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.
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