Why does the emission current decrease when a material has a higher work function?

In the context of a thermionic power converter, the electronic work function represents the minimum energy required to remove an electron from the surface of a material.12

The emission current decreases as the work function increases because the work function acts as an energy barrier that electrons must overcome to escape the material's surface. According to the Richardson–Dushman equation, the rate of electron emission is exponentially dependent on this energy barrier.342

At a given temperature, only a specific fraction of electrons within the material possess sufficient thermal energy to exceed the work function threshold. When the work function is higher, fewer electrons reach the necessary energy level to escape, resulting in a lower emission current density. Consequently, for efficient thermionic conversion, it is desirable to utilize emitter materials with a low work function that can also withstand high operating temperatures.24