1. The Atomic-scale Structure of the SiO2-Si(100) Interface
Simulating the Mechanism of Thermal Oxidation of Silicon

2. Outline Limitations of the well-known Deal-Grove model
A short dip into the studies by Bongiorno, A., Pasquarello, A., Car, R., Hybertsen, M. S., and Feldman, L. C.
Comparison of results from the respective papers and general outcome

3. The Deal-Grove model and its limitations
Diffusion governed by Fick’s 1st law:
𝐹 1 = 𝐷 𝑂 2 𝐶 ∗ − 𝐶 0 𝑡 𝑠𝑙
Pathway: Diffusion of oxygen or water through stagnant gas layer, through formed oxide layer till reaction at the oxide-silicon interface.
Fluxes at gas-oxide interface, bulk oxide, and oxide-silicon interface.
Equilibrium: F1 = F2 = F3

4. The Deal-Grove model and its limitations
Thick oxide: 𝑡 𝑜𝑥 2 ≈𝐵(𝑡+𝜏)
Thin oxide: 𝑡 𝑜𝑥 ≈ 𝐵 𝐴 𝑡+𝜏
Model cannot describe:
Oxidation kinetics for thin films
Atomic diffusion
Dynamic motion of bond formation

5. Papers 1. 3. 4. 2.

6. Questions and methods 1.
How does the Si-SiO2 interface appear?
Create interface by ab initio M.D. Let oxide and silicon substrate react by a thermal gradient, quench and relax.
Observe mechanism of oxide layer growth. 2.
How does the Si-SiO2 interface appear?
Combine ion-scattering experiments and reproducing experiments through ab initio M.D.
Calculate Si yield of partially oxidised Si and Si far out of lattice sites. 3.
How does the Si-SiO2 interface with incorporated experimental data form and appear?
Create interface by M.D. Manually change bonds and remove atoms. At last relax structure.
Simulate structures and their agreement with experimental values. 4.
How does oxygen proceed to react at the Si-SiO2 interface during Si oxidation?
Let O2 molecule diffuse through oxide to the interface, and react (by M.D.)
Observe O2 incorporation and dissociation mechanism and calculate energy barriers.
ab initio M.D.: ab initio molecular dynamics. In this case, classical molecular dynamics to create the interface by a thermal gradient calculating forces and potentials by first-principle methods, and relaxing the structures through density-functional relaxation methods.

7. Results 1. Excess of Si near the interface.
Incoming oxygen attacks Si-Si bonds near interface.
Rearrangements happen through a 3-fold coordinated O-atom. Process disrupts crystalline Si.
O-atoms carried into disrupted layer, creating new oxide.
Cycling of Si-Si bonds towards reaction layer, sustaining oxidation.

8. Results 2.
Consider transition structure in terms of Si yield (atoms displaced out of lattice position, and partially oxidised atoms).
Less structural order = better agreement.
Excess Si main contribution from distorted Si.
Two models correspond well: higher density of Si-Si dimers + O in backbonds with partially oxidised Si.

9. Results 3.
Models agree well with experimental values: low density of coordination defects, oxide layer near Si-substrate has slightly higher density, and transition layer contains correct amount of partially oxidised Si.
Disagreement in structural order between the models.

10. Results 4.
The reactions regarding the oxygen molecule are hindered by low energy barriers for incorporating and dissociating the molecule, compared to the energy gain in dissociating it. It may be interpreted as the oxidation process being governed more heavily by diffusion properties.
There is a dependency regarding charge states, where the spontaneous incorporation of O2 is more favourable when an excess negative charge is available.
Diffusion models require decrease in diffusion rate near interface, but may be achieved by a thin higher- density oxide layer near interface.

11. References
Bongiorno, A. and A. Pasquarello, Reaction of the oxygen molecule at the Si(100)-SiO2 interface during silicon oxidation. Phys Rev Lett, (8): p
Bongiorno, A., et al., Transition structure at the Si(100)-SiO2 interface. Phys Rev Lett, (18): p
Pasquarello, A., M.S. Hybertsen, and R. Car, Interface structure between silicon and its oxide by first-principles molecular dynamics. Nature, (6706): p
Bongiorno, A. and A. Pasquarello, Atomistic structure of the Si(100)–SiO2 interface: A synthesis of experimental data. Applied Physics Letters, (7): p
Campbell, Stephen A., and Stephen A. Campbell. Fabrication Engineering at the Micro and Nanoscale. New York: Oxford University Press, 2008.