How to calculate Fermi energy of metals?

[ashish dabral]

Hi, 

I would like to know how to calculate the fermi energy of metals using cp2k. 

For example, Cu has a fermi energy of around 7.0eV, which can also be 

calculated using the general formula involving carrier concentration (https://en.wikipedia.org/wiki/Fermi_energy, the

three dimensional case.) I would like to know how can I obtain this value (approximate) from the bulk metal unit cell. 

I am interested in transition metals mostly. 

Thanks

[Ari Paavo Seitsonen]

Dear Ashish Dabral,

  The only way _I_ know is to calculate a system with surface (well, two, slab model) and then align the Fermi energy via the potential in the middle of the slab - should be thick enough so that in the middle it is converged - and the potential in the middle of the vacuum. So the value of "Fermi energy" would be the work function. I guess that one would get the same value if one would then take the difference of the potential in the middle of the slab and potential in the vacuum, and then uses that after aliging the difference between the potential and the Fermi energy in a bulk system.

  With GGA one usually gets too small values of the work function if I remember correctly (self-interaction/asymptotics), by about 0.5-1 eV depending on the material.

    Greetings,

       apsi

2017-02-08 17:17 GMT+01:00 ashish dabral <ashishd...@gmail.com>:

Hi, 

I would like to know how to calculate the fermi energy of metals using cp2k. 

For example, Cu has a fermi energy of around 7.0eV, which can also be 

calculated using the general formula involving carrier concentration (https://en.wikipedia.org/wiki/Fermi_energy, the

three dimensional case.) I would like to know how can I obtain this value (approximate) from the bulk metal unit cell. 

Thanks

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[Matt W]

Hi,

the OP might need to be a bit careful with the definition of the fermi energy and explain what they are after. I think there are different conventions around.

I think the free-electron models he referred to, and that 7 eV for copper number, measure the chemical potential / fermi energy relative to the bottom of the band. So it corresponds to something like the energy from the lowest 4s copper states up to the highest occupied states. What you would use it for, I am not quite sure.

So I think it is not the same thing as a physical measure relative to the vacuum, i.e. work function.

Matt

On Wednesday, February 8, 2017 at 10:15:19 PM UTC, Ari Paavo Seitsonen wrote:

Dear Ashish Dabral,

  The only way _I_ know is to calculate a system with surface (well, two, slab model) and then align the Fermi energy via the potential in the middle of the slab - should be thick enough so that in the middle it is converged - and the potential in the middle of the vacuum. So the value of "Fermi energy" would be the work function. I guess that one would get the same value if one would then take the difference of the potential in the middle of the slab and potential in the vacuum, and then uses that after aliging the difference between the potential and the Fermi energy in a bulk system.

  With GGA one usually gets too small values of the work function if I remember correctly (self-interaction/asymptotics), by about 0.5-1 eV depending on the material.

    Greetings,

       apsi

2017-02-08 17:17 GMT+01:00 ashish dabral <ashishd...@gmail.com>:

Hi, 

I would like to know how to calculate the fermi energy of metals using cp2k. 

For example, Cu has a fermi energy of around 7.0eV, which can also be 

calculated using the general formula involving carrier concentration (https://en.wikipedia.org/wiki/Fermi_energy, the

three dimensional case.) I would like to know how can I obtain this value (approximate) from the bulk metal unit cell. 

Thanks

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[ashish dabral]

Thanks for your reply Ari. I am looking for the fermi energy from the bottom of the conduction band. I think what you are referring to is the work function. Matt has specified the same thing in the next reply. The information, nonetheless, is useful. Thanks.

On Wednesday, 8 February 2017 23:15:19 UTC+1, Ari Paavo Seitsonen wrote:

Dear Ashish Dabral,

  The only way _I_ know is to calculate a system with surface (well, two, slab model) and then align the Fermi energy via the potential in the middle of the slab - should be thick enough so that in the middle it is converged - and the potential in the middle of the vacuum. So the value of "Fermi energy" would be the work function. I guess that one would get the same value if one would then take the difference of the potential in the middle of the slab and potential in the vacuum, and then uses that after aliging the difference between the potential and the Fermi energy in a bulk system.

  With GGA one usually gets too small values of the work function if I remember correctly (self-interaction/asymptotics), by about 0.5-1 eV depending on the material.

    Greetings,

       apsi

2017-02-08 17:17 GMT+01:00 ashish dabral <ashishd...@gmail.com>:

Hi, 

I would like to know how to calculate the fermi energy of metals using cp2k. 

For example, Cu has a fermi energy of around 7.0eV, which can also be 

calculated using the general formula involving carrier concentration (https://en.wikipedia.org/wiki/Fermi_energy, the

three dimensional case.) I would like to know how can I obtain this value (approximate) from the bulk metal unit cell. 

Thanks

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[ashish dabral]

Hi Matt,

Yes, indeed I am looking for the chemical potential/ fermi energy (at 0K or otherwise, assuming it doesn't change much with temperature).

I need to find the the highest occupied states with respect to the bottom of conduction band for the metal. I would like to align semiconductors wrt

to the fermi energy to evaluate metal-semiconductor junction properties.

Thanks

[Matt W]

Hi,

you are approximately trying to find states that fit the free-electron model it seems. 

Best I could suggest is to look at projected density of states and see if you can see a clear increase in copper (or whatever element) s functions in a sensible energy range.

You could also look a band dispersion in k-space and try and find approximate parabolas leading up to the fermi level ...

Whether these features will be easy to spot in a real transition metal calculation, I don't know.

Matt

[ashish dabral]

Thanks for the suggestion. If I could find a reference for expermental data for fermi energies for metals, my problem

would be solved, but apparently that is not straightforward either.