So far you were considering a situation in which no voltage was applied at the probe tip, that is, electrons would be equally likely to be in the probe tip as in the sample. In a real scanning tunneling microscope, however, the probe tip can be placed at a positive voltage with respect to the sample, which means that the electrons (which have a negative charge) will be attracted towards the probe tip from the sample surface. Hence, electrons prefer to be in the probe tip, rather than in the sample.
Electrons, like everything else in nature, seek the lowest potential energy accessible. Given this fact, predict which side of the potential energy diagram (sample or probe tip) will have a greater electron population? Explain.
The potential energy diagram corresponding to the situation in which a positive voltage is applied to the probe tip will look like the figure below:
The thick dashed line is the original potential energy (when probe tip is at 0V). The solid line is the potential energy diagram when the probe tip is at a positive voltage.
Remember a positively charged object will have an electric field which will extend some distance from the object. The positive voltage at the probe tip causes the entire potential energy diagram on the right to move down by an amount which is equal to the positive voltage applied.
Consider the potential energy diagram drawn above. Does applying this voltage to the probe tip increase the probability that the electrons will move from the sample to the probe tip? Explain.
You can test your answer using the Quantum Tunneling program.
Change the barrier shape to the Trapezoidal option. Change the potential energy of the Left Height so the energy diagram is similar to the figure above. Click on the Redraw Graph button to view the wave function and check your prediction.
The final issue we need to look at to understand the role of tunneling in a STM is electron energy. In a real scanning tunneling microscope, electrons with a range of electrons will tunnel from the sample to the probe tip. The movement of a large number of these electrons constitutes a tunneling current. This current can be measured.
Based on the relationship between tunneling probability and tunneling current described above, how does tunneling current change when the probe tip is moved closer to the surface of the sample?
Refer to the diagram above.
Suppose the probe tip is moved along the vertical line P-Q as shown above. Consider your answer to the previous question and sketch a graph showing how tunneling current would depend on the vertical position of the probe.
Refer to your sketch, how does the current profile compare with the cross-sectional view of the sample?
In conclusion …
Earlier we listed three factors that increase tunneling probability: The width of the potential barrier decreases, The height of the potential barrier decreases, or The total energy of the electron increases.
From what we have discussed so far summarize how are these factors controlled in a scanning tunneling microscope?