Simulating Stm Images for the Gaas (110) Surface
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image does not match the theoretical predictions for atomic positions. One of the earliest examples concerns the graphitic surface. Based on the ideal surface of graphite, one would expect to see a honeycomb lattice; however, the first STM images yielded an image with half of the surface atoms missing. A possible explanation for this observation is straightforward: STM does not measure atomic positions. In graphite, the surface atoms are not equivalent in terms of their wave function character at the Fermi level. This difference can account for the STM observations [4]. Ag on the (111) surface of silicon provides another example. The bright spots in the STM image might be interpreted as arising from the Ag atoms. This appears not to be the case. Theoretical STM images yield a pattern in good correspondence to experiment, but the Ag atoms are not located at the bright spots. Again, the electronic structure dictates the emission pattern [5]. A final example concerns the symmetry of Si dimers on the free (100) Si surface. Experimentally, STM indicates a symmetric pattern; theoretically, the STM image should be asymmetric. The difference does not involve the electronic structure per se as the electronic structure is asymmetric. It is now believed that the STM tip alters the dimer geometry during the measurement [6]. These examples make it clear that without a complementary electronic structure calculation for the system in question the interpretation of STM images can be problematic. 49 Mat. Res. Soc. Symp. Proc. Vol. 492 © 1998 Materials Research Society
SIMULATING STM IMAGES We have applied the Tersoff-Hamann theory to generate STM images from the ab initio single-particle wave functions [3]. Within this formalism, the tunneling current is proportional to the local density of states at the tip position integrated over the energy range restricted by the applied bias voltage. hkElk(r)12 6(E - Efnk)dE.
I(r; V) OC±+E
To evaluate the tunneling current, we need to calculate the wave functions and eigenvalues for the surface in question. Our calculations for the electronic states were performed using the plane-wave pseudopotential method [7,8] within the local-density approximation [9,10].
To simulate the GaAs (110) surface, a slab geometry was used with periodic boundary conditions. We considered two geometries. One consisted of the free surface and the other consisted of a supercell to model a vacancy on the surface. The free surface can by modeled by a (1 x 1) surface unit cell. For the vacancy, the supercell was composed of a (4 x 2) surface unit cell. In both cases, the slab consisted of five atomic layers and five layers of "vacuum." The dangling bonds on one of the exposed surfaces (the bottom surface) were passivated
with fictitious hydrogens to minimize the interaction between two surfaces either through the atomic slab or across the vacuum region. For charged systems, a uniform compensating background was incorporated to maintain the charge neutrality of the supercell. We used Troullier-Martins pseudopotenti
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