PHYSICAL REVIEW B VOLUME 59, NUMBER 15 15 APRIL 1999-I Structure and oxidation kinetics of the Si„100…-SiO2 interface Kwok-On Ng and David Vanderbilt Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849 ~Received 28 October 1998! We present first-principles calculations of the structural and electronic properties of Si~001!-SiO2 interfaces. We first arrive at reasonable structures for the c-Si/a2SiO2 interface via a Monte Carlo simulated annealing applied to an empirical interatomic potential, and then relax these structures using first-principles calculations within the framework of the density-functional theory. We find a transition region at the interface, having a thickness on the order of 20 Å, in which there is some oxygen deficiency and a corresponding presence of suboxide Si species ~mostly Si12 and Si13). Distributions of bond lengths and bond angles, and the nature of the electronic states at the interface, are investigated and discussed. The behavior of atomic oxygen in a-SiO2 is also investigated. The peroxyl linkage configuration is found to be lower in energy than interstitial or threefold configurations. Based on these results, we suggest a possible mechanism for oxygen diffusion in a- SiO2 that may be relevant to the oxidation process. @S0163-1829~99!08115-1# I. INTRODUCTION model would introduce significant stress across the interface. A very recent paper by Pasquarello et al.18 has used first- Understanding the atomic structure of ultrathin silicon di- principles molecular dynamics to generate a model interface oxide films on Si~100! substrates is an outstanding problem structure. The generated structure reveals an unexpected ex- of great importance for microelectronic applications.1,2 The cess of silicon atoms at the interface, but it shows no bond- thickness of these films in commercial devices has dropped ing defects. A recent experimental paper suggests an abrupt well below 100 Å. Film thicknesses of 40 Å and below are interface model,19 as opposed to the graded interface sug- now being explored in experimental devices. Although such gested from earlier papers.8,9 Additional uncertainty has been ultrathin oxide films are in wide use, and considerable infor- generated by other studies about the interpretation of the mation about them has been amassed using a variety of dif- suboxide peaks observed.12,13 ferent experimental techniques,1,3–6 there is little consensus Another aspect that is of great interest is the oxidation about the microscopic structure and oxidation kinetics of the kinetics for thin films. The formation of thick oxide films films. Among the factors that have so far hindered detailed (.200 Å! is well-described phenomenologically by the 20 studies of the interface are the amorphous nature of the SiO2 Deal-Grove model, in which molecular oxygen diffuses to region, the difficulty of probing a buried interface, and the the SiO2 /Si interface and reacts with silicon at the interface. dependence of sample properties on preparation conditions. This model predicts a parabolic dependence of oxidation As a result, several issues relating to the detailed chemical time versus oxide thickness. However, it is well known that structure of the interface, and to the oxidation mechanism of the Deal-Grove model breaks down for the case of ultrathin thin oxide films, continue to be controversial. films (,100 Å!; in this case, the oxidation kinetics have Photoemission spectroscopy ~PES! or x-ray photoelectron been shown to be faster than would be expected from the spectroscopy ~XPS! have been the major experimental tech- linear relationship.5,14,21,22 However, there is little consensus niques used to study the interface structure. These experi- about the mechanisms of oxidation kinetics in this case. Sev- ments indicate the presence of a transition region of suboxi- eral phenomenological models have been proposed.22–24 dized Si near the interface, with all three intermediate partial Some of them fit the experimental data on oxidation kinetics oxidation states observed. However, different experiments quite satisfactorily with a large number of fitting parameters. suggest conflicting pictures of the structure.7–13 For example, However, most of the models are without direct experimental PES experiments indicate that the total suboxide is about two support. An analysis of kinetic results alone does not allow monolayers,7,8 while XPS results suggest it is 1-ML thick.9 one to distinguish among different models. A few key prob- Hattori11 argues in his paper that the total suboxide should be lems associated with the oxidation mechanism still remain 1 ML. Using medium-energy ion-scattering spectroscopy unresolved. For example, it is uncertain exactly where oxi- ~MEIS! to study the interface, Gusev and co-workers14,15 dation takes place, and the mechanism of oxygen diffusion have studied sequential isotopic exposures of oxygen and through the a-SiO2 region is not clear. found that the growth mechanism of interfaces depends on In this paper, we choose to address two main issues, the thickness of the films. Further complicating the task has namely, the microscopic structure of Si/SiO2 near the inter- been the lack of suitable interface models, which serve as face and the behavior of atomic oxygen in a-SiO2. First, we reference points for analysis of spectroscopic results. Theo- arrive at plausible structures for the Si/SiO2 interface by per- retical papers by Pasquarello et al.16,17 have attempted to forming Monte Carlo simulated annealing using an empirical construct interface models by attaching tridymite, a crystal- potential. Then we relax these structures and study their line form of SiO2,toSi~100!. Although different suboxide properties via first-principles density-functional calculations. states can be created, one would expect such an artificial We obtain the statistical distribution of suboxide species near 0163-1829/99/59~15!/10132~6!/$15.00PRB 59 10 132 ©1999 The American Physical Society PRB 59 STRUCTURE AND OXIDATION KINETICS OF THE . 10 133 the interface region, and find a graded transition region with a width of about 10 Å. Second, for excess atomic oxygen in a-SiO2, we compare the energy of the interstitial and peroxyl bridge configurations. It is found that the latter is always lower in energy. This suggests a possible mechanism of oxy- gen hopping among neighboring Si–Si bonds. The plan of the paper is as follows. Section II gives a brief description of the technique used to perform the calcu- lations. In Sec. III we present our study on the microscopic structure of the Si/SiO2 interface, and Sec. IV contains the results on oxidation kinetics of atomic oxygen in a-SiO2.We summarize the paper in Sec. V. II. METHODS Our theoretical analysis consists mainly of two parts. In the first part, we employ Metropolis Monte Carlo ~MC! simulations together with an empirical model potential rep- resenting the structural energies to arrive, via simulated an- nealing, at candidate structures for the c-Si/a-SiO2 interface. In the second part of the analysis, these candidate structures are relaxed and analyzed using first-principles plane-wave pseudopotential calculations. Because the structures of inter- est involve coordination changes, we have followed Hamann25 in employing a generalized gradient approxima- tion ~GGA! to the exchange-correlation potential, specifi- cally that of Perdew, Burke, and Ernzerhof ~PBE!.26 For use in generating the c-Si/a-SiO2 interface structures FIG. 1. The WWW bond-switching move ~Ref. 28! used in the within the MC approach, we designed a simple empirical- Monte Carlo simulations. ~a! Initial configuration. Atoms 1 and 4 potential model for the structural energy that is roughly are first neighbors, and atoms 1 and 7 are second neighbors. ~b! based on the formalism of Keating.27 The only degrees of After bond switch. Atoms 1 and 7 are now first neighbors, while freedom that appear in this model are the Si atom coordi- atoms 1 and 4 are second neighbors. nates; a direct Si–Si bond is designated as a ‘‘short’’ ~S! 28 bond, while a Si–O–Si bridge configuration is designated as rithm of Wooten, Winer, and Weaire ~WWW!. To random- ize the structure, one of the second neighbors of a randomly a ‘‘long’’ ~L! bond. In this way, the whole c-Si/a-SiO2 struc- ture is replaced by a network of ‘‘short’’ and ‘‘long’’ bonds chosen atom is switched to become its first neighbor, and between Si atoms. Its energy is taken to be that first neighbor becomes the second neighbor ~see Fig. 1!. Notice that the bonds being switched can be either S or L 1 1 bonds. For the bond conversion moves, a randomly chosen S E5 k~i!~d 2d~i!!21 k~ij!~c 2c~ij!!2. ~1! 2( r i 0 2( u ij 0 or L bond is swapped with a neighboring bond of opposite i iÞ j type. In all of the discrete moves, the total number of S and (i) L bonds are conserved, meaning that the number of oxygen The first term represents the bond stretching term, where kr (i) S 2 S atoms in the system does not change during the MC simula- and d0 take values kr 59.08 eV/Å and d052.35 Å for a L 2 L tions. After each move, the structure is relaxed within the ‘‘short’’ bond, or kr 51.89 eV/Å and d053.04 Å for a ‘‘long’’ bond. Similarly, the second term represents the Keating-like model, and the energy difference between the relaxed structures before and after the move is computed. bond-bending term, where k(ij) takes values kSS53.58 eV, u u The Metropolis algorithm is then employed to decide kSL53.81 eV, and kLL54.03 eV, where i and j are summed u u whether the new structure is to be accepted.