This thesis presents the systematic growth and characterization studies of the GaInNAs/GaAs Quantum Well (QW) and related GaNAs bulk material by Molecular Beam Epitaxy (MBE) technique. The motivation of this work lies in the significant advantage in growing optoelectronic devices on GaAs substrate compared to InP substrate. The availability of N plasma source and MBE ensure the incorporation of sufficient N in the GaInNAs material. They also make low temperature growth possible, which is essential for reducing phase separation in the material. As-grown and annealed GaInNAs/GaAs QWs were characterized by Photoluminescence (PL), Time-Resolved Photoluminescence (TR-PL), and X-Ray Diffraction (XRD) to examine their optical and structural quality. The integrity of the GaAs cap layer grown on the QW samples and annealed by Rapid Thermal Annealing (RTA) equipment was confirmed by Atomic Force Microscopy (AFM).