Vacuum/volume 41/numbers 1-3/pages 602 to 604/1990 0042-207X/9053.00 + .00 Printed in Great Britain © 1990 Pergamon Press plc Structure and energetics of Ge(111 )c(2 x 8) reconstruction W S Verwoerd and P Badziag, Department of Physics, University of South Africa, P.O Box 392, Pretoria 0001, Republic of South Africa We present self-consistent MNDO calculations of atomic clusters modelling the structure of adatom generated 2 x 2, ~/3 x x/3 and 2 x 8 reconstructions of the Ge(l 11) surface. Comparisons are made of the T4 and H3 adsorption sites and of closed shell singlet and open shell (spin triplet) RHF wavefunctions. We find that ~/3 x ~/3 prefers the T4 site energetically, but 2 x 2 prefers H3. Subsurface relaxation up to three layers deep plays a crucial role in the energetics and we also find significant charge transfers between rest atoms and adatoms as well as between layers. A consistent interpretation can be given of the similarities and differences between the configurations in terms of bond rehybridization and polarization effects as well as the different surface topologies. Introduction Considerable experimental '-6 and some theoretical 7 effort has been expended to understand the c(2 x 8) reconstruction of the Ge(111) surface, establishing a simple adatom model in a three- fold coordinated site, but the details remain uncertain. In particu- lar, it is not yet clear whether the adatom site is on top of the second layer (T4), or rather on the hollow above the fourth layer (H3). Furthermore, neither the role of charge redistribution close to the surface, nor the relation between the c(2 x 8) adatom terminated and the surface terminated by foreign atoms (usually in a x/3 x ,,/3 pattern) have been investigated in detail so far. This contribution addresses these unresolved issues from the point of view of semiempirical (self-consistent electronic struc- ture) total energy atomic cluster calculations. First we present the method of calculation and describe the investigated surface structures and model clusters, then the numerical results are listed and discussed, and finally the conclusions are summarized. Calculation and results We model the surface by atomic clusters representing a surface unit cell (SUC) and containing two to four atomic layers. The atomic geometry which minimizes the energy is calculated, subject to symmetry constraints appropriate to the correspond- ing surface periodicity. The energy calculation is done fully self consistently using the MOPAC 8 implementation of the MNDO 9 quantum chemical molecular Hamiltonian. Compared to previous surface cluster calculations, we use two innovations. Firstly, using the polymer options of the MOPAC program, the cluster is periodically repeated along one surface mesh unit vector, so that it represents an infinite ribbon from the surface. Secondly, the bonds embedding the ribbon in the crystal lattice are saturated by artificial 'capped bond' atoms (CB's). These are parametrized in MOPAC to form perfect covalent bonds, eliminating the problem of a polarized boundary which would occur with traditional bond saturating hydrogen atoms. By careful choice of the CB bond distance we have succeeded in 602 reducing all Ge atomic net charges in fully saturated bulk-like clusters to well below 0.1 e, which sets an accuracy standard for charge assignments calculated in the surface clusters. We have used two families of molecular clusters. The 2 x 2 and ~/3 x x/3 cases are modelled by including four 'substrate' atomic layers plus the adatoms, totalling about 22 Ge atoms. For the larger 2 x 4 and 2 x 8 unit cells we can only include two substrate layers, and have confirmed by repeating the 2 x 2 case with these shallow clusters that consistency with the deep clusters is maintained. In Figure 1 we show examples of the relation between the ribbon-like clusters used and the various reconstruction patterns modelled. In all clusters, the deepest layer is kept fixed, while atoms in all other layers are allowed to move vertically and first layer atoms are in addition free to move radially towards the adatom. The calculations reported here are based on restricted Hartree- Fock (closed shell singlet) wavefunctions. We also repeated the calculations with wavefunctions representing singly occupied dangling bond (open shell) states. No detailed conclusions could be made from the latter about the relative energies of the two kinds of states, because of certain inconsistencies in the open shell energy values, to be discussed in more detail elsewhere. Neverthe- less the atomic displacements, charges and hybridization in the open and closed shell calculations turn out to be quite similar and the results discussed below apply at least quantitatively to the open shell states as well. A comparison of our results for closed and open shell states, T4 and H3 sites, and x/3 × x/3 and 2 x 2 reconstruction patterns, may be summarized as follows: (a) The relative ordering of the four sites investigated, is the same for closed shell and open shell states. (b) The 2 x 2 reconstruction has a lower surface energy than the ,,/3 x ,,/3, in agreement with observation. (c) For x/3 x x/3, the T4 (on top) site is most favourable, as observed for foreign adatoms and as calculated by Northrup ~° also for Si(111)x/3 x x/3.