We present principles for tunnel-juhction (TJ) design optimization for use in intracavity contacted long-wavelength vertical-cavity surface-emitting lasers (LW-VCSELs). Using the WKB approximation, we find that layer thicknesses of 10 nm on the n++ side and 10 mn on the p++ side are large enough to maximize quantum tunneling probability and small enough to yield low optical free-carrier absorption loss. We also conjecture that our experimental test structures and actual devices have far lower active acceptor concentration than we expect based on an analytical model. Finally, we calculate the necessary doping levels to enable single-mode operation of LW-VCSELs and incorporate these conditions into a complete optimized model of our VCSELs. Based on optimal I-V curves, we can expect an increase in single-mode output power from 2 to 3.5 mW
