Band diagram of pn-junction diode at low temperature

[sunnyleekr]

Hi

What could be the band diagram of pn-junction diode at very low temperature where dopant ionzation is completely frozen out?

Would it still be like the band diagram at room temperature?

 

[DrDu]

I don't think that the band structure per se will change very much. It is more a question whether the physics at low temperatures can still be described within an independent electron picture.

 

[sunnyleekr]

I don't think that the band structure per se will change very much. It is more a question whether the physics at low temperatures can still be described within an independent electron picture.

Thank you for the reply but if the band diagram doesn't change much, how can we describe the built-in potential since there is no mobile(ionized) charge present?

 

[DrDu]

Ok, so you are asking whether it makes a difference to bring two junks of p and n doped semiconductor at room temperature or at low temperature?
I was thinking of cooling a diode.

 

[sunnyleekr]

Ok, so you are asking whether it makes a difference to bring two junks of p and n doped semiconductor at room temperature or at low temperature?
I was thinking of cooling a diode.

We usually learn semiconductor physics based on the fact that dopant ionization is present.
The simplest doped device we can think of will be pn-diode. And we know analytically what the depletion width, built-in potential and band diagram will be with given temperature and doping (Na/Nd).

But let's think of the behaviour of such device at very low temperature where there are absolutely no mobile carriers (extra charge from donor/acceptor is not at all ionized).

Where will be the fermi level of n/p-type semiconductor?
Can we draw band diagram if we attach p and n type semiconductor to build a pn diode?
What is the built-in potential of pn-diode?
No mobile charge but can we still apply room temperature analysis?

These are the questions I have.

 

[caffenta]

But let's think of the behaviour of such device at very low temperature where there are absolutely no mobile carriers (extra charge from donor/acceptor is not at all ionized).

The carriers freeze out on each side of the space-charge region. Inside the space-charge region, carriers are "pushed out" by the built-in field, so you still have ionized impurities.

Where will be the fermi level of n/p-type semiconductor?

At the energy where n_e=1/2. In semiconductor physics, the Fermi level is really the chemical potential term in the Fermi-Dirac statistics. The Fermi level does not move towards mid-gap when carriers freeze out (I think that's what you're thinking). Carriers freeze out because of the exp{(E-E_F)/kT} term in the denominator of the FD statistics.

Can we draw band diagram if we attach p and n type semiconductor to build a pn diode?

If you do it at T->0K? Well, in the degenerate case, you will never have complete freeze-out anyway. But if there was complete freeze-out, you would probably never reach equilibrium. Remeber that the "Fermi level must be the same evrywhere" condition applies to equilibrium.