© Kwok-Wai Ng, 1998.

Semiconductor crystal. For simplicity, let us assume there is only one conduction band, one valance band, and one donor band (i.e. degeneracy = 1 for each case) in this problem. The effective densities of state of the valance (N_v) and conduction (N_c) band are given as respectively, where m_e and m_h are masses of electron and hole respectively, and T is temperature. Now consider an intrinsic semiconductor of energy gap E_g = 1 eV, m_h = 0.5 m_e, and N_c = 3 10¹⁹ cm^-3 at T=300K. (a) Calculate n and p in cm^-3, the carrier density of electron and hole respectively. (b) Calculate the Fermi energy E_F. The semiconductor is now doped with a donor impurity at a concentration of 10¹³ cm^-3. The donor ionization energy is so small that they are essentially 100% ionized (i.e. N_D⁺ = N_D). (c) What is the new hole density (p) in cm^-3? (d) What is the new Fermi energy?

(a)

(b)

(c)

(d)