The mass action law states, that the product of electron concentration and hole concentration is equal to the square of the intrinsic carrier density. That applies to both intrinsic and extrinsic semiconductors. In an extrinsic N - type semiconductor the number of electrons in the conduction band increases and thus the propability of recombining is higher so the mass action law is satisfied by the increace of electron concentration and the decrease of hole concentration. What I don´t understand is, why that the generation rate is equal to the recombination rate at thermal equlibrium. Wasn´t it, that the recombination rate increases and the generation rate decreases? Please can someone help?
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$\begingroup$ won't you get out of neutral atoms otherwise? $\endgroup$– fraxinusCommented Jul 1, 2022 at 12:06
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4$\begingroup$ If more carriers generated than the amount of carriers that recombine, we are not in thermal equilibrium. $\endgroup$– Roger V.Commented Jul 1, 2022 at 14:06
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1 Answer
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It is all about counting and having a finite number of occupied and unoccupied states. You can also think about it in terms of a continuity equation.
Generation - you have to move the electron to an unoccupied state, and there has to be an electron available to be moved to the unoccupied state.
Recombination- there has to be an available hole and there has to be an electron available to recombine.
If you have more generation than recombination you will fill all the unoccupied states unless you run out of available electrons to be excited first. If there are no available states to be excited to, or no available electrons to be excited the generation rate would be zero. However there would be lots of opportunities for recombination.
If you have more recombination occurring than generation the opposite would happen.
The coefficients for the process can remain the same but the rates will depend on the numbers in the appropriate energy level.
The way you get the coefficients depends on the process, in the doped semiconductor case it could depend on the doping density and the temperature and where the dopant level is in the band gap. Going from band to band the temperature and band gap. But you only have so many dopant and so many states in the energy bands.
So if the semiconductors is just sitting there at some temperature there is some number of electrons jumping from the dopant level per volume per second to the conduction band, and some number of electrons per volume per second jumping from the valence band to the conduction band per second. But there has to be some number of electrons per second going back to the dopant atoms and some number per volume per second that will recombine with an available hole.
Those rates then have to be balanced or you won’t be in equilibrium.
If you shine light on the semiconductor you will have a generation rate for holes and electrons that depends on the absorption and intensity of light and initially the total generation of carriers will be higher than the total number of carriers recombining, but since you have excess numbers of electrons and holes the total number of carriers recombining will increase and in equilibrium the generation rate and recombination rates will be equal.
This is a little easier to see in a two level or three level system like a gas laser rate equations but the same principles hold for semiconductors.
