Multiscale modeling of the silicon oxidation process Angelo

Multiscale modeling of the silicon oxidation process Angelo Bongiorno and Alfredo Pasquarello

Outline I. III. IV. V. Introduction Oxygen diffusion through the oxide layer Structure of the Si(100)-Si. O 2 interface Oxidation reaction at the interface Conclusion

transition region Introduction MOS amorphous Si. O 2 poly-Si Si. O 2 Si 20 Å Si. Ox distorted Si crystalline Si The structure of the Si(100)-Si. O 2 interface The silicon oxidation process

The silicon oxidation process O 2 incorporation (h) Si. O 2 Si diffusion (D) reaction (k) e v o r l-G l e d mo Dea Exp. ~ 10 nm ØThe Deal-Grove model fails in the thin oxide regime ! ØNo atomistic insight ØLack of model interfaces matching experimental data

Multiscale approach Diffusion through the oxide layer Ø Ø oxidizing species diffusion mechanism energy landscape in a-Si. O 2 long-range diffusion in a-Si. O 2 Interface structure First-principles Classical / MD Lattice model / MC Oxidation reaction Ø c-Si/a-Si. O 2 interface Ø realistic model interfaces Ø oxidation reaction First-principles / classical MD / MC First-principles

Diffusion through the oxide layer Ø First-principles calculations (DFT/GGA) Ø O 2 is the most stable oxygen species in a-Si. O 2 Void distribution O 2 -O-O-O-

The diffusion mechanism Ø Minima Ø Barriers Ø Connections

Models for amorphous Si. O 2 ØClassical molecular dynamics simulations ØInteratomic potentials for Si. O 2 (BKS, 1990) ØLarge set of models (24 - 48 Si. O 2 units)

Potential energy landscape ØClassical scheme ØO 2–Si. O 2: fitted to first-principles results ØTransition states: ART, Barkema-Mousseau (1997) Minima l=0. 6 e. V Barriers l=0. 9 e. V Connections

O 2 long-range diffusion in a-Si. O 2 Barriers ØMonte-Carlo simulations Minima ØWe map distributions on lattice models ØEa=1. 12 e. V , exp. : 1. 04 -1. 26 e. V Missing connections 1500 K 1200 K E = 1. 12 e. V 1000 K

The transition region at the interface Ømodel Si(100)-Si. O 2 interfaces matching: üTEM & X-ray scattering üX-ray reflectivity üElectrical & ESR üAngle resolved XPS Ønew ion-scattering experiments (L. C. Feldman) Øion-scattering simulations Si. O 2 Øinverse scattering problem Si. Ox Si Si

Model Si(100)-Si. O 2 interfaces Two-step procedure 1. Classical molecular dynamics 2. - suitable connection between oxide and Si substrate 2. First-principles scheme - suboxide distribution and structural optimization

The inverse scattering problem Exp. Theory Si distortions 0. 8 ML

A B Consistent with ion-scattering experiments C

The oxidation reaction ØRealistic model Si(100)-Si. O 2 interfaces ØFirst-principles calculations ØConstrained molecular dynamics: - dragging towards the interface - dissociating the O 2 species ØNeutral and negatively charged O 2 O-O Si

O 2 at the Si(100)-Si. O 2 interface ØRegardless both the spin and charge state ØEincorp : 0. 0 -0. 4 e. V ~ kb. T (T=1000 o. C) ØEdiss : 0. 1 -0. 4 e. V O 2 approaches the interface O 2 incorporates in the network O 2 dissociation

Conclusions The silicon oxidation process ØO 2 hops between nearest neighbours interstitials of the oxide network. ØThe long range diffusion is a percolation process with an activation energy of 1. 12 e. V. ØAt the interface the oxidation reaction is nearly spontaneous. The Si(100)-Si. O 2 interface ØRealistic model Si(100)-Si. O 2 interfaces ØThe bond pattern at the interface ØAmount of Si distortions in the substrate