1 / 23

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

Bond-Order Potential for MD Simulation: Relaxation 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.

caradoc-clayton
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bond-Order Potential for MD Simulation:Relaxation 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

  2. 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

  3. Tight Binding exact diagonalisation two-center approximation: Slater-Koster integrals: electronic part (bandstructure) scaling part (elastic constants)

  4. Bond Order Potential Greens function: many atom expansion local density of states moment

  5. 2nd moment: contribution negligible normalized moment: angular function: reduced TB parameter:

  6. 4th moment approximation

  7. new contributions to  bond terms : torsion angle: on site term :

  8. contribution of largest at constant angle

  9. of most pronounced new angular dependence at constant angle

  10. Potential energy above Si(100) surface BOP2 BOP4 BOP4+ minimum minimum raised maximum

  11. Parametrization and Fit 7 parameter

  12. smooth promotion energy invested energy: promote one electron Gained energy: form new bonds

  13. propose and accept/reject fit via Monte Carlo/ Conjugate gradient fitness of set {r}:

  14. improved 4th moments and promotion energyfor pure carbon systems

  15. simulation of Si(100) waferbonding with rotational twist Scheerschmidt and Kuhlmann, Interface Science 12 (2004)

  16. recursion method and local density of states • solve Gii recursively: • LDOS approximated by moments: moments-theorem • semi-infinite linear chain: ai=a=0 eV bi=b=0.1 eV

  17. moments expansion of LDOS

  18. 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) = Nbrs^2 • 256 paths @ 16Nbrs vs. 16 paths @ 4Nbrs • 6th Moment : 64 vs. 4096 • low slopes (n,m) required by elasticity conflict with cutoff -> make a compromise

More Related