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Semiconductor

2007 Schools Wikipedia Selection. Related subjects: Electricity and
Electronics

   A semiconductor is a solid whose electrical conductivity can be
   controlled over a wide range, either permanently or dynamically.
   Semiconductors are tremendously important technologically and
   economically. Silicon is the most commercially important semiconductor,
   though dozens of others are important as well.

   Semiconductor devices, electronic components made of semiconductor
   materials, are essential in modern electrical devices, from computers
   to cellular phones to digital audio players.

Overview

   Semiconductors are very similar to insulators. The two categories of
   solids differ primarily in that insulators have larger band gaps —
   energies that electrons must acquire to be free to flow. In
   semiconductors at room temperature, just as in insulators, very few
   electrons gain enough thermal energy to leap the band gap, which is
   necessary for conduction. For this reason, pure semiconductors and
   insulators, in the absence of applied fields, have roughly similar
   electrical properties. The smaller bandgaps of semiconductors, however,
   allow for many other means besides temperature to control their
   electrical properties.

   Semiconductors' intrinsic electrical properties are very often
   permanently modified by introducing impurities, in a process known as
   doping. Usually it is reasonable to approximate that each impurity atom
   adds one electron or one "hole" (a concept to be discussed later) that
   may flow freely. Upon the addition of a sufficiently large proportion
   of dopants, semiconductors conduct electricity nearly as well as
   metals. Depending on kind of the impurity, a region of semiconductor
   can have more electrons or holes, and then it is called N-type or
   P-type semiconductor, respectively. Junctions between regions of N- and
   P-type semiconductors have built-in electric fields, which cause
   electrons and holes to escape from them, and are critical to
   semiconductor device operation. Also, a density difference of
   impurities produces in the region small electric field which is used to
   accelerate non-equilibrium electrons or holes in it.

   In addition to permanent modification through doping, the electrical
   properties of semiconductors are often dynamically modified by applying
   electric fields. The ability to control conductivity in small and
   well-defined regions of semiconductor material, both statically through
   doping and dynamically through the application of electric fields, has
   led to the development of a broad range of semiconductor devices, like
   transistors. Semiconductor devices with dynamically controlled
   conductivity are the building blocks of integrated circuits, like the
   microprocessor. These "active" semiconductor devices are combined with
   simpler passive components, such as semiconductor capacitors and
   resistors, to produce a variety of electronic devices.

   In certain semiconductors, when electrons fall from the conduction band
   to the valence band (the energy levels above and below the band gap),
   they often emit light. This photoemission process underlies the
   light-emitting diode (LED) and the semiconductor laser, both of which
   are very important commercially. Conversely, semiconductor absorption
   of light in photodetectors excites electrons from the valence band to
   the conduction band, facilitating reception of fibre optic
   communications, and providing the basis for energy from solar cells.

   Semiconductors may be elemental materials such as silicon and
   germanium, or compound semiconductors such as gallium arsenide and
   indium phosphide, or alloys such as silicon germanium or aluminium
   gallium arsenide.

Band structure

   Band structure of a semiconductor showing a full valence band and an
   empty conduction band.
   Band structure of a semiconductor showing a full valence band and an
   empty conduction band.

   Like other solids, the electrons in semiconductors can have energies
   only within certain bands between the energy of the ground state,
   corresponding to electrons tightly bound to the atomic nuclei of the
   material, and the free electron energy, which is the energy required
   for an electron to escape entirely from the material. The energy bands
   each correspond to a large number of discrete quantum states of the
   electrons, and most of the states with low energy are full, up to a
   particular band called the valence band. Semiconductors and insulators
   are distinguished from metals because the valence band in the former
   materials is very nearly full under normal conditions.

   The ease with which electrons in a semiconductor can be excited from
   the valence band to the conduction band depends on the band gap between
   the bands, and it is the size of this energy bandgap that serves as an
   arbitrary dividing line (roughly 4 eV) between semiconductors and
   insulators.

   The electrons must move between states to conduct electric current, and
   so due to the Pauli exclusion principle full bands do not contribute to
   the electrical conductivity. However, as the temperature of a
   semiconductor rises above absolute zero, the states of the electrons
   are increasingly randomized, or smeared out, and some electrons are
   likely to be found in states of the conduction band, which is the band
   immediately above the valence band. The current-carrying electrons in
   the conduction band are known as "free electrons", although they are
   often simply called "electrons" if context allows this usage to be
   clear.

   Electrons excited to the conduction band also leave behind electron
   holes, or unoccupied states in the valence band. Both the conduction
   band electrons and the valence band holes contribute to electrical
   conductivity. The holes themselves don't actually move, but a
   neighbouring electron can move to fill the hole, leaving a hole at the
   place it has just come from, and in this way the holes appear to move,
   and the holes behave as if they were actual positively charged
   particles.

   One covalent bond between neighboring atoms in the solid is ten times
   stronger than the binding of the single electron to the atom, so
   freeing the electron does not imply to destroy the crystal structure.

   The notion of holes, which was introduced for semiconductors, can also
   be applied to metals, where the Fermi level lies within the conduction
   band. With most metals the Hall effect reveals electrons to be the
   charge carriers, but some metals have a mostly filled conduction band,
   and the Hall effect reveals positive charge carriers, which are not the
   ion-cores, but holes. Contrast this to some conductors like solutions
   of salts, or plasma. In the case of a metal, only a small amount of
   energy is needed for the electrons to find other unoccupied states to
   move into, and hence for current to flow. Sometimes even in this case
   it may be said that a hole was left behind, to explain why the electron
   does not fall back to lower energies: It cannot find a hole. In the end
   in both materials electron-phonon scattering and defects are the
   dominant causes for resistance.
   Fermi-Dirac distribution. States with energy ε below the Fermi energy,
   here μ, have higher probability n to be occupied, and those above are
   less likely to be occupied. Smearing of the distribution increases with
   temperature.
   Fermi-Dirac distribution. States with energy ε below the Fermi energy,
   here μ, have higher probability n to be occupied, and those above are
   less likely to be occupied. Smearing of the distribution increases with
   temperature.

   The energy distribution of the electrons determines which of the states
   are filled and which are empty. This distribution is described by
   Fermi-Dirac statistics. The distribution is characterized by the
   temperature of the electrons, and the Fermi energy or Fermi level.
   Under absolute zero conditions the Fermi energy can be thought of as
   the energy up to which available electron states are occupied. At
   higher temperatures, the Fermi energy is the energy at which the
   probability of a state being occupied has fallen to 0.5.

   The dependence of the electron energy distribution on temperature also
   explains why the conductivity of a semiconductor has a strong
   temperature dependency, as a semiconductor operating at lower
   temperatures will have fewer available free electrons and holes able to
   do the work.

Energy–momentum dispersion

   In the preceding description an important fact is ignored for the sake
   of simplicity: the dispersion of the energy. The reason that the
   energies of the states are broadened into a band is that the energy
   depends on the value of the wave vector, or k-vector, of the electron.
   The k-vector, in quantum mechanics, is the representation of the
   momentum of a particle.

   The dispersion relationship determines the effective mass, m ^* , of
   electrons or holes in the semiconductor, according to the formula:

          m^{*} = \hbar^2 \cdot \left[ {{d^2 E(k)} \over {d k^2}}
          \right]^{-1}

   The effective mass is important as it affects many of the electrical
   properties of the semiconductor, such as the electron or hole mobility,
   which in turn influences the diffusivity of the charge carriers and the
   electrical conductivity of the semiconductor.

   Typically the effective mass of electrons and holes are different. This
   affects the relative performance of p-channel and n-channel IGFETs, for
   example (Muller & Kamins 1986:427).

   The top of the valence band and the bottom of the conduction band might
   not occur at that same value of k. Materials with this situation, such
   as silicon and germanium, are known as indirect bandgap materials.
   Materials in which the band extrema are aligned in k, for example
   gallium arsenide, are called direct bandgap semiconductors. Direct gap
   semiconductors are particularly important in optoelectronics because
   they are much more efficient as light emitters than indirect gap
   materials.

Carrier generation and recombination

   When ionizing radiation strikes a semiconductor, it may excite an
   electron out of its energy level and consequently leave a hole. This
   process is known as electron–hole pair generation. Electron-hole pairs
   are constantly generated from thermal energy as well, in the absence of
   any external energy source.

   Electron-hole pairs are also apt to recombine. Conservation of energy
   demands that these recombination events, in which an electron loses an
   amount of energy larger than the band gap, be accompanied by the
   emission of thermal energy (in the form of phonons) or radiation (in
   the form of photons).

   In the steady state, the generation and recombination of electron–hole
   pairs are in equipoise. The number of electron-hole pairs in the steady
   state at a given temperature is determined by quantum statistical
   mechanics. The precise quantum mechanical mechanisms of generation and
   recombination are governed by conservation of energy and conservation
   of momentum.

   As probability that electrons and holes meet together is proportional
   to the product of their amounts, the product is in steady state nearly
   constant at a given temperature, providing that there is no significant
   electric field (which might "flush" carriers of both types, or move
   them from neighbour regions containing more of them to meet together)
   or externally driven pair generation. The product is a function of the
   temperature, as the probability of getting enough thermal energy to
   produce a pair increases with temperature, being approximately
   1/exp(band gap / kT), where k is Boltzmann's constant and T is absolute
   temperature.

   The probability of meeting is increased by carrier traps – impurities
   or dislocations which can trap an electron or hole and hold it until a
   pair is completed. Such carrier traps are sometimes purposely added to
   reduce the time needed to reach the steady state.

Doping

   The property of semiconductors that makes them most useful for
   constructing electronic devices is that their conductivity may easily
   be modified by introducing impurities into their crystal lattice. The
   process of adding controlled impurities to a semiconductor is known as
   doping. The amount of impurity, or dopant, added to an intrinsic (pure)
   semiconductor varies its level of conductivity. Doped semiconductors
   are often referred to as extrinsic.

Dopants

   The materials chosen as suitable dopants depend on the atomic
   properties of both the dopant and the material to be doped. In general,
   dopants that produce the desired controlled changes are classified as
   either electron acceptors or donors. A donor atom that activates (that
   is, becomes incorporated into the crystal lattice) donates weakly-bound
   valence electrons to the material, creating excess negative charge
   carriers. These weakly-bound electrons can move about in the crystal
   lattice relatively freely and can facilitate conduction in the presence
   of an electric field. (The donor atoms introduce some states under, but
   very close to the conduction band edge. Electrons at these states can
   be easily excited to conduction band, becoming free electrons, at room
   temperature.) Conversely, an activated acceptor produces a hole.
   Semiconductors doped with donor impurities are called n-type, while
   those doped with acceptor impurities are known as p-type. The n and p
   type designations indicate which charge carrier acts as the material's
   majority carrier. The opposite carrier is called the minority carrier,
   which exists due to thermal excitation at a much lower concentration
   compared to the majority carrier.

   For example, the pure semiconductor silicon has four valence electrons.
   In silicon, the most common dopants are IUPAC group 13 (commonly known
   as group III) and group 15 (commonly known as group V) elements. Group
   13 elements all contain three valence electrons, causing them to
   function as acceptors when used to dope silicon. Group 15 elements have
   five valence electrons, which allows them to act as a donor. Therefore,
   a silicon crystal doped with boron creates a p-type semiconductor
   whereas one doped with phosphorus results in an n-type material.

Carrier concentration

   The concentration of dopant introduced to an intrinsic semiconductor
   determines its concentration and indirectly affects many of its
   electrical properties. The most important factor that doping directly
   affects is the material's carrier concentration. In an intrinsic
   semiconductor under thermal equilibrium, the concentration of electrons
   and holes is equivalent. That is,

          n = p = n[i]

   Where n is the concentration of conducting electrons, p is the electron
   hole concentration, and n[i] is the material's intrinsic carrier
   concentration. Intrinsic carrier concentration varies between materials
   and is dependent on temperature. Silicon's n[i], for example, is
   roughly 1×10^10 cm^-3 at 300 kelvins (room temperature).

   In general, an increase in doping concentration affords an increase in
   conductivity due to the higher concentration of carriers available for
   conduction. Degenerately (very highly) doped semiconductors have
   conductivity levels comparable to metals and are often used in modern
   integrated circuits as a replacement for metal. Often superscript plus
   and minus symbols are used to denote relative doping concentration in
   semiconductors. For example, n ^+ denotes an n-type semiconductor with
   a high, often degenerate, doping concentration. Similarly, p ^− would
   indicate a very lightly doped p-type material. It is useful to note
   that even degenerate levels of doping imply low concentrations of
   impurities with respect to the base semiconductor. In crystalline
   intrinsic silicon, there are approximately 5×10^22 atoms/cm³. Doping
   concentration for silicon semiconductors may range anywhere from 10^13
   cm^-3 to 10^18 cm^-3. Doping concentration above about 10^18 cm^-3 is
   considered degenerate at room temperature. Degenerately doped silicon
   contains a proportion of impurity to silicon in the order of parts per
   thousand. This proportion may be reduced to parts per billion in very
   lightly doped silicon. Typical concentration values fall somewhere in
   this range and are tailored to produce the desired properties in the
   device that the semiconductor is intended for.

Effect on band structure

   Band diagram of a p+n junction. The band bending is a result of the
   positioning of the Fermi levels in the p+ and n sides.
   Band diagram of a p^+n junction. The band bending is a result of the
   positioning of the Fermi levels in the p^+ and n sides.

   Doping a semiconductor crystal introduces allowed energy states within
   the band gap but very close to the energy band that corresponds with
   the dopant type. In other words, donor impurities create states near
   the conduction band while acceptors create states near the valence
   band. The gap between these energy states and the nearest energy band
   is usually referred to as dopant-site bonding energy or E[B] and is
   relatively small. For example, the E[B] for boron in silicon bulk is
   0.045 eV, compared with silicon's band gap of about 1.12 eV. Because
   E[B] is so small, it takes little energy to ionize the dopant atoms and
   create free carriers in the conduction or valence bands. Usually the
   thermal energy available at room temperature is sufficient to ionize
   most of the dopant.

   Dopants also have the important effect of shifting the material's Fermi
   level towards the energy band that corresponds with the dopant with the
   greatest concentration. Since the Fermi level must remain constant in a
   system in thermodynamic equilibrium, stacking layers of materials with
   different properties leads to many useful electrical properties. For
   example, the p-n junction's properties are due to the energy band
   bending that happens as a result of lining up the Fermi levels in
   contacting regions of p-type and n-type material.

   This effect is shown in a band diagram. The band diagram typically
   indicates the variation in the valence band and conduction band edges
   versus some spatial dimension, often denoted x. The Fermi energy is
   also usually indicated in the diagram. Sometimes the intrinsic Fermi
   energy, E[i], which is the Fermi level in the absence of doping, is
   shown. These diagrams are useful in explaining the operation of many
   kinds of semiconductor devices.

Preparation of semiconductor materials

   Semiconductors with predictable, reliable electronic properties are
   necessary for mass production. The level of chemical purity needed is
   extremely high because the presence of impurities even in very small
   proportions can have large effects on the properties of the material. A
   high degree of crystalline perfection is also required, since faults in
   crystal structure (such as dislocations, twins, and stacking faults)
   interfere with the semiconducting properties of the material.
   Crystalline faults are a major cause of defective semiconductor
   devices. The larger the crystal, the more difficult it is to achieve
   the necessary perfection. Current mass production processes use crystal
   ingots between four and twelve inches (300 mm) in diameter which are
   grown as cylinders and sliced into wafers.

   Because of the required level of chemical purity and the perfection of
   the crystal structure which are needed to make semiconductor devices,
   special methods have been developed to produce the initial
   semiconductor material. A technique for achieving high purity includes
   growing the crystal using the Czochralski process. An additional step
   that can be used to further increase purity is known as zone refining.
   In zone refining, part of a solid crystal is melted. The impurities
   tend to concentrate in the melted region, while the desired material
   recrystalizes leaving the solid material more pure and with fewer
   crystalline faults.

   In manufacturing semiconductor devices involving heterojunctions
   between different semiconductor materials, the lattice constant, which
   is the length of the repeating element of the crystal structure, is
   important for determining the compatibility of materials.

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