Carrier concentrations in extrinsic semiconductors

The number of holes created by the addition of the acceptors is equal to N, where the number of acceptor atoms per unit volume is Aa, and the number of acceptors that have gained an electron. 

Equations (13.4) and (13.5) allow the numbers of mobile charge carriers and the position of the Fermi level to be found as a function of dopant concentration, using a similar approach to that outlined in Section S4.8 for intrinsic semiconductors. Unfortunately, the results are not easily expressed analytically or displayed graphically. 

At elevated temperatures, most of the donors and acceptors will be ionised, and the electroneutrality condition. Equation (13.5), can be written as  

In cases where an n-type semiconductor contains only donors, and at high temperatures, so that the donors are completely ionised. Equations (13.4) and (13.6) give the number of electrons and holes as 

Similarly, for a p-type semiconductor crystal that contains only acceptors at high temperatures, the 

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