So far we have seen that the probability that tunneling can occur increases when: · The width of the potential barrier decreases, · The height of the potential barrier decreases, or · The total energy of the electron increases.
We will now see how these properties are applied to measuring the location of atoms on surfaces.
Recall that in a scanning tunneling microscope, the sample's surface is measured by a probe tip that "scans" the surface. In the figure below a probe tip is near the surface of a sample. We have rotated the figure so that the corresponding potential energy diagram can be displayed in the usual manner. As shown, the electron travels horizontally along the line from the A to B. The electron begins in the sample and ends up in the probe.
Inside the material the electrons are attracted to the atoms. Likewise the atoms attract electrons in side the probe tip. Because of these attractions the potential energy will be negative in both regions. A vacuum exits between the material and probe tip. The potential is zero in that region.
Take a moment to study the diagram and the potential - notice the similarity between the potential shape for the STM and the foil example we looked at earlier.
Make a sketch of the wave function you would expect with the probe at the point A-B.
Now suppose that you were to move the probe to the line C-D. Sketch the potential energy diagram and the wave function for the electron at C-D.
Compare the potential energy diagrams for the two probe positions A-B and C-D. How are they similar? How are they different?
Compare the wave functions for the two probe positions A-B and C-D. How are they similar? How are they different?
How does the tunneling probability compare for the two probe positions A-B and C-D?
Will some of the electrons in the sample appear in the probe tip? Explain.
The potential energy changes as the distance between the probe and surface changes. As a result the probability of electrons from the surface appearing in the probe also changes. This conclusion is the basis of the scanning tunneling microscope. The STM operator would measure the number of electrons that reach the probe. This number of electrons is related to the probability that tunneling occurs. So we can use quantum tunneling to construct a map of the surface.
Tunneling occurs without the surfaces touching. Because the probe does not touch the atoms, it does not move them. Thus quantum tunneling provides a way to map atoms on a surface accurately.