1. A certain semiconductor (m' - 0.12 me, mn - m,) is doped with acceptor impurities of density
N° - 10-23 m at the level EA - Eg 2. At the temperatures of interest Eg - 20kT and E, - SkT.
(a) the density of ionized impurities
(b) the electron density;
(c) the hole density;
(d) the temperature;
(e) the energy gap.
2. A system of electron spins is placed in a magnetic field of 2 Tesla. The number of spins parallel to the
magnetic field is twice as large as the number of anti parallel spins. Determine the temperature of the
3. A rectangular quantum wire with cross section 15 x 15 is realized in GaAs.
(a) Write an expression for the subband threshold energies of the quantum wire.
(b) Write a general expression for the electron dispersion in the quantum wire.
(c) In a table, list the quantized energies and their degeneracies (neglecting spin) for the first 15
(d) Plot the density of states of the wire over an energy range that includes the first fifteen subband
4. For this same wire:
(a) Write an expression for the electron density (per unit length) as a function of the Fermi energy of the
(b) Plot the variation of the electron density as a function of energy for a range that corresponds to
filling the first five distinct energy levels, taking proper account of level degeneracies.
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