Letter Atomistic simulation of SrTiO 3 and BaTiO 3 (110) surface relaxations E. Heifets a, * , E.A. Kotomin b,c a Materials and Processes Simulation Center, Beckman Institute, Caltech, Pasadena, CA 91125, USA b Fachbereich Physik, Universita Èt Osnabru Èck, D 49069 Osnabru Èck, Germany c Institute of Solid State Physics, University of Latvia, Kengaraga Strasse 8, Riga LV-1063, Latvia Received 21 June 1999; accepted 25 August 1999 Abstract The (110) surface relaxations were calculated for SrTiO 3 and BaTiO 3 perovskites in a cubic phase. Using a shell model, the positions of atoms in 16 near- surface layers placed atop a slab of rigid ions are calculated. The strong surface rumpling and induced surface dipole moments perpendicular to the surface are predicted for both the O-terminated and TiO-terminated surfaces. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Atomistic simulation; Surface and interface states 1. Introduction Thin ferroelectric ®lms are important for the development of high capacity memory cells, catalysis, optical wave- guides, integrated optics applications. They are also widely used as substrates for the cuprate superconductor growth [1± 3]. For many of these applications (e.g. epitaxial ®lm growth) the quality of surface structure is obviously impor- tant. In this Letter, we calculate the atomic structure of the SrTiO 3 and BaTiO 3 (110) surfaces in a cubic (paraelectric) phase of crystals. It should be reminded that at all tempera- tures bulk SrTiO 3 exhibits paraelectric properties whereas BaTiO 3 makes a transition from paraelectric to ferroelectric phase as the temperature decreases. Recently several ab initio studies were published for the (100) surface of these two crystals where a few near-surface planes were allowed to relax [4,5]. Due to many atomic coordinates to be calcu- lated, such calculations are very complicated and time consuming. An alternative approach is to use a classical, shell model (SM) [6]. This semiempirical approach has been very successfully used for many years for defect calcu- lations in the perovskite bulk [7±12]. The SM was very recently applied by us to the calculations of (100) surface relaxations for BaTiO 3 [13] and SrTiO 3 [14,15]. We discov- ered in these studies that approximately six near-surface planes are considerably disturbed as the surface is created, i.e. atoms are strongly displaced from their regular lattice sites. This results in appearance of a dipole moment perpen- dicular to the surface, even in a cubic phase of perovskite crystals. The great SM advantage is that it is well suited for the treatment of the polarization effects which are important for our study. A comparison of our SM results [13±15] with mentioned two ab initio calculations [4,5] and experimental low- energy-electron diffraction (LEED) study for SrTiO 3 (001) surface [16] clearly demonstrates [17] their good agreement for both the displacements of surface metal and oxygen atoms in opposite directions (the so-called rumpling) from their Ti-O perfect-plane sites and relative displacements of the second and third planes. This encouraged us in this study to perform calculations for more advanced (110) surfaces of these two crystals. The (110) surface was a subject of recent experimental studies using STM and UPS, XPS spectro- scopes [18] as well as Auger spectroscopy and LEED [19,20]. The atomic and electronic structure of (110) surface was found to be strongly dependent on the annealing temperature. We are not aware of any theoretical calcula- tions of the BaTiO 3 and SrTiO 3 (110) surfaces. In this pilot study we used an idealized model for a perfect and ¯at surface (see below). In particular, we focus on the rumpling effect since this is known to be quite considerable in many oxide crystals. For instance, an ab initio Hartree-Fock study of O relaxation on MgO (110) surface estimates it as large as 7% of the interlayer distance [21]. Sometimes oxide surface relaxation can reach even <70% (for the Al-terminated corundum surface [22]). Thin Solid Films 358 (2000) 1±5 0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S0040-6090(99)00686-0 www.elsevier.com/locate/tsf * Corresponding author. Tel.: 11-626-395-2722; fax: 11-626-585- 0918. E-mail address: heifets@wag.caltech.edu (E. Heifets)