Semiconductors

A Semiconductor is a kind of material that performs conductivity between conductors and insulators and has a conductivity value that lies between the conductor and an insulator.

In this article, we will be going through semiconductors, first, we will start our article with the introduction of the semiconductor, then we will go through holes and electrons with band gap theory, and after that we will go through properties and types of semiconductors, At last, we will conclude our article with solved examples, applications and advantages with some FAQs.

Semiconductor materials have some electrical properties that contribute to the operation of some electronic devices. In this, the resistivity falls as the temperature increases, whereas metal behaves differently in this term which is oppositely. It helps in the conduction of electricity in certain situations or conditions but not in all – the integrated circuits, transistors, and diodes all are made up of semiconductors. Apart from electricity conduction – it also functions to react to heat and light.

Holes and electronics are basically the charge carriers of the Semiconductor which results in the flow of current or electricity through it. Electrons, which carry a negative charge, orbit the nucleus of an atom. In semiconductors, they are assumed to be the primary carriers of electric charge. Within the semiconductor’s valence band, electrons are confined to atoms and exert limited influence on current flow. In a Semiconductor, when an electron leaves a place due to getting energy a place is left behind which is known as a hole. A hole in a Semiconductor represents a region of positive charge where an electron’s absence has left an opening in the covalent bond between atoms.

Mobility of Electrons and Holes

In Semiconductors like silicon, the mobility of the electrons surpass the holes due to their fundamental differences in their behavior within the material’s structure.

The Electrons reside and move within the conduction band of the semiconductor, while holes, which result from electrons transitioning to higher energy levels, move within the valence band. When an electric field is applied, electrons are comparatively less hindered in their movement than holes due to their greater freedom within the conduction band.Also electrons are negatively charged which makes them experience less resistance from the positively charged atomic nuclei as they traverse the lattice compared to holes, which possess a positive charge and thus encounter stronger repulsion from the nuclei.

In the given Silicon Bond Model, when a free electron moves from its lattice position, it leaves behind a hole with an opposite charge. These holes act as positive charge carriers within the lattice.

Given Below is the diagram for the Band Theory

As we can see from diagram of Band Gap of a Semiconductor, the following terms are expressed below:

• Insulators are the materials which have highest energy gap between conduction and valence band so even by applying some amount of energy electron cannot be moved from valence to conduction band so conduction of electricity is not possible in these materials according to band gap theory.

• Semiconductors are the materials which have energy gap between conductors and insulators. In this materials electrons can be moved from valence band to conduction band by applying some amount of energy. But they don’t conduct at normal conditions some energy equal to band gap between valence and conduction band need to be supplied for conductivity.

Valence Band and Conduction Band in Semiconductors

• Valence Band: It is the energy levels of valence electrons that represents the highest occupied energy band. As Compared to insulators, semiconductors have a smaller band gap, Which makes electrons in the valence band to move to the conduction band when external energy is provided.
• Conduction Band: It is situated below the valence band, consists of unoccupied energy levels and accommodates either positive charge carriers (holes) or negative charge carriers (free electrons).In semiconductors, the conduction band accepts electrons from the valence band.

As we can notice in above image that there is no band gap between conductors valence and conduction band are collapsed so in conductor materials no energy is need to be supplied to them in order to conduct.

The Fermi Energy level in the Semiconductors is referred as the energy level within the band gap Where the probability of finding an electron is 50%.At absolute zero temperature, the Fermi level is at the top of the valence band in an intrinsic semiconductor. However when the temperature increases, some electrons gain enough energy to move from the valence band to the conduction band, leaving behind holes in the valence band. This movement causes the Fermi level to shift towards the middle of the band gap. The Positioning of the fermi level with respect to energy bands effects the conductivity and other electronic properties of semiconductors.

On the basis of energy gap semiconductors can be divided into:

• Direct Band Gap Semiconductors
• Indirect Band Gap Semiconductors.

Direct Band Gap

As we can see from above image the bandgap is said to be direct if the top of valence band and the bottom of the conduction band are at same momentum. This means that the energy difference between the conduction band and the valence band is released in the form of a photon without any change in momentum.

As a result, direct bandgap semiconductors efficiently emit or absorb light (photons) during electronic transitions. The efficient emission of light makes direct bandgap semiconductors ideal for optoelectronic applications, such as light-emitting diodes (LEDs) and laser diodes.

Examples: Gallium arsenide (GaAs), Indium phosphide (InP), Gallium nitride (GaN) etc.

Indirect Bandgap

In Indirect Bandgap semiconductors the top of valence band and the bottom of conduction band don’t have same momentum. As a result, the energy difference between the conduction band and the valence band cannot be directly converted into a photon. Some change in the momentum and value of k is needed to convert the energy gap into photon.

Examples: Silicon (Si), Germanium (Ge) etc.

Some important properties of a Semiconductor are:

• Energy Gap: Semiconductors have a band gap, an energy range positioned between the valence band (with tightly bound electrons) and the conduction band (permitting electron movement), influencing their conductive or insulating nature.
• Dopant Introduction: Controlled introduction of impurities (doping) into semiconductors intentionally alters their electrical characteristics, generating excess charge carriers (N-type) or “holes” (P-type) for conductivity control.
• Temperature Responsiveness: Semiconductors’ conductivity varies with temperature, making them suitable for applications like thermistors and temperature sensors.
• Light Sensitivity: Certain semiconductors become more conductive upon light exposure, proving valuable in photodetectors and solar cells.
• Mechanical Influence: Semiconductors’ resistance can change with mechanical stress (piezo-resistivity), applied in strain gauges and pressure sensors.
• Heat Conductance: With intermediate thermal conductivity, semiconductors manage controlled heat dissipation, crucial for integrated circuits.
• Dielectric Qualities: Semiconductors can act as insulating dielectrics under specific circumstances, contributing to capacitors and energy storage mechanisms.
• Electroluminescence: When subjected to voltage, specific semiconductors emit light, essential in LEDs and displays.
• Quantum Aspects: On the nanoscale, semiconductors reveal quantum effects exploited in quantum dots and quantum well structures for advanced uses.
• Hall Effect: Semiconductors exhibit the Hall effect, where an electric field perpendicular to the current generates measurable voltage, applicable in Hall sensors and current measurement.
• Carrier Mobility: The movement ability of charge carriers (electrons and holes) within semiconductors is determined by carrier mobility, influencing device efficiency and speed.
• Resistivity (ρ): The resistivity decreases with the increase of temperature because of the increase in number of the mobile charge carriers and thus making the temperature coefficient negative.
• Conductivity (σ): The semiconductors act as insulators as zero kelvin but when the temperature increases they start working as the conductors.
• Carrier Concentration (n or p): In semiconductors, the carrier concentration refers to the number of charge carriers (electrons or holes) per unit volume. It’s given by the formula:

n = Nc * exp(Ec - Ef) / k * T

Where,

• n is the carrier concentration
• Nc is the effective state density
• Ec is level of energy of conduction band
• Ef is the Fermi energy level
• k is Boltzmann’s constant
• T is the temperature in Kelvin

Why Does the Resistivity of Semiconductors Go Down with Temperature?

The resistivity of the Semiconductor will decrease with the rise of temperature because the higher temperature will provide the more energy to the electron.The increase of the energy will make electron to jump from Valence band to the conduction band.

Semiconductors can be classified into two types on the basis of purity:

• Intrinsic Semiconductors
• Extrinsic Semiconductors

Intrinsic Semiconductors

Intrinsic Semiconductors are the pure semiconducting materials without any added impurity. No doping is done in this type of semiconductor materials. Intrinsic Semiconductor include elements from Group 4 of the Periodic Table. The mostly used elements for intrinsic semiconductor are Silicon and Germanium as they are tetravalent and bound to the covalent bond at 0 temperature. But s the temperature increases then the atoms get unbounded and becomes mobile charge carriers by leave their places and thus creating a hole in that positioning. The conductivity is less and the number of electrons and holes become equal.

Total current (I) =  I_h +  I_e

The Lattice of Pure Silicon Semiconductor at Different Temperatures

Given Below is the lattice bond theory of the Semiconductor

• Absolute Zero Kelvin Temperature: During this temperature the covalent bonds are strong with no free electrons which makes the semiconductor behave like a insulator.
• Above absolute temperature: By increasing the temperature, the valence bonds will go in conduction bond which will make the semiconductor behave as a poor conductor.

Given Below is the Energy band diagram of the Intrinsic Semiconductor

In this diagram we can see that with the finite temperature the probability of existing the electron in the conduction band will decrease exponentially with respect to the increase in the band gap(Eg).

[Tex]n=n_oe^{-E_g/2.Kb.T}[/Tex]

In the given equation,

Eg is the Energy band gap

Kb is the Boltzmann’s constant

Extrinsic Semiconductors

Extrinsic semiconductors are intentionally doped with impurity atoms to alter their electrical properties and increase their conductivity. Doping involves introducing a small number of foreign atoms into the crystal lattice of the intrinsic semiconductor. The most common dopants are from Group III (trivalent) and Group V (pentavalent) elements.

There are two main types of extrinsic semiconductors, depending on the type of dopant used:

• N-type Semiconductors
• P-type Semiconductors

N-type Semiconductors

In N-type Semiconductors, the semiconductor material is doped with atoms from Group V of the periodic table, such as phosphorus (P) or arsenic (As). These dopant atoms have one extra valence electron compared to the semiconductor material. When they replace some of the semiconductor atoms, they create extra electrons in the crystal lattice.

• Conductivity is mainly because of electrons.
• The material is entirely neutral.
• The current (I) is due to electron current (Ie), and the concentration of electrons (ne) is much greater than that of holes (nh).
• Majority carriers are electrons, and minority carriers are holes.

P-type Semiconductors

In order to form p type Semiconductor, trivalent impurity is added to it. These elements have three electrons in there valence shell and need 1 more electron. These are from Group III of the periodic table, such as Boron (B) or Aluminum (Al). These dopant atoms have one less valence electron compared to the semiconductor material. When they are added in semiconductor atoms they take one electron and create holes in the crystal lattice.

• Conductivity is mainly because of the holes.
• The material is entirely neutral.
• The current (I) is due to hole current (Ih), and the concentration of holes (nh) is much greater than that of electrons (ne).
• Majority carriers are holes, and minority carriers are electrons.

Formation of PN Junction by N and P type Semiconductor

• Creating P and N type Semiconductor by doping: P type semiconductor can be formed by doping the pure semiconductor such as germanium or silicon by adding impurities In P type Group 3 elements are added such as boron Aluminium. N type semiconductor can be made by adding impurities from atoms of Group 5 such as arsenic or phosphorus.
• Bringing the created N and P type Semiconductor together: We need to take the p and n type semiconductor closer in order to form PN Junction. The free electrons of negative N type region will move towards the P type semiconductor and the holes move in opposite direction towards n type region. The holes and the electrons recombine with each other a form a region where no free mobile charge carriers(charge carriers which have movement ) are present it is known as depletion region.

In a forward bias, when a positive voltage is applied to the P-side and negative voltage to the N-side, the potential barrier is reduced, and current can flow across the junction. In reverse bias, where the P-side is negative and the N-side is positive, the potential barrier increases, and the junction prevents significant current flow.

Here are the main differences between Intrinsic and Extrinsic Semiconductor:

For More: Difference Between Intrinsic and Extrinsic Semiconductor

Semiconductor materials are very useful in our everyday live below are some common examples-

• Computers: The chips and microprocessors which are called the core of computer are made of of semiconductors. These are the parts which helps the computers in processing data. Complex operations are not possible without these chips.
• Use in electronic devices: Basic electronic devices which we use such as Switches, electric circuits, diodes, transistors are made using semiconductors
• Light-emitting diodes (LEDs): LEDs are used in home for lightning these are semiconductor devices which produce light when current is passed through them. LEDs are used in everyday lighting applications, including energy-efficient bulbs for homes and offices, as well as in traffic signals, vehicle headlights, and electronic displays.
• Wearable Technology: The wearable devices such as smart watches now in latest smart rings have been built they are only possible using semiconductor technology. Because in them microprocessor chips are used which can be made using semiconductors
• Home Automation: Semiconductors are a crucial part of home automation systems, allowing for smart home devices like smart thermostats, smart lighting, smart security cameras, and voice-activated virtual assistants.

Given below are the day to day uses of Semiconductors

• Computers and Laptops: The CPUs and GPUs are made from Semiconductor technology.
• Televisions: The Modern day LED and OLED are made from Semiconductor materials.
• Communication: Many communication devices such as Routers ,Modems, Satellite and GPS Systems are made from semiconductor chips.
• Lighting: Lighting systems such as LED Light are made from semiconductor materials.

Importance of Semiconductors are

• Small Size: The Semiconductors are manufactured at microscopic scales which can be used for creating compact and portable device.
• Low Power Consumption: The Semiconductors require less input power compared to other technologies.
• Shockproof: Semiconductor devices are solid-state and have no moving parts which make them resistant to physical shocks and vibrations.
• Long Lifespan: The Semiconductors have large lifespan as compared to other technologies.
• Noise-Free Operation: The Semiconductor devices works with less electrical noise which improves its performance.

Here are some advantages of a semiconductor:

• Miniaturization: Semiconductors are used in extremely small devices such as microprocessors and chips. They allows miniaturization in so that the devices which took a lot of space, with help of semiconductors can be made in small sizes.
• Energy Efficiency: As compared to other materials semiconductor is an energy efficient device. They consume lower energy compared to other materials while the electronic operations are performed.
• Light Emission: Certain semiconductor have the property to emit light when the electric current is passed through them. This made the LEDs (Light Emitting Diodes) possible and also the laser diodes.
• High Switching Speed: The switching speed in semiconductors in comparatively very high which allows fast switching in devices. This is important property because it saves time and lowers the complexity and also allows them to perform fast digital operations.
• Formation of IC: Integrated circuits (ICs) can incorporate millions of semiconductor devices on a single chip, leading to complex functionalities in a compact form.

Some of the disadvantages of a Semiconductor are:

• Temperature Vulnerability: Semiconductor gadgets can react strongly to changes in temperature, leading to shifts in how they work and how dependable they are.
• Expensive Production: Making semiconductors involves intricate processes and specialized facilities, resulting in high initial manufacturing expenses.
• Heat Tolerance Limits: Some semiconductors can’t endure high temperatures well. This could lead to their performance dropping or even failing.
• Reliance on Purity: The efficiency of semiconductors heavily depends on how pure they are. Even minor impurities can drastically change their electrical characteristics.
• Issues with Consistency: Over time, specific semiconductor devices might degrade or wear out, negatively affecting their dependability and lifespan.

Calculate the electron concentration in a silicon semiconductor at room temperature (300 K) assuming the conduction band edge energy (Ec) is:- 1.12 eV and the Fermi energy (Ef) is 0.5 eV.

n = Nc * exp((1.12 eV – 0.5 eV) / (8.6173 × 10^-5 eV/K * 300 K))

(Values of Nc and constants should be looked up in a semiconductor physics reference for accurate calculations.)

d)Drift Current Density (Jd) Formula:

Jd = q * n * μ * E

Where Jd = Drift current density

• q = Elementary charge
• n = Carrier concentration
• μ = Mobility of carriers
• E = Electric field

Calculate the drift current density in a semiconductor with carrier concentration n = 1.5 x 10^16 cm^-3, mobility μ = 1000 cm^2/Vs, and electric field E = 200 V/cm.

Jd = (1.6 x 10^-19 C) * (1.5 x 10^16 cm^-3) * (1000 cm^2/Vs) * (200 V/cm)

= 4.8 x 10^-2 A/cm².

he chemical and electrical properties of Semiconductors help them to serve for the electronic devices LEDs , solar cell, etc. Without the use of the semiconductors, life would be complex and different. Semiconductor material the main reason behind them is they have moderate and controlled conductivity which can be changed by doping. Semiconductors have unique properties which make it favorable for making a lot of devices from them.

Who invented semiconductor?

Karl Braun in 1874.

What is the effect of heating on resistance of Semiconductor?

The resistance will decrease.

Highlight some advantages of Semiconductor devices?

Semiconductor devices are small in size, its low power consumption, higher reliability, fast switching speed, and ease of integration, making them the foundation of modern electronics and technology.

What recent advancements have impacted Semiconductor technology?

Some recent developments include the use of wide-bandgap semiconductors (like SiC and GaN) for power electronics and the exploration of novel materials, such as perovskite, for high-efficiency solar cells. Hence semiconductors are continuously evolving over time in form of there fabrication methods, device design etc.

What are the 2 most used semiconductors?

The two most commonly used semiconductors are:

• Silicon (Si)
• Gallium arsenide (GaAs)

What is the resistivity of pure silicon?

6000 Ω cm

How much impurity is added in extrinsic semiconductor as compared to intrinsic pure semiconductor?

1 atom for 10⁸ atoms