Current spreading in apertured vertical cavity lasers

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.