1225
« on: October 19, 2016, 00:19 »
To the best of my knowledge, experimental x-values reported for the indirect to direct band gap transition are quite scattered in the literature. So, I would not see 11% in the cited JAP paper as the reference number because the calculations are based on a highly empirical method with many parameters fitted to a particular experiment.
There is a comprehensive computational study of SnGe alloy given in Phys. Rev. B 89, 165201 (2014), where DFT-MGGA has been adopted. In the paper, one may find many computational details such as supercell size, k-point sampling and many other. Note that in the paper there exist references to recent experiments giving x for indirect to direct gap transition in the range of 0.06 < x < 0.08.
In ATK, you can also use DFT-MGGA for SnGe. I would suggest doing geometry optimization with LDA and the band structure calculation with MGGA, using the OMX-HIGH basis set. Note that MGGA might need to be tuned by changing the c-parameter to have band energies of bulk Ge closer to experiment. For example, the self-consistent MGGA (without spin-orbit interaction included) gives the c-parameter of 1.10028 for bulk Ge (for LDA optimized lattice constant of 5.641 Angs), and E_gap=E_L=0.88 eV, E_G = 0.98 eV in consistency with the PRB results, 0.82 and 0.97 eV, respectively.
Changing c-parameter to 1.0 will give E_gap=E_L=0.66 eV, E_G = 0.76 eV, and E_X (at the X-valley minimum) = 0.88 eV in agreement with room temperature experimental values E_gap=E_L=0.66 eV, E_G = 0.80 eV, and E_X (at the X-valley minimum) = 0.85 eV.
I would use the same c-parameter (of bulk Ge) for all Sn concentrations in SnGe alloy.
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