Compact silicon integrated lasers are of significant interest for various applications. We present a detailed investigation for realizing sub-mm long on-chip laser structures operating at λ = 1.533 µm on the silicon-on-insulator photonic platform by combining a multi-segment silicon waveguide structure and a recently demonstrated erbium-doped thin film deposition technology. Quarter-wave shifted distributed feedback structures (QWS-DFB) are designed and a detailed calculation of the lasing threshold conditions is quantitatively estimated and discussed. The results indicate that the requirements for efficient lasing can be obtained in various combinations of the designed waveguide DFB structures. Overall, the study proposes a path to the realization of compact (< 500 µm) on-chip lasers operating in the c-band through the hybrid integration of erbium-doped aluminum oxide processed by atomic layer deposition in the silicon photonic platform and operating under optical pumping powers of few mW at 1,470 nm. Silicon photonics has drawn a great interest in the past decades 1,2. The maturity of this field is such that its transition to an industrialization stage has already been achieved with the most important applications in the field of telecommunications and datacom 3-7. Nevertheless, there are still key points to be resolved, including the issue of the light source. Due to silicon's indirect band gap, one of the biggest challenges in silicon photonics is to realize compact, high efficiency, low power consumption and low cost on-chip lasers and amplifiers 8. Several methods have been investigated to address this problem. The hybrid integration of III/V based lasers on silicon can lead to high efficiency integrated lasers and is considered as the present dominant approach 9. This integration scheme is clearly controlled and effective, as the question of light coupling between active III/V zones and silicon waveguides has been solved in previous works 10,11. It nevertheless requires heterogeneous integration technologies, which are not directly complementary metal oxide semiconductor (CMOS) compatible with additional fabricating process steps. Any direct monolithic integration of materials deposited at temperatures compatible with a back-end CMOS process (≤ 500 °C) is therefore preferable. In this way, introducing rare-earth doped materials wildly employed in the development of optical fiber communication systems may be of interest 12. Recently, several key progresses related to the integration of rare-earth-doped amorphous aluminum oxides in silicon nitride waveguides have been reported 13-22. These works have enabled very interesting prospects by proposing integrated structures that have led to laser emission in several configurations, the most interesting one being probably that of optically pumped integrated DFB lasers. However, the demonstrated devices have footprint sizes of more than 2 cm 14 or even much larger 22. By comparing these dimensions with those required by advanced silicon photonics integration scheme...