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

ashish dabral ashishd... at gmail.com
Thu Feb 9 16:44:49 UTC 2017

```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.

On Thursday, 9 February 2017 15:39:46 UTC+1, Matt W wrote:
>
> 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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