# [CP2K:8672] How to calculate Fermi energy of metals?

Matt W MattWa... at gmail.com
Thu Feb 9 14:39:46 UTC 2017

```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

On Wednesday, February 8, 2017 at 11:15:54 PM UTC, ashish dabral wrote:
>
>
> 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
>
> On Wednesday, 8 February 2017 23:59:58 UTC+1, Matt W wrote:
>>
>> 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 <ashis... at 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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>>>
>>>
>>>
>>> --
>>>
>>> -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
>>>   Ari Paavo Seitsonen / Ari.P... at iki.fi / http://www.iki.fi/~apsi/
>>>     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
>>>     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935
>>>
>>
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