Ab initio studies of adatom vacancies on the Si„111…-„7 7… surface H. Lim,* K. Cho, R. B. Capaz, and J. D. Joannopoulos Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 K. D. Brommer Lockheed Sanders, Box 868, Nashua, New Hampshire 03051 B. E. Larson † Silicon Graphics Computer Systems, 1 Cavot Road, Hudson, Massachusetts 01749 Received 15 March 1996 Ab initio total-energy calculations are used to investigate adatom vacancies on the Si111-77 surface. In striking contrast to recent experimental estimates, vacancy formation energies are calculated to be 0.9 eV on average, with 0.1-eV variations depending on the type of adatom. We find that faulted or corner adatoms can be removed more easily than unfaulted or edge adatoms, respectively. Structural relaxations induce large changes in the electronic structure of the surface states. Calculation of scanning tunneling microscopy STM images show that the predicted variations should be readily observed in differential STM measurements. S0163-18299605324-6 The Si111 surface is the natural cleavage surface for silicon crystals and the structure of the 111 surface recon- struction has been extensively studied both experimentally and theoretically. More than 35 years have passed since the first identification by low-energy electron diffraction LEED of the (7 7) symmetry after annealing of the 111 surface 1 and the understanding of the structure of this large recon- struction unit has been one of the most outstanding surface problems since then. Currently, the Takayanagi dimer- adatom-stacking-fault DAS structure is generally accepted as the correct model for the structure of the (7 7) reconstruction. 2 Because of the complexity of the (7 7) reconstruction, first-principles theoretical investigations of the 111 surface have been a challenging task. Recently, ab initio calculations have shown that the Takayanagi DAS structure is indeed a low-energy structure of the 111 surface. 3,4 Almost as im- portant as the determination of the equilibrium structures, however, is the understanding of the microscopic dynamical processes in the phase transition of the surface reconstruction from the (7 7) symmetry to the (1 1) at around 870 °C. The (7 7) reconstruction rearranges the three topmost surface layer atoms from the bulk-truncated surface, and one can easily imagine the complexity of the rearrangement pro- cess from the number of rearranged atoms in each (7 7) unit i.e., 102 atoms. Among these three layers, the top sur- face layer consists of adatoms, and each adatom is expected to be weakly bound to the surface atoms’ four strained back- bonds. Because of this weak binding, removal of the adatom layer will naturally initiate the complicated dynamical pro- cesses of the surface phase transition. In this paper, we investigate the formation of adatom va- cancies using total-energy pseudopotential calculations. The average adatom vacancy formation energy is found to be 0.9 eV, with small ( 0.1 eV variations for the four types of surface adatoms. These results are in marked contrast to ex- perimental estimates which lie around 0.4 eV. 5 We also pre- dict changes in the electronic structure of surface states in- duced by local modifications in geometry at the vicinity of the vacancy. These changes should be readily observable in differential scanning tunneling microscopy STM. I. CALCULATIONS Total-energy pseudopotential density-functional calcula- tions are performed with the ab initio molecular-dynamics scheme implemented on Thinking Machines CM-5. 6,7 The surface system is modeled initially by a slab geometry in a supercell containing an adatom layer plus four surface layers, with hydrogen saturation in the bottom layer. Corrections for errors introduced by the finite size of the unit cell in the normal direction are subsequently estimated by calculating the 77 total energy with four-layer and eight-layer slabs using a tight-binding total-energy scheme as suggested by Qian and Chadi. 8 A more detailed description of the surface geometry is given elsewhere. 3 Initially all silicon atoms except for the bottom layer are allowed to relax according to Hellmann-Feynman forces un- til the forces become smaller than 0.10 eV/Å. Subsequently, one of the adatoms is removed from the supercell and the remaining system is again allowed to relax under the same conditions. This procedure is repeated for the four different types of adatoms see Fig. 1: corner or edge adatoms on the faulted or unfaulted half of the unit cell. The adatom vacancy formation energy E vac is then calculated as E vac =E  7 7  +vac +E bulk -E  7 7  , 1 where E (7 7) is the total energy of the perfect surface, E (7 7) +vac is the total energy of the surface with a vacancy, and E bulk is the total energy of a bulk silicon atom. PHYSICAL REVIEW B 15 JUNE 1996-I VOLUME 53, NUMBER 23 53 0163-1829/96/5323/154214/$10.00 15 421 © 1996 The American Physical Society