On the road towards next generation high efficiency solar cells, the ternary Indium Gallium Nitride (InGaN) alloy is a good passenger since it allows to cover the whole solar spectrum through the change in its Indium composition. The choice of the main structure of the InGaN solar cell is however crucial. Obtaining a high efficiency requires to improve the light absorption and the photogenerated carriers collection that depend on the layers parameters, including the Indium composition, p-and n-doping, device geometry.. . Unfortunately, one of the main drawbacks of InGaN is linked to its p-type doping, which is very difficult to realize since it involves complex technological processes that are difficult to master and that highly impact the layer quality. In this paper, the InGaN p-n junction (PN) and p-in junction (PIN) based solar cells are numerically studied using the most realistic models, and optimized through mathematically rigorous multivariate optimization approaches. This analysis evidences optimal efficiencies of 17.8% and 19.0% for the PN and PIN structures. It also leads to propose, analyze and optimize player free InGaN Schottky-Based Solar Cells (SBSC): the Schottky structure and a new MIN structure for which the optimal efficiencies are shown to be a little higher than for the conventional structures: respectively 18.2% and 19.8%. The tolerance that is allowed on each parameter for each of the proposed cells has been studied. The new MIN structure is shown to exhibit the widest tolerances on the layers thicknesses and dopings. In addition to its being player free, this is another advantage of the MIN structure since it implies its better reliability. Therefore, these new InGaN SBSC are shown to be alternatives to the conventional structures that allow removing the p-type doping of InGaN while giving photovoltaic (PV) performances at least comparable to the standard multilayers PN or PIN structures.