2. A rectangular quantum wire with cross section of 15 nm x 15 nm is microfabricated from GaAs. (a) Write an expression for the subband threshold energies of this quantum wire, by treating its cross-sectional area as a 2D infinite square well. (b) Write a general expression for the electron dispersion (i.e. energy as a function of k-vector) in this quantum wire. (c) In a table, list the quantized energies and their degeneracies (neglecting spin degeneracy) for the first 15 energetically-distinct subbands in the wire. (d) Plot the density of states of the wire over an energy range that includes the first fifteen subband energies. (A qualitative sketch with clearly-labelled axes and subband threshold energies is sufficient for this question, so use of Mathematica or similar software to plot your answer is optional.)

Fig: 1