Schottky Effect

 The Schottky effect is a reduction in the energy required to remove an electron from a solid surface in a vacuum that occurs by applying an electric field to the surface. It refers to an increase in the emission of electrons from the surface of a heated material due to the application of an electric field, which reduces the value of the energy required for electron discharge

In other words, we can say in the presence of an electric field, the energy required to remove electrons from a surface in a vacuum is less. The applied field reduces the barrier height. As a result, there is an increase in electron discharge from the surface. This process is the Schottky effect.

• The energy required for an electron to escape the surface of a material is known as the work function.
• As the electric field increases, at a point at which the value of the work function itself lowers. 
• With the increase of the field again, the work function continues to decrease, leading to an increase in electron emission current. 
• At very high values of the applied field, the electron emission increases because of the onset of a different emission called high-field emission or field emission, which is the Schottky effect, named after its discoverer, the German physicist Walter Schottky

Schottky-emitter electron source of an Electron microscope

Features:

• The phenomenon in physics reduces the energy required to remove electrons from a solid surface in a vacuum when we apply an electric field to the surface.
• Work function decreases and emission of electron current increases
• It affects the thermionic current, surface ionization energy, and photoelectric threshold.
• The Schottky effect, or field-enhanced thermionic emission, is a phenomenon in condensed matter physics

The Schottky effect is named after Walter H. Schottky and is significant for electron emission devices, especially electron guns.

 

In electron emission devices, particularly electron guns, the thermionic electron emitter is biased negatively relative to its surroundings. This situation creates an electric field of magnitude F at the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has a height W equal to the local work function. The electric field lowers the surface barrier by an amount of ΔW and increases the emission current. We can model it by modifying the Richardson equation, replacing W with (W − ΔW). This gives the equation[1][2].

We have the Richardson equation

J = AT² exp^(-w/kt)

 

^{J(F,T,W) = A}_GT²exp^{-(W - ΔW)/KT}

ΔW =√(q^3F/4πɛ₀)

Where J is the emission current density, T is the temperature of the metal, W is the work function of the metal, k is the Boltzmann constant, qe is the elementary charge, ε0 is the vacuum permittivity, and AG is the product of a universal constant A0 multiplied by a material-specific correction factor λR, which is typically of order 0.5.

• Electron emission happens in the field-and-temperature-regime where this modified equation applies and is often called Schottky emission.
• This equation is relatively accurate for electric field strengths lower than 108 V m−1.

 For electric field strengths higher than 108 V m−1, so-called Fowler–Nordheim (FN) tunneling begins to contribute significant emission current. We can model the combined effects of field-enhanced thermionic and field emission using the Murphy–Good equation for thermo-field (T-F) emission. [3] When the field is high, FN tunneling becomes the dominant electron emission mechanism, and the emitter operates in the so-called cold field electron emission (CFE) regime.

• Interaction with other forms of excitation, such as light, enhances thermionic emission [4].

For example, excited Cs-vapors in thermionic converters form clusters of Cs-Rydberg matter, which reduces the collector emitting work function from 1.5 eV to 1.0–0.7 eV. Due to the long-existing nature of Rydberg matter, this low work function remains low, which essentially increases the low-temperature converter’s efficiency. [5]

 

• Thermionic emission refers to the release of charge carriers (ions or electrons) from the surface of a material due to thermal energy given to it. 
• In solid materials,  one or two electrons per atom are typically 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 known as the work function. 

• The work function depends on the material type, crystal structure, surface condition, and surrounding environment. 
• The work function is inversely proportional to the thermionic emission current, meaning, that a lower work function results in higher electron emission.

Richardson’s law provides the relationship between thermionic emission, current density J, and the temperature T of a heated metal, which is mathematically analogous to the Arrhenius equation.

Now let me tell you something about the vacuum tubes

Vacuum tubes have a lot in common with an ordinary light bulb.

A vacuum is necessary for the filament to emit light in a bulb. The primary principle that the vacuum tube operates on is called thermionic emission. When the filament is hot, it emits electrons, and they are looking for a positive source to attract to it. 

It is the basis of the vacuum tube.

Do you have a microwave oven?

Yes?

You have a directly heated vacuum tube in your microwave oven.

A vacuum tube is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference exists.

The type known as a thermionic tube or thermionic valve utilizes the thermionic emission of electrons from a hot cathode for fundamental electronic functions such as signal amplification and current rectification. The electrons flow from the cathode to the anode by the electric field in the tube.

The simplest vacuum tube is the diode. It contains only a heated electron-emitting cathode and an anode. Electrons can flow in only one direction through the device, from the cathode to the anode. 

Diode

In the 1940s, the invention of semiconductor devices made it possible to produce solid-state devices, which are smaller, more efficient, reliable, durable, safer, and more economical than thermionic tubes. 

In the 1960s, the discovery of transistors led to thermionic tubes.   

away from circuits. However, the cathode-ray tube (CRT) remained the basis for television monitors and oscilloscopes until the early 21st century.

Classification based on active elements:

We can classify thermionic vacuum tubes by the number of active electrodes. 

A device with two active elements, anode and cathode, is a diode, usually used for rectification. 

Devices with three elements are triodes used for amplification and switching. It contains anode, cathode, and control grid.

Triode

By adjusting the voltage on the grids, we can control the current between the cathode and anode. [6]

Tetrode has four active elements: anode, cathode, control grid (g), and screen grid (r). The screen grid lowers the inter-electrode capacitance by creating an electrostatic shield.

Tetrode symbol

The pentode has five active elements: anode, cathode, control grid, screen grid, and suppressor grid. Multiple additional functions are made possible by the additional controllable electrodes.

Rydberg matter:

 

Rydberg matter is an exotic phase formed by Rydberg atoms. É. A. Manykin, M. I. Ozhovan, and P. P. Poluéktov predicted this in 1980. Its formation involves various elements, such as cesium, potassium, hydrogen, and nitrogen. They also studied the theoretical possibilities of Rydberg matter in sodium, beryllium, magnesium, and calcium. Researchers suggest that it is a material that diffuses interstellar bands.

References:

1. Kiziroglou, M. E.; Li, X.; Zhukov, A. A.; De Groot, P. A. J.; De Groot, C. H. (2008). "Thermionic field emission at electrodeposited Ni-Si Schottky barriers" (PDF). Solid-State Electronics. 52 (7): 1032–1038. Bibcode:2008SSEle..52.1032K. doi:10.1016/j.sse.2008.03.002.

2. ^ Orloff, J. (2008). "Schottky emission". Handbook of Charged Particle Optics (2nd ed.). CRC Press. pp. 5–6. ISBN 978-1-4200-4554-3.

3. ^ Murphy, E. L.; Good, G. H. (1956). "Thermionic Emission, Field Emission, and the Transition Region". Physical Review. 102 (6): 1464–1473. Bibcode:1956PhRv..102.1464M. doi:10.1103/PhysRev.102.1464.

4. ^ Mal'Shukov, A. G.; Chao, K. A. (2001). "Opto-Thermionic Refrigeration in Semiconductor Heterostructures". Physical Review Letters. 86 (24): 5570–5573. Bibcode:2001PhRvL..86.5570M. doi:10.1103/PhysRevLett.86.5570. PMID 11415303.

5. ^ Svensson, R.; Holmlid, L. (1992). "Very low work function surfaces from condensed excited states: Rydber matter of cesium". Surface Science. 269/270: 695–699. Bibcode:1992SurSc.269..695S. doi:10.1016/0039-6028(92)91335-9.

6. Wikipedia