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Differential carrier lifetimes and threshold carrier densities in vertical-cavity, surface-emitting lasers

Carrier lifetime measurements are an indispensable tool in semiconductor laser characterization. They allow determination of recombination rates, threshold current density, and other important device parameters. Experimental results on differential carrier lifetimes of gain-guided, proton-implanted and index-guided, oxide-defined vertical-cavity, surface-emitting lasers (VCSELs) are obtained from the laser impedance measurements at subthreshold currents. Differential carrier lifetimes can be derived directly from the impedance characteristics of the lasers. To apply this technique to VCSELs, a small-signal equivalent circuit model is developed. Carrier lifetimes are extracted by fitting the real and imaginary parts of the measured impedance with the circuit model. To confirm the obtained data and check the validity of the proposed equivalent circuit, the lifetimes were also measured using the traditional small-signal optical response technique. A measured response is corrected using already estimated circuit parameters to account for the frequency-dependent modulation amplitude, and fitted with a single-pole function. A good agreement is obtained between the lifetime values measured by electrical and optical techniques, indicating the validity of the equivalent circuit. For each device size, the threshold carrier density value and recombination parameters are obtained from the fit to lifetime dependence on the injection current.