Electrode temperature independent transmission spectrum?

[beark]

Recently, I come across some problems about the temperature dependency of current. In my opinion, although the electrode temperature has some physical meaning that it can be interpreted as the electron temperature in the electrode region, we are actually calculating the transport properties at zero temperature. Thus the transmission spectrum is independent of the electrode temperature. If I want to study current at different temperatures, I just need to calculate the transmission spectrum of certain temperature T₀ once, then I change the temperature in f_L-f_R and get the current from the Landauer-Büttiker formula.

I wonder if there is something wrong in my opinion? We cann't have the actually temperature dependent current from ab initio studys now?

[Anders Blom]

You are absolutely correct.

For T(E) to depend on the temperature, then we'd have to bring in phonons and other complicated things. The current, however, is another story, as then we also take the electron distribution into account. We may then for instance end up having a current that's dominated by thermionic emission rather than direct tunneling, as discussed in our tutorial on the graphene Z-shaped transistor structure.

[zhangguangping]

You are absolutely correct.

For T(E) to depend on the temperature, then we'd have to bring in phonons and other complicated things. The current, however, is another story, as then we also take the electron distribution into account. We may then for instance end up having a current that's dominated by thermionic emission rather than direct tunneling, as discussed in our tutorial on the graphene Z-shaped transistor structure.

Dear Anders Blom,
But when I changed the temperature,the transmission spectrum is also changed ,i.e. I have got a temperature dependent T(E).

[Anders Blom]

What I meant to say was, that if we want to model the real physical temperature-dependence of the current, we need phonons etc since the current computed by ATK in the ballistic regime are strictly zero-temperature results. As you noted in another post, the "temperature" used in ATK is rather a numerical trick to aid convergence. This trick may cause T(E) to depend on the "temperature", but the true result is obtained when the "temperature" is extrapolated (somehow) to zero.

(To avoid confusion on this point, it might be better not to use a temperature parameter, but rather specify the Fermi broadening explicitly, as an energy... What do you think?)