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Could someone please give me a good definition of the following electric terms? Despite what searching I have done, I have not come across a definition that I have found clear for me to understand:

  • Free electron
  • Mobile charge
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I assume that this is in the context of solid state, rather than, say, free electron lasers.

The heuristic picture is that when you have solids, the atomic orbitals overlap between nearby atoms and it is possible that some of these orbitals essentially change shape so much that one get orbitals which extend over the entire solid. The electrons in these extreme molecular orbitals are called "free", as opposed to the still localised ones which are referred to as "bound". These free electrons can then transport charge around and you have a conductor.

In metals that's about it, and there are lots and lots of electrons about. In a semiconductor however, the density of free electrons is much lower, and in fact one has in quantitatively similar amounts (this can be varied by doping) also holes, which are absences of electrons in an otherwise filled band. Undoped semiconductors would have them in a 1:1 ratio. These holes can be regarded as particles in their own right and can also move around and transport charge.

The difference is not just conceptual, as the two different charge carriers actually behave differently in a magnetic field, and through the Hall effect one can measure what the majority charge carriers are.

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