Twist-Wafer-Bonding

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

                                  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




                                         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


                                      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




                                         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 Emin translation at various
  temperatures
• Determine influence of temperature on total and
  interface energies and structure at the interface



                                                  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.



                            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)
                                                              
                                          1  N  e1 cos  e2 sin 
                                                         2       2
                                                              
                                          2  N  e1 sin  e2 cos 
                                                        2        2

                                             University of Illinois at Urbana-Champaign
Periodicity Cell




                   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




                                                       University of Illinois at Urbana-Champaign
                         Realistic Silicon Potentials



Stillinger-Weber Potential                                    Tight-binding Potential

   V 
         1
           
                                                       1
               (rij )   g (rij )g (rik )(cos  jik  ) 2       E tot   2  n | H TB |  n  E rep
         2 ij            ijk                           3                  n




• minimized at Ө = -arccos(1/3)                               • Compromise between classical
• Good description for bulk Si                                  and ab initio methods
• Not adequate for surface Si                                 • Total energy obtained by atoms’
  atoms                                                         set of orbitals (1s and 3p’s)
                                                              • Expensive and size-limited



                                                                              University of Illinois at Urbana-Champaign
Implementation of Nose-Hoover Thermostat

                                                                                                                                 s
                                                    p     2
                                                                  Q                    2                               
Extended Hamiltonian:             Eext                V ( q) 
                                                          i
                                                                      gkT                                                      gQ
                                                   2mi             2
                                                                                                                          ln s
                                              i

                                                                   t                              
                                         pin1 / 2  pin                 V (q n )   n pin 1 / 2 
                                                                   2  qi
                                                                      
                                                                                                     
                                                                                                     
                                                                  n 1            pin1 / 2
                                                              q   i       q  t
                                                                            n
                                                                            i
                                                                                   mi

                                                  n 1
                                                           nt     n 1 / 2
                                                                    pi                      2
                                                                                                         
                                                                                                     kT 
 Equations of motion:                                          Q i
                                                                      mi g                              
                                                                                                         

                                                                             t n1
                                                       n1   n 
                                                                             2
                                                                                    
                                                                                 n                  

                                                                  t                                 
                                      pin1  pin1 / 2                 V q n1    n1 pin1 / 2 
                                                                  2  qi
                                                                     
                                                                                                       
                                                                                                       

                  M. Tuckerman, B.J. Berne, G.J. Martyna, J. Chem. Phys., 97, 1990 (1992).


                                                                                            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




                                         University of Illinois at Urbana-Champaign
Effective Mass Effect on Nose Thermostat




      Q=100,000              Q=10


                            University of Illinois at Urbana-Champaign
Effect of Nose Thermostat




    Temperature is constant!!

                           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




                                           University of Illinois at Urbana-Champaign
Lattice Initialization via Steepest Descent




  •Initial lattice configuration   •1st iteration of sdmin
  has very little bonding          relaxes lattice and creates
  between slabs                    bonding @ interface

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




                               University of Illinois at Urbana-Champaign
        Lattice Translation Effect

• Different bonding coordination at interface for varying
  translations?




  High energy orientation        Low energy orientation

                                           University of Illinois at Urbana-Champaign
Temperature Effect on Interface Energy




 Surface energy/ unit area increases with increasing temperature

                                              University of Illinois at Urbana-Champaign
Temperature Effect on Total Energy




  Total energy constant with increasing temperature up to melting point

                                                    University of Illinois at Urbana-Champaign
Effect of Temperature on Lattice


• MOVIES!!!!  ???




                       University of Illinois at Urbana-Champaign
Effect of Temperature on Lattice




T = 200 ºK        T = 600 ºK




T = 1200 ºK      T = 2000 ºK

 FS-MRL / CMM           University of Illinois at Urbana-Champaign
            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)



                                                 University of Illinois at Urbana-Champaign
         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




                                                  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


                                                      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!!!!!!




                                      University of Illinois at Urbana-Champaign

				
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