I know that when an electron falls into a hole the number of mobile carriers reduces to zero from two. And when an electron jumps into conduction band the number of mobile carriers increases to two from zero.
But I cannot understand why recombination rate is proportional to the product of holes and conducting/mobile electrons. Does understanding this requires so much complicated math. I know basic probability but is this possible to explain this in high school level? How does the product of those is related to rate?
Best Answer
Let's look at this from the perspective of the electron:
Assume you have an electron at some point in a semiconductor. Now, you also need a hole in the vicinity. The probability of a hole is proportional to the overall number of holes.
Now, taking a step back, you'll need an electron first – and the probability of having a hole at a certain point is again proportional to the overall number of electrons.
So, it needs "luck" twice, getting an electron in a certain point, then getting a hole in the same. (the order doesn't actually matter – you need both.)
So, make an analogous experiment: Flip a coin (probability of say head=1/2) to figure out whether you get an electron, and roll a die to figure out whether you get a hole (probability of a say ⚅ = 1/6). What's the probability that you get an electron (head) and a hole (⚅) at the same time?
It's the product of these two probabilities, because both events are independent from each other.