How does thermionic emission allow electrons to escape from a heated metal surface?

In a thermionic power converter, electrons are liberated from a heated metal surface—the emitter—through a process known as thermionic emission.

While electrons are mobile within the metal's conduction band, they are held inside by an attractive force. To escape, an electron must acquire enough energy to overcome this barrier, which is defined as the electronic work function. This energy requirement is characteristic of the specific material and typically ranges from one to five electron volts.123

When the metal is heated to high temperatures, thermal collisions provide some electrons with sufficient kinetic energy to exceed the work function. These high-energy electrons can then break free from the surface of the metal. The rate of this emission is highly temperature-dependent and is described mathematically by the Richardson–Dushman equation, which shows that emission increases rapidly as the temperature rises. Once liberated, these electrons flow toward a cooler collector electrode, allowing the device to convert thermal energy directly into electrical energy.1324