Geometry and electronic structure of GaAs001…„24reconstructions W. G. Schmidt* and F. Bechstedt Friedrich-Schiller-Universita ¨t, Institut fu ¨r Festko ¨rpertheorie und Theoretische Optik, Max-Wien-Platz 1, 07743 Jena, Germany Received 23 May 1996 Structural and electronic properties of the As-rich GaAs00124reconstructions are investigated by means of converged first-principles total-energy calculations. For an As coverage of =3/4, we find the two-dimer 2 phase to be energetically preferred over the three-dimer phase. As the As chemical potential decreases, the phase of GaAs001represents the ground state of the surface. All geometries are character- ized by similar structural elements as As dimers with a length of about 2.5 Å, dimer vacancies, and a nearly planar configuration of the threefold-coordinated second-layer Ga atoms leading to a steepening of the dimer block. Consequently, the resulting electronic properties also have similar features. The surface band structures are dominated by filled As-dimer states and empty Ga dangling bonds close to the bulk valence- and conduction-band edge, respectively. The measured Fermi-level pinning cannot be related to intrinsic surface states. The calculated surface states and ionization energies support the 2 structure as the surface geometry for an As coverage of =3/4. S0163-18299604248-8 I. INTRODUCTION The GaAs001surface is one of the most studied polar semiconductor surfaces and has attracted much interest of both experimentalists and theoreticians because of its impor- tance for the growth of multilayer device structures. As-rich 24/c 28reconstructions, in which the surface is mainly terminated by various arrangements of As dimers are most important in molecular-beam epitaxy MBEof GaAs- based layered structures. Three different phases of the 2 4 surface have been identified by reflection high-energy electron-diffraction experiments. 1–3 The , , and phases correspond to a characteristic ratio of fractional order intensities. On grounds of a comparison with scanning tunneling microscopy STM images, Hashizume et al. 2,3 concluded that all three phases have the same outermost surface layer of the unit cell, which consists of two As dimers and two dimer vacancies. The phase is described by the two-dimer model of Farrel and Palmstro m 1 with a significant relaxation of the second-layer Ga atoms cf. Fig. 1. The phase corresponds to the two- dimer model originally introduced by Chadi, 4 which is char- acterized by an additional As dimer in the third layer. Ac- cording to the notation of Northrup and Froyen, 5 this structure will be called 2 in the following cf. Fig. 1. The phase was found to be a mixture of the phase and the c 44phase with the surface As coverage varying depend- ing on the actual growth conditions. On the other hand, three and two As dimers in the outermost surface layer in 2 4 unit cells are seemingly observed by STM Refs. 6–8and explained by the and structures shown in Fig. 1. Both the three-dimer structure and the two-dimer 2 structure correspond to the same As coverage of =3/4. Ab initio calculations by Ohno 9 and Northrup and Froyen 5 came to opposite conclusions concerning their energetical stability. Also the atomic structure of the phase is not clear. Northrup and Froyen 5 observed a dimerization of the second- layer Ga atoms in agreement with the early prediction by Chadi, 4 but in contrast to Ohno, 9 who ruled out a Ga-Ga bonding for the phase. There is also a lack of consensus on other structural details. Recent STM studies 8 indicated an apparent twisting of the As dimers in the structure. How- ever, symmetric dimers are found to be in best agreement with x-ray photoelectron diffraction XPDdata. 10 A rather wide range of As-As dimer bond lengths is reported. XPD studies 10 indicate a dimer length of 2.2 Å, energy-dependent photoelectron diffraction experiments 11 determined a value of 2.4 Å, and secondary-ion mass spectrometry investiga- tions 12 found the As dimer atoms to be 2.73 Å apart. An early theoretical study 13 considering As-As dimers in 2 1 surface unit cells predicts a dimer length of 2.52 Å. Recent ab initio calculations 14,15 state values of 2.39 and 2.60 Å, respectively. Other structural parameters as interplanar dis- tances and relaxations in deeper layers are even less well known than the precise dimer length and symmetry. Relatively little is known about the electronic structure of the GaAs001surface. The 2 4 reconstruction models con- sidered in this work satisfy the electron counting rule, i.e., the dangling bonds are filled on surface anions and are empty at surface cations. 16 The surface band structure should be semiconducting rather than metallic since there exists no partly occupied surface state. However, work function measurements 17 on p - and n -type samples indicate a Fermi- level pinning. Irrespective of the type of reconstruction the Fermi level lies about 0.5 0.1 eV above the valence-band maximum VBM. 18 Defects, in particular kinks, were made responsible for the band bending. 19 In contrast to the con- stant Fermi-level position for the different phases, a small dependence of the ionization energy on the reconstruction model was observed. 20 It assumes its maximum for the phase of the GaAs00124reconstructions. The occupied surface bands of the 24reconstruction have been mapped by angle-resolved photoemission spectroscopy ARPES. 21,22 Larsen et al. found weakly dispersive states with sp z char- acter in the energy range 0.5–1.6 eV below the VBM and a nearly dispersionless state near -3 eV. By applying the scat- tering theoretical method based on an empirical tight-binding TBscheme, these features were attributed to asymmetric PHYSICAL REVIEW B 15 DECEMBER 1996-I VOLUME 54, NUMBER 23 54 0163-1829/96/5423/167427/$10.00 16 742 © 1996 The American Physical Society