Question

( 10 points) Calculate the occupation probability f(E), that is the probability that a state will be occupied, at 293 K for a state at the bottom of the conduction band in germanium. The energy of the gap is Eg= 0.67 eV and assume that the Fermi energy lies in the middle of the gap.

Answer 1

It e Occupation. Probability fLE) (LE-E+) / KT where, Kis Boltzmann's constant (1.36X 10J/K) Tis the Temperature (293 K.(Giver)) Ef is the fermi Energy Es the energy at required point Energy of gap = 0.67 eV = Eg Es, Fermi energy = Eg = 0.67 0.335 eV Energy at bottom of conduction bands 2 2 E = + = +0.67 ev Hence, E-EE = 0.67-0.335 = 0.335 ev

KT = (1.38x 1023) (293) I C1-3&X 10-23) (293) et (1.6x 10-19 KI: - 2:53 x 10-2'= 0.0253 eV E-Eç = 0.335 eV (E-EF)/KI 0.335/0.0253 13.24 (E-EF)/KT = - 13.24 =e 562417.65 Hence, F(E) = It e (E-EP)/KT 156247 F(E) - 1:787106 562418.65 1.78 x 10-6 Answer