What is Schottky Effect?
The Schottky effect is a phenomenon in physics that reduces the energy required to remove electrons from a solid surface in a vacuum when an electric field is applied to the surface. This increases the discharge of electrons from the surface of a heated material and affects the thermionic current, the surface ionization energy, and the photoelectric threshold. The Schottky effect is named after Walter H. Schottky and is important for electron emission devices, especially electron guns.
Thermionic Emission and Work Function
To understand the Schottky effect, we need to first review some concepts related to thermionic emission and work function.
Thermionic emission is the emission (release) of charge carriers (ions or electrons) from the surface of a material due to the thermal energy given to it. In a solid material, there are usually one or two electrons for each atom that are free to move from one atom to another based on band theory. These electrons can escape from the surface if they have enough energy to overcome the potential barrier that binds them to the material.
The minimum amount of energy (produced due to thermal energy) necessary for an electron to escape from the surface of a material is called the work function. The work function depends on the type of material, its crystal structure, its surface condition, and the surrounding environment. The work function is inversely proportional to the thermionic emission current, which means that a lower work function leads to higher electron emission.
The relationship between the thermionic emission current density J and the temperature T of a heated metal is given by Richardson’s law, which is mathematically analogous to the Arrhenius equation:
where W is the work function of the metal, k is the Boltzmann constant, AG is the product of a universal constant A0 multiplied by a material-specific correction factor λR which is typically of order 0.5.
Electric Field and Barrier Lowering
Now, we can explain how the electric field affects thermionic emission and causes the Schottky effect.
When an electric field F is applied to a heated material, it lowers the potential barrier that prevents electrons from escaping from the surface. This results in decreasing the work function by an amount equal to ΔW and thereby increasing thermionic current. The amount of barrier lowering ΔW can be calculated by:
where qe is the elementary charge, and ϵ0 is the vacuum permittivity.
The modified Richardson equation that accounts for this barrier lowering is:
This equation describes the Schottky effect or field-enhanced thermionic emission, which occurs when a moderate electric field (lower than about 108 V/m) is applied to a heated material.
Field Emission and Fowler-Nordheim Tunneling
When a very high electric field (higher than about 108 V/m) is applied to a heated material, another type of electron emission takes place, which is called field emission or Fowler-Nordheim tunneling.
In this case, the electric field is so strong that it creates a very thin potential barrier that allows electrons to tunnel through it without having enough thermal energy. This type of emission or tunneling is independent of temperature and depends only on electric field strength.
The combined effects of field-enhanced thermionic and field emission can be modeled by the Murphy-Good equation for thermo-field (T-F) emission. At even higher fields, field emission becomes the dominant electron emission mechanism, and the emitter operates in the so-called “cold field electron emission (CFE)” regime.
Applications and Examples
The Schottky effect has many applications in various fields of science and engineering, such as:
- Electron microscopy: Electron microscopes use electron guns that rely on the Schottky effect to produce high-intensity electron beams for imaging microscopic objects.
- Vacuum tubes: Vacuum tubes use thermionic emitters that are biased and negative relative to their surroundings to create an electric field that enhances electron emission and improves performance.
- Gas discharge lamps: Gas discharge lamps use electrodes that are heated by electric current and emit electrons by the Schottky effect into a gas-filled chamber, where they ionize gas atoms and produce light.
- Solar cells: Solar cells use materials that have different work functions at their junctions to create an electric field that lowers the barrier for charge carriers and increases their flow.
- Nanotechnology: Nanotechnology uses nanoscale structures that have very high electric fields at their tips or edges, which can induce the Schottky effect or field emission of electrons or ions.
Some examples of materials that exhibit the Schottky effect are:
- Tungsten: Tungsten has a low work function of about 4.5 eV and is widely used as an electron emitter in various devices.
- Lanthanum hexaboride: Lanthanum hexaboride has a very low work function of about 2.6 eV and is used as an electron emitter in high-brightness electron guns.
- Carbon nanotubes: Carbon nanotubes have very high aspect ratios and can generate very high electric fields at their tips, which can cause the Schottky effect or field emission of electrons.
- Graphene: Graphene has a tunable work function that depends on its doping level and can be adjusted by applying an external electric field, which can modulate its thermionic emission.
Summary
The Schottky effect is a phenomenon in physics that reduces the energy required to remove electrons from a solid surface in a vacuum when an electric field is applied to the surface. It increases the discharge of electrons from the surface of a heated material and affects the thermionic current, the surface ionization energy, and the photoelectric threshold.
The Schottky effect occurs when a moderate electric field lowers the potential barrier that prevents electrons from escaping from the surface, which decreases the work function and increases thermionic current. The relationship between thermionic current density and temperature, work function, and electric field strength can be described by a modified Richardson equation.
When a very high electric field is applied to a heated material, another type of electron emission takes place, which is called field emission or Fowler-Nordheim tunneling. In this case, electrons tunnel through a very thin potential barrier without having enough thermal energy.
The Schottky effect has many applications in various fields of science and engineering, such as electron microscopy, vacuum tubes, gas discharge lamps, solar cells, nanotechnology, etc. Some examples of materials that exhibit the Schottky effect are tungsten, lanthanum hexaboride, carbon nanotubes, graphene, etc.
