Daniel Go, Alfonso Reina-Cecco, Benjamin Cho

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

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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

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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

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Experimental Procedure

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

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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.

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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)

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Periodicity Cell

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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

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Realistic Silicon Potentials

• Stillinger-Weber Potential
• minimized at ? -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 3ps)
• Expensive and size-limited

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

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Effective Mass Effect on Nose Thermostat
Q10
Q100,000
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Effect of Nose Thermostat
Temperature is constant!!
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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

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Lattice Initialization via Steepest Descent

• 1st iteration of sdmin relaxes lattice and
  creates bonding _at_ interface

• Initial lattice configuration has very little
  bonding between slabs

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Minimum Energy Rotated Lattice Configuration
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Lattice Translation Effect

• Different bonding coordination at interface for
  varying translations?

Low energy orientation
High energy orientation
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Temperature Effect on Interface Energy
Surface energy/ unit area increases with
increasing temperature
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Temperature Effect on Total Energy
Total energy constant with increasing temperature
up to melting point
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Effect of Temperature on Lattice

• MOVIES!!!! ? ???

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Effect of Temperature on Lattice
T 600 ºK
T 200 ºK
T 1200 ºK
T 2000 ºK
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Summary of Results

• 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)

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Physical Interpretation

• 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

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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

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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, TAs and classmates!!!!!!