Flat band potential

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In semiconductor physics, the flat band potential of a semiconductor defines the potential at which there is no depletion layer at the junction between a semiconductor and an electrolyte [1] or p-n-junction. This is a consequence of the condition that the redox Fermi level of the electrolyte must be equal to the Fermi level of the semiconductor [1] and therefore preventing any band bending of the conduction and valence band. An application of the flat band potential can be found in the determining the width of the space charge region in a semiconductor-electrolyte junction. [2] Furthermore, it is used in the Mott-Schottky equation to determine the capacitance of the semiconductor-electrolyte junction [3] [4] [5] and plays a role in the photocurrent of a photoelectrochemical cell. [2] [5] The value of the flat band potential depends on many factors, such as the material, pH and crystal structure of the material [3] [6] [7]

Background semiconductor physics

In semiconductors, valence electrons are located in energy bands. According to band theory, [8] [9] the electrons are either located in the valence band (lower energy) or the conduction band (higher energy), which are separated by an energy gap. In general, electrons will occupy different energy levels following the Fermi-Dirac distribution; for energy levels higher than the Fermi energy Ef, the occupation will be minimal. Electrons in lower levels can be excited into the higher levels through thermal or photoelectric excitations, leaving a positively-charged hole in the band they left. [9] [8] Due to conservation of net charge, the concentration of electrons (n) and of protons or holes (p) in a (pure) semiconductor must always be equal. Semiconductors can be doped to increase these concentrations: n-doping increases the concentration of electrons while p-doping increases the concentration of holes. This also affects the Fermi energy of the electrons: n-doped means a higher Fermi energy, while p-doped means a lower energy. At the interface between a n-doped and p-doped region in a semiconductor, band bending will occur. [9] [8] Due to the different charge distributions in the regions, an electric field will be induced, creating a so-called depletion region at the interface. Similar interfaces also appear at junctions between (doped) semiconductors and other materials, such as metals/electrolytes. A way to counteract this band bending is by applying a potential to the system. This potential would have to be the flat band potential and is defined to be the applied potential at which the conduction and valence bands become flat [9]

Related Research Articles

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.

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">Schottky barrier</span> Potential energy barrier in metal–semiconductor junctions

A Schottky barrier, named after Walter H. Schottky, is a potential energy barrier for electrons formed at a metal–semiconductor junction. Schottky barriers have rectifying characteristics, suitable for use as a diode. One of the primary characteristics of a Schottky barrier is the Schottky barrier height, denoted by ΦB. The value of ΦB depends on the combination of metal and semiconductor.

<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 semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region, or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or forced away by an electric field. The only elements left in the depletion region are ionized donor or acceptor impurities. This region of uncovered positive and negative ions is called the depletion region due to the depletion of carriers in this region, leaving none to carry a current. Understanding the depletion region is key to explaining modern semiconductor electronics: diodes, bipolar junction transistors, field-effect transistors, and variable capacitance diodes all rely on depletion region phenomena.

Capacitance–voltage profiling is a technique for characterizing semiconductor materials and devices. The applied voltage is varied, and the capacitance is measured and plotted as a function of voltage. The technique uses a metal–semiconductor junction or a p–n junction or a MOSFET to create a depletion region, a region which is empty of conducting electrons and holes, but may contain ionized donors and electrically active defects or traps. The depletion region with its ionized charges inside behaves like a capacitor. By varying the voltage applied to the junction it is possible to vary the depletion width. The dependence of the depletion width upon the applied voltage provides information on the semiconductor's internal characteristics, such as its doping profile and electrically active defect densities., Measurements may be done at DC, or using both DC and a small-signal AC signal, or using a large-signal transient voltage.

<span class="mw-page-title-main">Anderson's rule</span>

Anderson's rule is used for the construction of energy band diagrams of the heterojunction between two semiconductor materials. Anderson's rule states that when constructing an energy band diagram, the vacuum levels of the two semiconductors on either side of the heterojunction should be aligned.

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

In solid-state physics of semiconductors, a band diagram is a diagram plotting various key electron energy levels as a function of some spatial dimension, which is often denoted x. These diagrams help to explain the operation of many kinds of semiconductor devices and to visualize how bands change with position. The bands may be coloured to distinguish level filling.

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.

In solid-state physics, a metal–semiconductor (M–S) junction is a type of electrical junction in which a metal comes in close contact with a semiconductor material. It is the oldest practical semiconductor device. M–S junctions can either be rectifying or non-rectifying. The rectifying metal–semiconductor junction forms a Schottky barrier, making a device known as a Schottky diode, while the non-rectifying junction is called an ohmic contact.

In bulk semiconductor band structure calculations, it is assumed that the crystal lattice of the material is infinite. When the finite size of a crystal is taken into account, the wavefunctions of electrons are altered and states that are forbidden within the bulk semiconductor gap are allowed at the surface. Similarly, when a metal is deposited onto a semiconductor, the wavefunction of an electron in the semiconductor must match that of an electron in the metal at the interface. Since the Fermi levels of the two materials must match at the interface, there exists gap states that decay deeper into the semiconductor.

A quasi Fermi level is a term used in quantum mechanics and especially in solid state physics for the Fermi level that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from equilibrium. This displacement could be caused by the application of an external voltage, or by exposure to light of energy , which alter the populations of electrons in the conduction band and valence band. Since recombination rate tends to be much slower than the energy relaxation rate within each band, the conduction band and valence band can each have an individual population that is internally in equilibrium, even though the bands are not in equilibrium with respect to exchange of electrons. The displacement from equilibrium is such that the carrier populations can no longer be described by a single Fermi level, however it is possible to describe using concept of separate quasi-Fermi levels for each band.

In electronics and semiconductor physics, the law of mass action relates the concentrations of free electrons and electron holes under thermal equilibrium. It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration . The intrinsic carrier concentration is a function of temperature.

Photoelectrochemistry is a subfield of study within physical chemistry concerned with the interaction of light with electrochemical systems. It is an active domain of investigation. One of the pioneers of this field of electrochemistry was the German electrochemist Heinz Gerischer. The interest in this domain is high in the context of development of renewable energy conversion and storage technology.

<span class="mw-page-title-main">Moss–Burstein effect</span>

The Moss-Burstein effect, also known as the Burstein–Moss shift, is the phenomenon in which the apparent band gap of a semiconductor is increased as the absorption edge is pushed to higher energies as a result of some states close to the conduction band being populated. This is observed for a degenerate electron distribution such as that found in some degenerate semiconductors and is known as a Moss–Burstein shift.

This article provides a more detailed explanation of p–n diode behavior than is found in the articles p–n junction or diode.

<span class="mw-page-title-main">Field effect (semiconductor)</span>

In physics, the field effect refers to the modulation of the electrical conductivity of a material by the application of an external electric field.

<span class="mw-page-title-main">Valence and conduction bands</span> Electron energy bands which determine the electrical conductivity of a material

In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a semiconducting material, the valence band is located below the Fermi level, while the conduction band is located above it.

<span class="mw-page-title-main">Mott–Schottky plot</span>

In semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of capacitance versus the potential difference between bulk semiconductor and bulk electrolyte. In many theories, and in many experimental measurements, the plot is linear. The use of Mott–Schottky plots to determine system properties is termed Mott–Schottky analysis.

In solid-state physics, band bending refers to the process in which the electronic band structure in a material curves up or down near a junction or interface. It does not involve any physical (spatial) bending. When the electrochemical potential of the free charge carriers around an interface of a semiconductor is dissimilar, charge carriers are transferred between the two materials until an equilibrium state is reached whereby the potential difference vanishes. The band bending concept was first developed in 1938 when Mott, Davidov and Schottky all published theories of the rectifying effect of metal-semiconductor contacts. The use of semiconductor junctions sparked the computer revolution in 1990. Devices such as the diode, the transistor, the photocell and many more still play an important role in technology.

References

  1. 1 2 Sixto Giménez and Juan Bisquert. Photoelectrochemical Solar Fuel Production. Springer, Switzerland, 2016.
  2. 1 2 M Sharon. An Introduction to the Physics and Electrochemistry of Semiconductors. John Wiley & sons, inc and Scrivener Publishing LLC, New Jersey and Beverly, 2016.
  3. 1 2 K. Gelderman, L. Lee, and S. W. Donne. Flat-band potential of a semiconductor: Using the mott–schottky equation. Journal of Chemical Education, 84(4):685, 2007.
  4. W. John Albery, Gerald J. O’Shea, and Alec L. Smith. Interpretation and use of mott–schottky plots at the semiconductor/electrolyte interface. J. Chem. Soc., Faraday Trans., 92:4083–4085, 1996.
  5. 1 2 Anna Hankin, Franky E. Bedoya-Lora, John C. Alexander, Anna Regoutz, and Geoff H. Kelsall. Flat band potential determination: avoiding the pitfalls. J. Mater. Chem. A, 7:26162–26176, 2019.
  6. M. Radecka, M. Rekas, A. Trenczek-Zajac, and K. Zakrzewska. Importance of the band gap energy and flat band potential for application of modified tio2 photoanodes in water photolysis. Journal of Power Sources, 181(1):46 – 55, 2008. SPECIAL SECTION Selected papers from the 1st POLISH FORUM ON FUEL CELLS AND HYDROGEN.
  7. E. C. Dutoit, F. Cardon, and W. P. Gomes. Electrochemical properties of the semiconducting tio2 (rutile) single crystal electrode. Berichte der Bunsengesellschaft f¨ur physikalische Chemie, 80(6):475–481, 1976.
  8. 1 2 3 Steven H. Simon. The Oxford Solid State Basics. Oxford, Oxford, 2013.
  9. 1 2 3 4 Giménez, Sixto; Bisquert, Juan (29 April 2016). Photoelectrochemical solar fuel production : from basic principles to advanced devices. Switzerland. ISBN   978-3-319-29641-8. OCLC   948632302.{{cite book}}: CS1 maint: location missing publisher (link)