Question

Fermi Energy Eqn. 4.22 in Kasap gives the Fermi energy (at 0 K) as is the conduction electron concentration. This is equivalent to the equation we derived in class. Kasap Eqn. 4.23 gives the Fermi energy as a function of temperature: EFEF1 a. If each copper atom contributes one conduction electron, what is the Fermi energy of copper at 29:3 b. Since this Fermi energy was derived from the Sommerfeld model, the energy is entirely kinetic 12 LEFo K? energy (the energy in the infinite 3D box was zero). Thus, what is the speed ve for conduction electrons in copper with energies near the Fermi energy calculated in part (a)? If the conduction electrons in copper were treated as an ideal gas following Maxwell-Boltzmann c. statistics with 1/2K7 per degre of fredom and 3 degree of reedom, what would be their thermal speed vth? d. Comment on the difference (or ratio) ofV to Vth by comparing your results from parts (b) and (c). What fundamental quantum mechanical phenomena leads to this difference? e. The electron drift mobility in copper, from Hall effect measurements, is 33 cm2 V-1 s1. This mobility can be used to calculate the mean free time (or mean scattering time) t. Calculate the mean free path l for electrons with speed vp

Answer 1

8m 3A84 32 x 10 % 83 3.14 T 293 k : 11xlo ' | '-@w) 198 x lev 1-6xto 's so can be cementol into ov ② Permi velocity v at T=29.3K 9.1x10-31 3 2 2.3 rm

d) fermi velocity is the maximum possible velocity in a material as Fermi energy is the energy of highest occupied energy level .

In case of metals due to quantum effects, random collisions are possible at higher energy levels because of the presence of empty levels there leading to high velocity as the case in Fermi velocity....