034 In a simplified model of an undoped semiconductor, the ac- tual distribution of energy states may be replaced by one in which there are N, states in the valence band, all these states having the same energy E,, and N, states in the conduction band, all these states having the same energy E. The number of electrons in the conduction band equals the number of holes in the valence band. (a) Show that this last condition implies that N. exp(AEJKT) + 1 exp(AE,IkT) + 1 N in which AE. = E. - EF and AE, = -(E, – Er). %3D (b) If the Fermi level is in the gap between the two bands and its dis- tance from each band is large relative to kT, then the exponentials dominate in the denominators. Under these conditions, show that (E. + E,) EF 2 kT In(N,/N) 2 and that, if N, - N the Fermi level for the undoped semiconduc- tor is close to the gap's center.

034 In a simplified model of an undoped semiconductor, the ac- tual distribution of energy states may be replaced by one in which there are N, states in the valence band, all these states having the same energy E,, and N, states in the conduction band, all these states having the same energy E. The number of electrons in the conduction band equals the number of holes in the valence band. (a) Show that this last condition implies that N. exp(AEJKT) + 1 exp(AE,IkT) + 1 N in which AE. = E. - EF and AE, = -(E, – Er). %3D (b) If the Fermi level is in the gap between the two bands and its dis- tance from each band is large relative to kT, then the exponentials dominate in the denominators. Under these conditions, show that (E. + E,) EF 2 kT In(N,/N) 2 and that, if N, - N the Fermi level for the undoped semiconduc- tor is close to the gap's center.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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