(a) Show that for E ? 0, the Fermi factor may be written as

(b) Show that if C?>> e^?E/kT, f(E) = Ae^?E/kT

(d) Using the result obtained in part (c), show that the classical approximation is applicable when the electron concentration is very small and/or the temperature is very high.

(e) Most semiconductors have impurities added in a process called doping, which increases the free electron concentration so that it is about 10¹⁷/cm³ at room temperature. Show that for these systems, the classical distribution function is applicable.

1 %3D f(E)% = CEEKT +1