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 leave through the mirrors, both facets together, rather than being lost inside the cavity:

where ${\alpha }_m=(1\mathrm{/}L)\ln (1\mathrm{/}R)$ 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 $1\mathrm{/}{\eta }_d$ versus $L$ for a set of nominally identical devices with different cavity lengths produces a straight line:

• Slope = ${\alpha }_i\mathrm{/}({\eta }_i\ln (1\mathrm{/}R))$
• Intercept ($L\to 0$) = $1\mathrm{/}{\eta }_i$

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:

Above threshold the carrier density in the active region is clamped, so the recombination there, radiative or not, stays at its threshold rate, and the extra current goes into stimulated emission unless it fails to reach the active region. A low ${\eta }_i$ therefore points mainly to leakage: carriers escaping over the heterobarriers around the active region, which increases with temperature, or current spreading past it. Non-radiative recombination in the active region, such as Auger recombination in long-wavelength III–V devices or Shockley–Read–Hall recombination through defect states, raises the threshold current rather than lowering ${\eta }_i$. Measured single-device ${\eta }_d$ alone cannot distinguish whether low efficiency comes from ${\eta }_i$ or from facet design.

References: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012). G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993). S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007).