We investigate a growth mechanism which allows for the fabrication of catalyst-free InAs nanowires on Si (111) substrates by chemical beam epitaxy. Our growth protocol consists of successive low-temperature (LT) nucleation and high-temperature growth steps. This method produces non-tapered InAs nanowires with controllable length and diameter. We show that InAs nanowires evolve from the islands formed during the LT nucleation step and grow truly catalyst-free, without any indium droplets at the tip. The impact of different growth parameters on the nanowire morphology is presented. In particular, good control over nanowire aspect ratio is demonstrated. A better understanding of the growth process is obtained through the development of a theoretical model combining the diffusion-induced growth scenario with some specific features of the catalyst-free growth mechanism, along with the analysis of the V/III flow ratio influencing material incorporation. As a result, we perform a full mapping of the nanowire morphology versus growth parameters which provides useful general guidelines on the self-induced formation of III-V nanowires on silicon.