Problem 1: The electron energy near the top of the valence band in a semiconductor is given by

ε = -10^-37k²J

where k is the wavevector. An electron is removed from the state

k = 10⁹k^{^}_xm^-1

where k^{^}x is a unit vector along the x axis. Calculate (a) the effective mass, (b) the energy, (c) the momentum and (d) the velocity of the resulting hole.

Problem 2. Indium antimonide has dielectric constant ε = 17 and electron effective mass m_c = 0.014m. Calculate:

(a) the donor ionization energy,

(b) the radius of the ground state orbit, and

(c) the donor concentration at which orbits around adjacent impurities begin to overlap. What effects occur at about this concentration, and why?

Problem 3. Use the data to estimate a value of the donor ionization energy for arsenic Impurities in germanium.