Recombination Equation

[qiushidaren]

recombination equation

For recombination, here is the equation dn/dt=-Δn/tau, but here is a question, dn/dt is an instantaneous quantity, but -Δn/tau is a quantity for the recombination procedure, does it mean tau is very small so -Δn/tau can be considered as an instantaneous procedure, I am very confused about this equation.
Your comments and suggestions will be appreciated!

 

[aryajur]

recombination equation, hole

In this equation Δn is the excess electron concentration, ie. in excess of the normal concentration of electrons in the the semiconductor. This is a function of time since as time goes by these excess electrons will recombine with a time constant of tau. So this actually is the equation that defines it. You can solve the equation to get the rate of Δn=Δn0 exp(-t/tau)

 

[qiushidaren]

In this equation Δn is the excess electron concentration, ie. in excess of the normal concentration of electrons in the the semiconductor. This is a function of time since as time goes by these excess electrons will recombine with a time constant of tau. So this actually is the equation that defines it. You can solve the equation to get the rate of Δn=Δn0 exp(-t/tau)

Yes I know that, but what I can't understand very clearly is that Δn/tau is not an instantaneous quantity in my opinion but dn/dt is a instantaneous quantity, so how can these two be equal? Are there any underlying default assumptions for this equation, e. g., tau is so small that Δn/tau can be considered as an instantaneous quantity?
Thank you in advance!

 

[aryajur]

dn/dt is the rate of increase of electron concentration. Δn is the excess electron concentration, and the equation states (if there is no generation):
dn/dt = -Δn/tau

Δn/tau is the recombination rate at any instant, it changes every instant because Δn is changing every instant. So Δn/tau is actually an instantaneous quantity, recombination rate at any instant that is.

 

[qiushidaren]

dn/dt is the rate of increase of electron concentration. Δn is the excess electron concentration, and the equation states (if there is no generation):
dn/dt = -Δn/tau

Δn/tau is the recombination rate at any instant, it changes every instant because Δn is changing every instant. So Δn/tau is actually an instantaneous quantity, recombination rate at any instant that is.

I still can't understand your explanation, in my opinion, Δn is a constant, tau is also a constant, so why Δn/tau is an instantaneous quantity because Δn/tau is a constant in my opinion? Your help will be highly appreciated!

 

[aryajur]

Well, all I can tell you is Δn cannot be constant. Just review a chapter from Streetman, or maybe Sze. The basic explanation is that in equilibrium when there are no excess carriers the rate of recombination=rate of generation of carriers and this is proportional to the product of electron and hole concentrations. This is the basic fact from which that differential equation came. So now when you have excess carriers the rate of recombination which is proportional to the product of the electron and hole concentrations is increased while the rate of generation will be the same as it was in equilibrium. So whenever you have excess carriers there will be a faster recombination rate of the excess carriers, and that is what is represented mathematically by this equation. So if the excess carriers are recombining, how can they be constant!
So Δn which is the excess carrier concentration is not a constant but a number which is changing continuously with time. I don't know how I can explain any clearer than this.