Generation and recombination in stationary state

[LydiaAC]

I know that in a semiconductor in thermal equilibrium generation and recombination are equivalent. This is obvious from continuity equation since in thermal equilibrium there is no time derivatives nor spatial gradients.
However, I have read that in "stationary state" generation and recombination are also equivalent. That does not have sense to me. You do not have time derivatives but you keep space gradients and it is possible to have a current to compensate for the difference in generation and recombination rates.
Is there something that I am not understanding well?

 

[matteo83]

I know that in a semiconductor in thermal equilibrium generation and recombination are equivalent. This is obvious from continuity equation since in thermal equilibrium there is no time derivatives nor spatial gradients.
However, I have read that in "stationary state" generation and recombination are also equivalent. That does not have sense to me. You do not have time derivatives but you keep space gradients and it is possible to have a current to compensate for the difference in generation and recombination rates.
Is there something that I am not understanding well?

I have only read about "equivalent generation and recombination in stationary state" when the system is homogeneous, since carriers concentration are constant and spatial derivatives vanishes.

 

[LydiaAC]

Hello Matteo83:
But if the system is homogeneous and carrier concentrations are constant. Are not you in thermal equilibrium?
Lydia

 

[matteo83]

Hello Matteo83:
But if the system is homogeneous and carrier concentrations are constant. Are not you in thermal equilibrium?
Lydia

Your question is very interesting.
I have never reflected on thermal equilibrium concept in these systems, but I think that solution is in the difference between thermal equilibrium and "equilibrium" that set up in not homogeneous system without external biasing where in every point of space so called "virtual" drift currents are equivalent to "virtual" diffusive currents. "Equilibrium" is then defined by the condition divJ=0.
Not homogeneous systems are intrinsically out of thermal equilibrium but may be in "equilibrium" as for example a pn-junction without biasing.
So if you takes continuity equation in the form \frac{dp}{dt}=-1/e div J_{h} + U_{h} you can see that stationary "equilibrium" state in not homogeneous system may have equivalent generation and recombination.

I' m not sure that this is the right explanation but it seems to be coherent.
If you find a different one I'll be glad to know it.

Matteo

 

[Gokul43201]

However, I have read that in "stationary state" generation and recombination are also equivalent. That does not have sense to me. You do not have time derivatives but you keep space gradients and it is possible to have a current to compensate for the difference in generation and recombination rates.

It looks to me like you will need a divergenceless (i.e., solenoidal) current along a finite path of field-free space.

 

[no_math_plz]

it is possible to have a current to compensate for the difference in generation and recombination rates.

it's possible to have a current to compensate for the difference in generation and recombination rates, sure, but for a single kind of carrier. in stationary state, electron and holes currents give a total current whithout net flux, so NET recombination rates for electrons and NET recombination rates for holes are perfectly equivalent (for example, if I have an excess of holes entering a volume, I have a net flux of holes that recombinate, and so an excess of electrons entering in that volume, bringing to a null net flux of current but not necessarily to a null current). don't confuse diffusive equilibrium, that implicates NULL currents, with stationary condition