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Quantum Mechanical Tunnelling.

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Quantum Mechanical Tunnelling

        The infinite potential walled particle in a box theory does not allow any of the wave function to escape the box as it would have to have more than infinity energy to cross the barrier. Allowing the potential energy well to be a finite number has the effect of making it possible for the wave function of a particle that is trapped in this potential well, to partially escape and thus have a presence outside the confines of the box.

The wave function can transverse the potential barrier, although it will decay exponentially through the barrier. Assuming that the wave function does not totally decay away before the end of the barrier, the particle can have a physical presence on the other side of the potential barrier.

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        The essential aspect of STM is the extreme sensitivity of the tunnelling current to the tip sample separation. It is therefore important to realise that the tunnelling current is a quantum phenomenon. In classical physics the current could not flow across a gap.

Modes of Operation

Constant height mode - In this mode the vertical position of the tip is not changed, equivalent to a slow or disabled feedback. The tunnelling current varies depending on topography and the local surface electronic properties of the sample. The current as a function of lateral position represents the surface image. This mode is only appropriate for atomically flat surfaces. If the surface was not flat, the STM tip would crash. An advantage of constant height mode is that it can be used at high scanning frequencies (up to 10 kHz).



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(http://instruct1.cit.cornell.edu/courses/ee476/FinalProjects/s2002/sm242/stmdesign.htm, 12/10/03).

Tip etching

        The construction of the tip is one of the most crucial aspects of STM. The tip must be approximately one atom thick in order for the STM to be carried out effectively. “Surface pictures can appear to be distorted due to the presence of more than one sharp protrusion”, (………). Some important characteristics of a tip are

  • Sharp tips which allow high resolution STM observations
  • Small resonance area
  • Thick taper to reduce tip oscillation during STM scans

  (http://www.mme.wsu.edu/~reu/poster2000/Ronald2000/ronald/ppframe.htm, 14/10/03)

It appears that multiple tips are formed when suspended particles are picked up from the etching solution, (……same as above).

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