Posted by Saad on April 17, 2015, 11:44 pm
In your book on page 191 (and in the lectures), you deduced that the DOS for electrons in conduction band and holes in valence band are similar to the free electron case, with changes in mass and range. However, these expressions hold strictly near the bottom and top of the conduction and valence bands respectively, since it is only there that the energy has a quadratic dependence on k. So, how can we use these expressions for DOS in the integrals for n(T) and p(T) when the limits of the integral are extended far beyond that range? 
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