Question

(2) In a semiconductor with an energy gap Eg between the valence and the conduction bands we can take Ef (the Fermi energy) to be halfway between the bands (see figure below): Conduction band Energy gap Eg Valence band Semiconductor a. Show that for a typical semiconductor or insulator at room temperature the Fermi- Dirac factor is approximately equal to exp(-E 2kBT). (Typical Eg for semi-conductors ranges from about 0.5eV to 6eV at T-293K.) b. In heavily doped n-type silicon, there are 1016 electrons per cm at room temperature. The donor level is located 0.05 eV below the conduction band. The current carrier concentration as a function of temperature may be expressed as Eg /2kT At what temperature are there essentially no charge carriers (< 1 cm-3)?

Answer 1

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​​​​que (b) contains proof of (a) also. So I gave a combined ans.