Solid state Physics
Assignment set II
May 13, 2023
1. The actual energy gap at 0 K in lead is 2.73 × 10−3 eV. (a) What is the prediction of the BCS
theory for this energy gap? (b) Radiation of what minimum frequency could break apart Cooper
pairs in lead at 0 K ? In what part of the em spectrum is such radiation ?
2. Consider silicon at T = 300 K. A Hall effect device is fabricated with the following geometry: d
= 5 × 10−3 cm, W = 5 × 10−2 cm, L = 0.5 cm. The electrical parameters measured are: Ix =
0.50 mA, Vx = 1.25 V, and Bz = 650 gauss. The Hall field is EH = −16.5 m V/cm. Determine
(a) the Hall voltage, (b) the conductivity type, (c) the majority carrier concentration, and (d)
the majority carrier mobility.
3. Calculate the intrinsic carrier concentration, ni at T = 200, 400, and 600 K for (a) silicon, (b)
germanium, and (c) gallium arsenide.
4. Two semiconductor materials have exactly the same properties except material A has a bandgap
energy of 0.90 eV and material B has a bandgap energy of 1.10 eV. Determine the ratio of ni of
material B to that of material A for (a) T = 200 K, and (b) T = 300 K.
5. (a) The carrier effective masses in a semiconductor are m⋆n = 1.21m0 and m⋆p = 0.7m0 . Determine the position of the intrinsic Fermi level with respect to the center of the bandgap at T =
300 K.
6. The value of p0 in silicon at T = 300 K is 2 × 1016 cm−3 . (a) Determine EF − Ev . (b) Calculate
the value of Ec − EF . (c) What is the value of n0 ? (d) Determine EF i − EF .
7. The Fermi energy level in silicon at T = 300 K is 0.22 eV above the intrinsic Fermi level.
Determine n0 and p0 .
8. 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.
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