip has potential energy -U compared to one in vacuum. (We are assuming for the moment that the surface and tip are made of the same material. We will comment on this assumption shortly.) The kinetic energy of an electron in the surface is E so that an amount of energy equal to (U - E) must be given to an electron to remove it from the surface. Thus (U - E) is the work function of an electron in the surface.

For the potential energy curve of Figure 4, one could expect as much tunneling from the surface into the tip as in the opposite direction. In an STM, the direction in which electrons tend to cross the barrier is controlled by applying a voltage between the surface and the tip. With preferential tunneling from the surface into the tip, the tip samples the distribution of electrons in and above the surface. Because of this "bias" voltage, the work functions of surface and tip are different, giving a preferred direction of tunneling. This is also automatically the case if the surface and tip are made of different materials. In addition, the top of the barrier in Figure 4 will not be flat but will be tilted to reflect the electric field between the surface and the tip. However, if the barrier energy U is large compared to the difference between the surface and tip work functions, and if the bias voltage is small compared to Æ = U/q, we can ignore these complications in our calculations.

The characteristic scale of length for tunneling is set by the work function (U - E). For a typical value (U - E) = 4.0 eV, this scale of length is

 

 

 

 

The probability that a given electron will tunnel across the barrier is the transmission coefficient , where L is the barrier width. If the separation L between surface and tip is not small compared to d , then the barrier is "wide" and we can use an approximate result for T. The current of electrons tunneling across the barrier is simply proportional to T. The tunneling current density can be shown to be

 

 

In this expression e is the charge of the electron and V is the bias voltage between surface and tip.

We can see from this expression that the STM is very sensitive to the separation L between tip and surface. This is because of the exponential dependence of the tunneling current on L (this is much more important than the 1/L dependence). As we saw above, typically d =1.0 Å. Hence increasing the distance L by just 0.01 Å causes the tunneling current to be multiplied by a factor e=-2(o.01Å)/(1.0 Å)» 0.98; i.e., the current decreases by 2% -- a change that is measurable. For distances L greater than 10 Å (that is, beyond a few atomic diameters), essentially no tunneling takes place. This sensitivity to L is the basis of the operation of the STM: monitoring the tunneling current as the tip is scanned over the surface gives a sensitive measure of the topography of the surface. In this way the STM can measure the height of surface features to within 0.01 Å, or approximately one one-hundredth of an atomic diameter.

The STM also has excellent lateral resolution, that is, resolution of features in the plane of the surface. This is because the tips used are very sharp indeed, typically only an atom or two wide at their extreme end. Thus the tip samples the surface electrons only in a very tiny region approximately 2 Å wide, and so can "see" very fine detail. You might think that making such tips would be extremely difficult, but in fact it's relatively easy: sometimes just sharpening the tip on a fine grinding stone (or even with fine sandpaper) is enough to cause the tip atoms to rearrange by themselves into an atomically sharp configuration. (If you find this surprising, you're not alone. Binnig and Rohrer were no less surprised when they discovered this.)

There are two modes of operation for the STM, shown in Figure 5. In the constant current mode a convenient operating voltage (typically between 2 millivolts and 2 volts) is first established between surface and tip. The tip is then brought close enough to the surface to obtain measurable tunneling current. The tip is then scanned over the surface while the tunneling current I is measured. A feedback network changes the vertical position of the tip, z, to keep the tunneling current constant, thereby keeping the separation L between surface and tip constant. An image of the surface is made by plotting z versus lateral position (x, y). The simplest scheme for plotting the image is shown in the graph below the schematic view. The height z is plotted versus the scan position x. An image consists of multiple scans displaced laterally from each other in the y direction.

The constant current mode was historically the first to be used, and has the advantage that it can be used to track surfaces that are not atomically flat (as in Figure 1). However, the feedback network requires that the scanning be done relatively slowly. As a result, the sample being scanned must be held fixed in place for relatively long times to prevent image distortion.

Alternatively, in the constant height mode the tip is scanned across the surface at constant voltage and nearly constant height while the current is monitored. In this case the feedback network responds only rapidly enough to keep the average current constant, which means that the tip maintains the same average separation from the surface. The image is then a plot of current I versus lateral position (x, y), as shown in the graph below the schematic. Again, multiple scans along x are displayed laterally displaced in the y direction. The image shows the substantial variation of tunneling current as the tip passes over surface features such as individual atoms.

The constant height mode allows much faster scanning of atomically flat surfaces (100 times faster than the constant current mode), since the tip does not have to be moved up and down over the surface "terrain." This fast scanning means that making an image of a surface requires only a short "exposure time." By making a sequence of such images, researchers may be able to study in real-time processes in which the surfaces rearrange themselves -- in effect making an STM "movie."

Individual atoms have been imaged on a variety of surfaces, including those of so-called layered materials in which atoms are naturally arranged into two-dimensional layers. Figure 6 shows an example of atoms on one of these layered materials. In this image it is fascinating not only to see individual atoms, but also to note that some atoms are missing. Specifically, there are three atoms missing from Figure 6. Can you find the places where they belong?

Another remarkable aspect of the STM image in Figure 6 is that it was obtained with the surface and tip immersed in liquid nitrogen. While we assumed earlier in this essay that the space between the surface and tip must be empty, in fact electron tunneling can take place not just through vacuum but also through gases and liquids-- even water. This seems very surprising since we think of water, especially water with salts dissolved in it, as a conductor. But water is only an ionic conductor. For electrons, water behaves as an insulator just as vacuum behaves as an insulator. Thus electrons can flow through water only by tunneling, which makes scanning tunneling microscopy possible "under water."

As an example, Figure 7 shows individual carbon atoms on a graphite surface. It was obtained for a surface immersed in a silver plating solution, which is highly conductive for ions but behaves as an insulator for electrons. (The sides of the conducting probe were sheathed with a nonconductor, so that the predominant current into the probe comes from electrons tunneling into the exposed tip. The design of STM used to make this particular image is the one shown in Figure 2.) Sonnenfeld and Schardt observed atoms on this graphite surface before plating it with silver, after "islands" of silver atoms were plated onto the surface, and after the silver was electrochemically stripped from the surface. Their work illustrates the promise of the scanning tunneling microscope for seeing processes that take place on an atomic scale.

While the original STMs were one-of-a-kind laboratory devices, commercial STMs have recently become available. Figure 8 is an image of a graphite surface in air made with such a commercial STM. Note the high quality of this image and the recognizable rings of carbon atoms. You may be able to see that three of the six carbon atoms in each ring appear lower than the other three. All six atoms are in fact at the same level, but the three that appear lower are bonded to carbon atoms lying directly beneath them in the underlying atomic layer. The atoms in the surface layer that appear higher do not lie directly over subsurface atoms, and hence are not bonded to carbon atoms beneath them. For the higher-appearing atoms, some of the electron density that would have been involved in bonding to atoms beneath the surface instead extends into the space above the surface. This extra electron density makes these atoms appear higher in Figure 8, since what the STM maps is the topography of the electron distribution.

The availability of commercial instruments should speed the use of scanning tunneling microscopy in a variety of applications (Figure 9). These include characterizing electrodes for electrochemistry (while the electrode is still in the electrolyte), characterizing the roughness of surfaces, measuring the quality of optical gratings, and even imaging replicas of biological structures.

Perhaps the most remarkable thing about the scanning tunneling microscope is that its operation is based on a quantum mechanical phenomenon -- tunneling -- that was well understood in the 1920s, yet the STM itself wasn't built until the 1980s. What other applications of quantum mechanics may yet be waiting to be discovered?

Suggested Readings

Binnig, G., H. Rohrer, Ch. Gerber, and E. Weibel, Physical Review Letters 49: 57, 1982. The first description of the operation of a scanning tunneling microscope.

Binnig, G., and H. Rohrer, Sci. American, August 1985, p. 50. A popular description of the STM and its applications.

Quate, C.F., Physics Today, August 1986, p. 26. An overview of the field of scanning tunneling microscopy, including insights into how it came to be developed.

Hansma, P.K., and J. Tersoff, Journal of Applied Physics 61: R1, 1987. A comprehensive review of the "state of the art" in scanning tunneling microscopy.

Binnig, G., and H. Rohrer, Reviews of Modern Physics 59: 615, 1987. The text of the lecture given on the occasion of the presentation of the 1986 Nobel Prize in Physics.

Questions

  1. The density of the earth's atmosphere of air depends on altitude z according to, where z0, the "scale height" of the atmosphere, is 8430 meters. What is the scale height for the electron "atmosphere" above a conductor? Give both a formula and a numerical estimate.

  2. Our discussion of STM operation was based on the assumption that the conducting probe has only a single tip. In fact a probe may have a number of protrusions on its end, each of which acts as a "tip." Hence it might be expected that such a probe would give multiple STM images of the surface, greatly complicating the analysis. Explain why there is in fact no problem with multiple images, provided that the multiple tips differ in proximity to the surface by 20 Å or more.

  3. The STM, while using physical concepts that date from the 1920s, was not developed until the 1980s. Suggest some reasons why the STM was not invented half a century earlier.

  4. It was stated in the essay that for conventional microscopes, the resolution is limited by the wavelength of the waves used to make the image. To see whether this guideline applies to the STM, estimate the wavelength of an electron in the surface of a conductor and compare your estimate to the vertical resolution (about 0.01 Å) and lateral resolution (about 2 Å). Does the guideline apply to the two resolutions? Why or why not?

Figure Legends

Figure 1
Scanning tunneling microscope image of the surface of crystalline gold. The divisions on the scale are 5 Å. Successive scans are approximately 1.5 Å apart. The figure is from G. Binning, H. Rohrer, Ch. Gerber, and E. Stoll, Surface Science 144:321, 1984

Figure 2
Drawing of an actual STM head and base showing the essential components. Also depicted are the three screw used for controlling the mechanical approach of the tip to the sample. Three keys to a successful STM design are (1) A smooth mechanical approach mechanism, (2) rigidity, and (3) convenience in changing the sample and tip. (Based on a drawing from P.K. Hansma, V,B. Elings, O. Marti, and C.E. Bracker, Science 242:209-16, 1988. © 1988 by the AAAS,)

Figure 3

  1. The wave function of an electron in the surface of the material to be studied. The wave function extends beyond the surface into the empty region.
  2. The sharp tip of a conducting probe is brought close to the surface. The wave function of a surface electron penetrates into the tip, so that the electron can "tunnel" from surface to tip.

Figure 4
The potential energy versus position for an electron in a metal. The potential energy is öU when the electron is in the metal (x < 0) and is proportional to x outside the metal (x > 0). An electron with energy E can escape the metal by tunneling from x = 0 to the point x2.

Figure 5
A schematic view of an STM. The tip, shown as a rounded cone, is mounted on a piezoelectric x,y,z scanner. A scan of the tip over the sample can reveal contours of the surface down to the atomic level. An STM image is composed of a series of scans displaced laterally from one another such as shown in Figure 6. (Based on a drawing from P.K. Hansma, V.B. Elings, O, Marti, and E,E, Bracker, Science 242:209-16. ©1988 by the AAAS.)

Figure 6
Image of atoms on a surface4 of tantalum disulfide (TzS2) immersed in liquid nitrogen. The figure is from C.G. Slough, W.W. McNairy, R.V. Coleman, B. Drake, and P.K. Hansma, Physical Review B. 34:994, 1986

Figure 7
Image of a graphite electrode in an electrolyte used for silver plating. The figure is from R. Sonnenfeld and B. Schardt, Applied Physics Letters 49:1172, 1986

Figure 8
The surface of graphite as "viewed" with a scanning tunneling microscope. This technique enables scientists to see small details on surfaces, with a resolution of about 2 Å. The contours seen here represent the arrangement of individual atoms on the crystal surface. (Obtained with a commercial STM: the Nanoscope II from Digital Instruments in Goleta, California.

Figure 9
Examples of technological applications of the STM.

  1. A 6m m by 6m m scan of gold diffraction-grating master. The grating has 375 lines per millimeter, and the steps are 120 nm high.
  2. A thin-film magnetic recording head. The magnetic material is about 0.5 m m wide. Measurements show that the material is undercut about 20 nm below the surrounding material during lapping.
  3. Bumps on a compact disk stamper. Five track are shown in this image.
  4. The sharpened edge of a diamond-cutting tool. The diamond is a type 2B blue diamond which is conductive enough for the STM to image. The scale sin all of these figures are in nanometers. These images were also obtained with the Nanoscope II. (Figure from P.K. Hansma, V.B. Elings, O. Marti, and C.E. Bracker, Science 242:209-16, 1988 © 1988 by the AAAS.)

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