VOLUME 86, NUMBER 16 PHYSICAL REVIEW LETTERS 16 APRIL 2001 Subsurface Dimerization in III-V Semiconductor (001) Surfaces C. Kumpf, 1, * L. D. Marks, 2 D. Ellis, 3 D. Smilgies, 1 E. Landemark, 1 M. Nielsen, 1 R. Feidenhans’l, 1 J. Zegenhagen, 4 O. Bunk, 5 J. H. Zeysing, 5 Y. Su, 5 and R. L. Johnson 5 1 Condensed Matter Physics and Chemistry Department, Risø National Laboratory, DK-4000 Roskilde, Denmark 2 Department of Material Science and Engineering, Northwestern University, Evanston, Illinois 60208 3 Department of Chemistry, Northwestern University, Evanston, Illinois 60208 4 European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France 5 II. Institut f ür Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany (Received 21 September 2000; revised manuscript received 17 January 2001) We present the atomic structure of the c8 3 2reconstructions of InSb-, InAs-, and GaAs-(001) surfaces as determined by surface x-ray diffraction using direct methods. Contrary to common belief, group III dimers are not prominent on the surface, instead subsurface dimerization of group III atoms takes place in the second bilayer, accompanied by a major rearrangement of the surface atoms above the dimers to form linear arrays. By varying the occupancies of four surface sites the 001-c8 3 2 reconstructions of III-V semiconductors can be described in a unified model. DOI: 10.1103/PhysRevLett.86.3586 PACS numbers: 68.35.Bs, 61.10.–i, 81.05.Ea The (001) surfaces of III-V compound semiconductors show a wealth of surface reconstructions that play an important role in both homoepitaxial and heteroepitax- ial growth. Knowledge of the atomic structure of these surfaces is particularly important because a wide variety of high-speed electronic and optoelectronic devices used in communications technology and fundamental studies (e.g., quantum transport) are fabricated on (001) wafers. It is generally believed that the basic building blocks in these reconstructions are dimers [1]. The presence of group V dimers on V-rich surfaces has been clearly es- tablished, e.g., Sb dimers on the InSb001-c4 3 4sur- face by scanning tunneling microscopy (STM) [2], and As dimers on InAs001-b2-2 3 4by surface x-ray diffrac- tion (SXRD) [3]. It has been assumed that group III dimers are the primary structural element on III-rich (001) surfaces [4–10] as suggested in the early STM study by Biegelsen et al. on in situ grown GaAs(001) surfaces [4]. However, on the Ga-rich surface it is difficult in STM to es- tablish whether the features attributed to dimers are really made up of one or two atoms. If dimers at the surface are not the key structural element in III-rich surfaces, a sub- stantial rethinking of the physics of III-V compound semi- conductor surfaces would be required. Our surface x-ray diffraction results presented here demonstrate that this is indeed the case, since an essential part of the structure is subsurface dimerization of group III atoms in the second bilayer accompanied by the formation of linear chains of the atoms in the topmost layer. A fundamental difficulty in structure determination is to identify whether the correct solution, i.e., the global mini- mum, or a local minimum, of the goodness-of-fit function has been found. For 3D structure determination with x-ray diffraction the ambiguity has been largely removed by us- ing what are called direct methods [11]. Direct methods find probable values for the phases of the measured reflec- tions, consistent with the atomicity of the crystal structure. Combining the phases with the measured amplitudes al- lows approximate charge density maps to be calculated, and placing atoms at the peaks in these maps yields a good approximation to the structure. Direct methods elimi- nate the need to guess starting models for the structural refinement. While direct methods have been used success- fully on two-dimensional SXRD or transmission electron surface diffraction data [12,13], extending them to three- dimensional SXRD data is not simple. We have recently shown that the mathematical approach of “feasible sets” [14] developed for image restoration problems can be ap- plied to crystallographic problems [15], permitting addi- tional constraints to be introduced that enable full, ab initio surface structure determination to be performed in three dimensions [16]. Since this is a truly model-independent approach, group III dimers will arise only in the data analysis if they are an intrinsic part of the structure. All samples, GaAs, InAs, and InSb, were prepared in an ultrahigh vacuum (UHV) system by sputtering and an- nealing cycles as described in the literature [7,8]. STM images were measured prior to the SXRD measurements and were consistent with the images in the literature [7,8]. After preparation the samples were transferred to a small UHV chamber and brought to the BW2 wiggler beam line at Hamburg synchrotron radiation laboratory (HASYLAB) for the x-ray measurements. Extended in-plane and out-of- plane data sets were measured on all three systems at wavelengths between 1.24 and 1.42 Å. The intensity of each reflection was measured in a rocking scan by rotat- ing the sample about its surface normal (v scan). The scans were integrated, background subtracted, and cor- rected for the Lorentz factor, polarization factor, active sample area, and rod interception [17]. In the zinc-blende structure the III-terminated (001) surface has twofold rota- tional symmetry so there was only a single rotational do- main. By averaging equivalent reflections using a c2mm symmetry, systematic errors in jFj 2 of 7.2%, 7.8%, and 3586 0031-900701 86(16) 3586(4)$15.00 © 2001 The American Physical Society