<title>Current spreading in apertured vertical-cavity lasers</title>

Abstract

Scaling of the threshold current density in apertured vertical cavity lasers is limited by scattering losses, current spreading, and carrier diffusion. We consider the contributions of all three effects, but focus on current spreading. We analyze a vertical cavity laser (VCL) with low scattering losses so the scaling of the threshold current density is dominated by current spreading under the aperture. We show that a simple analytic estimate (appropriate for circular geometry) for the increase in threshold matches experimental data extremely well without any fitting parameters. One can also conveniently apply the estimate of current spreading to VCLs with double apertures or multiple layers of different resistivities. We also show that current spreading should only negligibly reduce the differential efficiency as implied by experiment.

High-performance small vertical-cavity lasers: a comparison of measured improvements in optical and current confinement in devices using tapered apertures

“…We see no strong variation with size which suggests that additional carriers injected above threshold going into unclamped regions relative to clamped regions changes negligibly with size. There are a number of assumptions which keep us from unequivocally concluding the lateral injection efficiency is not changing with size, but these data provide strong evidence that there is little variation laterally, which is in agreement with theoretical predictions [8]. Lastly, we should note that these measurements are on devices with low scattering losses.…”

“…Previous studies have indicated that lateral current spreading between the aperture and the active region can be significant in apertured devices [4], [8], [10]. In Fig.…”

“…Therefore, most of the change in threshold current density relative to the broadarea threshold is due to current confinement only. To make this point clearer, it is useful to compare with the model developed in [8] for the spreading when there is a purely resistive region between the aperture and an active region with a diode J-V characteristic. In that model, (in the absence of excess loss) should scale as (2) where for a layer of uniform resistivity and thickness .…”

“…One might expect the unclamped voltage at the aperture to increase the current spreading above threshold and drop the slope efficiency, but an estimate of this increased spreading above threshold suggests it should not be significant even at diameters of 1 m [8]. Even so, the contribution of current spreading to threshold is significant at much larger diameters.…”

Ultra-Low Threshold Vertical-Cavity Surface-Emitting Lasers for USAF Applications

“…The expansion coefficients a α j and b α j for each region are found by back substitution through (40) and (36).…”