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김세진 1,2 , 김상필 1,3 , 최정혜 1 , 이승철 1 , 이광렬 1 , 김도연 2 , S. Plimpton 4 PowerPoint PPT Presentation


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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.

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김세진 1,2 , 김상필 1,3 , 최정혜 1 , 이승철 1 , 이광렬 1 , 김도연 2 , S. Plimpton 4

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1 2 1 3 1 1 1 2 s plimpton 4

제34회 동계 진공학회

Fixed charge problem of Modified-BMH potential during molecular dynamic simulation of Si/SiO2 interface

김세진1,2, 김상필1,3, 최정혜1, 이승철1, 이광렬1, 김도연2, S. Plimpton4

1한국과학기술연구원 계산과학센터, 2서울대학교 재료공학부, 3한양대학교 신소재공학부, 4Sandia National Lab.


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http://www.intel.com/

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.

수정!!

구체적인 문구로...

  • atomic configuration ?

  • oxidation diffusion process ?


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Time Evolution of

Each Atom

Molecular Dynamics (MD)

Interatomic

Distance

Time Integration

Interatomic Potential

as a function of distance

E: energy

F: force

a: acceleration

v: velocity

s: position or distance

m: atomic mass

Newton’s equation of motion

Ionic Structure  Coulombic Energy,


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O

O

O

O

Si

Si

Si

Si

O

O

O

O

O

O

O

O

Si

Si

Si

Si

O

O

O

O

O

O

O

O

Si

Si

Si

Si

O

O

O

O

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

MD Potentials for Si-O

  • Si potentials

  • - Tersoff : good for bulk

  • - Strenger-Webber : good for dimers on surface

  • SiO2 potentials

  • - Buckingham, Born-Mayer-Huggins(BMH),Morse ……

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


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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.

2-body interaction

3-body interaction


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Cutoff

O

Si

(a)

Si

(b)

(c)

(d)

(e)

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)~(d) : M-BMH(e) Tersoff


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O : -2

Si : 4

0

300K for 0.3ps

M-BMH

M-BMH + Tersoff

M-BMH vs. M-BMH with Tersoff

  • Bottom of the bulk silicon layer fixed by Tersoff potential.

  • Strong repulsive force between silicon with fixed charge(+4) makes SiOx amorphous layer separating from bulk silicon region.


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O atom in Si lattice

Si atom in O lattice

-2

-2

4

4

0.25

-2

4

-0.5

0.142

-2

1st Approximation

  • Atomic charge is depends on number and type of atoms within cutoff radius.

  • Same types of atoms have same charge within cutoff radius.


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q( )

2nd Approximation

  • Atomic charges are exponentially decreased for increasing the atomic distance.

  • Same types of atoms can have different charge, depends on neighbor configuration.


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0.142

-2

Charge Generating Function

0.142

0.015

0.029

0.047


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1st vs. 2nd Approx.

Top view

  • 300K, 0.3 ps MD calculation

  • 2nd approximation shows more various charge distribution.

  • Si-O bonding by Coulombic force is confirmed by 2nd approximation.

Side view

Side view

1st Appx.

1st Appx.

2nd Appx.

2nd Appx.


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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


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Supplement

MD Results (1,000 MD steps @ 300K)

1st approx.

2nd approx.


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Cutoff

O

Si

(a)

Si

(b)

(c)

(d)

(e)

Future Work

Based on the 2nd approximation,

M-BMH competes with Tersoff potential between Si-Si interactions

(a), (b): M-BMH

(c), (d) : M-BMH & Tersoff

(e): Tersoff

(a)~(d) : M-BMH(e) Tersoff


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