Continuity Equation Semiconductor Derivation Part 1 

You are welcome! Glad you are finally able to wrap your head around it, it's probably the most challenging topic in intro semiconductors. I had to learn it several different ways before I finally started to understand what was going on.

Great question, it makes some approximations which are only valid for minority carriers.

P (total number) goes to p (Number Density or total Number per Volume)

Thanks, I was having the same doubt when dividing by ∆V

Excellent question. I'm approximating the derivative using a finite ∆V, implicitly assuming that the time derivative is a function of the small volume element. dV would be more in keeping with calculus notation, and would work just as well.

Initially we assume that G=R, but strictly speaking this is only true under steady-state. Transiently, it isn’t true. Additionally, G and R might actually be functions! (Of space or time), and so to solve the continuity equation you need to include their full functional form.

Solar cells as an counterexample where G is larger than R (hopefully haha)

These days I use photoshop, but I used to use sketchbook.

Means

@@girivardhangiri4324 maybe the answer is late but the drift current is the current caused by the electric field