[DFTB-Plus-User] DOS and Transmission units
Théo Giverne
theo.giverne at etu.u-bordeaux.fr
Thu Feb 18 11:07:24 CET 2021
Dear A. Pecchia,
First thank you again for your help. How ever some interrogations remains. As I understand DOS is normed as "number of states per eV" and not as "number of states per volume unit per eV ».
Here is my method to compute mobility by integrating over E from fermi energy to infinity the DOS factor F-D distribution at a given temperature I should obtain the density of charge carrier (free electrons) but this is if DOS is also per unit of volume. And then if i integrate this time over the whole energy i should get the total density of electron. My question is how can I norm the DOS in such a way that it is also per unit of volume. Do I divide it by the size of my system or by the size of the system with the k-points repetition or am I on the wrong way x).
Finally I have further question about transmission. In the Electron transport calculations in armchair nanoribbon the transmission graphs show transmission above 1 which shouldn’t be possible as transmission I a fraction, like percentage, but it is not the case for transmission with TunnellingAndDos and I am not sure i understand the difference between the two transmission calculation.
Again thank you for your help 🙏🏻,
Best regards,
Théo Giverne
> Le 18 févr. 2021 à 09:17, Alessandro Pecchia <alessandro.pecchia at cnr.it> a écrit :
>
>
> I realized I wrote "total number of electrons" but I obviously ment "total number of states".
> The correct Fermi occupation and spin degeneracy gives the total number of electrons.
>
> A Pecchia
>
> -----Messaggio originale-----
> Da: DFTB-Plus-User [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto di Alessandro Pecchia
> Inviato: mercoledì 17 febbraio 2021 23:24
> A: 'User list for DFTB+ related questions'
> Oggetto: [DFTB-Plus-User] R: R: DOS and Transmission units
>
> Dear Giverne,
>
> yes in that case it is exact. You can check yourself that the files obtained from ProjectStates (region*.out) add up exactly to the total number of electrons. Then dp_dos simply smears using gaussians or other functions. Gaussians are normalized hence the integration should give back the total number of electrons beside some quadrature error.
>
> Regards,
>
> A Pecchia
>
> -----Messaggio originale-----
> Da: DFTB-Plus-User [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto di Université
> Inviato: mercoledì 17 febbraio 2021 15:19
> A: User list for DFTB+ related questions
> Oggetto: Re: [DFTB-Plus-User] R: DOS and Transmission units
>
> Dear A. Pecchia,
>
> Thank you for these helpful explications. But now what about the DOS computed by dp_dos from the band.out file. Can I integrate it to obtain the number of electrons in the conduction band for instance?
>
> Best regards,
>
> T. Giverne
>
>> Le 17 févr. 2021 à 12:50, Alessandro Pecchia <alessandro.pecchia at cnr.it> a écrit :
>>
>> Dear Théo Giverne,
>>
>> 'Transmission' is already a dimensionless quantity
>> . It is the transmission of all travelling states at a given energy, E.
>> Mind however that, as defined in most literature of transport, T(E) is the quantity entering the Landauer formula for current, J = 2e/h Integral[ T(E) (f1(E) - f2(E)) dE ]. This means that the T(E) contains the number of states. For a perfectly ideal system it counts the number of bands at a given energy. This also means that T(E) is size-dependent. It depends on cross-section of the conductor.
>>
>> Concerning the density of states computed by TunnelingAndDos, this is the "trace" of the Retarded Green's function on the central region. DOS(E) = -1/pi Im{Trace[GR(E)]}
>>
>> The PDOS is the projection on given atoms/orbitals obtained by sub-tracing the matrix on related atoms/orbitals, such that for instance:
>> PDOS(atom==n, E) = -1/pi Im{ Sum_i GR_ii(E)}, where i are the orbitals of atom n.
>>
>> HOWEVER, it should be noted that integrating this quantity over E does *not* give back exactly the number of electrons in the central region. In order to sum-up to N, the correct formula should be:
>> PDOS(atom==n, E) = -1/pi Im{ Sum_i Sum_j GR_ij(E) S_ji}, where S_ij is the overlap matrix.
>>
>> This was not done because internally GR is restricted to the central region, whereas the sum over j should extend to overlapping regions between central and contacts. In order to get the overlapping parts of GR more computations are needed. Note that such an extra work was done for the density matrix in order to compute correct SCC charges.
>>
>> It should be said that the DOS computed neglecting the overlap reproduces the main information needed to correlate the transmission to the electronic states and localization.
>>
>> Regards,
>>
>> A Pecchia
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> -----Messaggio originale-----
>> Da: DFTB-Plus-User [mailto:dftb-plus-user-bounces at mailman.zfn.uni-bremen.de] Per conto di Théo Giverne
>> Inviato: mercoledì 17 febbraio 2021 10:58
>> A: User list for DFTB+ related questions
>> Oggetto: Re: [DFTB-Plus-User] DOS and Transmission units
>>
>> Dear users,
>>
>> Where can I find in what unit are normalised DOS and Transmission. Without this information the DOS and Transmission are practically useless as they can’t be que quantitatively but only qualitatively.
>> Your answer will be greatly appreciate, thank you,
>>
>> Sincerely,
>>
>> Théo Giverne
>>
>> theo.giverne at etu.u-bordeaux.fr
>>
>>
>>
>>> Le 11 févr. 2021 à 11:05, Théo Giverne <theo.giverne at etu.u-bordeaux.fr> a écrit :
>>> Dear users,
>>> I am currently using the DOS and Transmission results from DFTB+ do obtain some electronic properties.
>>> However I need to know in what units DFTB+ gives the DOS and the Transmission, I couldn’t find any information on this matter, does anyone have a clue ?
>>> Thank you,
>>> Sincerely,
>>> Théo Giverne
>>> theo.giverne at etu.u-bordeaux.fr
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