Stephen Cunningham

Using the method of Chadi and Cohen, we present, for each of the two-dimensional lattice types, the mean-value point, the set of generating wave vectors, and the sets of special points in the two-dimensional Brillouin zone which are the most efficient in finding accurate averages of a periodic function over the Brillouin zone.

We have solved Maxwell's equations for the fields localized near the surface of a doped semiconductor possessing either a depletion layer, an accumulation layer, or an inversion layer. We present the dispersion relation for the frequency of the surface plasmon polariton as a function of the wave vector parallel to the surface for each of the three cases. The effect of the space charge at the surface is taken into account by dividing the surface region into layers and assuming a linear position dependence for the free-carrier concentration and the local dielectric constant within each layer. We have found the solution for the fields within each layer and have satisfied the boundary conditions for the normal and tangential components of the fields at each interface between layers. We show that the features of the dispersion curve can be used to obtain information about the space-charge region. For illustration, we compare our calculations with measured dispersion curves of $n$-type InSb.

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We present a theory of long-wavelength acoustic phonons localized at the apex of a variable-angle semi-infinite wedge made up of an isotropic cubic elastic medium. Stress-free boundary conditions are incorporated into the calculation by assuming position-dependent elastic constants. The equations of motion are solved numerically by first performing a linear mapping of the wedge into a right-angle wedge, and then expanding each displacement component in a double series of Laguerre functions. When the Cauchy relation is satisfied and when the interior angle of the wedge is between 125\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{}, the speed of the lowest-frequency edge mode, which is of ${\ensuremath{\Gamma}}_{1}$ symmetry, is very nearly equal to the speed of Rayleigh surface waves. For wedge angles less than 100\ifmmode^\circ\else\textdegree\fi{}, the speed of the lowest-frequency edge mode, which is now of ${\ensuremath{\Gamma}}_{2}$ symmetry, decreases rapidly with angle and appears to vanish in the limit as the angle approaches 0\ifmmode^\circ\else\textdegree\fi{}. For these acute angles, additional edge modes of ${\ensuremath{\Gamma}}_{2}$ symmetry appear with speeds below the Rayleigh value.