Fermi Levels in Extrinsic Semiconductors

For reasons that will become clear in Chapter 21, it is very important to understand the influence of doping on the Fermi level. From Equation 20.18, 

Computed carrier concentration in n-doped Si as a function of reciprocal temperature at various doping levels. 

Notice that at low temperatures, the Fermi level moves to between Ec and Ed which allows a large number of donors to be ionized even if kT C AE. 

Next consider the saturated region n n =Nu- Using Equation 20.23, Equation 20.24 becomes 

One can see that adding donors raises the Fermi level. We see from Equation 20.24 that it is possible to raise the Ep above the conduction band in order to make the material ohmic (metal-like) by making n Neu- One is tempted to think that this could be accomplished by setting Nu = Neff- However, exp(AE/ET) = 6.66 at 300 K for Si. So as Nq — Ngg, the approximation used in Equation 20.26 is no longer valid and the Fermi level must be foimd by using Equation 20.21 with Equation 20.24. 

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