1. University of Illinois at Urbana-Champaign Daniel Go, Alfonso Reina-Cecco, Benjamin Cho Simulation of Silicon Twist Wafer Bonding MATSE 385 Final Project Presentation December 20, 2003

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

3. University of Illinois at Urbana-Champaign 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. University of Illinois at Urbana-Champaign Objectives 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

5. University of Illinois at Urbana-Champaign Experimental Procedure 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 E min translation at various temperatures Determine influence of temperature on total and interface energies and structure at the interface

6. University of Illinois at Urbana-Champaign Lattice Implementation 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.

7. University of Illinois at Urbana-Champaign Coincidence Site Lattice Theory 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)

8. University of Illinois at Urbana-Champaign Periodicity Cell

9. University of Illinois at Urbana-Champaign Minimum Energy Rotated Lattice Configuration 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

10. University of Illinois at Urbana-Champaign Realistic Silicon Potentials 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

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

12. University of Illinois at Urbana-Champaign Implementing Thermostat in OHMMS 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

13. University of Illinois at Urbana-Champaign Effective Mass Effect on Nose Thermostat Q=100,000 Q=10

14. University of Illinois at Urbana-Champaign Effect of Nose Thermostat Temperature is constant!!

15. University of Illinois at Urbana-Champaign Outline of Computational Procedure 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

16. University of Illinois at Urbana-Champaign Lattice Initialization via Steepest Descent Initial lattice configuration has very little bonding between slabs 1 st iteration of sdmin relaxes lattice and creates bonding @ interface

17. University of Illinois at Urbana-Champaign Minimum Energy Rotated Lattice Configuration

18. University of Illinois at Urbana-Champaign Lattice Translation Effect Different bonding coordination at interface for varying translations? High energy orientation Low energy orientation

19. University of Illinois at Urbana-Champaign Temperature Effect on Interface Energy Surface energy/ unit area increases with increasing temperature

20. University of Illinois at Urbana-Champaign Temperature Effect on Total Energy Total energy constant with increasing temperature up to melting point

21. University of Illinois at Urbana-Champaign Effect of Temperature on Lattice MOVIES!!!! ???

22. University of Illinois at Urbana-Champaign FS-MRL / CMM Effect of Temperature on Lattice T = 200 ºK T = 600 ºK T = 1200 ºK T = 2000 ºK

23. University of Illinois at Urbana-Champaign Summary of Results Nose thermostat sucessfully implemented 1 st 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 T m = 1687 ºK)

24. University of Illinois at Urbana-Champaign Physical Interpretation 1 st 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

25. University of Illinois at Urbana-Champaign Areas of Future Research 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

26. University of Illinois at Urbana-Champaign Our Many Thanks Go to… 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!!!!!!