The histogram method for computing density of states spectra is simplified considerably for the cubic lattices. As an example we treat the fcc lattice by randomly sampling a cube in k space (composed of octants from two adjacent Wigner-Seitz cells of the reciprocal lattice). Graphical results for the magnitude of the group velocity are used to locate the critical points that cause the singularities in the density of states. Illustrations are given that show how this can be used to improve the resolution of singularities that are not clearly resolved by the histogram method. A utility dispersion relation has been used for the examples, and it can be applied to spin waves as well as to electrons in the tight-binding approximation. Students can gain much insight into solid state research from this method since it helps to bridge the gap between the standard textbook treatments and the highly technical discussions of the research literature. The authors have used this method in a detailed study of the spectra of fcc lattices that will be presented elsewhere.

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The mechanical relaxation of strained semiconducting stripes is studied. The deformation tensor is calculated using a classical approach of elasticity problem with predeformations; the electronic band structure is then simulated using an 8 band kp model including strain. To confirm the models developed, compressively and tensely strained stripes were fabricated and characterized by photoluminescence measurements. Theoretical and experimental results are in very good agreement and show the importance of mechanical anisotropic relaxation phenomena in optoelectronic devices like waveguide structures, modulators, or lasers.