1.
Calculate the probability that an energy state in the conduction band at E = Ec + kT is
occupied by an electron and calculate the thermal equilibrium electron concentration in silicon
at T = 300 K. Assume the Fermi energy is 0.20 eV below the conduction band energy Ec. The
value of Nc for silicon at T = 300 K is Nc = 2.8 x 1019 cm-3.
2.
Calculate the thermal equilibrium electron concentration in silicon at T = 300 K for the case
when the Fermi level is 0.25 eV below the conduction-band energy.
3.
Calculate the probability that an energy state in the valence band at E = Ev – kT is empty of an
electron and calculate the thermal-equilibrium hole concentration in silicon at T = 350 K.
Assume the Fermi energy is 0.25 eV above the valence-band energy. The value of Nv for
silicon at T = 300 K is Nv = 1.04 x 1019 cm-3.
4.
Calculate the thermal-equilibrium hole concentration in silicon at T = 300 K for the case when
the Fermi level is 0.20 eV above the valence-band energy.
Calculate the intrinsic carrier concentration in silicon at T = 350 K and at T = 400 K. The
values of Nc and Nv vary as T3/2. As a first approximation, neglect any variation of bandgap
energy with temperature. Assume that the bandgap energy of silicon is 1.12 eV. The value of
kT at 350 K is
5.
 350 
kT  (0.0259 )
  0.0302 eV
 300 
and the value of kT at 400 K is
 400 
kT  (0.0259 )
  0.0345 eV
 300 
6.
Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi
energy. Consider silicon at T = 300 K. Assume that the Fermi level is 0.25 eV above the
valence-band energy. If we assume the bandgap energy of silicon is 1.12 eV, then the Fermi
energy will be 0.87 below the conduction-band energy.
7.
Determine the hole concentration in silicon at T = 300 K given the electron concentration.
Assume the electron concentration is n0 = 1 x 1016cm-3.
8.
Consider a germanium sample at T = 300 K in which Nd = 5 x 1013cm-3 and Na = 0. Assume
that ni = 2.4 x 1013cm-3. Calculate the thermal-equilibrium electron and hole concentrations.
9.
A silicon power device with n-type material is to be operated at T = 475 K. At this
temperature, the intrinsic carrier concentration must contribute no more than 3 percent of the
total electron concentration. Determine the minimum doping concentration required to meet
this specification. (As a first approximation, neglect the variation of Eg with temperature.)