In this paper, we present a systematic analysis for the design of Si-rich-nitride (SRN) based interposer waveguide layers interfacing InP-based devices and Si3N4 waveguides, towards monolithic co-integration of active and passive elements through a Back-End-Of-Line process. The investigation is performed via extensive 2D-eigenvalue and 3D-FDTD electromagnetic simulations and focuses on three different interposer designs, where performance in terms of coupling loss and back reflections is exchanged for fabrication complexity. In addition, a tolerance analysis is performed for the demonstration of the proposed coupling scheme's resilience to fabrication misalignments. The calculations use for the refractive index of the SRN interposer, real values extracted from ellipsometry measurements of a novel ultra-Si-rich-nitride material developed and engineered for this purpose. This new material provides tunability in the real part of the refractive index with low-stress crack free samples grown up to 500nm thickness. Test structures with cutbacks featuring waveguides of 500 × 500nm2 cross section formed via e-beam lithography reveal 15dB/cm propagation losses in line with similar amorphous silicon-rich nitride (aSi:N) materials. The proposed coupling concept although assumes an InP active medium, can be applied also with GaAs based lasers and dual facet devices such as Semiconductor Optical Amplifiers (SOAs) and electroabsorption modulators. In addition, all proposed designs are compatible in terms of critical dimensions with low cost 248nm DUV lithography targeting to maximize the low-cost advantage of the Si3N4 platform with very high coupling performance. Our results are expected to pave the way for the generation of a versatile, low cost, high performance monolithic InP-Quantum-Dot (QD)/Si3N4 platform on a common Si substrate.