Editing Electron hole (section)

== Simplified analogy: Empty seat in an auditorium ==
[[File:15-puzzle-02.jpg|thumb|A children's puzzle which illustrates the mobility of holes in an atomic lattice. The tiles are analogous to electrons, while the missing tile ''(lower right corner)'' is analogous to a hole.  Just as the position of the missing tile can be moved to different locations by moving the tiles, a hole in a crystal lattice can move to different positions in the lattice by the motion of the surrounding electrons.]]

Hole conduction in a [[valence band]] can be explained by the following analogy:

Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so he jumps over the back of the seat into another row, and walks out. The empty row is analogous to the [[conduction band]], and the person walking out is analogous to a conduction electron.

Now imagine someone else comes along and wants to sit down. The empty row has a poor view; so he does not want to sit there. Instead, a person in the crowded row moves into the empty seat the first person left behind. The empty seat moves one spot closer to the edge and the person waiting to sit down. The next person follows, and the next, et cetera. One could say that the empty seat moves towards the edge of the row. Once the empty seat reaches the edge, the new person can sit down.

In the process everyone in the row has moved along. If those people were negatively charged (like electrons), this movement would constitute [[Electrical resistivity and conductivity|conduction]]. If the seats themselves were positively charged, then only the vacant seat would be positive. This is a very simple model of how hole conduction works.

Instead of analyzing the movement of an empty state in the valence band as the movement of many separate electrons, a single equivalent imaginary particle called a "hole" is considered. In an applied [[electric field]], the electrons move in one direction, corresponding to the hole moving in the other. If a hole associates itself with a neutral atom, that atom loses an electron and becomes positive. Therefore, the hole is taken to have positive [[electric charge|charge]] of +''e'', precisely the opposite of the electron charge.

In reality, due to the [[uncertainty principle]] of [[quantum mechanics]], combined with the [[Bloch's theorem|energy levels available in the crystal]], the hole is not localizable to a single position as described in the previous example. Rather, the positive charge which represents the hole spans an area in the crystal lattice covering many hundreds of [[crystal structure|unit cells]]. This is equivalent to being unable to tell which broken bond corresponds to the "missing" electron.  Conduction band electrons are similarly delocalized.