Transcribed Text
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.
5
Determine
(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
system.
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
energetically-distinct subbands.
(d) Plot the density of states of the wire over an energy range that includes the first fifteen subband
energies.
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
wire.
(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.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.