김세진 1,2 , 김상필 1,3 , 최정혜 1 , 이승철 1 , 이광렬 1 , 김도연 2 , s....

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