A double heterojunction InGaAsP LED operating at $1310 \mathrm{~nm}$ has radiative and non-radiative recombination times of 30 and $100 \mathrm{~ns}$ respectively. The current injected is $40 \mathrm{Ma}$. Calculate, Bulk recombination lifetime. Internal quantum efficiency Internal power level.

Solution:

$ \lambda=1310 \mathrm{~nm}=(1.31 \times 10-6 \mathrm{~m})\\ $

$ \begin{aligned}\\ & \tau \mathrm{rr}=30 \mathrm{~ns} \\\\ & \mathrm{\tau rr}=100 \mathrm{~ns}\\ \end{aligned} $

Bulk Recombination Lifetime (τ):

$ \eta_{i n t}=\frac{\tau}{\tau_r}\\ $

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

Internal quantum efficiency (ηint):

$ \begin{aligned} & \eta_{i n t}=\frac{23.07}{30} \\\\ & \eta_{i n t}=\mathbf{0 . 7 6 9}\\ \end{aligned} $

Internal power level (Pint):

$ P_{\text {int }}=\eta_{\text {int }} \cdot \frac{\mathrm{hc} \mathrm{I}}{\mathrm{q} \lambda}\\ $