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

1. 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.

2. 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 ?

3. 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,

4. 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

5. 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

6. 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

7. 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.

8. 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.

9. 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.

10. 0.142 -2 Charge Generating Function 0.142 0.015 0.029 0.047

11. 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.

12. 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

13. Supplement MD Results (1,000 MD steps @ 300K) 1st approx. 2nd approx.

14. 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