Thermal Emission of Electrons

What thermionic emission is. Every free electron inside a metal is held back from escaping into the surrounding space by an energy barrier at the metal's surface, called the work function $\phi$ of that metal -- the minimum energy a conduction electron must be given to leave the metal entirely. At ordinary room temperature, the thermal energy available to an electron is far too small to overcome this barrier for all but a vanishingly small fraction of electrons, so a cold metal emits essentially no electrons at all.

Heating the metal. If the metal is heated strongly -- typically to a temperature of $1000$-$2500\ \text{K}$, well below its melting point, using a filament carrying an electric current -- a much larger fraction of its free electrons acquire enough thermal kinetic energy to overcome the work-function barrier and escape from the surface into the surrounding vacuum. This process, called thermionic emission (or thermal emission), is the source of the free electrons that every vacuum-tube device -- the vacuum diode (Section 9.3) and the triode valve (Section 9.4) -- depends on.

Factors governing the rate of emission. The number of electrons emitted per second from a given surface depends principally on two factors. First, the temperature of the emitting surface: the emission rate rises extremely steeply (very close to exponentially) with temperature, so even a modest increase in filament temperature produces a large increase in the emission current. Second, the work function of the emitting material: a LOWER work function allows a given temperature to release far more electrons, which is why real thermionic emitters are rarely made of a plain, high-work-function metal alone. …