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  • Created 29 Jun 2010

Problems reproducing TB results for a quantum well

  1. James Jehiel Ramsey

    To put NEMO5 through its paces and debug my own understanding of its use, I’ve been trying to reproduce the results from Franceschi, Jancu, and Beltram in Phys. Rev. B 59, 9691–9694 (1999), which uses the tight-binding parameters of Jancu et al., Phys. Rev. B 57, 6493–6507 (1998). Toward this end, I made a database file with the appropriate parameters for both GaAs and AlAs, which should be in the attached archive.

    So far, though, I’ve had little luck reproducing the tight-binding results from the paper by Franceschi et al. Some eigenvalues from the NEMO5 results cluster somewhere around the valence band results as determined from nextnano3 (, but there are spurious states in the band gap, and the conduction band results are barely a match at all. EPS files should be in the attached archive as well.

    I’m not sure what I’m doing wrong here. The simulation domain is mostly a long thin column of AlAs, 65 nm tall, with a 5 nm layer of GaAs across the middle of the column. There are periodic boundary conditions along the 100 and 010 directions, but not along the growth direction, 001. I checked to make sure that there are hydrogens passivating the ends of the column, and the TB parameters for the hydrogens are borrowed from NEMO5’s main material database, though the parameters were originally for gallium and indium:

    passivation_potential = 100;

    V_S_S_Sigma_Al_H = -10; V_S_P_Sigma_H_Al = 10; V_S_D_Sigma_H_Al = -0; V_S_S_Sigma_As_H = -10; V_S_P_Sigma_H_As = 10; V_S_D_Sigma_H_As = -0; V_Sstar_S_Sigma_As_H = -0; V_Sstar_S_Sigma_Al_H = -0; V_S_Sstar_Sigma_H_As = -0; V_S_Sstar_Sigma_H_Al = -0;

    The valence band offset is set to -0.5 eV for AlAs and 0.0 for GaAs.

    I don’t know if this is a reasonable set-up or not, and judging from the results I’m getting, I’m sure I must be missing something.

    Input, output, and Gnuplot files for NEMO5 runs

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  2. Tillmann Christoph Kubis

    Looking at your inputdeck, I can see that you did not include the passivation in the Schroedinger solver: Please include the option “passivate_H” in the job_list of “find_bands”. That should move the surface states out of the band gap to very high energies. The passivation parameters are fine. However, recently we realized (and updated the database) that the tight binding coupling parameters with H-atoms V_S_P_Sigma_… should be -sqrt(3)*V_S_S_Sigma_…, if you want to be more consistent with previous publications. In your case, you should write V_S_P_Sigma_AL_H= 10 * sqrt(3), etc. Please let us know whether that helped.

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  3. James Jehiel Ramsey

    Adding “passivate_H” got rid of the states in the gap, but agreement between the tight-binding results and the envelope function results is still iffy, as seen in the attached file. For example, in the uppermost valence band, there are no tight-binding results that correspond with the envelope function results for k-vectors along the negative 100 direction. Maybe I just need to tweak the shift parameter? (So far, I’ve used shift=1 to find conduction band results and shift = 0 for the valence band results, with 40 eigenvalues per shift.)

    It doesn’t seem to matter much whether I have the passivation parameters be V_S_P_Sigma_AL_H= 10, etc. or V_S_P_Sigma_AL_H= 10 * sqrt(3), etc.


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  4. James Jehiel Ramsey

    Once I changed the eigensolver to ARPACK, I now have more tight-binding results whose energy values are in the same range as the envelope function results, which both makes for a clearer comparison between the two sets of results, and a much better agreement with the paper Phys. Rev. B 59, 9691-9694 (1999). What I’ve got now looks reasonable.


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