Physics of Semiconductor Devices

Average electron energy in a metal

For a metal at a temperature of T = 0 K, the conduction electrons at the bottom of the band have an energy E = 0 and the conduction electrons with the highest energy have an energy E = E_f. Assuming that the density of states is given by N(E) = 8π√2m³E/h³, what is the average energy of the conduction electrons?

An expression for the average energy should be given in terms of Planck's constant h, the Fermi energy Ef, the effective mass m, pi = 3.14159... and numerical constants. The functions sin, cos, tan, asin, acos, exp, ln, and sqrt can be used. For instance, 2*sin(h*m)*exp(Ef) is a valid (but wrong) answer. Be sure to include a * to indicate multiplication; write 2*h*m not 2hm to multiply 2 times h times m.

Hint: Not all of the constants h, m, Ef, and pi appear in the answer.