Semiconductors Devices Formula, Definition, Examples, & Facts

Semiconductors are a crucial class of materials that play a fundamental role in modern electronics and technology. They bridge the gap between conductors, which allow the easy flow of electric current, and insulators, which inhibit the flow of current. This unique property of semiconductors has revolutionized the world.

In a semiconductor, the conductivity lies between that of a conductor (like copper) and an insulator (like rubber). The behavior of semiconductors is governed by the movement of electrons and "holes" (the absence of an electron) within their atomic structure. This movement can be manipulated and controlled through the application of electric fields, temperature changes, or light.

Some Important Formulas:

• Carrier Concentration (Intrinsic Semiconductor):

For electrons ( n ) and holes ( p ) in intrinsic semiconductor:

n = p = ni

where ni is the intrinsic carrier concentration.

• Carrier Concentration (Extrinsic Semiconductor):

1. 1. For electrons ( n ) in an n-type semiconductor:

n=N _d

1. For holes (p) in a p-type semiconductor:

p=N _a

• n is the electron concentration (intrinsic electrons + donor electrons in n-type material)
• p is the hole concentration (intrinsic holes + acceptor holes in p-type material)
• N _d is the donor impurity concentration (number of donor atoms per unit volume) in n-type material
• N _a is the acceptor impurity concentration (number of acceptor atoms per unit volume) in p-type material .
• Drift Current Density (n-type or p-type):

1. 1. Jn = q μn  n  E
   2. Jp = q μp  p  E
   3. where Jn and Jp are the drift current densities for electrons and holes, q is the elementary charge, μn and μp are the electron and hole mobilities, n and p are the electron and hole concentrations, and E is the electric field.

• Diffusion Current Density (n-type or p-type):

1. 1. Jn = qDn (∂n/∂x)
   2. Jp = qDp (∂p/∂x)
   3. where Jn and Jp are the diffusion current densities for electrons and holes, Dn and Dp are the electron and hole diffusion coefficients, (∂n/∂x) and (∂n/∂x) are the concentration gradients.

• Einstein Relation (Relating Mobility and Diffusivity):

1. 1. μn = qDn / k T
   2. μp = qDp / k T
   3. where μn and μp are the electron and hole mobilities, Dn and Dp are the electron and hole diffusion coefficients, q is the elementary charge, K is Boltzmann's constant, and T is temperature in Kelvin.

• Current Continuity Equation:

1. 1. ∂n/∂t + ∂(Jn)/∂x = G - R
   2. ∂p/∂t - ∂(Jp)/∂x = G - R
   3. where G is the generation rate of electron-hole pairs, R is the recombination rate.

• Shockley-Read-Hall (SRH) Recombination Rate:

1. 1. R = (np - ni ² ) / τ
   2. where n and p are the electron and hole concentrations, ni is the intrinsic carrier concentration, and T is the average lifetime of carriers due to recombination.

Also Read - Wave Motion Formula

Holes and Electrons in Semiconductors

The behavior of holes and electrons in semiconductors is crucial for understanding their electronic properties and how semiconductor devices operate.

1. Electrons in Semiconductors: Electrons are negatively charged subatomic particles that play a significant role in the electrical behavior of semiconductors. In a pure semiconductor crystal, such as silicon (Si) or germanium (Ge), electrons are bound to their respective atoms in the crystal lattice. However, at finite temperatures, some electrons can gain enough energy to break free from their atomic bonds and move through the crystal lattice. When an external electric field is applied to a semiconductor, these free electrons can move in response to the field, contributing to the flow of electric current.
2. Holes in Semiconductors: Holes are essentially the absence of an electron in the valence band of a semiconductor material. When an electron leaves its position in the valence band (leaving behind an empty state), it creates a hole. Holes can move through the crystal lattice in a manner similar to how electrons move. In a sense, you can think of holes as positive charge carriers, even though they are not actual particles. They represent the movement of missing electrons. Holes play a significant role in the movement of charge in semiconductor materials. Many semiconductor devices are designed and analyzed using the concept of holes to describe charge transport and carrier dynamics.
3. Electron-Hole Pairs (Excitons): When an electron moves from the valence band to the conduction band. This movement of an electron creates an electron-hole pair, also known as an exciton. Excitons are important in the absorption and emission of light in semiconductors. When an electron recombines with a hole, it releases energy in the form of a photon (light), which is the principle behind light-emitting diodes (LEDs).

Mobility of Electrons and Holes

Let's discuss the mobility of electrons and holes and how they contribute to the conductivity of materials.

1. Electron Mobility: Electron mobility refers to the ease with which electrons can move through a material in response to an electric field. In a semiconductor, electrons are the charge carriers responsible for carrying the current. Electrons experience a force that accelerates them, leading to a net movement of electrons in a particular direction. However, electron mobility can be hindered by various factors, including lattice vibrations (phonons), impurities, and defects in the crystal structure.
2. Hole Mobility: Holes are essentially the absence of an electron in the valence band of a semiconductor crystal lattice. In a simplified way, they can be thought of as positively charged carriers that move in the opposite direction of electrons. When an electron leaves a valence band (leaving a hole behind), neighboring electrons can move to fill the vacant position, creating a movement of holes. Like electrons, holes can also contribute to electric current and have a mobility that describes how easily they can move.

Also Read - Thermoelectricity Formula

Factors Affecting Mobility

Several factors influence the mobility of electrons and holes in a semiconductor:

1. Crystal Structure: The crystalline arrangement of atoms in a semiconductor affects the scattering of charge carriers. A more ordered crystal lattice generally leads to higher mobility.
2. Temperature: Higher temperatures can increase lattice vibrations (phonons), leading to increased scattering of charge carriers and reduced mobility.
3. Doping: The intentional introduction of impurities (dopants) into a semiconductor can significantly affect the mobility of charge carriers. N-type doping (introducing extra electrons) can enhance electron mobility, while P-type doping (introducing holes) can enhance hole mobility.
4. Electric Field: Mobility can be influenced by the strength of the applied electric field. At high electric fields, carriers can experience velocity saturation, where their mobility decreases due to interactions with the crystal lattice.
5. Scattering Mechanisms : Various scattering mechanisms, such as phonon scattering, ionized impurity scattering, and alloy scattering, can limit the mobility of charge carriers.

Band Theory of Semiconductors

The Band Theory of Semiconductors is a fundamental concept in condensed matter physics and materials science that explains the electronic behavior of semiconductors and insulators. It provides a framework for understanding how electrons are organized in the energy levels of a solid material, particularly in terms of energy bands and band gaps.

1. Energy Bands: In a solid material, the energy levels of individual atoms merge and form continuous energy bands. These bands are classified as valence bands and conduction bands.
2. Val ence Band: This band is the range of energy levels that are occupied by the electrons in the ground state of a material.
3. Conduction Band: It lies above the valence band and represents energy levels that are vacant or sparsely populated by electrons. Electrons in the conduction band have higher energy and are free to move throughout the material, contributing to electrical conduction.
4. Band Gap: The band gap is the energy range between the valence band and the conduction band where no electron energy levels exist. This energy gap determines the insulating or semiconducting properties of a material.
5. Insulators: Materials with large band gaps have a clear separation. As a result, these materials are poor conductors of electricity.
6. Semiconductors: Materials with moderate band gaps have a smaller separation such as the application of external energy (e.g., heat or light).
7. Intrinsic and Extrinsic Semiconductors: Semiconductors can be classified as intrinsic or extrinsic based on their level of impurities.
8. Intrinsic Semiconductors: Pure semiconductors with no intentional impurities.
9. Extrinsic Semiconductors: Semiconductors intentionally doped with specific impurities to alter their electrical properties. Creating more charge carriers and enhancing conductivity. Two common types of extrinsic semiconductors are n-type (donor-doped) and p-type (acceptor-doped) semiconductors.

Also Read - Elasticity Formula

Properties of Semiconductors

1. Carrier Concentration: Semiconductors can have either majority electrons (N-type) or majority holes (P-type) as the dominant charge carriers. The concentration of these carriers affects the material's conductivity.
2. Mobility: Mobility refers to the ease with which charge carriers move through a semiconductor material when subjected to an electric field. It depends on factors like carrier concentration, temperature, and scattering mechanisms.
3. Thermal Conductivity: Semiconductors typically have lower thermal conductivity compared to metals. This property is important for managing heat in electronic devices.
4. Temperature Sensitivity: The electrical properties of semiconductors are sensitive to temperature changes. As the temperature increases, the number of charge carriers may increase, altering the conductivity.
5. Photoconductivity: Some semiconductors become more conductive when exposed to light, a property exploited in photodetectors and solar cells.
6. Rectification: Semiconductors can exhibit rectification behavior, allowing current to flow more easily in one direction than the other. This property is the basis for diodes, which are essential components in electronic circuits.

Uses of Semiconductors in Everyday Life

1. Electronics and Integrated Circuits (ICs): Semiconductors are the foundation of electronic devices and integrated circuits, commonly known as chips or microchips. These chips are found in virtually all electronic devices, such as smartphones, computers, televisions, and home appliances. They perform various functions, including processing information, storing data, and controlling devices.
2. Transistors: Transistors are fundamental semiconductor devices used in amplification and switching circuits. They are a key component of electronic devices like radios, televisions, and computers. The development of smaller and more efficient transistors has driven the miniaturization and advancement of electronics.
3. Solar Cells: Photovoltaic cells, commonly known as solar cells, convert sunlight into electricity using semiconductors like silicon. Solar panels on rooftops and in solar farms generate clean and renewable energy.
4. Optoelectronics: Semiconductors are used in optoelectronic devices, which involve the interaction of light and electrical signals. Examples include lasers, photodetectors, and optical communication systems like fiber optics for high-speed data transmission.
5. Memory Devices: Semiconductors are essential for various types of memory devices. These technologies are used in computer memory, USB drives, solid-state drives (SSDs), and memory cards for cameras and smartphones.