An ab initio cluster study of the structure of the Si(001) surface

Abstract

Ab initio calculations, employing double zeta plus polarization (DZP) basis sets and generalized valence bond (GVB) wave functions, have been performed on clusters of varying size, to investigate the utility of such clusters as prototypes for the study of silicon surfaces, and to investigate the effect of the level of theory used on predicted results. This work builds on landmark papers by Goddard in 1982 and Paulus in 1998 that demonstrate that a single reference wave function description of the silicon dimer bond is incorrect, and that a multireference description results in a symmetric dimer in a silicon cluster containing one dimer. In this work, it is shown that the imposition of arbitrary geometrical constraints (fixing subsurface atoms at lattice positions) on cluster models of the Si(100) surface can also lead to nonphysical results. Calculations on the largest clusters, without geometrical constraints, reveal that surface rearrangement due to dimer bond formation is “felt” several layers into the bulk. The predicted subsurface displacements compare favorably to experiment. Thus, small clusters, such as Si9H12, cannot adequately represent bulk behavior. Vibrational analysis shows that dimer buckling modes require minimal excitation energy, so the experimental observation of buckled dimers on silicon surfaces may reflect the ease with which a symmetric dimer can be perturbed from its minimum energy structure. In the study of surface reconstruction and relaxation, and the associated issue of the buckling of dimer surfaces, it is critical to use adequate wave functions. As shown in this work and previously by Goddard and Paulus, this generally means that multireference treatments are needed to correctly treat the dangling bonds.