# Cut-off frequency of an LED [closed]

I'm trying to solve this problem:

A GaAs LED is at $$300 K$$ when the current density is 100 $$A/cm^2$$ . The width of the active region is $$1 µm$$. Assume that, for that current, we are in the strong injection regime, and that the bimolecular coefficient is $$10^{-10} cm^3 /s$$. Calculate the cut-off frequency for that current density.

I know the answer is 4 MHz.

I know that the cut-off frequency relates do the carrier's lifetime.

$$f_c=\frac{1}{2 \pi \tau}$$

Right, so now I need to calculate the carrier's lifetime. I know that since this is strong injection we would have:

$$\tau=\frac{1}{B \Delta n_0}$$

where B is the bimolecular coefficient. So now I need to calculate $$\Delta n_0$$.

My question now is how can I use the temperature, the current density and the width of the active region to calculate $$\Delta n_0$$? I feel that I might need some parameters of GaAs at 300 K, but I'm having trouble understanding what parameters.