Hi, all.
I calculated the bands structure and am trying to compare its vary with doping.
I would like to align the highest occupied and lowest unoccupied energy level of SrTiO3 like the attachment file.
My question is how to set the baseline? I mean I calculated the highest occupied and lowest unoccupied energy level of SrTiO3 are around 10 eV using Quantum ESPRESSO, but in the attachment they are negative.
Please help me. Many thanks.
Calculate the total density-of-states D(ε) from the bandstructure you have calculated (summing over all the k points of the 1BZ and over all the band indices and spin indices), multiply it by the Fermi function f(ε-μ,T), integrate with respect to ε and divide the result by the volume of the unit cell. This gives you a number. Vary the chemical potential μ until this number is equal to the number of electrons in the unit cell. The calculated μ is the sought-after chemical potential at temperature T.
Irrespective of the values, you can just plot them in a graph as y axis contains energy gap (HOMO and LUMO energy values) and x axis contains the doped elements, then you will get the picture like above
You need to calculate the vacuum level by doing a slab calculation. This sets the absolute energy scale (all materials have the same vacuum level!). Then your HOMO and LUMO which represent wrt to the vacuum level the ionization potential and electron affinity respectively (this is approximate as DFT is not an exact theory) are quantities intrinsic to your material (and chosen surface). These numbers are also experimentally available; so if you have them for 2 different materials, you would know how their conduction (or valence) bands are positioned with respect to each other.
After an eventual charge transfer the 2 Fermi levels will lineup and you will get your band bending.
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