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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. 제 34 회 동계 진공학회

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Introduction Simulations of Si and SiO 2 have been studied for a long time. As the size of gate oxide decrease, device performance is largely affected by Si/SiO 2 interface structure. http://www.intel.com/ atomic configuration ? oxidation diffusion process ? 수정 !! 구체적인 문구로...

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Time Integration Interatomic Distance Interatomic Potential as a function of distance Time Evolution of Each Atom Newton’s equation of motion E: energy F: force a: acceleration v: velocity s: position or distance m: atomic mass Ionic Structure Coulombic Energy, Molecular Dynamics (MD)

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Difficult to describe interface because of - Different bonding style - Various phase & structure of SiO x - Charge problem - Reaction, interface definition …… What we want to see is atomic structure of interface between Si and SiO 2 MD Potentials for Si-O Si O O O O O O O O O O O O O O O O O O O O O O O O Si potentials - Tersoff : good for bulk - Strenger-Webber : good for dimers on surface SiO 2 potentials - Buckingham, Born-Mayer-Huggins(BMH),Morse ……

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M-BHM Potential Improved Born-Mayer-Huggins’ SiO 2 potential Based on Coulombic interaction of two particle with three body term Advantage - Useful at various SiO 2 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

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(a)~(d) : M-BMH(e) Tersoff Si Cutoff (c) (d) (e) (b) (a) O Si 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

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M-BMH M-BMH + Tersoff 0 O : -2 Si : 4 300K for 0.3ps Bottom of the bulk silicon layer fixed by Tersoff potential. Strong repulsive force between silicon with fixed charge(+4) makes SiO x amorphous layer separating from bulk silicon region. M-BMH vs. M-BMH with Tersoff

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O atom in Si lattice -2 4 0.25 Si atom in O lattice 4 -2 4 -0.5 1 st 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.

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2 nd Approximation Atomic charges are exponentially decreased for increasing the atomic distance. Same types of atoms can have different charge, depends on neighbor configuration. q( )

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0.142 -2 Charge Generating Function 0.142 0.047 0.029 0.015

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1 st Appx. 2 nd Appx. 300K, 0.3 ps MD calculation 2 nd approximation shows more various charge distribution. Si-O bonding by Coulombic force is confirmed by 2 nd approximation. 1 st vs. 2 nd Approx. Top view Side view

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Summary We found the fixed charge problem in Modified-BMH potential for using in Si/SiO 2 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/SiO 2 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) 1 st approx.2 nd approx.

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Future Work Based on the 2 nd approximation, M-BMH competes with Tersoff potential between Si-Si interactions (a)~(d) : M-BMH(e) Tersoff Si Cutoff (c) (d) (e) (b) (a) O Si (a), (b): M-BMH (c), (d) : M-BMH & Tersoff (e): Tersoff

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