Theory of optical reflectance anisotropy of the natural Si„110… surface Bernardo S. Mendoza* Centro de Investigaciones en Optica, A.C., Leo ´n Guanajuato, Mexico Rodolfo Del Sole † Istituto Nazionale per al Fisicadella Materia, Dipartimento di Fisica, II Universita ` di Roma Tor Vergata, Rome, Italy Anatoli I. Shkrebtii ‡ Department of Physics, University of Toronto, Toronto, Canada Received 23 January 1998 We investigate theoretically the optical reflectance anisotropy of the natural Si110 surface, including the surface intrinsic anisotropy and the surface local-field effect. We model a rough Si110 surface, determining a number of defect structures by total-energy minimization. We show that a structure with missing Si atoms and partial H coverage gives a reflectance anisotropy in agreement with experiment, in contrast to previous calculations for the ideally H-terminated Si110 surface. We show that both the intrinsic anisotropy and the surface local-field effect are essential for such an agreement. S0163-18299851720-1 Reflectance anisotropy spectroscopy RAS is one of the few optical techniques that can probe the surface and inter- face structure of cubic materials. 1–7 It measures the differ- ence between the normal-incidence optical reflectance of light polarized along the two principal axes in the surface plane as a function of the photon energy. Since the bulk optical properties of cubic crystals are isotropic, any ob- served anisotropy must be related to the lower symmetry of the surface. RAS data are typically obtained in the visible- ultraviolet spectral range, thus providing information about electronic structure modifications due to the creation of the surface, reconstructions, adsorbates, etc. Theoretical calcula- tions of the reflectance anisotropy RA for a few important clean and adsorbate covered semiconductor surfaces are in reasonable agreement with experiments. 8–11 For a clean sur- face of a cubic semiconductor, an important contribution to the RA comes from surface states and surface recon- struction. 6,12 However, RA has also been found at the natural oxygen or hydrogen passivated unreconstructed Si110 surface, 1,7 where no optically active surface states are ex- pected in the frequency range of interest. In this case, the RA may arise due to the intrinsic anisotropy IA coming from the effect of wave-function termination at the surface, and to the surface local-field effect LFE. The LFE alone yields a RA in good agreement with experiment for the natural Ge110Ref. 13 and Si110Ref. 14 surfaces; while the calculated IA line shape is substantially different from the experiment. 8 On the other hand, when the two effects are combined for the ideal Si110:H, 14 the surface LFE modifies the IA line shape, making it closer to the experimental RA of the natural surfaces. However, relevant discrepancies with experiment still remain, especially above 4 eV. Hence, de- spite the definite progress of the theory for the clean and adsorbate covered well ordered surfaces, 8–11,15 the RA of the natural Si110 surface is not yet understood. Nevertheless, because of its stability and reproducibility, it has been pro- posed as a RAS standard. 16 Therefore, there is still a need to understand the physical mechanism underlying the RAS of natural Si110, and the purpose of this paper is to investigate systematically this surface. Actually, the key point seems to be in the prepara- tion of the samples. As Ye et al. have recently shown, 17 etch- ing is indeed crucial to preparing an ideal that is, well or- dered and ideally H-terminated Si110 surface. Depending on the etching time and conditions, one can go from an atomically rough surface to a practically ideal termination. Moreover, not only etching conditions, but also the hydroge- nation process, determines the surface structure. For in- stance, as Watanabe has recently shown, 18 hydrogenating the surface in hydrofluoric acid or in hot deoxygenated water gives a surface with missing Si atoms or ideally H covered, respectively. It seems that all available RAS measurements at natural Si110 have been performed on surfaces of the former type, that is with many defects. 1,7 In view of this evidence, we model the natural Si110 surface as a surface with atomic defects. We determine vari- ous defect structures by total-energy minimization and use them to calculate RA spectra according to the LFE-IA model. We show that a rough Si110 surface, with missing Si atoms and partial H coverage, produces a RA in good agreement with experiment. Following Ref. 14, we briefly sketch the procedure taken to calculate the RA. To model the semi-infinite crystal we use a slab consisting of N atomic 110 layers, extending from z =0 to z =Nd , d being the interlayer distance. We define the RA signal as S RA   R / R   01 ¯ 0 -  R / R   001  , 1 where we have taken the normally incident light to be polar- ized along 001 ( x ) or 11 ¯ 0 ( y ). Neglecting the LFE, the surface contribution to normal-incidence reflectance is given by 19   R / R  i =4   / c  Im 4  D  ii hs    /   B    -1   , 2 RAPID COMMUNICATIONS PHYSICAL REVIEW B 15 MAY 1998-II VOLUME 57, NUMBER 20 57 0163-1829/98/5720/127094/$15.00 R12 709 © 1998 The American Physical Society