Solid-state thermionic power generators are an alternative to thermoelectric modules. In this presentation, we report an analytical model to investigate the performance of these generators in the non-linear regime. We identify dimensionless parameters determining their performance and provide measures to estimate acceptable range of thermal and electrical resistances of thermionic generators. We find the relation between the optimum load resistance and the internal resistance and suggest guide lines for the design of thermionic power generators. Finally, we discuss the possiblity of using layered 2D heterostructures to design nanoscale thermionic coolers capable of working at relatively low temperatures.