Electron injector (EI) technology has already been proven capable of achieving unprecedented sensitivity in the shortwave infrared (SWIR), surpassing the current performance of commercial cameras. As on-chip optical interconnects have drawn increasing attention over the past few years, the need for energy-efficient (<10 fJ/bit) and fast (<10 Gbps) IR receivers has spurred new interest in detectors that can meet such requirements. However, heterojunction phototransistors typically suffer from a large power dependence of the gain-bandwidth product, which constitutes an intrinsic limitation to the realization of high-sensitivity, high-bandwidth photodetectors. We present a comprehensive analysis of the gain and bandwidth of the EI detectors as a function of optical power, for different device architectures. At low light level, as the optical power level increases, the recombination centers in the base are saturated by the higher excess carrier density, and as a result the gain-bandwidth product increases. At higher light level, however, the gain of the phototransistor drastically drops due to Kirk effect. As a result, the gain-bandwidth product peaks at a given power level, which is dependent on the band alignment, doping and defect density in the base. The presented results demonstrate a wide tunability of the EI detectors gain-bandwidth product as a function of the device architecture, and hence constitute a valuable platform for the design of novel detectors that can simultaneously achieve high sensitivity and high bandwidth at the desired optical power level depending on the envisaged application.