Stable laser emission with narrow linewidth is of critical importance in many applications, including coherent communications, LIDAR, and remote sensing. In this work, the physics underlying spectral narrowing of self-injection-locked on-chip lasers to Hz-level lasing linewidth is investigated using a composite-cavity structure. Heterogeneously integrated III–V/SiN lasers operating with quantum-dot and quantum-well active regions are analyzed with a focus on the effects of carrier quantum confinement. The intrinsic differences are associated with gain saturation and carrier-induced refractive index, which are directly connected with 0- and 2-dimensional carrier densities of states. Results from parametric studies are presented for tradeoffs involved with tailoring the linewidth, output power, and injection current for different device configurations. Though both quantum-well and quantum-dot devices show similar linewidth-narrowing capabilities, the former emits at a higher optical power in the self-injection-locked state, while the latter is more energy-efficient. Lastly, a multi-objective optimization analysis is provided to optimize the operation and design parameters. For the quantum-well laser, minimizing the number of quantum-well layers is found to decrease the threshold current without significantly reducing the output power. For the quantum-dot laser, increasing the quantum-dot layers or density in each layer increases the output power without significantly increasing the threshold current. These findings serve to guide more detailed parametric studies to produce timely results for engineering design.