The Fermi-Dirac factor is expressed in Equation(9.34) as FFD 1exp3b1E EF 2 4 1 In a
Chapter 11, Problem 18(choose chapter or problem)
The Fermi-Dirac factor is expressed in Equation(9.34) as FFD 1exp3b1E EF 2 4 1 In a semiconductor or insulator, with an energy gapEg between the valence and conduction bands, we cantake EF to be halfway between the bands, so that EF Eg/2. (a) Show that for a typical semiconductor orinsulator at room temperature the Fermi-Dirac factoris approximately equal to exp (Eg/2kT). (b) Usethe result in (a) to compute the Fermi-Dirac factorfor a typical insulator, with Eg 8.0 eV at T 300 K.(c) Repeat for a semiconductor, silicon, with Eg 1.11 eV at T 293 K. (d) Your result in (c) is stillsmall, but suffi ciently large to explain why there willbe conduction. Explain.
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