The radiative and nonradiative recombination lifetimes of minority carriers in the active region of a double heterojunction LED are $60 \mathrm{nsec}$ and $90 \mathrm{nsec}$ respectively. Determine the total carrier recombination lifetime and optical power generated internally if the peak emission wavelength si $870 \mathrm{~nm}$ and the drive current is $40 \mathrm{~mA}$.

Solution:

Given:

λ = 870 nm 0.87 x 10-6 m

τr = 60 nsec.

τnr = 90 nsec.

I = 40 mA = 0.04 Amp.

i) Total carrier recombination lifetime:

$ \frac{1}{\tau}=\frac{1}{\tau_r}+\frac{1}{\tau_{n r}} $

$ \begin{aligned} & \frac{1}{\tau}=\frac{1}{60}+\frac{1}{90} \\\\ & \frac{1}{\tau}=\frac{150}{5400}\\ \end{aligned} $

ii) Internal optical power.

$ \mathrm{P}_{\text {int …