What's the physical insight of the variation of HOMO and LUMO with bias voltage?

[fan0221]

Hello everyone,
       
        I calculated a little molecule with Si electrode and got the energy of HOMO and LUMO in various bias voltage. I  found that the energy of the HOMO and LUMO shifted together with different bias voltage. What's the physical insight of the variation of HOMO and LUMO with bias voltage?

Thank you if you could give me some advices.

[fan0221]

nobody

[nori]

Dear fan0221,

One of the main reason is the potential shift due to applied bias voltage.
However, there is another factor to get MPSH spectrum changed, which is non-equilibrium density matrix.

In your case from Vb = 0V to Vb = 1V, HOMO and LUMO shift are almost the same because only the potential shift seem to affect the spectrum shift.
But above Vb = 1V, the electric structure gets drastically changed because LUMO is included in non-equilibrium density matrix,
 so that the spectrum shift get more complex.

It is the general suggestion, so the detailed analysis for your specific system is needed to understand more precisely why the spectrum get such a change under finite bias.

I'd be happy if my advice can help you.

[fan0221]

Thanks for your answer!

[Anders Blom]

What complicates matter in this case is that your electrodes are semi-conducting. Thus, I suspect you have no current in the low-bias calculations. However, as the bias exceeds the band gap, you start to get tunneling from the valence band of the left electrode to the conduction band of the right one, via the molecule. I imagine this somehow pins the HOMO to the valence band top of the left electrode, perhaps.

[fan0221]

Thanks for your help!