PHYSICAL REVIEW B 85, 205314 (2012) Microscopic mechanisms of initial oxidation of Si(100): Reaction pathways and free-energy barriers Kenichi Koizumi, 1,* Mauro Boero, 2 Yasuteru Shigeta, 3 and Atsushi Oshiyama 1 1 Department of Applied Physics, The University of Tokyo, Hongo, Tokyo 113-8656, Japan 2 IPCMS, UMR 7504 CNRS and University of Strasbourg, F-67034 Strasbourg 2, France 3 Department of Materials Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan (Received 2 February 2012; published 16 May 2012) Various reaction pathways and corresponding activation barriers in the initial oxidation of Si(100) surfaces are clarified by free-energy sampling techniques combined with the Car-Parrinello molecular dynamics. We find a crucial stable geometry which is ubiquitous during the oxidation and links the dissociation of O 2 molecules and the oxidation of subsurfaces. The calculated free-energy landscape provides a comprehensive picture of the various competing reaction pathways. DOI: 10.1103/PhysRevB.85.205314 PACS number(s): 68.43.Bc, 71.15.Pd, 81.65.Mq, 82.65.+r I. INTRODUCTION Oxygen is ubiquitous on earth and oxidation of materials is common in human life. The understanding of the oxidation process is thus fundamental to our knowledge of nature. In various stages in technology ranging from cutting edge miniaturization of semiconductor devices 1,2 to biocompatible applications, 3 oxide films of silicon are widely utilized to fabricate complex structures and also to generate functions of devices. In current semiconductor technology, 4 the thickness of Si oxide becomes less than 1 nm and a new class of materials named high k is combined with Si oxide to ensure its durability. 4–6 It is thus mandatory to get a comprehensive atomic-level insight into the mechanisms of the oxidation in order to clarify and tune the properties of the oxide films. After several pioneering theoretical works, 7–9 a realistic atomic-level insight about the Si oxidation was given by Kato and coworkers. 10,11 Their static density-functional calculations have shown that oxidation of the Si(100) surface proceeds via backbond oxidation. Recently, Ciacchi and Payne revisited the Si(100) oxidation process via first-principles molecular dynamics (FPMD) in the NVE ensemble. 12 Their results indicate a different thermally activated mechanism for the backbond oxidation, underscoring the importance of dynam- ical study. For the atomistic understanding of the oxidation process, however, it is imperative to identify reaction pathways for dissociation of oxygen molecules and then formation of Si-O bonds, and furthermore to obtain the corresponding free-energy barriers. Since the typical barrier is about a half eV or more, it is difficult to simulate these elementary processes by standard FPMD methods. To resolve the difficulty, we here investigate the reaction mechanisms of the initial oxidation processes on Si(100) by Car-Parrinello molecular dynamics (CPMD) simulations 13 combined with the blue moon (BM) ensemble 14 and the metadynamics (MTD) free-energy sampling approaches, 15,16 which have been shown to possess accuracy and versatility in a wide range of applications. 17,18 We find a crucial configuration which links the dissociation of O 2 molecules and further oxidation of subsurfaces. Detailed reaction pathways and corresponding free-energy barriers are provided for the first time. II. CALCULATIONS In the calculations, valence electrons are expanded in the plane-wave basis set with an energy cutoff of 70 Ry and the core-valence interaction is described by norm-conserving pseudopotentials. 19 All simulations are done within the gen- eralized gradient approximation 20 with a spin-unrestricted approach. The Si(100) surface is modeled by a slab of six Si layers and the exposed area corresponds to a c(4 × 4) surface, wide enough to allow for a sampling of the Brillouin zone to the Ŵ point only. Above the surface a vacuum space of 8.6 ˚ A allows for a good separation of repeated images of the simulation cell. The ionic temperature is controlled by Nos´ e-Hoover thermostat 21 in NVT simulations. III. RESULTS AND DISCUSSION A. Reaction pathways described by metadynamics We have first examined various configurations of an O 2 molecule on Si(100) via unconstrained NVT simulations at 300 K, since experiments suggest an initial oxidation occurring at room temperature. 22 Our results confirm the findings of Ref. 11 within an error bar of 1%: namely an O 2 dissociation energy of 5.66 eV and an adsorption energy of O 2 to a Si dimer at the Si(100) of 2.92 eV. We have then investigated the dissociation of O 2 from the most probable O 2 configuration in which both O atoms are absorbed on top of a dimer [the minimum (A) configuration of Fig. 1(c)] by using MTD. To this aim, we use two different sets of collective variables (CVs) in our MTD simulations. In the first case, the CVs are the two distances between each of the two O atoms and the center of the closest Si-Si bond in the first layer, as shown in Fig. 1(a). In the second case, the two CVs are the distances between each of the two O atoms and the nearest Si atoms belonging to the first layer [Fig. 1(b)]. Each MTD simulation lasted for about 70 ps, to ensure a good convergence of the free-energy sampling as specified in Ref. 23. Both simulations result essentially in an identical reaction pathway. Specifically, the chemical bond between the two O atoms is cleaved and the O atom bound to the upper Si atom of the Si-Si dimer moves toward the backbond site. Simultaneously, the second O atom is displaced very rapidly into the on-dimer site, as shown in the minimum (B) configuration of Fig. 1(c). This process can be 205314-1 1098-0121/2012/85(20)/205314(4) ©2012 American Physical Society