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A modification of the form of Shaw's optimized model potential is proposed so as (a) to decrease the energy dependence of the model potential parameters and (b) to increase the flexibility, and thereby the applicability, of the model potential. Calculations of the Fermi surface distortions of K, Rb and Cs metals using the present proposed model pseudopotential show significant improvements in the results over those obtained from Shaw's optimized model potential. The phonon dispersion relations of K, Rb, Cs and P b are also calculated and the results obtained lend support to the necessity of the modification of the form of Shaw's optimized model potential. In addition, the present pseudopotential calculation of the phonon dispersion relations for metallic Pb is discussed in relation to previous calculations by other authors. It is found that, if a well determined first-principles pseudopotential is used, the higher-order perturbation corrections to the phonon frequencies calculated by second-order pseudopotential perturbation theory of lattice dynamics are not as significant as is implied by previous work.

We fabricated two dimensional photonic crystals (a square and a triangular lattice) with a photonic band gap (PBG) in the visible light range by periodically arranging Si nanopillars with a period of 270 nm. The pillar diameter and height are 50 nm and 1 µm, respectively. The fabrication process uses iron clusters as nuclei for self-formation of etching masks during electron cyclotron plasma etching with SF 6 gas at −135 • C to obtain high-aspect-ratio Si nanopillars. The iron clusters are arranged by electron beam lithography. The reflection spectra of the square lattice photonic crystal have a peak around 570 nm for transverse magnetic polarization light while that for transverse electric polarization have a peak around 550 nm. This is consistent with our theoretical calculation that the photonic crystal has a PBG at these wavelengths.