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Comparison of Si/SiOComparison of Si/SiOxx Potentials Potentials
for Oxidation Behaviors on Sifor Oxidation Behaviors on Si
Sang-Pil Kim, Sae-Jin Kim and Kwang-Ryeol Lee
Computational Science CenterKorea Institute of Science and Technology, Seoul, Korea
PS-21
Introduction• Simulations of Si and SiO2 have been studied for a long time.
• As the size of gate oxide decrease, device performance is largely affected by Si/SiO2 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.
MD Potentials for Inter-bonding System
Metallic bondMetallic bond
Covalent bondCovalent bond Ionic bondIonic bond
• Modified EAM• Modified Tersoff InertInert
GasGas
ZBL, Moliere
ZBL, Moliere 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)
Difficult to describe interface because of- Different bonding style - Various phase & structure of SiOx
- Charge problem- Reaction, interface definition ……
What we want to see is atomic structure of interface between Si and SiO2
MD Potentials for Si-O
Si
Si
Si
Si
Si
Si Si
Si
Si SiSi
Si
Si
Si Si Si
Si
SiSi
SiSiSi
Si Si
Si Si SiSi
O O O O
O O O O
O O O OO O O O
O O O O
O O O O
• Si potentials- Tersoff : good for bulk- Strenger-Webber : good for dimers on surface
• SiO2 potentials - Born-Mayer-Huggins(BMH), BKS, Buckingham Morse ……
Covalent-Ionic Potentials
Covalent bondCovalent bond Ionic bondIonic 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
Si
Cutoff
(c)(d) (e)
(b)
(a)
OSi
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
M-BHM Potential
• Improved Born-Mayer-Huggins’ SiO2 potential
• Based on Coulombic interaction of two particle with three body term
• Advantage
- Useful at various SiO2 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
Result - Tersoff + M-BMHCutoff = 3.0 Å
0 50 100 150 200 250 300-40
-30
-20
-10
0
10
Net
Ch
arg
e
MD steps (x10)
1000 MDs
2000 MDs
3000 MDs
Jiang & Brown’s Suggestion
kjiji
ijii
i kjivjivqeE ,,, 32
(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 function2.Bond-softening function3. 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 (SiOx)
Result - SW + BKS
10 MDs0 500 1000 1500 2000 2500 3000
-1.0x10-3
-8.0x10-4
-6.0x10-4
-4.0x10-4
-2.0x10-4
0.0
2.0x10-4
4.0x10-4
6.0x10-4
8.0x10-4
1.0x10-3
Net
Ch
arg
e
MD steps
50 MDs
100 MDs 300 MDs
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 (Ionizatio
n potential)
Long-range force calculation by Ewald sum or erfc