Puzzles on Fermi energy defined in EPW

[amosyang]

Dear all EPW users,

Recently, I am puzzled with the definition of Fermi energy in the input file of epw.in. According to the wikipedia, the Fermi energy is the energy difference between the highest and lowest occupation states of single-particle. And its definition needs one reference. So there comes the puzzle, how can we define the Fermi energy in epw. Is it equal to the Fermi level? In the example of GaN, the fermi energy is defined as 9.9775 eV, while the energy of highest occupation level is 10.7349 eV. In this way, it seems that the Fermi energy is lower than the highest occupation level. Is it right?

On the other hand, the Fermi level lies in the middle of energy gap of intrinsic semiconductor. With the highest occupation energy level, such as 10.7349, then can I say that the Fermi level of intrinsic semiconductor GaN is 10.7349+Eg/2, where Eg is the energy gap.

Best

Jiayue Yang
RWTH Aachen University

[carla.verdi]

Dear Jiayue

We use Fermi energy with the common meaning of Fermi level.
The calculation of the Fermi level in QE (efermig routine) will give an arbitrary number between the highest occupied state and the lowest unoccupied state in the case of a semiconductor, hence why it's useful to be able to input the fermi level. You can change the number in the example and put a value that corresponds to the middle of the gap.
There are other cases in which it is useful to input the value of the Fermi level. For example, if you want to calculate some properties on a k-path in the BZ, then the Fermi level determined by the call to efermig would be inaccurate even for a metal, because instead of integrating on a fine uniform grid you are integrating on a k path instead.

Best
Carla

[amosyang]

[code]Dear Carla,

Thanks very much for your explanation of Fermi energy used in EPW. Following the idea, I try to correlate the doping concentration with the Fermi level in the example of GaN. After the scf calculation, I have obtained the highest occupation level (that is Fermi level) of 10.952293 eV. On the other hand, since the intrinsic carrier concentration is 1.6xe-10 cm-3, if I want to have the n-doping concentration of 1e19 cm-3, I have to shift the Fermi level 1.7 eV upwards. Based on this, I change the Fermi value to 12.652293 eV in the input file of epw following the rigid band approximation.

However, all I get for the lamda are zero and the gamma are zero, too. I don't know how to solve this. Please help me.

Best

Jiayue Yang
RWTH Aachen University, Germany

[carla.verdi]

Dear Jiayue

If I am correct, the Fermi level you have in your input is still inside the gap. However, the imaginary part of the phonon self-energy that you are trying to calculate contains a difference between the Fermi occupations at k and k+q, multiplied by an energy conserving delta function [Eq. 1 in CPC 181 (2010) 2140], therefore you will obtain zeros if the Fermi level is inside the gap.

Best
Carla

[Nandan]

To continue this thread, since I am also using GaN as my example.
I am also trying to artificially push the Fermi energy ~2KT below conduction band minima. But I always get "NaN" as the Im(Sigma). Why should this happen?
From the earlier email I understand that it could be zero but I do not understand why I get a "NaN".

Golden Rule strictly enforced with T = 0.030161 eV
Gaussian Broadening: 0.010000 eV, ngauss= 1
DOS = -0.000000 states/spin/eV/Unit Cell at Ef= 9.216200 eV

WARNING: only the eigenstates within the Fermi window are meaningful

ik = 1 coord.: 0.0000000 0.0000000 0.0000000
-------------------------------------------------------------------
E( 1 )= -18.4839 eV Re[Sigma]= NaN meV Im[Sigma]= NaN meV Z= NaN lam= NaN
E( 2 )= -16.4028 eV Re[Sigma]= NaN meV Im[Sigma]= NaN meV Z= NaN lam= NaN
E( 3 )= -10.0716 eV Re[Sigma]= NaN meV Im[Sigma]= NaN meV Z= NaN lam= NaN
E( 4 )= -3.9470 eV Re[Sigma]= NaN meV Im[Sigma]= NaN meV Z= NaN lam= NaN

Thanks and Regards,

Nandan.

[sponce]

Dear Nandan,

Nan can be caused by a bug (I fixed one so it could be solved in the next QE 6.0 release that should come out very soon), by a compilation problem or by very large numbers (overflow).

Can you confirm that it works if you place the Fermi level in the middle of the gap?

If so can you try to place the Fermi level closer but not as close ?

Best,

Samuel

[Nandan]

Dear Samuel,

Thanks for the reply. I will check what happens when the Fermi level is in the middle of the gap.

My example works fine when I am not reading the fermi energy from the input file.

I don't think it is relevant, but an example of AlAs using an executable on a different machine, works without errors.
So it might just be compilation related.
Although there is no change in the scattering rates by shifting the Fermi energy.

Nandan.

[sponce]

Dear Nandan,

Off course, result wont change if the Fermi level is in the gap (wherever) except if you are within kT or if your smearing is very large and you are relatively close to a band.

Best,

Samuel