Regarding sigma calculation in AMSET

AMSET
1

Dear Sir,

I want to calculate electronic conductivity (sigma) as a function of temperature for both n and p type carriers using AMSET. How can I identify the conductivity for a specific carrier? What are the required steps?

There is a parameter present in settings.yaml file, high frequency dielectric. Will it be the same as the static dielectric?

Thank you in advance.

With regards,
Shiladitya

2

Dear Shiladitya,

Apologies for my delayed response.

  1. In amset, n-type doping concentrations are specified by negative doping concentrations, and p-type carriers are specified by positive doping concentrations. See the documentation for more details.

  2. In general, people discuss two dielectric constants:

  • The high-frequency dielectric constant (\epsilon_\infty), sometimes called the “optical dielectric constant”, is the value deduced from the refraction of electromagnetic waves with frequencies high compared to lattice vibrations (phonons).
  • The static-dielectric constant (\epsilon_\mathrm{S}) is the total dielectric screening from the high-frequency response and the vibrational response (lattice). I.e, static = high-frequency + ionic dielectric constants.

Unfortunately, the terminology used by VASP for the dielectric constants is not very precise. If you do a DFPT+LEPSILON calculation, as described in the calculation section of the documentation, the OUTCAR will contain a number of dielectric constants, each with very similar names.

For example, these are taken from the OUTCAR for a DFPT calculation on SnS.

 MACROSCOPIC STATIC DIELECTRIC TENSOR (including local field effects in DFT)
 ------------------------------------------------------
          17.540787     0.000000     0.000000
           0.000000    21.425820     0.000000
           0.000000     0.000000    17.487301
 ------------------------------------------------------

...

 MACROSCOPIC STATIC DIELECTRIC TENSOR IONIC CONTRIBUTION
 ------------------------------------------------------
          19.848112    -0.000007    -0.000001
          -0.000007    41.125796     0.000008
          -0.000001     0.000008    21.693346
 ------------------------------------------------------

Here, the first dielectric constant is actually the high-frequency dielectric constant NOT the static dielectric. The second tensor is the ionic contribution to the static dielectric. To get the final static dielectric constant you have to take the high-frequency dielectric + ionic contribution.

Therefore, the inputs to amset would be:

static_dielectric: 
  - [37.39, 0, 0]
  - [0, 62.56, 0]
  - [0, 0, 39.18]

high_frequency_dielectric:
  - [17.54, 0, 0]
  - [0, 21.43, 0]
  - [0, 0, 17.49]

I hope that helps.

Best,
Alex