Phonon Calculations in Covalent Semiconductors using a Vector Computer
In the past decade two ab-initio methods have been developed to calculate phonon dispersion curves of covalent semiconductors: the dielectric screening formalism and the total energy difference method. In the first method linear response theory is applied in order to evaluate the effect of the ionic displacements on the electronic system. The electronic structure is calculated in the framework of the local density approximation. Starting from a local ionic pseudopotential a self-consistent pseudopotential band calculation is performed to find the electron wave functions and energies. The lattice constant is not taken from experiment but obtained from minimali nation of the total crystalline energy with respect to ionic displacements. The convergence of the phonon frequencies as a function of the number of reciprocal lattice vectors used in the Hamiltonian and in the linear response matrices is investigated in detail. Because the programs to mare the above described calculations take a large amount of computer time the codes have been vectorized during the past year. They were executed on a CDC Cyber 205 (1-pipe, 2 M words) giving a gain in time (with respect to the scalar mode) by a factor 5. This number refers to the whole program. In some parts the factor was as high as 45.
KeywordsIonic Potential Local Density Approximation Phonon Frequency Electron Wave Function Hamiltonian Matrix
Unable to display preview. Download preview PDF.
- 4.J.A. Appelbaum, D.R. Hamann, Phys. Rev B8, 1777 (1973).Google Scholar
- 7.P.E. Van Camp, V.E. Van Doren, J.T. Devreese,Phys. Rev. B24, 1096 (1981)Google Scholar
- 9.P.E. Van Camp, V.E. Van Doren, J.T. Devreese in “Ab-initio Calculation of Phonon Spectra”, eds. J.T. Devreese, V.E. Van Doren, P.E. Van Camp, Plenum, New York (1983)Google Scholar
- 10.P.E. Van Camp, V.E. Van Doren, J.T. Devreese in “Proceedings of the 6th General Conference of the European Physical Society”, Prague, to be published (1984).Google Scholar
- 11.CDC-Cyber 200 Fortran Version 2 Reference Manual, publication number 60485000, Sunnyvale, Ca. (1981).Google Scholar
- 12.J. Donahue, “The Structure of the Elements”, Wiley, New York (1972).Google Scholar