[DFTB-Plus-User] Fermi Energy

Gabriele Penazzi gabriele.penazzi at bccms.uni-bremen.de
Tue May 14 21:18:53 CEST 2013

On 05/14/2013 06:53 PM, Xiaobao wrote:
>  Dear dftb+ users:
> I am currently working on carbon nanotube using the nonequilibrium 
> Green's function part of the code . First, I have some fundamental 
> questions about setting up the Fermi energy in a transport 
> calculation. Currently, I take the fermi energy calculated from the 
> source/drain calculation step. However, when I perform a 
> self-consistent calculation on a longer tube (source+device + drain 
> region) to determine the fermi energy, its value changes slightly. 
> Which approach is more appropriate for obtaining the fermi energy?


I am not sure what you mean with "when I perform a self-consistent 
calculation on a longer tube (source+device + drain region) to determine 
the fermi energy". Are we still speaking of a periodic boundary 
conditions calculation? If yes, the result should be consistent with the 
contact calculation apart numerical error or different k-point sampling.

> The second question is relating to the first one. The transport 
> direction in my calculation is set to be along the tube axis. I am 
> interested in obtaining accumulate charge density under gate bias. 
> Please be mindful that the bias, is applied along the gate direction, 
> not the transport direction. The applied voltage along the transport 
> is set to zero. My preliminary results didn't show any correlation 
> between the charge accumulation and the applied gated bias. I am 
> looking for the charge change in the order of 10^-4 to 10^-5 in 
> electron unit. Are there anything else I need to be careful about, 
> despite the Fermi energy setting?
> Best wishes,

You're performing a calculation which is for sure quite delicate, 
numerically speaking, as the charge change you expect is pretty small. 
It's very important that the Fermi level you start with is very precise, 
I reccomend you to use a "paranoid" k-point sampling. Check that at 
equilibrium (gate bias zero) the charges in the device area are 
negligible respect to the quantity you're expecting to measure. If the 
fermi level is precise enough, there should be a negligible charge 
difference. Typically, you'll need convergence to the 2nd or 3rd 
decimal, but check it yourself!

Also, when you start to apply gate bias, be sure that your contact are 
far enough from the gate, otherwise you could still converge but you 
could see some artificious charge pinning due to boundary conditions. It 
could be a good idea to check that increasing the device region length 
doesn't change the accumulated charge.

Previous authors (I'm not one of them) made similar calculations, so it 
should be possible.

Another opportunity is to calculate the fermi level which ensure charge 
neutrality in the system, implementing some kind of iterative line 
search scripting. Nevertheless, it should be possible to calculate the 
fermi level with enough accuracy to get a neutral system.

I hope this help to get meaningful results.


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Dr. Gabriele Penazzi
BCCMS - University of Bremen


phone: +49 (0) 421 218 62337
fax: +49 (0) 421 218 62770

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