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| In [[semiconductor physics]], the [[band gap]] of a [[semiconductor]] is always one of two types, a '''direct band gap''' or an '''indirect band gap'''. The minimal-energy state in the [[conduction band]] and the maximal-energy state in the [[valence band]] are each characterized by a certain [[crystal momentum]] (k-vector) in the [[Brillouin zone]]. If the k-vectors are the same, it is called a "direct gap". If they are different, it is called an "indirect gap". The band gap is called "direct" if the [[momentum]] of electrons and holes is the same in both the [[conduction band]] and the [[valence band]]; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
| | Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. This is a service where people write articles using a specific keyword you have given them. s and intelligently including a substantial amount of key words in the title tags, image links, etc. If you have any queries pertaining to where by and how to use [http://zpib.com/backup_plugin_664797 wordpress backup plugin], you can contact us at our own webpage. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. But as expected the level of support you get with them can be hit or miss based on the developer's free time and desire. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. <br><br>Here are a few reasons as to why people prefer Word - Press over other software's. The nominee in each category with the most votes was crowned the 2010 Parents Picks Awards WINNER and has been established as the best product, tip or place in that category. Whether or not it's an viewers on your web page, your social media pages, or your web page, those who have a present and effective viewers of "fans" are best best for provide provides, reductions, and deals to help re-invigorate their viewers and add to their main point here. Storing write-ups in advance would have to be neccessary with the auto blogs. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration. <br><br>Numerous bloggers are utilizing Word - Press and with good reason. php file in the Word - Press root folder and look for this line (line 73 in our example):. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. Word - Press offers constant updated services and products, that too, absolutely free of cost. <br><br>He loves sharing information regarding wordpress, Majento, Drupal and Joomla development tips & tricks. Sanjeev Chuadhary is an expert writer who shares his knowledge about web development through their published articles and other resource. This allows updates to be sent anyone who wants them via an RSS reader or directly to their email. Extra investment in Drupal must be bypassed as value for money is what Drupal provides. The 2010 voting took place from July 7 through August 31, 2010. |
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| [[Image:Indirect Bandgap.svg|thumb|350px|right|Energy vs. [[crystal momentum]] for a semiconductor with an indirect band gap, showing that an electron cannot shift from the lowest-energy state in the conduction band (green) to the highest-energy state in the valence band (red) without a change in momentum. Here, almost all of the energy comes from a [[photon]] (vertical arrow), while almost all of the momentum comes from a [[phonon]] (horizontal arrow).]]
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| [[Image:Direct.svg|thumb|350px|right|Energy vs. [[crystal momentum]] for a semiconductor with a direct band gap, showing that an electron can shift from the lowest-energy state in the conduction band (green) to the highest-energy state in the valence band (red) without a change in [[crystal momentum]]. Depicted is a transition in which a photon excites an electron from the valence band to the conduction band.]]
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| ==Implications for radiative recombination==
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| {{see also|Radiative recombination}}
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| Interactions among [[electron]]s, [[electron hole|holes]], [[phonon]]s, [[photon]]s, and other particles are required to satisfy [[conservation of energy]] and [[crystal momentum]] (i.e., conservation of total k-vector). A photon with an energy near a semiconductor band gap has almost zero momentum. One important process is called [[radiative recombination]], where an electron in the conduction band annihilates a hole in the valence band, releasing the excess energy as a photon. This is possible in a direct band gap semiconductor if the electron has a k-vector near the conduction band minima (the hole will share the same k-vector), but not possible in an indirect band gap semiconductor, as photons cannot carry crystal momentum, and thus conservation of crystal momentum would be violated. For radiative recombination to occur in an indirect band gap material, the process must also involve the absorption or emission of a [[phonon]], where the phonon momentum equals the difference between the electron and hole momentum. (It can also, instead, involve a [[crystallographic defect]], which performs essentially the same role.) The involvement of the phonon makes this process much less likely to occur in a given span of time, which is why ''radiative recombination is far slower in indirect band gap materials than direct band gap ones''. This is why [[Light-emitting diode|light-emitting]] and [[laser diode]]s are almost always made of direct band gap materials, and not indirect band gap ones like [[silicon]].
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| The fact that radiative recombination is slow in indirect band gap materials also means that, under most circumstances, radiative recombinations will be a small proportion of total recombinations, with most recombinations being non-radiative, taking place at point defects or at grain boundaries. However, if the excited electrons are prevented from reaching these recombination places, they have no choice but to eventually fall back into the valence band by radiative recombination. This can be done by creating a [[dislocation]] loop in the material. At the edge of the loop, the planes above and beneath the "dislocation disk" are pulled apart, creating a negative pressure, which raises the energy of the conduction band substantially, with the result that the electrons cannot pass this edge. Provided that the area directly above the dislocation loop is defect-free (no non-radiative recombination possible), the electrons will fall back into the valence shell by radiative recombination, thus emitting light. This is the principle on which "DELEDs" (Dislocation Engineered LEDs) are based.
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| ==Implications for light absorption==
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| The exact reverse of radiative recombination is light absorption. For the same reason as above, light with a photon energy close to the band gap can penetrate much farther before being absorbed in an indirect band gap material than a direct band gap one (at least insofar as the light absorption is due to exciting electrons across the band gap).
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| This fact is very important for [[photovoltaics]] (solar cells). Silicon is the most common solar-cell material, despite the fact that it is indirect-gap and therefore does not absorb light very well. Silicon solar cells are typically hundreds of [[micrometre]]s thick; if it was much thinner, much of the light (particularly in the infrared) would simply pass through. On the other hand, [[thin-film solar cell]]s are made of direct band gap materials (such as [[Cadmium telluride|CdTe]], [[Copper indium gallium selenide|CIGS]] or [[CZTS]]), which absorb the light in a much thinner region, and consequently can be made with a very thin active layer (often less than 1 micrometre thick).
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| The absorption spectrum of an indirect band gap material usually depends more on temperature than that of a direct material, because at low temperatures there are fewer phonons, and therefore it is less likely that a photon and phonon can be simultaneously absorbed to create an indirect transition. For example, silicon is opaque to visible light at room temperature, but transparent to red light at [[liquid helium]] temperatures, because red photons can only be absorbed in an indirect transition.
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| ===Formulae for absorption===
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| A common and simple method for determining whether a band gap is direct or indirect uses [[absorption spectroscopy]]. By plotting certain powers of the [[absorption coefficient]] against photon energy, one can normally tell both what value the band gap has, and whether or not it is direct.
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| For a direct band gap, the [[absorption coefficient]] <math>\alpha</math> is related to light frequency according to the following formula:<ref>''Optoelectronics'', by E. Rosencher, 2002, equation (7.25).</ref><ref>Pankove has the same equation, but with an apparently different prefactor <math>A^*</math>. However, in the Pankove version, the units / dimensional analysis appears not to work out.</ref>
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| :<math>\alpha \approx A^*\sqrt{h\nu - E_{\text{g}}}</math>, with <math>A^*=\frac{q^2 x_{vc}^2 (2m_{\text{r}})^{3/2}}{\lambda_0 \epsilon_0 \hbar^3 n}</math>
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| where:
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| * <math>\alpha</math> is the [[absorption coefficient]], a function of light frequency
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| *<math>\nu</math> is light frequency
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| *<math>h</math> is [[Planck's constant]] (<math>h\nu</math> is the energy of a [[photon]] with frequency <math>\nu</math>)
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| *<math>\hbar</math> is [[reduced Planck's constant]] (<math>\hbar=h/2\pi</math>)
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| *<math>E_{\text{g}}</math> is the band gap energy
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| *<math>A^*</math> is a certain frequency-independent constant, with formula above
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| *<math>m_{\text{r}}=\frac{m_{\text{h}}^* m_{\text{e}}^*}{m_{\text{h}}^* + m_{\text{e}}^*}</math>, where <math>m_{\text{e}}^*</math> and <math>m_{\text{h}}^*</math> are the [[effective mass (solid-state physics)|effective mass]]es of the electron and hole, respectively (<math>m_{\text{r}}</math> is called a "[[reduced mass]]")
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| *<math>q</math> is the [[elementary charge]]
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| *<math>n</math> is the (real) [[index of refraction]]
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| *<math>\epsilon_0</math> is the [[vacuum permittivity]]
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| *<math>x_{vc}</math> is a "matrix element", with units of length and typical value the same order of magnitude as the [[lattice constant]].
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| This formula is valid only for light with photon energy larger, but not too much larger, than the band gap (more specifically, this formula assumes the bands are approximately parabolic), and ignores all other sources of absorption other than the band-to-band absorption in question, as well as the electrical attraction between the newly created electron and hole (see [[exciton]]). It is also invalid in the case that the direct transition is [[forbidden transition|forbidden]], or in the case that many of the valence band states are empty or conduction band states are full.<ref name=Pankove>J.I. Pankove, ''Optical Processes in Semiconductors''. Dover, 1971.</ref>
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| On the other hand, for an indirect band gap, the formula is:<ref name=Pankove/>
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| :<math>\alpha \propto \frac{(h\nu-E_{\text{g}}+E_{\text{p}})^2}{\exp(\frac{E_{\text{p}}}{kT})-1} + \frac{(h\nu-E_{\text{g}}-E_{\text{p}})^2}{1-\exp(-\frac{E_{\text{p}}}{kT})}</math>
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| where:
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| *<math>E_{\text{p}}</math> is the energy of the [[phonon]] that assists in the transition
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| *<math>k</math> is [[Boltzmann's constant]]
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| *<math>T</math> is the [[thermodynamic temperature]]
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| (This formula involves the same approximations mentioned above.)
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| Therefore, if a plot of <math>h\nu</math> versus <math>\alpha^2</math> forms a straight line, it can normally be inferred that there is a direct band gap, measurable by extrapolating the straight line to the <math>\alpha=0</math> axis. On the other hand, if a plot of <math>h\nu</math> versus <math>\alpha^{1/2}</math> forms a straight line, it can normally be inferred that there is an indirect band gap, measurable by extrapolating the straight line to the <math>\alpha=0</math> axis (assuming <math>E_{\text{p}}\approx 0</math>).
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| ==Other aspects==
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| In some materials with an indirect gap, the value of the gap is negative. The top of the valence band is higher than the bottom of the conduction band in energy. Such materials are known as [[semimetal]]s.
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://ece-www.colorado.edu/~bart/book/book/chapter4/ch4_6.htm B. Van Zeghbroeck's Principles of Semiconductor Devices] at Electrical and Computer Engineering Department of University of Colorado at Boulder
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| [[Category:Electronic band structures]]
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| [[Category:Optoelectronics]]
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| [[de:Bandlücke#Arten]]
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| [[ja:直接遷移]]
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He loves sharing information regarding wordpress, Majento, Drupal and Joomla development tips & tricks. Sanjeev Chuadhary is an expert writer who shares his knowledge about web development through their published articles and other resource. This allows updates to be sent anyone who wants them via an RSS reader or directly to their email. Extra investment in Drupal must be bypassed as value for money is what Drupal provides. The 2010 voting took place from July 7 through August 31, 2010.