The silicon avalanche-mode light-emitting diode (AMLED) opens a route for on-chip opto-electronic applications in standard CMOS, both due to its relatively broad spectral overlap with the spectral responsivity of silicon photodiodes and due to its high speed capability. This work presents closed form models for the key figures of merit (FOMs) of AMLEDs, namely, current (or power) density, cut-off frequency, radiative efficiency, and specifically for optical data communication energy cost per photon. Their derivations are based on one-dimensional analyses of an abrupt single-sided (p + n or n + p) junction and of a p-i-n diode. TCAD simulations for optimized device structures, including the recently reported superjunction (SJ) LED, were performed to validate the model. Measurements on single-sided abrupt junctions and SJ diodes are shown to validate some of the modelled trends. The results show that a p-i-n or an SJ diode is favorable to a conventional single-sided junction diode for the AMLED design. In addition, as confirmed for conventional AMLEDs by earlier reports, the results indicate that for a yet higher efficiency the carrier supply should be increased. For this a combination of a separate minority carrier injector and SJLED is proposed, referred to as the injection-avalanche CMOS SJLED. However, more experimental optical data (e.g., absolute photon flux) are needed for a more accurate model validation.