First Principles Calculation of the Energy Band Structure of Diamond

Abstract

A first principles calculation of the energy band structure of diamond is performed using a muffin tin potential constructed from atomic functions and including the parametrized exchange term due to Slater. The crystal wave functions are expanded in 2s and 2p like functions obtained by integrating the Schrodinger equation for a single atom with a potential equal to the muffin tin potential inside the muffin tin radius and a constant elsewhere. The method gives a good valence band but a poorer conduction band. Excludiiig three centre integrals, varying the parametcr in the exchange term and altering the electron configuration of the carbon atom does not appreciably change the band structure. Finally, including non muffin tin parts of the crystal potential improves the conduction band.Es wird eine Berechnung der Energiebandstruktur von Diamsnt von ,,first principles" aus mit einem ,,muffin-tin"-Potential aus Atomfunktionen und mit dem parametrisierten Anstauschterm nach Slater durchgefuhrt. Die Kristallwellenfunktionen werden nach 2s-und 2p-Funktionen entwickelt, die durch Integration der Schrodingergleichung fur ein einzelnes Atom mit einem ,,muffintin"-Potential innerhalb des ,,muffin-tin"-Radius und einer Konstante aunerhalb davon erhalten werden. Die Methode liefert ein gutes Valenzband jedoch ein schlechteres Leitungsband. Eliminierung von Dreizentrenintegralen, Variation der Parameter im Austauschterm und h d e r u n g der Elektronenkonfiguration der Kohlenstoffatome iindern die Bandstruktur nicht wesentlich. SchlieBlich l l B t sich durch Einbeziehung von nicht ,,muffin-tin"-Anteilen des Kristallpotentials das Leitungsband verbessern.

Electron state associated with the unreconstructed (111) surface in diamond

“…As the method has been described in detail elsewhere [7] we only repeat the major steps in the calculation of the Slater-Koster parameters. Starting with atomic functions we evaluated the atomic electron density e. By solving Poisson's equation and adding the Coulomb term from the nucleus we obt,ained the atomic potential V,, The basis functions, qa, used in the expansion of the crystal wave functions were the 2s-and 2p-like solutions of the Schrodinger equation for a single atom with a potential equal to the muffin-tin potential inside the muffin-tin radius and constant elsewhere, i.e.…”

“…I n the present calculation we have used a set of first principles Slater-Koster parameters [7]. As self-consistency has proved to be important in surface calculations we made a second calculat,ion in which we included non-spherical parts of the crystal potential in the matrix elements for the surface atom.…”

Electron States Associated With Partial Dislocations in Diamond

“…As the method has been described in detail elsewhere [3] we only repeat the major steps in the calculation of the Slater-Koster parameters. Starting with atomic functions we evaluated the atomic electron density Q.…”

“…parallel to the dislocation line. The Slater-Koster parameters used were evaluated for a muffin-tin potential based on an atomic 2s2p3 configuration and the parameter (x in the Slater exchange term equal to 0.76 [3]. Interactions up to thirdnearest neighbours were considered.…”

“…As was reported in our previous paper [3] for diamond we have calculated a set of first-principles Slater-Koster parameters. I n the present paper we use the evaluated parameters to study dislocations in diamond.…”