Physics · Ch 11 — Dual Nature of Radiation and Matter
Electron Emission
Electron Emission
The Free Electron and the Surface Barrier
Metals conduct electricity because they contain a sea of free electrons — negatively charged particles that are not bound to any particular atom and can drift through the lattice. But if these electrons are so free, why don't they simply float out of the metal?
The answer lies at the surface. When an electron tries to leave, the metal surface immediately acquires a net positive charge (because positive ions are left behind). This positive charge exerts an attractive force that pulls the electron back. The free electron is therefore trapped inside the metal by the electrostatic attraction of the positive ion cores. To escape, the electron must have enough energy to overcome this pull.
Think of the metal surface as a potential-energy cliff. Inside the metal, an electron's energy is relatively low. To get out, it must climb up a potential-energy wall. The height of that wall is the work function.
Work Function — The Escape Energy
The minimum energy that must be given to an electron to pull it out from the surface of a metal is called the work function of that metal. It is denoted by (phi-zero) and is measured in electron volts (eV).
Definition of 1 eV: One electron volt is the energy gained by an electron when it is accelerated through a potential difference of 1 volt.
This unit is standard in atomic and nuclear physics because the energies involved are tiny fractions of a joule.
The work function is not a universal constant. It depends on two things:
- The properties of the metal (its atomic structure and electron configuration).
- The nature of its surface (cleanliness, crystal face, oxidation, etc.).
Different metals have different work functions. For example, cesium has a low work function (around 2.1 eV), while platinum has a high one (around 5.6 eV).
Three Ways to Supply the Escape Energy
The free electrons inside a metal already possess some thermal energy at room temperature, but it is far below the work function for most metals. To eject an electron, we must supply the missing energy. There are three distinct physical processes by which this can be done.
(i) Thermionic Emission
If the metal is heated to a sufficiently high temperature, the free electrons gain thermal energy. When the thermal energy of an electron exceeds the work function, it can overcome the surface barrier and escape. This is the principle behind the old vacuum tubes (valves) and cathode-ray tubes — a heated filament emits electrons.
The higher the temperature, the greater the number of electrons that have enough energy to escape. The emission current increases dramatically with temperature, following Richardson's law (which you will study in detail later).
(ii) Field Emission
Instead of heating the metal, you can apply an extremely strong electric field — of the order of — to the metal surface. Such a strong field distorts the potential-energy barrier at the surface, making it thinner. Electrons can then tunnel through this thin barrier (a quantum-mechanical effect) and escape. This is what happens in a spark plug: the intense electric field pulls electrons out of the metal electrode, initiating the spark.
Field emission requires enormous electric fields — V/m is a hundred million volts per metre. Ordinary household fields are nowhere near strong enough to cause this effect.