1) Semiconductor band diagrams. Consider a heterojunction consisting of GaAs / InAs. The
electron affinity of GaAs is 4.07 eV; its band gap is 1.42 eV. The electron affinity of InAs is 4.9
eV; its band gap is 0.36 eV.
a) Draw the band alignments before the materials are adjoined. Make sure that the relative
valence band positions are accurately drawn.
b) Assume that the InAs layer is intrinsic and the GaAs layers have a work function of 4.37 eV.
Draw the band alignments of this formed heterojunction (the materials are now adjoined).
c) Keeping InAs intrinsic; what position of the Fermi level within the GaAs layers is needed to
removal all band bending (to have flat bands up to the interface)?
d) In the scenario of (c), is GaAs p-type, intrinsic, or n-type?
1e) Finally, consider the situation where the GaAs layer is replaced by silver, forming an Ag/InAs
junction. Assume the workfunction of the InAs layer is 5.0 eV and that of the Ag layer is 4.3 eV.
Draw the band alignments of the metal-semiconductor junction after the materials are
2) Phonons and Thermal Properties.
a) How are acoustic and optical phonon modes different? As part of your answer, include a
phonon dispersion (E vs k) diagram.
b) How is the sound of speed related to phonons?
3) Magnetic Materials
a) Both antiferromagnet and paramagnetic materials have zero magnetization in the absence of
an applied magnetic field and a similar magnetic susceptibility. What distinguishes
antiferromagnetism from paramagnetism? It may be helpful to draw a diagram.
b) Draw an example of the density of states (both spin up and spin down) as a function of E for
a ferromagnetic material and a paramagnetic material in the absence of an applied magnetic
field (H = 0).
c) Draw an example of the density of states (both spin up and spin down) as a function of E for a
ferromagnetic material and a paramagnetic material in the presence of an applied magnetic
field (H ≠ 0).
4) Electronic Structure. Consider the following portion of a band structure for a material in
which the near Fermi level band structure consists of 5 d bands and 1 p band.
a) Is this material a metal or an insulator? Why?
b) Are the majority carriers electrons or holes?
c) Which bands (xy, z2
, z, etc) are fully occupied? Which bands are fully unoccupied?
d) Complete the empty figure to the right of the E vs k diagram by drawing the approximate
density of states (DOS) as a function of energy.
e) At the k = /a point, which band will have the smallest effective mass for electrons? Which
band will have the largest effective mass for electrons?
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