The structure of p-i-n InGaN/GaN based solar cell having a photonic crystal (PhC)-based light trapping structure (LTS) at the top assisted by the planar metallic (aluminum) back reflector (BR) is proposed. We propose two different designs for efficiency enhancement: in one we keep the PhC structure etching depth extending from the top antireflective coating (ARC) of indium tin oxide (ITO) up to the p-GaN layer (which is beneath the ITO and above the active layer), whereas in the other design, the PhC LTS etching depth has been extended up to the absorbing layer, starting from the top ITO layer. The theoretical optical simulation studies and optimization of the required parameters of the structure, which help to investigate and demonstrate the effectiveness of the LTS in the efficiency enhancement of the structure, are presented. The work also demonstrates the Lambertian light trapping limits for the practical indium concentrations in a active layer cell. The paper also presents the comparison between the proposed designs and compares their results with that of a planar reference cell. The studies are carried out for various indium concentrations. The results indicate considerable enhancement in the efficiency due to the PhC LTS, mainly because of better coupling, low reflectance, and diffraction capability of the proposed LTS, although it is still under the Lambertian limits. The performance evaluation of the proposed structure with respect to the angle of incident light has also been done, indicating improved performance. The parameters have been optimized and calculated by means of rigorous coupled wave analysis (RCWA) method.