Internal quantum efficiency (η_i)

Internal quantum efficiency $\eta_i$ describes the conversion of above-threshold injected current to stimulated photons inside the cavity:

where $I_\text{stim}$ is the current contributing to stimulated emission and $I - I_\text{th}$ is the total above-threshold drive current. Bounded by unity for any single-junction device.

The external differential quantum efficiency $\eta_d$ combines $\eta_i$ with the fraction of intracavity photons that escape through the front facet:

where $\alpha_m = (1/L) \ln(1/R)$ is the mirror loss (in units of length$^{-1}$), $\alpha_i$ is the internal cavity loss, and $L$ is the cavity length. Inverting:

Extraction by length-dependence. Plotting $1/\eta_d$ versus $L$ for a set of nominally identical devices with different cavity lengths produces a straight line:

• Slope = $\alpha_i / (\eta_i \ln(1/R))$
• Intercept ($L \to 0$) = $1/\eta_i$

This method simultaneously yields $\eta_i$ and the internal loss $\alpha_i$, providing intrinsic material parameters independent of facet design. The technique is the standard for active-region characterization in III–V epitaxy development.

Typical values:

Low $\eta_i$ indicates excess non-radiative recombination — often dominated by Auger recombination in long-wavelength III–V devices, or by Shockley–Read–Hall recombination through defect states in immature material systems. Measured single-device $\eta_d$ alone cannot distinguish whether low efficiency comes from $\eta_i$ or from facet design.