After reading the first few articles ( stranks et. al and xing et. al), I understood that they use one dimensional diffusion model to fit the carrier population decay rate as,

dn/dt = D d2n/dx2 -k n;

Now I understand where the diffusion term is coming from. But the second term is attributed to decay of excited state population by electron or hole quenching in presence of electron transport material and hole transporting material respectively. So I am assuming they modeled it as:

electrons + ETM -------- ETM-

dn/dt = -k'n [ETM]; assuming [ETM] doesn't change, 

dn/dt = -kn

however, have they taken account of electron hole recombination within the perovskite layer which would also decrease the excited state population. Recently, Kamat et. al showed that excited state decay mostly via electron hole bimolecular recombination or,

e- + h+ ---- [eh]

dn/dt = k'' n2 ; (assuming same number of electrons and holes)

So shouldn't the overall equation be:

dn/dt = D d2n/dx2 -k n - k'' n2  to calculate the diffusion coefficient D.

And then use L = sqrt (D*lifetime of perovskite films)

Or is it, exciton relaxation rather than electrons and hole bimolecular recombination, which suggests,

(e-------h+) ---------(eh)

So dn/dt = k'' n

and then dn/dt = D d2n/dx2 -k n - k'' n = D d2n/dx2 -k' n;

I am not sure if I interpreted the model right. Can anyone please explain if I am not thinking it right?? Thank you!

Saurabh Chauhan