1. Comparison of Si/SiO x Potentials for Oxidation Behaviors on Si Sang-Pil Kim, Sae-Jin Kim and Kwang-Ryeol Lee Computational Science Center Korea Institute of Science and Technology, Seoul, Korea PS-21

2. Introduction Simulations of Si and SiO 2 have been studied for a long time. As the size of gate oxide decrease, device performance is largely affected by Si/SiO 2 interface structure. http://www.intel.com/ Deal-Grove model report that below 10nm scale, molecular diffusion shows different feature. Not only diffusion tendency, other characteristic such as atomic structure, oxidization mechanism could be different in nanoscale. MD is effective tool for investigating atomistic scale behavior at the thin films.

3. MD Potentials for Inter-bonding System Metallic bond Covalent bond Ionic bond Modified EAM Modified TersoffInertGas ZBL, Moliere Lennard-Jones (LJ) Stillinger-Weber (SW) Tersoff Brenner (also hydrocarbon) Environment-dependent Interatomic potential (EDIP) Biswa-Hamann (BH) Born-Mayer-Huggins (BMH) Vashishta Beest-Kramer-van Santen (BKS) Demiralp-Cagin-Goddard (DCG) Tangney-Scandolo (TS) Tsuneyuki-Tsukada-Aoki-Matsui (TTAM) Embedded atom method (EAM) Effective medium theory (EMT) Glue-models TB-SMA Finnis-Sinclair EAM+ Electrostatic (ES) - Streitz-Mintmire - Zhou-Wadley Modified SW SW+BKS Augmented Tersoff Yasukawa Charge optimized many body potentials (COMB)

4. Difficult to describe interface because of - Different bonding style - Various phase & structure of SiO x - Charge problem - Reaction, interface definition …… What we want to see is atomic structure of interface between Si and SiO 2 MD Potentials for Si-O Si O O O O O O O O O O O O O O O O O O O O O O O O Si potentials - Tersoff : good for bulk - Strenger-Webber : good for dimers on surface SiO 2 potentials - Born-Mayer-Huggins(BMH), BKS, Buckingham Morse ……

5. Covalent-Ionic Potentials Covalent bond Ionic bond Stillinger-Weber (SW) Tersoff Brenner (also hydrocarbon) Environment-dependent Interatomic potential (EDIP) Biswa-Hamann (BH) Born-Mayer-Huggins (BMH) Vashishta Beest-Kramer-van Santen (BKS) Demiralp-Cagin-Goddard (DCG) Tangney-Scandolo (TS) Tsuneyuki-Tsukada-Aoki-Matsui (TTAM) Co-use of covalent and ionic potentials Modified covalent or ionic potentials Novel potentials for describing both system simultaneously Possible candidates We employed the effective interatomic potential which combines Tersoff + M-BMH vs. SW + BKS

6. Si Cutoff (c) (d) (e) (b) (a) O Si M-BMH with Tersoff Tersoff potential is used with for describing Si covalent bond. Oxygen and silicon atom within oxygen cutoff  M-BMH force-field Silicon atom beyond oxygen cutoff  Tersoff force-field (a)~(c) : M-BMH (d)~(e) Tersoff

7. M-BHM Potential Improved Born-Mayer-Huggins’ SiO 2 potential Based on Coulombic interaction of two particle with three body term Advantage - Useful at various SiO 2 crystal and amorphous structure. - Can be used with other elements. (silica, silicate glass and surfaces, alumina, water interactions with silica & silicate etc) Disadvantage : Atomic charge is fixed for each atom - Cannot describe Si covalent bonding. - Is limited in the system with unbalanced charge. 3-body interaction2-body interaction

8. Result - Tersoff + M-BMH Cutoff = 3.0 Å 1000 MDs 2000 MDs 3000 MDs

9. Jiang & Brown’s Suggestion (a) (b)(c) (a)Ionization energy: 1-body potential, contributed from each atom ‘i’ (b)Pair energy: 2-body potential, energy for the distance (c)Angular energy: 3-body potential, energy for the angle 1.Charge-transfer function 2.Bond-softening function 3.Ionization energy Three NEW components are introduced to describe mixed bonding between oxygen and silicon atoms Z. Jiang and R.A. Brown, Chem. Eng. Sci. 49, 2991 (1994) Z. Jiang and R.A. Brown, Phys. Rev. Lett. 74, 2046 (1995) SW (Si) + BKS (SiO x )

10. Result - SW + BKS 10 MDs 50 MDs 100 MDs 300 MDs

11. Future Works -Jiang & Brown’s suggestion is a suitable for simulating Si oxidation process. -Remained problems should be solved.  Exact force calculation in charge transfer function  Exact force calculation in one-body potential (Ionization potential)  Long-range force calculation by Ewald sum or erfc