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. If the potential barrier is long range, then the wave function will decay away exponentially and tend towards zero. Upon reaching the end of the potential barrier, the particle will have an infinite small wave function and zero presence on the other side of the barrier. This property is known as quantum mechanical tunnelling.

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(http://www.chembio.uoguelph.ca/educmat/chm729/STMpage/stmdet.htm,10/10/03).

        The quantum mechanical phenomenon creates the high degree of sensitivity necessary for atomic scale imaging of surfaces. The quantum mechanical tunnelling current is highly dependent on the tip-surface distance. The distance between tip and surface is usually of the order of 0.3 nm and the tunnelling voltage V ranges from a few mV up to a few V, depending on the conductivity of the surface. The tunnelling current typically varies between 10 pA and 1 nA, (http://www.fys.kuleuven.ac.be/vsm /spm/introduction.html12/10/03).

        The essential aspect of STM is the extreme sensitivity of the tunnelling current to the tip sample separation. ...

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