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Optical emission in carbon nanotube devices has potential for many technological applications. Electroluminescence in a recently demonstrated carbon nanotube transistor, with a partially suspended geometry, is attributed to excitonic recombination. Here, we report detailed device simulations for this device structure, treating the excitonic and phonon scattering effects on transport. We confirm the localized generation of excitons near the trench-substrate junction, and the bias dependence of emission characteristics. Furthermore, we provide insight into device operation, exploring device optimization schemes; specifically, the effects of the trench depth and of high-k substrate oxides. We observe a moderate increase in emission efficiency for high-aspect ratio trenches, while high-k oxides could lead to significant improvements.