Bond-Order Potential for MD Simulation: Relaxation of Semiconductor Nanostructures

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Bond-Order Potential for MD SimulationRelaxation
of Semiconductor Nanostructures

• tight binding and bond order
• 4th moment approximation
• parameterization and fit
• some examples

Volker Kuhlmann and Kurt Scheerschmidt Max
Planck-Institute of Microstructure Physics Halle
- Germany
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large time and length scales
accurate atomistic potential
quantum mechanics of electrons (slow)
empirical potential (fast)
pair potential many-body cluster expansion
bond order potential
density functional theory

• - transferable
• few parameter
• chemical bonds

tight binding
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Tight Binding
exact diagonalisation
two-center approximation
Slater-Koster integrals
electronic part (bandstructure)
scaling part (elastic constants)
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Bond Order Potential
Greens function
many atom expansion
moment
local density of states
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2nd moment contribution negligible
normalized moment
angular function
reduced TB parameter
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4th moment approximation
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new contributions to
? bond terms
torsion angle
on site term
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contribution
at constant angle
of largest
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at constant angle
of most pronounced new angular dependence
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Potential energy above Si(100) surface
BOP2
BOP4 BOP4
minimum
minimum raised
maximum
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Parametrization and Fit
7 parameter
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smooth promotion energy
invested energy promote one electron
Gained energy form new bonds
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fit via Monte Carlo/ Conjugate gradient

• propose and accept/reject

fitness of set r
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improved 4th moments and promotion energyfor
pure carbon systems
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simulation of Si(100) waferbonding with
rotational twist
Scheerschmidt and Kuhlmann, Interface Science 12
(2004)
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recursion method and local density of states

• solve Gii recursively
• LDOS approximated by moments moments-theorem
• semi-infinite linear chain aia0 eV bib0.1
  eV

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moments expansion of LDOS
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• adjust parameter to
• recover properties
• (Ro,Ucoh,B,C11,)
• s(r) must die out suffic.
• before cut off via spline
• must cut off before 2nd nearest neighbors
• of paths of length 4 (4th moment) Nbrs2
• 256 paths _at_ 16Nbrs vs. 16 paths _at_ 4Nbrs
• 6th Moment 64 vs. 4096
• low slopes (n,m) required by elasticity conflict
  with cutoff
• -gt make a compromise