Daniel Go, Alfonso Reina-Cecco, Benjamin Cho

1. Simulation of Silicon Twist Wafer Bonding Daniel Go, Alfonso Reina-Cecco, Benjamin Cho MATSE 385 Final Project PresentationDecember 20, 2003

2. Determine effects of interfacial alignment on crystal energetics Creation of unique interface reconstructions Application to grain boundary interfaces Fundamental mechanisms similar to atomic friction Motivation for Studying Twist Bonding

3. Technological Significance of Silicon Wafer Bonding • Silicon on Insulator (SOI) Overcome the physical limit of silicon gate technology by offering higher clocked CPUs and lowering power consumptions simultaneously • Theoretical studies on atomic friction due to plucking of atoms, an interesting phenomenon in nanoelectronics

4. Generate atom positions for a silicon bicrystal by rotation of 2 supercells Implement Nose-Hoover thermostat for constant temperature simulation Examine energetics of bulk system and interfaces as a function of lateral translation and temperature Objectives

5. Define coordinates for original and rotated lattices Apply 10 different lateral lattice translations Determine minimum energy translation: Perform steepest descent @ 0ºK to initialize lattice MD run @ 1000ºK Steepest descent @ 0ºK MD runs using this Emin translation at various temperatures Determine influence of temperature on total and interface energies and structure at the interface Experimental Procedure

6. Define atom coordinates corresponding to diamond FCC Si unit cell expanded to 5x5x2 Create new slab by expanding basic lattice to new quadrants Rotate Discard all points outside original boundaries. Lattice Implementation

7. Lattice points of original unit cell must coincide with rotated lattice Pythagorean triplet relationship between a, b, N ex: (3,4,5), (9,40,41), (25,312,313) Coincidence Site Lattice Theory

8. Periodicity Cell

9. Using basic rotated lattice coordinates, laterally translate to a variety of positions: 5 translation distances in each of 2 directions 0º, 45º: increments of L/10, L(2)1/2/10 Perform steepest descent to find minimum energy configuration Sdmin at 0 ºK on original lattice MD Nose at 1000 ºK Sdmin at 0 ºK Look at interface and system energy Minimum Energy Rotated Lattice Configuration

10. Stillinger-Weber Potential minimized at Ө = -arccos(1/3) Good description for bulk Si Not adequate for surface Si atoms Tight-binding Potential Compromise between classical and ab initio methods Total energy obtained by atoms’ set of orbitals (1s and 3p’s) Expensive and size-limited Realistic Silicon Potentials

11. Implementation of Nose-Hoover Thermostat Extended Hamiltonian: Equations of motion: M. Tuckerman, B.J. Berne, G.J. Martyna, J. Chem. Phys., 97, 1990 (1992).

12. OHHMS (Object-Oriented High Performance Multiscale Materials Simulator) Written in C++ Contains propagator classes for easy addition of new integrators Our implementation is a LeapFrog variant Implementing Thermostat in OHMMS

13. Effective Mass Effect on Nose Thermostat Q=10 Q=100,000

14. Effect of Nose Thermostat Temperature is constant!!

15. Use lowest energy lattice configuration Perform OHMMS simulation at elevated temperature (200, 400, 800, 1000, 1200, 1400, 1600, 2000, 3000 ºK) Cool to ~0 ºK, repeat steepest descent Examine system and interface energy Check behavior of high energy lattice configuration for comparison Outline of Computational Procedure

16. Lattice Initialization via Steepest Descent • 1st iteration of sdmin relaxes lattice and creates bonding @ interface • Initial lattice configuration has very little bonding between slabs

17. Minimum Energy Rotated Lattice Configuration

18. Different bonding coordination at interface for varying translations? Lattice Translation Effect Low energy orientation High energy orientation

19. Temperature Effect on Interface Energy Surface energy/ unit area increases with increasing temperature

20. Temperature Effect on Total Energy Total energy constant with increasing temperature up to melting point

21. MOVIES!!!!  ??? Effect of Temperature on Lattice

22. Effect of Temperature on Lattice T = 600 ºK T = 200 ºK T = 1200 ºK T = 2000 ºK

23. Nose thermostat sucessfully implemented 1st sdmin step results in creation of a significant number of 4-fold coordinated atoms at interface Translation vector for minimum energy configuration of rotated lattice identified. With increasing temperature : Increasing disorder of slabs Increasing interfacial energy Constant total energy (up to melting point, agrees well with actual Tm = 1687 ºK) Summary of Results

24. 1st sdmin step initializes the system to a realistic state Energy minima exist for specific combinations of rotation angle and lattice translation: low energy surface reconstructed state Increasing temperature causes: increased thermal motion of atoms causing fluctuation around equilibrium positions Increase in disorder at interface and disruption of 4-fold symmetry causes increased interfacial energy Physical Interpretation

25. Quantitative statistical analysis of interfacial bonding states/structure as a function of : Temperature Lateral translation (interface/system energy) Spacing between slabs Other rotation angles Additional discrete angles corresponding to pythagorean triplets Implementation of generic lattice expansion algorithm to allow automatic calculation of coincidence site geometry (BEST!) Geometric considerations: pipe effects at edges of cell Round off error at cell boundaries Comparison of energetics with different potentials ex. MEAM, tight-binding Areas of Future Research

26. Dr. Jeongnim Kim, MCC Coordinator Dr. Stephen Bond, Department of Computer Science Dr. Kurt Scheerschmidt, Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany Dr. Duane Johnson, TA’s and classmates!!!!!! Our Many Thanks Go to…