EPW Forum

Dear all,

In a mobility calculation, I set a specific carrier concentration (ncarrier), for example, -1.5E21(hole mobility). However, after the Progression iq (fine) step, the program prints the temperature, Fermi level, and hole density, but the reported hole density is 0.227147E+21 instead.

I would like to ask:

1) Which parameters could influence this discrepancy? I noticed that increasing fsthick and refining the grid does not significantly change the result.
2) Is the mobility result valid for the given output density, or should I disregard it completely?

Thank you in advance for your help!

Best regards,
Giuseppe

Hi Giuseppe,

The Fermi-level is found by using a bisection method (iterative) since its a root-finding problem. However, there is an upper-bound to the number of iterations. That means, once the max number of iterations is reached and the relative error (which is 1e-5) between previous and current step is still higher than the threshold (which is 1e-5), the code returns the last computed Fermi-level along with the hole/electron density for that Fermi-level.

This rarely happens when carrier concentration is low but since your carrier concentration is quite high, it makes sense. Coming to your question 2, the mobility is valid for the carrier-concentration returned by EPW.

Best regards,
Sabya.

Hi Sabya,

Thank you very much for your reply. I tried to verify whether the discrepancy between the input and output hole density was due to reaching the maximum number of iterations, but this does not seem to be the case for two reasons.

First, there is no "too many iterations in bisection" warning in the output—though I wouldn’t focus too much on this. The key point is that when I perform a calculation in Quantum ESPRESSO using tot_charge corresponding to my input hole density (1.5E21), a Fermi-Dirac smearing matching the temperature, and the same mesh as in the mobility calculation, I obtain a Fermi level very close to the one printed in the EPW output after the bisection step. This suggests that the Fermi level is correct and corresponds to the intended hole density.

However, what remains unclear is why EPW prints a different hole density. To confirm this, I ran another test with Quantum ESPRESSO, setting the hole density to the value reported in EPW’s output. In this case, the resulting Fermi level was significantly different from the one given by EPW. This suggests that the Fermi level and hole density reported by EPW are inconsistent with each other.

I would really appreciate any further insights into this issue.

Thanks again for your help!

Best regards,
Giuseppe

You could check whether the parameter fsthick is large enough.

I also considered the possibility that the fsthick parameter was not large enough. To test this, I increased its value and observed the following behavior: with fsthick = 0.4, I obtained the same hole density as before; increasing it to 0.5 resulted in 0.227540E+21, and at 0.6, the hole density became 0.227543E+21.

Regarding the Fermi level, EPW reports a value of 5.3033, and using 0.6 I reach (starting from the valence band maximum) 5.0491 for the included states. Given this trend, it seems unlikely that further increasing fsthick would allow me to reach the target hole density

Hi,

The calculation of carrier concentration assumes the Fermi level is in the gap. The concentration at the order of 10^21 is rather high. So it may be near the band edge. Please check the doped Fermi level carefully. Or you can start from a lower carrier concentration, like 10^16

Best,
Zhe