Fermi energy location in band diagram for ATK and VASP

[kaypu]

Dear Quantumwise staff:
 Hi, i found the Fermi energy in band diagram is different for VASP and ATK. Take MoS2 for example, For VASP, the Fermi energy is near valence band (See VASP.jpg). However, for ATK. the Fermi energy locates about half of valence and conduction (see ATK.jpg). So, i want to know, how to determine Fermi energy in ATK? DOS integration from the lowest energy to Fermi energy=total electron?

[filipr]

In QuantumATK (and I presume the same is true for VASP) the Fermi level is calculated as the root of the equation sum_{k,n} f(e_{k,n} - Ef) - N = 0, i.e. the energy Ef for which the sum of state occupations equals the number of electrons. The value of the Fermi level will thus depend on the state eigenvalues, the occupation method, the broadening and the precision of the root finding algorithm.

For large band gaps and small occupation broadenings the values of the eigenvalues should not matter much, and in the limit of broadening going to zero (but not exactly zero) one can show that using this algorithm the Fermi level will always be exactly in the middle of the band gap. In your examples I guess the reason for the discrepancy is that your VASP and QuantumATK calculations use different occupation methods or broadenings. You can read more about occupation methods here: https://docs.quantumatk.com/manual/technicalnotes/occupation_methods/occupation_methods.html

In any case, for a system with a band gap the exact value of the Fermi level is irrelevant as long as it is inside the band gap. In both the VASP and QuantumATK case the density of states will integrate to the total number of electrons as the density of states is zero inside the band gap (integrating zero equals zero). As such the Fermi level for a semiconductor/insulator calculated using DFT is somewhat meaningless and only used for defining a zero value when plotting band structures and DOS. Instead meaningful quantities should be based on the valence band maximum or conduction band minimum.