I will try to define a derive an expression for the lifetime as it is agreed upon in the semicondcutor literature. The radiative recombination rate R

can be expressed by

R = k np, where k is a constant, n and p are the electron and electron concentrations

assuming n=p for intrinsic material as undoped perovskites, then

R=k n^2

The emitted photon flux epsi is proportional to R= dn/dt

epsi =dn/dt= k n^2

depsi/dt= d2n/dn^2= 2k n,

By definition R=n/Tau where Tau is the lifetime.

kn^2= n/Tau

Tau= I/kn

depsi/dt= 2/Tau

Tau= 2/(depsi/dt)

After this definitions and derivations we see that

The lifetime according to the definition above is equal to double the inverse slope of the photolumenance with time.

Best wishes

I will try to define a derive an expression for the lifetime as it is agreed upon in the semicondcutor literature. The radiative recombination rate R

can be expressed by

R = k np, where k is a constant, n and p are the electron and electron concentrations

assuming n=p for intrinsic material as undoped perovskites, then

R=k n^2

The emitted photon flux epsi is proportional to R= dn/dt

epsi =dn/dt= k n^2

depsi/dt= d2n/dn^2= 2k n,

By definition R=n/Tau where Tau is the lifetime.

kn^2= n/Tau

Tau= I/kn

depsi/dt= 2/Tau

Tau= 2/(depsi/dt)

After this definitions and derivations we see that

The lifetime according to the definition above is equal to double the inverse slope of the photolumenance with time.

Best wishes

Relationship between free carrier lifetime and PL decay time constants will depend on measurement conditions. The simplest case is when injection level is high so that any space charge fields are screened by photo generated carriers, and trap density (not recombination center density) is negligible so that trapping-re-emission is not taking place. Then one only needs to deal with diffusion and recombination and TRPL decay is usually bi-exponential. Short time constant is then related to diffusion and interface recombination, long time constant to bulk recombination. To find the lifetime one would need to solve continuity equation either numerically or analytically. There is a lot of literature on this. For relative sample-to-sample comparisons, one can simply fit TRPL decay with two exponents and use longer time constant “Tau2” as a metric.

Just keep in mind that you will calculate the recombination lifetime determined only by radiative recombination. If you carry out PL measurements at room temperature (close to working conditions of a solar cell) there is a chance that you will have a significant non-radiative recombination channel in addition to the radiative one. Thus, the determined recombination lifetime based on PL measurements will be overestimated and will not correctly represent the total recombination losses in your device.