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| wienfaq [2014/05/21 12:09] – janettate | wienfaq [2020/03/06 09:12] (current) – external edit 127.0.0.1 |
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| * Q. //Why does Wien get the band gap of Si wrong?// | * Q. //Why does Wien get the band gap of Si wrong?// |
| A. Density Functional Theory underestimates the band gaps of insulators and semiconductors. This is a well-known shortcoming, and there are ways to estimate the gap better, but they are computationally more expensive. Theories that take account of many-body interactions in the solid, including the "exchange interaction", can be expected to reproduce the excited state structure of the solid far more accurately. The "GW" approximation is one such. Many papers address the topic. One that uses Si as an example is Yakovkin //et al//., Surface Review and Letters 14 (2007) 481. | A. Density Functional Theory underestimates the band gaps of insulators and semiconductors. This is a well-known shortcoming, and there are ways to estimate the gap better, but they are computationally more expensive. Theories that take account of many-body interactions in the solid, including the "exchange interaction", can be expected to reproduce the excited state structure of the solid far more accurately. The "GW" approximation is one such. Many papers address the topic. One that uses Si as an example is Yakovkin //et al//., Surface Review and Letters 14 (2007) 481. There is another discussion at the [[https://www.materialsproject.org/wiki/index.php/Calculations_Manual#Accuracy_of_Band_Structures|Materials Project bandstructure webpage]]. |
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| * Q. //Why are rhombohedral spacegroups troublesome?// | * Q. //Why are rhombohedral spacegroups troublesome?// |
| A. Rhombohedral spacegroups (those that start with R, like R3m for example) are tricky because there are 2 ways to describe a material with rhombohedral symmetry. One way is the true rhombohedral coordinates: a=b=c, and alpha=beta=gamma, and the associated positions for that system. Another way is to create a hexagonal unit cell with 3 times the volume with a'=b' not= c' and alpha'=beta'=90˚ and gamma'=120˚ and use the positions for those. Google "hexagonal to rhombohedral conversion" and look [[http://en.wikipedia.org/wiki/Trigonal_crystal_system#Rhombohedral_lattice_system|here]]. In Bi2Te3, for example (SG = R3barm = #166), using the hexagonal lattice parameters and placing Bi at (u,u,u) x=0.4 and Te1 and (0,0,0) and Te2 at (v,v,v) v=0.792 generates the correct 5-atom cell. | A. Rhombohedral spacegroups (those that start with R, like R3m for example) are tricky because there are 2 ways to describe a material with rhombohedral symmetry. One way is the true rhombohedral coordinates: a=b=c, and alpha=beta=gamma, and the associated positions for that system. Another way is to create a hexagonal unit cell with 3 times the volume with a'=b' not= c' and alpha'=beta'=90˚ and gamma'=120˚ and use the positions for those. Google "hexagonal to rhombohedral conversion" and look [[http://en.wikipedia.org/wiki/Trigonal_crystal_system#Rhombohedral_lattice_system|here]]. In Bi2Te3, for example (SG = R3barm = #166), using the hexagonal lattice parameters and placing Bi at (u,u,u) x=0.4 and Te1 and (0,0,0) and Te2 at (v,v,v) v=0.792 generates the correct 5-atom cell. |
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