- Schottky Effect Definition: The Schottky effect is a phenomenon that reduces the energy required to remove electrons from a solid surface in a vacuum when an electric field is applied.
- Thermionic Emission: Thermionic emission involves the release of electrons from a material due to thermal energy, allowing them to escape the surface.
- Electric Field’s Role: An electric field lowers the barrier for electron escape, enhancing thermionic emission by reducing the work function.
- Field Emission: At very high electric fields, electrons tunnel through the barrier without needing thermal energy, known as field emission.
- Applications: The Schottky effect is utilized in devices like electron microscopes, vacuum tubes, gas discharge lamps, solar cells, and in nanotechnology.
What is Schottky Effect?
The Schottky effect is the lowering of an electron-emission barrier at a surface in vacuum when an applied electric field combines with the electron’s image-force potential. A heated cathode then emits more electrons than it would at the same temperature with no applied field. The effect changes the effective barrier during operation; it does not permanently change the surface’s zero-field work function.
Thermionic Emission and Work Function
The Schottky effect builds on thermionic emission and the surface work function.
Thermionic electron emission occurs when the electron-energy distribution in a heated material gives some electrons enough energy to cross the surface barrier into vacuum. The supply of electrons, their energy distribution and the surface condition all influence the current. Emitted ions can occur in other surface processes, but the standard Richardson-Schottky treatment here concerns electrons.
The work function is the minimum energy needed to move an electron from the material’s Fermi level to the vacuum level immediately outside a stated surface. It depends on composition, crystal face, adsorbates, contamination and surface treatment. Heating changes the population able to cross the barrier; it is not part of the definition of work function.
For an ideal thermionic regime with negligible field lowering and space-charge limitation, the Richardson-Dushman relation gives emission current density J as a function of absolute temperature T:
Here W is the zero-field work function, k is the Boltzmann constant and AG is an effective emission constant for the material and surface. Its measured value can differ from the ideal Richardson constant because of crystal orientation, surface chemistry, non-uniform work function and experimental geometry.
Electric Field and Barrier Lowering
An electric field normal to the surface tilts the vacuum potential. The electron’s image-force attraction rounds the barrier, moving its maximum closer to the surface and lowering its height.
The lowering ΔW increases with the square root of the local surface field. When ΔW and W use the same energy units, the Richardson exponent can use the effective barrier W – ΔW. The local field can differ greatly from the average applied field near a sharp tip or microscopic protrusion.
In the barrier-lowering expression, qe is the magnitude of the elementary charge, ϵ0 is the vacuum permittivity and E is the local normal electric field. The exact form depends on whether ΔW is written in joules, electronvolts or volts.
Substituting the field-lowered barrier into the thermionic relation gives the Richardson-Schottky form:
This approximation describes field-enhanced thermionic emission when electrons mainly pass over the lowered barrier. There is no universal electric-field threshold for this regime. Temperature, zero-field work function, local field and surface geometry determine when tunnelling becomes important.
Field Emission and Fowler-Nordheim Tunneling
As the local field increases, the surface barrier becomes thin enough for electrons below its top to tunnel into vacuum. This is field electron emission. A cold field-emission source operates at low temperature and high field, while a Schottky source deliberately combines emitter heating with a strong field.
In the cold-field limiting regime, emission depends strongly on local electric field strength and work function, with relatively weak temperature dependence. Real emitters can also experience resistive heating, adsorbate changes and geometric field enhancement, so current does not depend on field alone.
Murphy-Good theory treats thermionic emission, cold field emission and the thermo-field transition within one framework. The Richardson-Schottky and Fowler-Nordheim-type equations are limiting approximations. Which mechanism dominates must be judged from local field, temperature and work function rather than a single fixed field value.
Applications and Examples
Direct and related applications include:
- Electron microscopy: Schottky electron guns heat a sharp tungsten emitter, commonly with a zirconium-oxide surface layer, while applying a strong extraction field. They provide a bright and stable source for SEM, TEM, Auger analysis and electron-beam lithography.
- Vacuum tubes: Applied fields can increase emission from a hot cathode, but measured tube current also depends on space charge, electrode geometry, surface condition and supply voltage.
- Gas discharge lamps: Heated or high-field electrodes can supply the initiating electric current. Gas pressure, electrode fall, secondary emission and collisions with gas atoms also govern the discharge, so Schottky lowering may be only one contribution.
- Solar cells: Metal-semiconductor devices can show image-force barrier lowering at a Schottky junction. That interface-current effect is related mathematically but is not the same vacuum-emission application described for an electron gun.
- Nanotechnology: Sharp nanoscale tips create large local fields. Depending on temperature and field, they may operate through cold field emission, thermo-field emission or field-enhanced thermionic emission.
Representative emitter materials include:
- Tungsten: A clean tungsten surface has a work function around 4.5 eV, depending on crystal face and condition. Its high melting point and mechanical robustness make it a common thermionic and field-emitter base.
- Lanthanum hexaboride: LaB6 has a lower work function near 2.7 eV and can provide higher thermionic brightness at a lower temperature than tungsten, but it needs a better vacuum.
- Carbon nanotubes: Their high aspect ratio can concentrate the local field at an apex. Operation is commonly dominated by tunnelling field emission rather than pure Richardson-Schottky emission.
- Graphene: Work function and emission depend on layer structure, doping, substrate, edges and temperature. Device-specific models are needed before assigning a thermionic or field-emission mechanism.
Summary
The Schottky effect lowers the effective surface barrier for electron emission into vacuum. It arises from the combination of an external field and image-force potential. The zero-field work function remains a material-and-surface property, while the operating barrier becomes W – ΔW.
In a thermionic regime, the field-lowered barrier increases current according to the Richardson-Schottky relation. The increase depends exponentially on barrier lowering relative to kT, so temperature and local surface field must both be known.
At higher field or lower temperature, tunnelling contributes and can become dominant. Murphy-Good theory covers the transition between thermionic, thermo-field and cold field emission more accurately than a hard field threshold.
Heated Schottky electron guns are the clearest practical example. Vacuum tubes and gas discharges can contain the same barrier-lowering physics, while ordinary solar-cell operation and cold nanotube emission need different device models.
