# Effect of vacuum on carrier mobility

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

Dear Alex,

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

2. The transport coefficients shouldnâ€™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

Thanks Alex.

This helps.

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.

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 â€śeffectiveâ€ť 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

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

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

@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

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

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Thank you very much.