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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.

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