# Can transmission spectrum value exceed 1 within bias window?

I'm trying to simulate a ZnO nanoribbon structure using TranSIESTA in the siesta package. When I performed the transport calculations, for a few bias points within the bias window, the transmission spectrum value exceeded 1.
The transmission spectrum gives the probability of transmission of electrons. Since it is a probability function, its value shouldn't exceed 1.

Are my simulation results correct?

• The transmission is between 0 and 1 PER conductive channel. So if you have a single chain of metallic atoms the transmissson won't exceed 1. If there are multiple channels the transmission is the sum of the probabillities associated with each channel. Sep 7 at 6:23
• Sorry, sir, I couldn't get exactly what you meant by multiple channels. I have constructed ZnONR channel region by repeating the single ribbon of 4 atom width using the supercell cell approach. The same single ribbon structure is used as the electrode by repeating twice. Does this mean I have multiple channels? Sep 7 at 7:44

Each electron has an associated transmission probability, put in another common nomenclature is that for every channel you'll have a transmission probability between 0 and 1. So if you have 2 channels you can get between 0 and 2 and so forth.

So your simulations seems perfectly fine.

For bulk systems you can see the number of channels in the bandstructure. Basically each energy crosses a set number of bands, for bulk systems the transmission equals the number of bands crossed at that energy.
Only when introducing defects will you see fractional transmissions that can still maximally be the number of bands for the electrodes at the given energy (remember the electrons originate from the electrodes).

When applying a bias the electrodes are still in equilibrium since one only shifts the electronic structure. This is the basis for NEGF calculations in TranSiesta, OpenMX, ATK etc.. I.e. the eigenspectrum of an electrode at $$\mu$$ gets all eigenvalues shifted according to $$\epsilon(\mu) = \epsilon(0) + \mu$$.

So the same procedure about examining the bandstructures from the electrodes applies, simply examine energies while taking into account the chemical potentials.

• Thank Your sir for your reply. But I'm little confused about the statement "Basically each energy crosses a set number of bands, for bulk systems the transmission equals the number of bands crossed at that energy." Upon applying the bias voltage doesn't the bandstructure of the channel/scattering region change? If so then how do I know how many number of energy bands are crossing the Fermi level at a particular bias point. Do we need to check the energy bands of the electrodes? Could you please elaborate in this aspect. Thank you. Sep 8 at 9:32