Thermionic energy converter (TEC) has recently received significant attention, for it holds potential for clean energy generation with a very high theoretical conversion efficiency (60%). For the latter to be achieved, some of the key hurdles are to be overcome. This paper discusses all these key hurdles along with modelling of solar energy conversion using a TEC with nano-materials and metals, using the modified Richardson-Dushman equation, which best describes the thermionic emission current density from these materials. Using two scenarios: allowing natural heat radiation from the back surface of the collector and using controlled heat collection from the collector to maintain it at a fixed temperature. We then discuss results of simulation of the conversion efficiency as a function of temperatures of emitter and collector, work functions and Fermi energy of emitter and collector at absolute zero temperature, solar insolation, the radius of parabolic concentrator and emissivity of radiating surfaces. We discuss the impact of neglecting the radiation losses on the efficiency evaluation as has been done by other workers recently. We suggest some innovative ways to reduce significantly the space charge effect to make a solar TEC a reality.