Sample Questions on Semiconductor
1. Assume the Boltzmann approximation in a semiconductor is valid.
Determine the ratio of n(E) = gc(E) fF(E) at E = Ec +4kT to that at E = Ec
+ kT/2.
2. In a particular semiconductor material, the effective density of states
functions is given by Nc =Nco (T)3/2 and Nv = Nvo (T)3/2 where Nco and Nvo
are constants independent of temperature. The experimentally determined
intrinsic carrier concentrations as a function of temperature are given in
following table. Determine the product NcoNvo and the bandgap energy Eg
(Assume Eg is independent of temperature.)
Figure: Intrinsic concentration as a function of temperature
3. If the density of states function in the conduction band of a particular
semiconductor is a constant equal to K, derive the expression for the
thermal-equilibrium concentration of electrons in the conduction hand,
assuming Fermi-Dirac statistics and assuming the Boltzmann
approximation is valid.
4. Calculate the ionization energy and radius of the donor electron in
germanium using the Bohr theory. (Use the density of states effective
mass as a first approximation.)
5. A) If Ec - EF = 0.25 eV in gallium arsenide at T = 400 K. calculate the
values of no and po. B) Assuming the value of no from part (a) remains
constant, determine Ec – EF and po at T = 300 K.
6. A sample of silicon at T = 450 K is doped with boron at a concentration
of 1.5 x 1015 cm-3 and with arsenic at a concentration of 8 x 1014 cm-3. A)
Is the material n or p type? (b) Determine the electron and hole
concentrations. (c) Calculate the total ionized impurity concentration.
PYL-125(2021-I)
7. Silicon at T = 300 K is doped with acceptor atoms at a concentration of
Na = 7 x1015 cm-3. (a) Determine EF-Ev b) Calculate the concentration of
additional acceptor atoms that must be added to move the Fermi level a
distance kT closer to the valence-band edge.
8. Four electrons exist in a one-dimensional infinite potential well of width
a = 10Å. Assuming the free electron mass, what is the Fermi energy at T
= 0 K.
PYL-125(2021-I)