(a) that when the number of electrons in the conduction band equals the number of holes in the valence band, it implies N c exp ⁡ ∆ E c k T + 1 = N v exp ⁡ ∆ E v k T + 1 in which ∆E c = E c - E F and ∆E v = - (E v - E F ). (b) that under the conditions when the Fermi level is in the gap between the two bands and its distance from each band is large relative to kT E f = E c + E v 2 + k T l n ( N v N c ) 2

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Chapter 41, Problem 34P

To determine

To show:

(a) that when the number of electrons in the conduction band equals the number of holes in the valence band, it implies

Ncexp⁡∆EckT+1 = Nvexp⁡∆EvkT+1

in which ∆E_c = E_c - E_F and ∆E_v = - (E_v - E_F).

(b) that under the conditions when the Fermi level is in the gap between the two bands and its distance from each band is large relative to kT

Ef = Ec+ Ev2+kT ln (NvNc)2

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