Something's wrong in the transmission spectrum of silicon pn junction tutorial

[narin]

Hi,

I did the silicon pn junction tutorial (http://quantumwise.com/publications/tutorials/item/828-silicon-p-n-junction) exactly as stated. When I inspect the transmission from the I-V curve object there seems something weird. In the V=-1V bias, the transmission looks like this:
 


The transmission is reported as 4.88E-16 in the bias window. At V=1V bias, where pn junction is conducting, the transmission spectrum is this:

.

The transmission at V=1V bias is reported as 3.61E-23 in the bias window.

The current calculation is this:



The current at V=-1V is zero while at V=1V bias, there's the forward current of 0.9nA. According to the transmissions, current of V=-1V should be higher than the current at V=1V. Why is there a contradiction here like this? I ask for your kind help. Thanks in advance.

[Umberto Martinez]

In the transmission analyzer window you can also see the value of the current which correspond to the IV plot.
The current is calculated, from the transmission coefficients and the fermi functions. see notes here: http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.transmissionspectrum.html

Better to plot the IV curve on a logarithmic scale. You will see that you have an exponential behavior both at negative and positive bias.
There is a script in the tutorials which you can use to do that.

Finally, note that inelastic scattering is indeed important for a silicon p-n junction.
This effect is described in this tutorial: http://quantumwise.com/publications/tutorials/item/837-inelastic-transmission
and you can see that indeed the current increase at negative bias by including e-p interaction.

[Anders Blom]

What these two figures show you, and it could be expected from just comparing the size of the Si band gap to the applied bias, is that the current is not conducted at the Fermi level, but in the tails of the transmission spectrum outside the bias window level, where the Fermi distributions anyway do not decay to zero so quickly, so they pick up the conduction band states (the rising part of T(E) above 0.6 eV = Eg/2).

Just looking at the transmission values at E=0 is therefore meaningless - the transmission there is for all practical purposes zero for all values of the bias.

[narin]

Thank you for your replies. I got it now. And a connected question (may be a recurring question) is that when I do the doping same as the silicon pn junction in a graphene nanoribbon pn junction (as attached) where left is p-doping and right hand side is n-doping, the current-voltage relationship is like this:



I couldn't solve why it is the origin symmetric of the silicon pn characteristics. When the junction is p-n, p side is anode and n side is cathode and the current should  be as in the silicon pn junction. I coulnd't figure this out for 2 weeks. Your kind help is appreciated. Best regards.

[Anders Blom]

The 1D graphene band structure is a lot different compared to buk Si, so a direct comparison is not necessarily possible.

Can you show the "Additional plot" also, so we can see the individual transmission spectra at each bias? Also, what you really should do is plot the LDOS at zero, positive, and negative bias, like at the end of the pn junction tutorial. From that, it will probably be possible to understand the relationship between the bias and the current.

[narin]

Hi,

Thank you very much for your reply. Here's the Iv curve with additional plots:



Also, DDOS at 0V, -1V and 1V biases are as follows consequently:


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IMO, the DDOS images have no similarity with the DDOS images of the silicon pn junction tutorial. Also not compilant with the DOS of a pn junction given in http://wanda.fiu.edu/teaching/courses/Modern_lab_manual/pn_junction.html referenced in the tutorial.  Is it the screening length or the doping error, how can I obtain a proper pn junction with soped GNR in ATK, your help would be very much appreciated. Regards.