Mobility of Electrons and Holes

The speed at which an electron can travel in an electrical field through a solid describes the mobility of electron particles. Mathematically, the electron mobility formula is

v_d = μE

Where is the speed of the electron, μ is the mobility, and E is the electrical field. The same formula is not applicable to hole mobility as holes are simply the absence of electrons in a solid. Electrons are negatively charged in nature, this polarity is reversed in holes, and they are positively charged. Holes exist when an electron moves out of the outer ring of an atom due to high energy levels.

Mobility in solids

The Mobility of electron particles is higher than that of holes, as holes have a higher mass. This is because holes move in a fixed orbit around an atom and are generally the gap created by missing electrons. As they are on a fixed path, their speed and density are limited, whereas free-flowing electrons are lighter and faster in an electrically charged field.

Mobility in semiconductors

Semiconductors are elements or elemental compounds that can neither be charged completely nor stop an electric charge from passing through them. They possess the qualities of good conductors of electricity and bad conductors of electricity. Mobility in semiconductors is very important to understand the performance of any device that runs on electricity. The higher the mobility, the better the performance. Semiconductor compounds can be formed naturally or artificially to enhance electrical conductivity, as mobility in semiconductors is essential.

Band theory

Electrons display different levels of energy in different places within an atom. When the atoms collide to form solids, the energy levels of these electrons are considerably increased. Sometimes, the energy is high enough for some electrons to break away from the atom structure and float freely around the solid-state. The area left behind by the electron in the atom is a hole. 

The orbit or band around an atom which contains the electrons or holes is known as a valence band. When an electron separates from the atom, it is free-floating; however, it revolves around the composite structure of the solid material itself. This revolution band, or the structure in which the free-electron led the conduction band. The mobility of electron particles is higher in the conduction band as they can have different levels of energy and speed at which electricity can flow through them.

This is due to the fact that electrons have more space and are free from any fixed path movements. This is why free-flowing electrons have a lower mass and negatively allow for electricity to flow through them.

Importance of mobility

As described in the above sections, mobility is one of the most important aspects of studying the electrical charge in metals and semiconductors. This helps us determine the electrical compatibility or strength that can be utilized in creating electronic devices and require a stable flow of electricity to function. The mobility of electron particles plays a huge role in confirming this decision. Free-flowing electrons have a higher propensity to channel electricity than holes. So materials with high mobility like graphene, carbon, and some gases are used when a high voltage electrical supply is required to travel over a huge distance. 

This is why silicon microchips are used in almost all electronic devices, as they are found in abundance. Their electrical conductivity is a huge factor in transmitting data and intelligence safely through electric current in the form of minute processors. Silicon is also used popularly because it can resist temperature changes while delivering electricity safely through solids. As discussed earlier, temperature changes can vastly affect the mobility of a solid. This is largely contained in silicon.

In some cases, the presence of both free electrons and holes is necessary for safe conduction. The number of free-floating electrons and holes in an atom or solid structure defines the amount of electricity that can be passed through them per unit of volume. This is measured as cm²/V·s  centimeters squared per volt-second.

Conclusion

Electron mobility is the ability of an electron to travel across a metal or semiconductor in the presence of an applied electric field. However, when a voltage or electric field is placed across the semiconductor, each free electron begins to travel faster in a certain direction. In a vacuum, electrons travel incredibly quickly. Free electrons do not move very rapidly in metals or semiconductors, instead of at a limited average velocity known as drift velocity. Hole mobility is the ability of a hole to travel across a metal or semiconductor in the presence of an applied electric field. However, electron mobility is unaffected by the applied electric field, i.e., a change in the electric field does not affect electron mobility.