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