How does increasing temperature affect the electron emission current?

In a thermionic power converter, the rate of electron emission increases rapidly as the temperature of the emitter increases. This relationship is described by the Richardson-Dushman equation, which mathematically relates the emission current density to the absolute temperature of the material.123

Because the emission of electrons is fundamental to the operation of these devices, higher temperatures allow a greater proportion of electrons within the emitter to overcome the electronic work function—the energy barrier required for an electron to escape the surface. While increasing the temperature enhances this emission, practical performance can be limited by the space-charge effect, where the buildup of emitted electrons creates a negative cloud that repels further emission. To maintain efficient power conversion, engineers often use techniques such as reducing electrode spacing or introducing positive ions to neutralize this charge.12