What is meant by thermionic emission?

In a conducting solid, we have many free electrons which are responsible for conduction. The electrons are free in the sense that they are allowed to move freely within the crystal lattice of the solid.

They however, are not allowed to leave the conductor due to attraction from positive ions.

Thus, in order to pull out an electron from a solid, we somehow need to supply energy from outside the system so that the electron can overcome the electrostatic attraction due to the positive ions in the solid and come out of it into the surroundings.

The minimum energy required to pull an electron outside the solid is called it's work function. This energy may be supplied in a number of ways.

One such way is by heating the solid. We ofcourse know that heating a solid means supplying thermal energy to it and thus to it's constituent particles. The electrons upon getting sufficiently energized due to this energy may leave the metal under certain conditions.

Suppose, we take a cathode and an anode in a low pressure CRT.
Now, upon introducing a negative voltage at the cathode and positive voltage to anode, we find that no current flows through the gas. (Assuming that voltage is not as high as to pull electrons out which in case would be the case of cold emission)

Now,the we heat up that cathode. At a certain temperature, we will find that a current flows through the circuit i.e. through the CRT. What happens is that, due to imparting thermal energy to the cathode and thus to it's electrons, they are sufficiently energized to leave the metal. As soon as they leave it, they are attracted by the positive anode and thus the flow of current is justified.

One can derive an equation specifying thermionic emission as,

#J=AT^2exp(-(ephi)/(k_BT))# which is called the Richardson-Dushman equation.
Where, #A# is a constant independent of the metal,
#T# is the temperature, #ephi# the work function and #k_B# is the Boltzmann constant.

#J# signifies the thermionic emission current density.