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Phonon dispersion calculation

Phonon dispersion calculation. spin-relaxation rates depends on τ m Momentum relaxation time ( τ m )  electron-phonon scattering electron-phonon scattering  phonon spectrum (dispersion). Lattice vibrations in mono-atomic crystals. Lattice vibrations in ….

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Phonon dispersion calculation

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  1. Phonon dispersion calculation • spin-relaxation rates depends on τm • Momentum relaxation time (τm ) electron-phonon scattering • electron-phonon scattering phonon spectrum (dispersion)

  2. Lattice vibrations in mono-atomic crystals Daryoush Shiri, IQC

  3. Lattice vibrations in … Daryoush Shiri, IQC

  4. Lattice vibrations in Diatomic lattice… It is instructive to consider the boundaries and limiting cases e.g. k=0 and k=π/a. WHAT if we have a more complex solid? e.g. Bulk Si , ge, GaAs crystals Nanowires Amorphous Si, oxide, atomic clusters u Daryoush Shiri, IQC

  5. Dynamical Matrix Method • The generalization of the previous method to large solids • Challenges: Computationally intensive for large number of atoms • In the last example (1 and 2 atoms in each unit cell of a periodic 1D solid)  we found 1 and 2 modes, respectively. • What about bulk Si and Ge? • What about a nanowire? W. L. Park et al, Nano Letters, 19 August 2008 Daryoush Shiri, IQC

  6. Dynamical Matrix Method Daryoush Shiri, IQC

  7. Daryoush Shiri, IQC

  8. Daryoush Shiri, IQC

  9. Daryoush Shiri, IQC

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  21. Daryoush Shiri, IQC

  22. SIESTA calculation of phonon spectrum bulkGe_phonon.fdf STEP 1: Building a super-cell from the unit cell of a given structure e.g. bulk Si or Ge (2 atoms per unit cell) Dynamic Matrix Equation is solved in SIESTA using Vibra package (see: http://departments.icmab.es/leem/siesta/Documentation/Tutorials/index.html ) Daryoush Shiri, IQC, Waterloo

  23. SIESTA …. • LOCAL MACHINE: • After downloading, unzipping & installing SIESTA you can go directly to Vibra/Src and copy your .fdffiles there. Make sure you have a Fortran compiler to compile fcbuild.f, Vibra.fetc • SUPERCOMPUTING FACILITY: • If you have access to e.g. SHARCNET (www.sharcnet.ca), just copy /Srcfrom your local machine to your work directory. Daryoush Shiri, IQC, Waterloo

  24. bulkGe_phonon_2014.ifc.fdf SIESTA …. • STEP 2: Displace the atoms and calculate the IFC • $siesta path/./siesta < example.ifc.fdf > example.ifc.out • OR in my example I used MPI version of SIESTA on Sharcnet Daryoush Shiri, IQC, Waterloo

  25. SIESTA …. • BandLinesScale pi/a • %block BandLines • 1 0.000 0.000 0.000 \Gamma • 45 2.000 0.000 0.000 X • 17 2.000 0.500 0.500 K • 48 2.000 2.000 2.000 \Gamma • 1.000 1.000 1.000 L • %endblockBandLines • STEP 3: Computing Dynamical matrix and Diagonalize • A Fourier transform carries Force matrix from position to momentum(k-space) • K grid points are defined in example.fdf file. • $path/Utils/Vibra/Src/./vibrator <bulkGe_phonon.fdf •  OUTPUT: Ge_bulk_2014.bands • $path/ ./bandline.x < Ge_bulk_2014.bands > Ge_bulk_2014.gnubands.dat Daryoush Shiri, IQC, Waterloo

  26. SIESTA calculated phonon spectrum of Bulk Ge 1/cm = 2.997 93 x 10+10 Hz • BandLinesScale pi/a • %block BandLines • 1 0.000 0.000 0.000 \Gamma • 45 2.000 0.000 0.000 X • 17 2.000 0.500 0.500 K • 48 2.000 2.000 2.000 \Gamma • 1.000 1.000 1.000 L • %endblockBandLines Daryoush Shiri, IQC, Waterloo

  27. LO TO

  28. [110] Si nanowire d = 1.7nm Phonon dispersion Electronic dispersion From: J. Appl. Phys. 104, 053716 2008

  29. Daryoush Shiri, IQC

  30. Quantization of phonon modes

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