DETERMINING THE ELECTRONIC-PROPERTIES OF SEMIINFINITE CRYSTALS

A self-consistent method for the calculation of the electronic structu re of crystalline surfaces is described. It is based on a semi-infinit e geometry with individual surface atomic layers stacked onto an infin ite number of bulk layers. Contrary to models based on slab or superla ttice geometries there is no artificial distortion of the correct asym ptotic behavior of the wave functions so that an exact distinction bet ween surface and bulk effects is possible. Furthermore there are no pr incipal restrictions on the shape of the self-consistent potential. A special form of wave-function matching is used to construct the discre te surface states as well as the continuum of bulk states from complet e sets of solutions of the Schrodinger equation in each single layer. The semiinfinite substrate is treated as a whole by means of the compl ex band structure which appears as an easily obtainable side-product o f the theory. The main improvement at this step is the complete avoida nce of the inherent numerical instability which prevented the applicat ion of similar matching techniques to other than very simple materials so far. The layer solutions of the Schrodinger equation are obtained by means of the spline-augmented-plane-wave method providing very accu rate wave functions. As a first application the (001) and (111) surfac es of aluminum were investigated. The results obtained include the sel f-consistent charge density, the work function, and the complete band structure of the surface states and resonances. All calculations are f ound to be in good quantitative agreement with experiment. [S0163-1829 (98)00124-6].