Generation and recombination in stationary state

In summary: EQUIVALENT currents. In summary, in a semiconductor in thermal equilibrium generation and recombination are equivalent. However, in a "stationary state" generation and recombination are also equivalent. This does not have sense to me because in stationary state there is no time derivatives nor spatial gradients. You will need a divergenceless (i.e., solenoidal) current along a finite path of field-free space to compensate for the difference in generation and recombination rates.
  • #1
LydiaAC
Gold Member
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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?
 
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  • #2
LydiaAC said:
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.
 
  • #3
Hello Matteo83:
But if the system is homogeneous and carrier concentrations are constant. Are not you in thermal equilibrium?
Lydia
 
  • #4
LydiaAC said:
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 [tex]\frac{dp}{dt}[/tex]=-1/e div J[tex]_{h}[/tex] + U[tex]_{h}[/tex] 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
 
  • #5
LydiaAC said:
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.
 
  • #6
LydiaAC said:
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
 

What is generation and recombination in stationary state?

Generation and recombination in stationary state refers to the processes by which charge carriers (electrons and holes) are created and destroyed in a semiconductor material. In this state, the number of carriers entering and leaving a particular region is equal, resulting in a steady state of charge carriers.

What factors affect generation and recombination in stationary state?

The rate of generation and recombination in stationary state is influenced by several factors, including temperature, doping concentration, and the presence of impurities or defects in the material. Additionally, the material's bandgap, carrier lifetime, and electric field can also impact the rate of generation and recombination.

Why is understanding generation and recombination important in semiconductor devices?

Generation and recombination play a crucial role in the operation of semiconductor devices such as transistors and solar cells. The balance between these processes affects the device's performance and efficiency. Therefore, understanding and controlling generation and recombination are essential for optimizing the performance of these devices.

What is the difference between generation and recombination?

Generation and recombination are opposite processes that occur in semiconductors. Generation involves the creation of charge carriers, while recombination involves the destruction of these carriers. In the stationary state, the rates of generation and recombination are equal, resulting in a balance of carriers in the material.

How is generation and recombination measured in a semiconductor material?

The rate of generation and recombination in a semiconductor material can be measured using techniques such as photoconductivity, photoluminescence, and transient photocurrent. These methods involve shining light on the material and measuring the resulting changes in its electrical and optical properties.

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