Progress Report

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Progress Report

• Xiaobin Niu

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Outline

• Experimental results
• Level Method
• Some changes we made in the code
• Some simulation results
• Conclusion

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Experimental Results of Xies Group

• Ge QDs preferentially nucleate over the buried
  misfit dislocations.
• Dislocation lines are buried underneath.
• Lead to strain field
• This can alter potential energy surface
• Anisotropic diffusion
• Spatially varying diffusion
• Nucleation occurs in regions of fast diffusion

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Ge0.25Si0.75
Ge0.10Si0.90
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Level-Set Model. Why?

• The Level Set model is an island dynamics model
  for the simulation of thin film growth. In this
  model, the motion of island boundaries of
  discrete atomic layers is determined by the time
  evolution of a continuous level-set function f.
  The adatom concentration is treated in a mean
  field manner. It is obtained by solving the
  diffusion equation.
• Computational advantage. Not limited to time
  scale of adatom hopping (KMC) but still retain
  spatial information.
• More control over the growth nucleation
  dynamics. Allowing us to see what are the correct
  models and physical relevance of the various
  sources of stochasticity in the process.

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Schematic of the Level Method
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The Level-Set Model
1. The level set function evolves according to
2. An adatom density field over the substrate is
evolved according to a driven diffusion equation.
3. The island normal velocities from the gradient
of the adatom density at the island boundary.
4. The nucleation rate.
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Level set simulations of submonolayer growth on
patterned surface. (left) Diffusion coefficient
Dx vs. x due to strain from buried dislocation
line. (right) Island growth at 12 coverage.
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For Anisotropic diffusion
1. The diffusion coefficient is replaced by
matrix
2. The diffusion equation is changed to
3. The velocity become
4. The nucleation rate
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Dy
Dx
Dy
Dx
Dx 103-109 Dy 106
Dy 103-109 Dx 106
Dxx
Daverage 106 Edge diffusion coefficient 10
Detachment rate 500 Edge diff (reversible)
105
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Introduce the potential energy surface and drift
term into the code
1. Introducing of transition energy and
absorption energy
-LnD
2. The diffusion coefficient is determined by the
energy barrier
3. The drift term is proportional to the grads of
absorption energy
4. The diffusion equation
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Without nucleation
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Without nucleation
Etrany
Eabs
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Without nucleation
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Conclusion

• The level-set method indicates that an undulating
  diffusion coefficient of Ge adatoms could account
  the experimental observation that Ge QDs
  preferentially nucleate over the buried misfit
  dislocations.
• Changes in the code D ? Dxx introduction of the
  potential energy surface and the drift term
• When the variation of absorption energy become
  large, the drift term dominate the process.