김세진 1,2 , 김상필 1,3 , 최정혜 1 , 이승철 1 , 이광렬 1 , 김도연 2 , s....
DESCRIPTION
제 34 회 동계 진공학회. Fixed charge problem of Modified-BMH potential during molecular dynamic simulation of Si/SiO 2 interface. 김세진 1,2 , 김상필 1,3 , 최정혜 1 , 이승철 1 , 이광렬 1 , 김도연 2 , S. Plimpton 4 1 한국과학기술연구원 계산과학센터 , 2 서울대학교 재료공학부 , 3 한양대학교 신소재공학부 , 4 Sandia National Lab. - PowerPoint PPT PresentationTRANSCRIPT
Fixed charge problem of Modified-BMH potential during molecular dynamic
simulation of Si/SiO2 interface
김세진 1,2, 김상필 1,3, 최정혜 1, 이승철 1, 이광렬 1, 김도연 2, S. Plimpton4
1 한국과학기술연구원 계산과학센터 , 2 서울대학교 재료공학부 , 3 한양대학교 신소재공학부 , 4Sandia National Lab.
제 34 회 동계 진공학회
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/
• atomic configuration ?• oxidation diffusion process ?
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Time Integration
InteratomicDistance
Interatomic PotentialInteratomic Potentialas a function of distanceas a function of distance Time Evolution of Time Evolution of
Each AtomEach Atom
)(sE
dtvs dtav m
Fa
dr
dEF
Newton’s equation of motionE: energyF: forcea: accelerationv: velocitys: position or distancem: atomic mass
t
Ionic Structure Coulombic Energy, 2( ) i jq qE r C
r
Molecular Dynamics (MD)
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 - Buckingham, Born-Mayer-Huggins(BMH),Morse ……
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
(a)~(d) : M-BMH (e) Tersoff
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
M-BMH M-BMH + Tersoff
0 O : -2Si : 4
300K for 0.3ps
• Bottom of the bulk silicon layer fixed by Tersoff potential. • Strong repulsive force between silicon with fixed charge(+4) mak
es SiOx amorphous layer separating from bulk silicon region.
M-BMH vs. M-BMH with Tersoff
O atom in Si lattice
-2
4
-2
0.25
Si atom in O lattice
4-2
4
-0.5
1st Approximation
0.142
-2
• Atomic charge is depends on number and type of atoms within cutoff radius.
• Same types of atoms have same charge within cutoff radius.
2nd Approximation
• Atomic charges are exponentially decreased for increasing the atomic distance.
• Same types of atoms can have different charge, depends on neighbor configuration.
q( ) )(2
)(2
22
11
rFnum
rFnum
2r1r
2r
2
1)cos(
2
1)(
12
1
rr
rrrS
))61.1(exp()( rrf
)(rF
A B C
6.8013 )(: rFA
)(8013.6)(: rfrFB )()(8013.6)(: rSrfrFC
0.142
-2
Charge Generating Function
0.142
0.0470.029
0.015
1st Appx.
1st Appx. 2nd Appx. 2nd Appx.
• 300K, 0.3 ps MD calculation
• 2nd approximation shows more various charge distribution.
• Si-O bonding by Coulombic force is confirmed by 2nd approximation.
1st vs. 2nd Approx.Top view
Side view Side view
Summary
• We found the fixed charge problem in Modified-BMH potential for using in Si/SiO2 interface and modified this as follows:- Modified charge generating function- Combining with Tersoff potential for describing pure Si
• These approximations can be used to simulate Si/SiO2 interface which has a charge distribution.
• Remained problem: - Overestimation of repulsion between partially charged Si atoms near oxygen
Supplement
MD Results (1,000 MD steps @ 300K)
1st approx. 2nd approx.
Future Work
Based on the 2nd approximation, M-BMH competes with Tersoff potential between Si-Si interactions
(a)~(d) : M-BMH (e) Tersoff
Si
Cutoff
(c)(d) (e)
(b)
(a)
OSi
(a), (b): M-BMH(c), (d) : M-BMH & Tersoff(e): Tersoff