Semiconductors

Semiconductors

In general, semiconductors are inorganic or organic materials that can control their conduction depending on chemical structure, temperature, illumination, and the presence of dopants. The name semiconductor comes from the fact that these materials have electrical conductivity between a metal, like copper, gold, etc., and an insulator, like glass. They have an energy gap of less than 4eV (about 1eV). In solid-state physics, this energy gap or band gap is an energy range between the valence band and conduction band where electron states are forbidden. In contrast to conductors, semiconductors’ electrons must obtain energy (e.g., from ionizing radiation) to cross the band gap and reach the conduction band. The properties of semiconductors are determined by the energy gap between valence and conduction bands.

Application of Semiconductors

Semiconductors are materials that have electrical conductivity between that of a conductor and an insulator, making them useful for a wide range of electronic applications. Some of the key applications of semiconductors include:

1. Electronic devices: Semiconductors are used to create a wide range of electronic devices, including transistors, diodes, and integrated circuits. These devices are used in everything from smartphones and computers to cars and airplanes.
2. Solar cells: Semiconductors like silicon are commonly used in the production of solar cells. When light strikes the semiconductor material, it creates a flow of electrons that can be harnessed to produce electrical power.
3. Lighting: Light-emitting diodes (LEDs) are a type of semiconductor device that can produce light when an electric current is applied. LEDs are used in a wide range of lighting applications, from streetlights to televisions.
4. Power electronics: Semiconductors are used in power electronics applications, such as inverter systems, power converters, and voltage regulators. These devices are used to control and convert electrical power for a range of applications, including electric vehicles, renewable energy systems, and industrial machinery.
5. Sensors: Semiconductors can also be used to create sensors that can detect and measure a wide range of physical properties, including temperature, pressure, and light. These sensors are used in a wide range of applications, from automotive and aerospace systems to medical devices and environmental monitoring.

Characteristics of Semiconductors

Some of the key characteristics of semiconductors include:

1. Variable conductivity: Semiconductors can be made to conduct electricity under certain conditions, such as when exposed to light or heat. They can also be made to act as insulators under different conditions.
2. Bandgap: Semiconductors have a bandgap, which is the energy required to move an electron from the valence band to the conduction band. The size of the bandgap determines the energy required for the semiconductor to become a conductor.
3. Doping: Semiconductors can be doped with impurities to modify their electrical properties. Doping introduces additional electrons or “holes” into the material, which can increase or decrease its conductivity.
4. Temperature dependence: The electrical conductivity of semiconductors is highly dependent on temperature. As the temperature increases, the conductivity of the material generally increases as well.
5. Light sensitivity: Some semiconductors are sensitive to light and can be used in applications such as photovoltaic cells, light sensors, and LEDs.
6. Minority carriers: In semiconductors, electrons and holes are known as minority carriers. These carriers can be manipulated and controlled to produce desired electrical properties in the material.

Here is a table with 3 intrinsic semiconductors and 2 p-type and n-type semiconductors, along with 4 key properties:

Semiconductor	Type	Band Gap (eV)	Electron Mobility (cm²/Vs)	Hole Mobility (cm²/Vs)	Thermal Conductivity (W/mK)
Silicon (Si)	Intrinsic	1.12	1500	450	150
Germanium (Ge)	Intrinsic	0.67	3900	1900	60
Gallium Arsenide (GaAs)	Intrinsic	1.43	8500	400	46
Boron-doped Silicon (p-Si)	p-type	1.12	1500	1800	150
Phosphorus-doped Silicon (n-Si)	n-type	1.12	1500	4500	150
Aluminum-doped Gallium Arsenide (p-GaAs)	p-type	1.43	8500	200	46
Silicon-doped Gallium Arsenide (n-GaAs)	n-type	1.43	8500	800	46

Types of Semiconductors

Semiconductors can be classified into two basic types based on their electronic properties:

1. Intrinsic Semiconductors: These are pure semiconductors that are made up of a single element (e.g., Silicon, Germanium) and have no intentional doping with impurities. Intrinsic semiconductors have a specific number of electrons in their valence band and conduction band. They conduct electricity when they are heated, and some electrons gain sufficient energy to break free from their bonds and become free electrons in the conduction band.
2. Extrinsic Semiconductors: These are impure semiconductors that are intentionally doped with impurities to change their electronic properties. Extrinsic semiconductors can be further classified into two types:
   1. p-type semiconductors: In p-type semiconductors, impurity atoms such as boron are introduced into the semiconductor material. These impurities have fewer valence electrons than the semiconductor material, which results in “holes” (absence of electrons) being created in the valence band. These holes can conduct current like positive charge carriers, which gives the material its p-type designation.
   2. n-type semiconductors: In n-type semiconductors, impurity atoms such as phosphorus are introduced into the semiconductor material. These impurities have more valence electrons than the semiconductor material, which creates excess electrons in the conduction band. These excess electrons can conduct current like negative charge carriers, which gives the material its n-type designation.

Semiconductor Materials

There are many types of semiconductors in nature and others synthesized in laboratories; however, the best known are silicon (Si) and germanium (Ge).

Types of semiconductors:

• Silicon. Silicon is a chemical element with the atomic number 14, meaning there are 14 protons and 14 electrons in the atomic structure. The chemical symbol for Silicon is Si. Silicon is a hard and brittle crystalline solid with a blue-grey metallic luster, and it is a tetravalent metalloid and semiconductor. Silicon is mainly used for charged particle detectors (especially for tracking charged particles) and soft X-ray detectors. The large band-gap energy (Egap= 1.12 eV) allows us to operate the detector at room temperature, but cooling is preferred to reduce noise. Silicon-based detectors are very important in high-energy physics. Since silicon-based detectors are very good for tracking charged particles, they constitute a substantial part of the detection system at the LHC in CERN.
• Germanium. Germanium is a chemical element with the atomic number 32, which means there are 32 protons and 32 electrons in the atomic structure. The chemical symbol for Germanium is Ge. Germanium is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbors, tin and silicon. Pure germanium is a semiconductor with an appearance similar to elemental silicon. Germanium is widely used for gamma-ray spectroscopy. In gamma spectroscopy, germanium is preferred due to its atomic number being much higher than silicon, increasing the probability of gamma-ray interaction. Germanium is more used than silicon for radiation detection because the average energy necessary to create an electron-hole pair is 3.6 eV for silicon and 2.9 eV for germanium, which provides the latter a better resolution in energy. On the other hand, germanium has a small band gap energy (E_gap = 0.67 eV), which requires operating the detector at cryogenic temperatures.
• Diamond. Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Diamonds are also very good electrical insulators, which are both useful and problematic for electrical devices. Diamond is a wide-bandgap semiconductor (Egap= 5.47 eV) with high potential as an electronic device material in many devices. Diamond detectors have many similarities with silicon detectors but are expected to offer significant advantages, particularly high radiation hardness and very low drift currents.
• CdTe and CdZnTe. Cadmium telluride (CdTe) and cadmium zinc telluride (CdZnTe) are promising semiconductor materials for hard X-ray and gamma-ray detection. These materials’ high atomic number and density mean they can effectively attenuate X-rays and gamma rays with energies greater than 20 keV that traditional silicon-based sensors cannot detect. This significantly increases their quantum efficiency in comparison with silicon-based. The large band-gap energy (Egap= 1.44 eV) allows us to operate the detector at room temperature. On the other hand, a considerable amount of charge loss in these detectors produces a reduced energy resolution.

Intrinsic Semiconductor – Pure Semiconductor

An intrinsic semiconductor is completely pure without any significant dopant species. Therefore, intrinsic semiconductors are also known as pure semiconductors or i-type semiconductors.

The number of charge carriers at a certain temperature is therefore determined by the material’s properties instead of the number of impurities. Note that a 1 cm³ sample of pure germanium at 20 °C contains about 4.2×10²² atoms but also contains about 2.5 x 10¹³ free electrons and 2.5 x 10¹³ holes. These charge carriers are produced by thermal excitation. In intrinsic semiconductors, the number of excited electrons and the number of holes are equal: n = p. Electrons and holes are created by the excitation of electrons from the valence band to the conduction band. An electron-hole (often simply called a hole) is the lack of an electron at a position where one could exist in an atom or atomic lattice. This equality may even be the case after doping the semiconductor, though only if it is doped with both donors and acceptors equally. In this case, n = p still holds, and the semiconductor remains intrinsic, though doped.

Semiconductors have an energy gap of less than 4eV (about 1eV). Band gaps are naturally different for different materials. For example, diamond is a wide-bandgap semiconductor (Egap= 5.47 eV) with high potential as an electronic device material in many devices. On the other side, germanium has a small band gap energy (E_gap = 0.67 eV), which requires operating the detector at cryogenic temperatures. In solid-state physics, this energy gap or band gap is an energy range between the valence band and conduction band where electron states are forbidden. In contrast to conductors, semiconductors’ electrons must obtain energy (e.g., from ionizing radiation) to cross the band gap and reach the conduction band.

Intrinsic semiconductors, however, are not very useful, as they are neither very good insulators nor very good conductors. However, one important feature of semiconductors is that their conductivity can be increased and controlled by doping with impurities and gating with electric fields. Recall that a 1 cm³ sample of pure germanium at 20 °C contains about 4.2×10²² atoms but also contains about 2.5 x 10¹³ free electrons and 2.5 x 10¹³ holes constantly generated from thermal energy. Total absorption of a 1 MeV photon produces around 3 x 10⁵ electron-hole pairs. This value is minor compared to the total number of free carriers in a 1 cm³ intrinsic semiconductor. As can be seen, the signal-to-noise ratio (S/N) would be minimal. Adding 0.001% of arsenic (an impurity) donates an extra 10¹⁷ free electrons in the same volume, and the electrical conductivity is increased by a factor of 10,000. The signal-to-noise ratio (S/N) would be even smaller in doped material. Because germanium has a relatively low band gap, these detectors must be cooled to reduce the thermal generation of charge carriers to an acceptable level. Otherwise, leakage current-induced noise destroys the energy resolution of the detector. Doping and gating move the conduction or valence band much closer to the Fermi level and greatly increase the number of partially filled states.

Extrinsic Semiconductors – Doped Semiconductors

An extrinsic semiconductor, or doped semiconductor, is a semiconductor that was intentionally doped to modulate its electrical, optical, and structural properties. In the case of semiconductor detectors of ionizing radiation, doping is the intentional introduction of impurities into an intrinsic semiconductor for the purpose of changes in their electrical properties. Therefore, intrinsic semiconductors are also known as pure semiconductors or i-type semiconductors.

The addition of a small percentage of foreign atoms in the regular crystal lattice of silicon or germanium produces dramatic changes in their electrical properties since these foreign atoms incorporated into the crystal structure of the semiconductor provide free charge carriers (electrons or electron holes) in the semiconductor. In an extrinsic semiconductor, these foreign dopant atoms in the crystal lattice mainly provide the charge carriers that carry electric current through the crystal. Two types of dopant atoms generally result in two types of extrinsic semiconductors. These dopants that produce the desired controlled changes are classified as either electron acceptors or donors, and the corresponding doped semiconductors are known as:

• n-type Semiconductors.
• p-type Semiconductors.

Extrinsic semiconductors are components of many common electrical devices, as well as many detectors of ionizing radiation. For these purposes, a semiconductor diode (devices that allow current in only one direction) usually consists of p-type and n-type semiconductors placed in a junction with one another.

n-type Semiconductors

An extrinsic semiconductor doped with electron donor atoms is called an n-type semiconductor because most charge carriers in the crystal are negative electrons. Since silicon is a tetravalent element, the normal crystal structure contains 4 covalent bonds from four valence electrons. The most common dopants in silicon are group III and V elements. Group V elements (pentavalent) have five valence electrons, allowing them to act as donors. That means adding these pentavalent impurities such as arsenic, antimony, or phosphorus contributes to free electrons, greatly increasing the conductivity of the intrinsic semiconductor. For example, a silicon crystal doped with boron (group III) creates a p-type semiconductor, whereas a crystal doped with phosphorus (group V) results in an n-type semiconductor.

The conduction electrons are completely dominated by the number of donor electrons. Therefore:

The total number of conduction electrons is approximately equal to the number of donor sites, n≈N_D.

The charge neutrality of semiconductor material is maintained because excited donor sites balance the conduction electrons. The net result is that the number of conduction electrons increases while the number of holes is reduced. The imbalance of the carrier concentration in the respective bands is expressed by the different absolute number of electrons and holes. Electrons are majority carriers, while holes are minority carriers in n-type material.

p-type Semiconductors

An extrinsic semiconductor doped with electron acceptor atoms is called a p-type semiconductor because most charge carriers in the crystal are electron holes (positive charge carriers). The pure semiconductor silicon is a tetravalent element, and the normal crystal structure contains 4 covalent bonds from four valence electrons. In silicon, the most common dopants are group III and group V elements. Group III elements (trivalent) all contain three valence electrons, causing them to function as acceptors when used to dope silicon. When an acceptor atom replaces a tetravalent silicon atom in the crystal, a vacant state (an electron-hole) is created. An electron-hole (often simply called a hole) is the lack of an electron at a position where one could exist in an atom or atomic lattice. It is one of the two charge carriers responsible for creating an electric current in semiconducting materials. These positively charged holes can move from atom to atom in semiconducting materials as electrons leave their positions. Adding trivalent impurities such as boron, aluminum, or gallium to an intrinsic semiconductor creates these positive electron holes in the structure. For example, a silicon crystal doped with boron (group III) creates a p-type semiconductor, whereas a crystal doped with phosphorus (group V) results in an n-type semiconductor.

The number of acceptor sites completely dominates the number of electron holes. Therefore:

The total number of holes is approximately equal to the number of donor sites, p ≈ N_A.

The charge neutrality of this semiconductor material is also maintained. The net result is that the number of electron holes is increased while the number of conduction electrons is reduced. The imbalance of the carrier concentration in the respective bands is expressed by the different absolute number of electrons and holes. Electron holes are majority carriers, while electrons are minority carriers in p-type material.

The P-N Junction – Reverse Biased Junction

The semiconductor detector operates much better as a radiation detector if an external voltage is applied across the junction in the reverse-biased direction. The depletion region will function as a radiation detector. Improvement can be achieved by using a reverse-bias voltage to the P-N junction to deplete the detector of free carriers, which is the principle of most semiconductor detectors. Reverse biasing a junction increases the thickness of the depletion region because the potential difference across the junction is enhanced. Germanium detectors have a p-i-n structure in which the intrinsic (i) region is sensitive to ionizing radiation, particularly X and gamma rays. Under reverse bias, an electric field extends across the intrinsic or depleted region. In this case, a negative voltage is applied to the p-side and positive to the second one. Holes in the p-region are attracted from the junction towards the p contact and similarly for electrons and the n contact. In proportion to the energy deposited in the detector by the incoming photon, this charge is converted into a voltage pulse by an integral charge-sensitive preamplifier.

See also: Germanium Detectors, MIRION Technologies. <available from: https://www.mirion.com/products/germanium-detectors>.

Theory of Semiconductors

The theory of semiconductors is based on the behavior of electrons and holes in a crystalline lattice structure. This theory is known as the electronic band structure.

The electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).

Semiconductors have a valence band, which is the highest energy band that is completely filled with electrons, and a conduction band, which is the next higher energy band that is empty or only partially filled with electrons. The energy gap between the valence and conduction bands is called the band gap.

At absolute zero temperature, all of the electrons in a semiconductor are in the valence band and there are no free electrons in the conduction band. However, at room temperature or higher, some electrons in the valence band can be excited by thermal energy or by an external energy source, such as light or an electric field, and jump into the conduction band, leaving behind a hole in the valence band.

The movement of these free electrons and holes in the crystal lattice structure of the semiconductor can be described by the laws of quantum mechanics. The behavior of these charge carriers is influenced by factors such as the crystal structure, the doping concentration and type, the temperature, and the presence of impurities or defects in the crystal lattice.

Intrinsic semiconductors have a perfectly balanced number of free electrons and holes, and their conductivity is determined by the intrinsic concentration of free electrons and holes, which increases exponentially with temperature. Extrinsic semiconductors, which are doped with impurities, have a much higher concentration of free electrons or holes, which dramatically increases their conductivity and makes them useful for electronic devices.