Optical emission from carbon nanotube transistors (CNTFETs) has recently attracted significant attention due to its potential applications. In this paper, we use a self-consistent numerical solution of the Boltzmann transport equation in the presence of both phonon and exciton scattering to present a detailed study of the operation of a partially suspended CNTFET light emitter, which has been discussed in a recent experiment. We determine the energy distribution of hot carriers in the CNTFET and, as reported in the experiment, observe localized generation of excitons near the trench-substrate junction and an exponential increase in emission intensity with a linear increase in current versus gate voltage. We further provide detailed insight into device operation and propose optimization schemes for efficient exciton generation; a deeper trench increases the generation efficiency, and use of high-k substrate oxides could lead to even larger enhancements.