Effect of vacuum on carrier mobility

AMSET
1

Dear Developers,

I am using amset to model carrier mobilities in 2D materials. I have following queries:

  1. How to take into account effect of vacuum on elastic constants?
  2. As the transport coeffcient will have dependence on volume- wiill it have some effect of r mobility as well? Should we scale the output mobilities by volume and thickness of 2D layer?

Any pointer on this will be very helpful.

Best,
AK

2

Dear Alex,

  1. Iā€™m not familiar with calculating the elastic constants of 2D materials, so it isnā€™t obvious to me how to take the vacuum into account.

  2. The transport coefficients shouldnā€™t have a dependence on the vacuum height, unless there is some interaction occurring across the layers. There is no need to scale the output mobilities.

Best,
Alex

3

Thanks Alex.

This helps.

4

Dear Alex,
I hope you are doing well.
There is a volume term in the denominator of electrical conductivity. For 2D system, I think we need to multiply the factor (cell height (thickness+vacuum)/original thickness of the 2D system) to electrical conductivity to get accurate result.

5

Dear Alex_Kent and Aamir_Shafique,

For 2D materials, you should consider the area instead of volume. In order to compare with 3D, 2D can also convert to ā€œeffectiveā€ 3D, such as elastic constant. You multiply the vacuum and divide the thickness, that is all! More useful details can be found in this paper: https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.6b03921

Best wishes,
Zhibin

6

Thank you Zhibin. In the future I will update AMSET to support 2D materials more efficiently.

7

Thanks @Zhibin_GAO.

Yes I was using similar approach.

However, I think there is one issue when using these scaled elastic constants in amset (perhaps @alex can give some insights here). By design amset takes the full 3D elastic tensor in 6x6 Voigt notations. For 2D materials some component will be zero. I find that in some cases this leads to diverging solution with the error SVD did not convergence. Not sure if these are related - I am just throwing it out there.

best,
kent

8

@Aamir_Shafique - Just wanted to ask if you able to good results for 2D materials mobility in amset? For me amset works perfectly for bulk, but I have not had much luck for 2D materials.

TIA.
AK

9

Hi Alex,

There are some other factors I will have to consider when enabling proper support for 2D systems. Not only will the set of available q-vectors for scattering be constrained to the 2D plane, but the actual form of the scattering rate equations will be different too. For example, polar optical phonon scattering has a different form, as detailed in this paper.

Implementing these changes will take some time but I will update you when it is done.

Best,
Alex

1 Like
10

Thank you very much. :slightly_smiling_face:

11

Dear Zhibin,

I am using AMSET to calculate scattering rates, relaxation times, and mobility for a 2D monolayer using a vacuum-containing supercell.

I understand that the output mobility should not be scaled by the vacuum height. However, should the 3D mobility or relaxation time be converted to a 2D value using c/deff, i.e.

Ī¼2D=Ī¼3D*C/deff

and similarly for Ļ„, or should both mobility and relaxation time be used directly as obtained from AMSET without any c/deff correction?

12

Dear Shivam_Pandey, I am also working on calculating the carrier mobility of 2D materials using AMSET, and I encounter the same issue of how to handle the vacuum layer, especially regarding the elastic constants and piezoelectric constants. What do the symbols C and the deff distribution in the formula represent? Does Ī¼3D refer to the calculation results without any vacuumā€‘layer correction? Thank you very muchļ¼

13

Dear wyzong, As amset takes carrier concentration only in 3d format, therefore we use the above formula to convert carrier concentration from 2d to 3d. normally the carrier concentration for 2d material lies between1e11 to 1e14,

14

Dear Shivam_Pandey, Thanks for your reply. I donā€™t think we need to convert the carrier concentration, because what is set in settings.yaml is already the 3D carrier concentration with the unit cm-3. I think that 2D corrections are not needed for the deformation potentials or the dielectric constants. The key question is whether the elastic constants and piezoelectric constants need to be corrected, and how to correct them reasonably.

15

Dear Alex,

I am calculating the carrier mobility of a 2D Janus material considering acoustic deformation-potential (ADP) and polar optical phonon (POP) scattering.

For ADP scattering, I calculate the mobility analytically using a 2D deformation-potential model:

Ī¼ADPā€‹=6350 C2D/ T ā€‹ā€‹(māˆ—)^2 DP^2ā€‹

This gives a mobility that is essentially independent of carrier concentration and depends mainly on temperature.

For POP scattering, I am using AMSET, since AMSET gives POP mobility at different concentration, shall i take average of all the concentration and then use methissian rule to calculate mobilityā€¦

Best regards,

Shivam Pandey