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The main difference is the factor 1/2 in front of the exponential term.

The distribution function for acceptors differs also because of the different possible ways to occupy the acceptor level. The neutral acceptor contains two electrons with opposite spin, the ionized acceptor still contains one electron which can have either spin, while the doubly positive state is not allowed since this would require a different energy. This restriction would yield a factor of 2 in front of the exponential term. In addition, one finds that most commonly used semiconductors have a two-fold degenerate valence band, which causes this factor to increase to 4 yielding:


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