Transcript Document 7822996

PS-21
Comparison of Si/SiOx 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
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
• Embedded atom method (EAM)
• Effective medium theory (EMT)
• Glue-models
• TB-SMA
• Finnis-Sinclair
Metallic bond
ZBL, Moliere
• Modified EAM
• Modified Tersoff
ZBL, Moliere
Inert
Gas
• EAM+ Electrostatic (ES)
- Streitz-Mintmire
- Zhou-Wadley
ZBL, Moliere
Lennard-Jones (LJ)
Covalent bond
• Stillinger-Weber (SW)
• Tersoff
• Brenner (also hydrocarbon)
• Environment-dependent
Interatomic potential (EDIP)
• Biswa-Hamann (BH)
Ionic bond
• Modified SW
• SW+BKS
• Augmented Tersoff
• Yasukawa
• Charge optimized
many body potentials
(COMB)
• Born-Mayer-Huggins (BMH)
• Vashishta
• Beest-Kramer-van Santen (BKS)
• Demiralp-Cagin-Goddard (DCG)
• Tangney-Scandolo (TS)
• Tsuneyuki-Tsukada-Aoki-Matsui (TTAM)
MD Potentials for Si-O
• Si potentials
- Tersoff : good for bulk
- Strenger-Webber : good for dimers on surface
• SiO2 potentials
- Born-Mayer-Huggins(BMH), BKS, Buckingham Morse ……
O
O
O
Si
O
Si
Si
O
O
O
Si
Si
Si
Si
Si
O
Si
O
O
Si
Si
O
O
O
O
O
O
O
O
Si
O
O
O
O
O
Si
Si
O
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
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
Si
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)
Possible candidates
 Co-use of covalent and ionic potentials
 Modified covalent or ionic potentials
 Novel potentials for describing both system simultaneously
We employed the effective interatomic potential which combines
Tersoff + M-BMH vs. SW + BKS
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
Cutoff
(a)
(b)
(c)
(d)
Si
(a)~(c) : M-BMH
(d)~(e) Tersoff
(e)
O
Si
M-BHM Potential
• Improved Born-Mayer-Huggins’ SiO2 potential
• Based on Coulombic interaction of two particle with three body term
2-body interaction
3-body interaction
• 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.
Result - Tersoff + M-BMH
Cutoff = 3.0 Å
1000 MDs
10
Net Charge
0
2000 MDs
-10
-20
-30
-40
0
50
100
150
200
MD steps (x10)
250
300
3000 MDs
Jiang & Brown’s Suggestion
SW (Si) + BKS (SiOx)

  v i, j, k 
E   ei qi    v2 i, j   ij 
i j
i
(a)
(b)
i j k
3
(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
Three NEW components
are introduced to describe
mixed bonding between
oxygen and silicon atoms
1. Charge-transfer function
2. Bond-softening function
3. Ionization energy
Z. Jiang and R.A. Brown, Chem. Eng. Sci. 49, 2991 (1994)
Z. Jiang and R.A. Brown, Phys. Rev. Lett. 74, 2046 (1995)
Result - SW + BKS
-3
1.0x10
-4
8.0x10
-4
6.0x10
-4
Net Charge
4.0x10
-4
2.0x10
0.0
-4
-2.0x10
-4
-4.0x10
-4
-6.0x10
-4
-8.0x10
10 MDs
50 MDs
100 MDs
300 MDs
-3
-1.0x10
0
500
1000
1500
2000
2500
3000
MD steps
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