Ionized impurity scattering

Last updated

In quantum mechanics, ionized impurity scattering is the scattering of charge carriers by ionization in the lattice. The most primitive models can be conceptually understood as a particle responding to unbalanced local charge that arises near a crystal impurity; similar to an electron encountering an electric field. [1] This effect is the mechanism by which doping decreases mobility.

Contents

In the current quantum mechanical picture of conductivity the ease with which electrons traverse a crystal lattice is dependent on the near perfectly regular spacing of ions in that lattice. Only when a lattice contains perfectly regular spacing can the ion-lattice interaction (scattering) lead to almost transparent behavior of the lattice. Impurity atoms in a crystal have an effect similar to thermal vibrations where conductivity has a direct relationship with temperature.

A crystal with impurities is less regular than a pure crystal, and a reduction in electron mean free paths occurs. Impure crystals have lower conductivity than pure crystals with less temperature sensitivity in that lattice. [2]

See also

Related Research Articles

<span class="mw-page-title-main">Electric current</span> Flow of electric charge

An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons.

A semiconductor is a material that has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity generally falls as its temperature rises; metals behave in the opposite way. In many cases their conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common semiconductor and is used in laser diodes, solar cells, microwave-frequency integrated circuits, and others. Silicon is a critical element for fabricating most electronic circuits.

<span class="mw-page-title-main">Exciton</span> Quasiparticle which is a bound state of an electron and an electron hole

An electron and an electron hole that are attracted to each other by the Coulomb force can form a bound state called an exciton. It is an electrically neutral quasiparticle that exists mainly in condensed matter, including insulators, semiconductors, some metals, but also in certain atoms, molecules and liquids. The exciton is regarded as an elementary excitation that can transport energy without transporting net electric charge.

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or and is measured in W·m−1·K−1.

Electrical resistivity is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

<span class="mw-page-title-main">Band gap</span> Energy range in a solid where no electron states exist

In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band to the conduction band, then current can flow. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances having large band gaps are generally insulators, those with small band gaps are semiconductor, and conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.

<span class="mw-page-title-main">Electrical conductor</span> Object or material which allows the flow of electric charge with little energy loss

In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge in one or more directions. Materials made of metal are common electrical conductors. The flow of negatively charged electrons generates electric current, positively charged holes, and positive or negative ions in some cases.

In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used most commonly in solid state physics. In a conducting medium, an electric field can exert force on these free particles, causing a net motion of the particles through the medium; this is what constitutes an electric current. The electron and the proton are the elementary charge carriers, each carrying one elementary charge (e), of the same magnitude and opposite sign.

<span class="mw-page-title-main">F-center</span> Type of crystallographic defect

An F center or Farbe center is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more unpaired electrons. Electrons in such a vacancy in a crystal lattice tend to absorb light in the visible spectrum such that a material that is usually transparent becomes colored. The greater the number of F centers, the more intense the color of the compound. F centers are a type of color center.

In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.

<span class="mw-page-title-main">Semimetal</span>

A semimetal is a material with a very small overlap between the bottom of the conduction band and the top of the valence band. According to electronic band theory, solids can be classified as insulators, semiconductors, semimetals, or metals. In insulators and semiconductors the filled valence band is separated from an empty conduction band by a band gap. For insulators, the magnitude of the band gap is larger than that of a semiconductor. Because of the slight overlap between the conduction and valence bands, semimetals have no band gap and a negligible density of states at the Fermi level. A metal, by contrast, has an appreciable density of states at the Fermi level because the conduction band is partially filled.

<span class="mw-page-title-main">Doping (semiconductor)</span> Intentional introduction of impurities into an intrinsic semiconductor

In semiconductor production, doping is the intentional introduction of impurities into an intrinsic (undoped) semiconductor for the purpose of modulating its electrical, optical and structural properties. The doped material is referred to as an extrinsic semiconductor.

In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.

<span class="mw-page-title-main">Madison Symmetric Torus</span>

The Madison Symmetric Torus (MST) is a reversed field pinch (RFP) physics experiment with applications to both fusion energy research and astrophysical plasmas.

An intrinsic semiconductor, also called a pure semiconductor, undoped semiconductor or i-type semiconductor, is a semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p. This may be the case even 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. This means that some conductors are both intrinsic as well as extrinsic but only if n is equal to p.

In mesoscopic physics, ballistic conduction is the unimpeded flow of charge carriers, or energy-carrying particles, over relatively long distances in a material. In general, the resistivity of a material exists because an electron, while moving inside a medium, is scattered by impurities, defects, thermal fluctuations of ions in a crystalline solid, or, generally, by any freely-moving atom/molecule composing a gas or liquid. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning and electrostatic interactions likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below.

An extrinsic semiconductor is one that has been doped; during manufacture of the semiconductor crystal a trace element or chemical called a doping agent has been incorporated chemically into the crystal, for the purpose of giving it different electrical properties than the pure semiconductor crystal, which is called an intrinsic semiconductor. In an extrinsic semiconductor it is these foreign dopant atoms in the crystal lattice that mainly provide the charge carriers which carry electric current through the crystal. The doping agents used are of two types, resulting in two types of extrinsic semiconductor. An electron donor dopant is an atom which, when incorporated in the crystal, releases a mobile conduction electron into the crystal lattice. An extrinsic semiconductor that has been doped with electron donor atoms is called an n-type semiconductor, because the majority of charge carriers in the crystal are negative electrons. An electron acceptor dopant is an atom which accepts an electron from the lattice, creating a vacancy where an electron should be called a hole which can move through the crystal like a positively charged particle. An extrinsic semiconductor which has been doped with electron acceptor atoms is called a p-type semiconductor, because the majority of charge carriers in the crystal are positive holes.

The Rigid-Band Model is one of the models used to describe the behavior of metal alloys. In some cases the model is even used for non-metal alloys such as Si alloys. According to the RBM the shape of the constant energy surfaces and curve of density of states of the alloy are the same as those of the solvent metal under the following conditions:

  1. The excess charge of the solute atoms localizes around them.
  2. The mean free path of the electrons is much greater than the lattice spacing of the alloy.
  3. The electron states of interest in the pure solvent are all in one energy band, which is greatly separated in energy from the other bands.
<span class="mw-page-title-main">Lattice scattering</span>

Lattice scattering is the scattering of ions by interaction with atoms in a lattice. This effect can be qualitatively understood as phonons colliding with charge carriers.

References

  1. "Ionized impurity scattering" . Retrieved September 26, 2011.
  2. Kip, Arthur F. (1969). Fundamentals of Electricity and Magnetism . McGraw-Hill. pp.  211–213. ISBN   0-07-034780-8.

Lundstrom, Mark (2000). Fundamentals of carrier transport . Cambridge University Press 2000. pp.  58–60. ISBN   0-521-63134-3.