3.3 The scanning tunnelling microscope
The first scanning probe microscope, the scanning tunnelling microscope (STM), was invented by Heinrich Rohrer and Gerd Binnig in 1981, and used the quantum-mechanical effect of electron tunnelling (in which electrons ‘tunnel’ through an energy barrier that classical physics would suggest is too high to cross). In this instance, the energy barrier is the tendency of the metal of the probe tip to want to hang on to its electrons. In effect, as you try to remove an electron from the surface of the metal, it is attracted to the metal, and an electric field strong enough to overcome this attraction is needed to pull the electron off. In this context, tunnelling is the phenomenon of being able to get some electrons off using an electric field much weaker than the calculations would suggest was needed. One of the counter-intuitive results of quantum mechanics is that the electron is not a hard particle confined to a specific location. Rather, it is a blurred region of ‘electron-ness’, such that at any instantaneous time you look, you're most likely to find it in some preferred part of this region, but there's also a finite chance of finding it some distance from there. So, when the STM tip is brought close enough to the surface of an electrically conducting sample (a separation of about a nanometre), even a small voltage, of the order of 1 V or so, between tip and sample enables enough electrons to absent themselves from the tip and reappear in the material across the gap. This transfer of electrons produces a measurable current.
The current is very strongly dependent on the width of the gap – it falls exponentially as the gap increases, halving every 0.04 nm or so. It can be maintained at a constant value by moving the probe up and down, using a piezoelectric crystal actuator, as it scans across the sample. The voltage applied to the actuator to cause this vertical movement then contains the information about how the height of the sample surface varies as the probe tip is scanned over it. Traces from successive side-by-side scans can then be laid together to produce a topographical map of the surface, with a vertical resolution of 1/100th of a nanometre (compare this with the atomic radius of carbon – about seven times this distance).
As I mentioned earlier when I was talking about the graphite surface, the local density of states also plays a part in forming the image. The LDOS refers to the number of energy states an electron from the tip of the STM has available to it when it arrives on the surface. The more of these there are, the higher is the likelihood that an electron will tunnel across from the tip to the surface, and therefore the larger will be the tunnelling current. It's a little like a cat jumping across a gap. If its landing site is the small square top of a fence post, it will find it more difficult to ensure it has the right momentum to stay balanced on it than if it has a whole rooftop to aim at. The cat opposite the roof (with a higher density of states) will be more likely to risk the jump. The larger current due to a higher LDOS is indistinguishable from one due to the surface getting closer to the tip: an increase in the LDOS will look to the STM like a bump on the surface.
The development in microscopy that the STM represented was considered so significant that Rohrer and Binnig received the Nobel Prize in 1986, only three years after describing their invention. It is interesting to note that they shared the prize that year with August Ruska, who was honoured for inventing the electron microscope over fifty years earlier.