Electronic States near Surfaces - a) Analysis of calculation methods using semi-infinite boundary conditions; b) Sensitive detection using laser photoelectron spectroscopy

Abstract

Photoelectron spectroscopy with pulsed laser excitation can provide a low-background, sensitive view of electronic states in the band gap and photo-populated states above the Fermi level. Measurements of photoelectron emission for ultra-high vacuum cleaved surfaces of CdSe, excited by 4.5 and 5.9 eV Ti:sapphire laser pulses of 150 femtosecond duration are reported. One- and two-photon excitation processes are observed and analyzed in terms of features of the electronic structure. In order to distinguish defect and surface contributions from the bulk properties of these systems, computer modeling methods are needed. The "SI-PAW" method is designed to solve the Kohn-Sham equations within the projector augmented wave "PAW" formalism with boundary conditions appropriate for the semi-infinite geometry of material surfaces. This method, which directly distinguishes between bulk, surface, and defect states, is an extension of the very successful Appelbaum-Hamann method, modified to accommodate non-local potential terms in the PAW formalism. In the bulk region, the wave functions are composed of linear combinations of Bloch waves of the converged self-consistent periodic lattice. In the vacuum region, the wave functions are composed of functions which decay or propagate into the vacuum. In the interface region, the wavefunctions are composed of extensions of the Bloch wavefunctions or surface states which decay into the material. The interface wavefunctions are determined by putting the Kohn-Sham equations in the form of boundary value problems, using the Numerov algorithm to approximate the differential equations and the GMRES algorithm to solve them efficiently.