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| {{distinguish|band structure}}
| | The author is called Wilber Pegues. Since he was eighteen he's been operating as an info officer but he ideas on altering it. The favorite pastime for him and his children is to perform lacross and he would never give it up. Her family lives in Ohio but her spouse wants them to move.<br><br>Also visit my blog :: free online tarot card readings ([http://help.ksu.edu.sa/node/65129 http://help.ksu.edu.sa]) |
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| [[File:Pn-junction zero bias.png|thumb|'''Band diagram''' for [[p-n junction|''p–n'' junction]] at equilibrium. The [[depletion region]] is shaded.]]
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| [[File:PnJunction-LED-E.svg|thumb|The inner workings of a [[light emitting diode]], showing circuit (top) and band diagram when under bias (bottom)]]
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| [[File:Schottky barrier zero bias.svg|thumb|'''Band diagram''' for [[Schottky barrier]] at equilibrium.]]
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| [[File:Straddling gap heterojunction band diagram.svg|thumb|'''Band diagram''' for semiconductor [[heterojunction]] at equilibrium.]]
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| In [[solid-state physics]] of [[semiconductors]], a band diagram is a diagram plotting various key electron energy levels ([[Fermi level]] and nearby [[energy band]] edges) as a function of some spatial dimension, which is often denoted ''x''.<ref>http://ecee.colorado.edu/~bart/book/moseb.htm</ref>
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| These diagrams help to explain the operation of many kinds of [[semiconductor device]]s and to visualize [[band bending]].
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| A band diagram should not be confused with a [[band structure]] plot. In both a band diagram and a band structure plot, the vertical axis corresponds to the energy of an electron. The difference is that in a band structure plot the horizontal axis represents the [[wavevector]] of an electron in an infinitely large, homogeneous material (a crystal or vacuum), whereas in a band diagram the horizontal axis represents position in space, usually passing through multiple materials. The bands may be coloured to distinguish [[Fermi-Dirac statistics|level filling]].
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| A band diagram does however try to show the ''changes'' in the band structure from place to place.
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| In doing so, there is an intrinsic conflict due to the [[Heisenberg uncertainty principle]]: the band structure relies on momentum which is only precisely defined for large length scales.
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| For this reason, the band diagram can only accurately depict evolution of band structures over long length scales, and has difficulty in showing the microscopic picture of sharp, atomic scale interfaces between different materials (or between a material and vacuum).
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| Typically, an interface must be depicted as a "black box", though its long-distance effects can be shown in the band diagram as asymptotic [[band bending]].<ref>http://academic.brooklyn.cuny.edu/physics/tung/Schottky/index.htm</ref>
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| == Anatomy of a band diagram ==
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| The vertical axis of the band diagram represents the energy of an electron, which includes both kinetic and potential energy.
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| The horizontal axis represents position, often not being drawn to scale. Note that the [[Heisenberg uncertainty principle]] prevents the band diagram from being drawn with a high positional resolution, since the band diagram shows energy bands (as resulting from a momentum-dependent [[band structure]]).
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| While a basic band diagram only shows electron energy levels, often a band diagram will be decorated with further features.
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| It is common to see cartoon depictions of the motion in energy and position of an electron (or [[electron hole]]) as it drifts, is excited by a light source, or relaxes from an excited state.
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| The band diagram may be shown connected to a [[circuit diagram]] showing how bias voltages are applied, how charges flow, etc.
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| The bands may be colored to indicate [[Fermi Dirac statistics|filling of energy levels]], or sometimes the [[band gap]]s will be colored instead.
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| === Energy levels ===
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| Depending on the material and the degree of detail desired, a variety of energy levels will be plotted against position:
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| * ''E''<sub>F</sub> or ''μ'': Although it is not a band quantity, the ''[[Fermi level]]'' ([[total chemical potential]] of electrons) is a crucial level in the band diagram. The Fermi level is set by the device's electrodes. For a device at equilibrium, the [[Fermi level]] is a constant and thus will be shown in the band diagram as a flat line. Out of equilibrium (e.g., when voltage differences are applied), the Fermi level will not be flat. Furthermore, in semiconductors out of equilibrium it may be necessary to indicate multiple [[quasi-Fermi level]]s for different [[energy band]]s, whereas in an out-of-equilibrium insulator or vacuum it may not be possible to give a quasi-equilibrium description, and no Fermi level can be defined.
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| * ''E''<sub>C</sub>: The ''conduction band edge'' should be indicated in situations where electrons might be transported at the bottom of the conduction band, such as in an [[N-type semiconductor|''n''-type semiconductor]]. The conduction band edge may also be indicated in an insulator, simply to demonstrate [[band bending]] effects.
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| * ''E''<sub>V</sub>: The ''valence band edge'' likewise should be indicated in situations where electrons (or [[electron hole|hole]]s) are transported through the top of the valence band such as in a [[P-type semiconductor|''p''-type semiconductor]].
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| * ''E''<sub>i</sub>: The ''intrinsic Fermi level'' may be included in a semiconductor, to show where the Fermi level would have to be for the material to be neutrally doped (i.e., an equal number of mobile electrons and holes).
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| * ''E''<sub>imp</sub>: ''Impurity energy level''. Many defects and dopants add states inside the [[band gap]] of a semiconductor or insulator. It can be useful to plot their energy level to see whether they are ionized or not.<ref>http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dsem.html</ref>
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| * ''E''<sub>vac</sub>: In a vacuum, the ''vacuum level'' shows the energy <math>-e\phi</math>, where <math>\phi</math> is the [[electrostatic potential]]. The vacuum can be considered as a sort of insulator, with ''E''<sub>vac</sub> playing the role of the conduction band edge. At a vacuum-material interface, the vacuum energy level is fixed by the sum of [[work function]] and [[Fermi level]] of the material.
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| * ''Electron affinity level'': Occasionally, a "vacuum level" is plotted even ''inside materials'', at a fixed height above the conduction band, determined by the [[electron affinity]]. This "vacuum level" does not correspond to any actual energy band and is poorly defined (electron affinity strictly speaking is a surface, not bulk, property); however, it may be a helpful guide in the use of approximations such as [[Anderson's rule]] or the [[Schottky-Mott rule]].
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| ==References==
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| {{commons category|Band diagram}}
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| {{reflist}}
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| [[Category:Condensed matter physics]]
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| [[Category:Electronic band structures]]
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The author is called Wilber Pegues. Since he was eighteen he's been operating as an info officer but he ideas on altering it. The favorite pastime for him and his children is to perform lacross and he would never give it up. Her family lives in Ohio but her spouse wants them to move.
Also visit my blog :: free online tarot card readings (http://help.ksu.edu.sa)