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| '''Quantum capacitance (density)''' is a physical value first introduced by Serge Luryi (1988)<ref name =Luryi>Serge Luryi (1988). "Quantum capacitance devices". ''Appl.Phys.Lett.'' 52(6). [http://www.ece.sunysb.edu/~serge/63.pdf Pdf]</ref> to describe the [[2DEG|2D-electronic systems]] in silicon surfaces and [[Heterojunction|GaAs junctions]]. This capacitance was defined through standard density of states in the solids. Quantum capacitance could be used in the [[quantum Hall effect]] (integer and fractional) investigations as a new approach which uses [[quantum LC circuit]].
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| == Theory ==
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| In the general case 2D-density of states in a solid could be defined by the following:
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| :<math>D_{2D} = \frac{m^*}{\pi \hbar^2}</math>,
| | by Nas, is very fitting and the film agrees with it. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. If you are using videos on your site then this is the plugin to use. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. <br><br>Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. Apart from these, you are also required to give some backlinks on other sites as well. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites. <br><br>It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. For a much deeper understanding of simple wordpress themes", check out Upon browsing such, you'll be able to know valuable facts. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory. <br><br>If you have any queries concerning where by and how to use [http://miniURL.fouiner.info/backup_plugin_813850 backup plugin], you can get hold of us at the website. Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. The SEOPressor Word - Press SEO Plugin works by analysing each page and post against your chosen keyword (or keyword phrase) and giving a score, with instructions on how to improve it. Specialty about our themes are that they are easy to load, compatible with latest wordpress version and are also SEO friendly. Word - Press is the most popular open source content management system (CMS) in the world today. This includes enriching the content with proper key words, tactfully defining the tags and URL. <br><br>Website security has become a major concern among individuals all over the world. Automated deal feed integration option to populate your blog with relevant deals. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. ) Remote Login: With the process of PSD to Wordpress conversion comes the advantage of flexibility. Get started today so that people searching for your type of business will be directed to you. |
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| where <math>m^* = \xi m_0 </math> is a current carrier's effective mass in a solid, <math>m_0 </math> is the electron mass, and <math>\xi </math> is a dimensionless parameter which considers the zone structure of a solid. So, the quantum capacitance can be defined as follows:
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| :<math>C_{QL} = e^2\cdot D_{2D} = \xi \cdot C_{Q0}</math>,
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| where <math>C_{Q0} = 8\pi \alpha \cdot C_{QY} \ </math> - the ‘‘ideal value’’ of quantum capacitance at <math>\xi = 1 \ </math> and another ideal quantum capacitance:
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| :<math>C_{QY} = \frac{\epsilon_0}{\lambda_0} = 3.649\;2417\;\mathrm{F/m^2}</math>,
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| where <math>\epsilon_0 - \ </math> [[Vacuum permittivity|dielectric constant]], <math>\alpha - \ </math> [[fine structure constant]] and <math>\lambda_0 - \ </math> [[Compton wavelength|Compton wave length]] of electron, first defined by Yakymakha (1994) )<ref name =Yakym1>Yakymakha O.L., Kalnibolotskij Y.M. (1994). "Very-low-frequency resonance of [[MOSFET]] [[amplifier]] parameters". ''Solid- State Electronics'' 37(10),1739-1751 [http://dx.doi.org/10.1016/0038-1101(94)00152-6 pdf]</ref> in the spectroscopic investigations of the silicon MOSFETs.
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| == Experiments ==
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| === Heterostructure tunnel junctions ===
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| The first attempt of quantum capacitance experimental confirmation in the 21st century were made by Qingmin Liu and Alan Seabaugh from the [[Notre Dame University]] (2001).<ref name =Liu>Qingmin Liu and Alan Seabaugh (2001). "New Physical Understanding of the Resonant Tunneling Diode Small-Signal Equivalent Circuit". Notre Dame University Publications. [http://www.nd.edu/~nano/publications/3a0623LiuDRC.pdf Notre Dame University Publications][http://arxiv.org/abs/0812.3927 Pdf]</ref> They investigated GaAs heterostructure tunnel junctions. It is evident that tunnel junction capacity is defined by the metallurgic tunnel junction surface:
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| :<math>C_{TD} = \frac{\epsilon_0 S_{TD}}{a_{TD}} \approx 6 \times 10^{-14}\;\mathrm{F} = 60\;\mathrm{fF}</math>
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| where <math>S_{TD} = (1.6 \times 10^{-6}\;\mathrm{m})^2 - \ </math>
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| AlAs/InGaAs/AlAs- metallurgic tunnel junction surface, <math>a_{TD} = 3.84\times 10^{-10}\;\mathrm{m} - \ </math> junction thickness (its value could be estimated by heterostructure lattice constant). For the aim of comparison, the quantum capacitance (Yakymakha) in this case should be:
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| :<math>C_{TDQ} = \frac{\epsilon_0 S_{TD}}{\lambda_0} \approx 9.34 \times 10^{-12}\;\mathrm{F} = 9.32\;\mathrm{pF} \ </math>.
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| Therefore this value is significantly greater than the experimental value obtained by Seabaugh. Thus, in the general case of tunnel junction, neither Yakymakha, nor Luryi (there are no 2D- density of states in the 1D- dimension) approaches could be used.
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| === Graphene MOSFETs ===
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| One publication on the theme was made by Zhihong Chen and Joerg Appenzeller<ref name =Chen>Zhihong Chen, Joerg Appenzeller (2008). "Mobility Extraction and Quantum Capacitance Impact in High Performance Graphene Field-effect Transistor Devices". Electron Devices Meeting, 2008. IEDM 2008. IEEE International. San Francisco, CA, USA. ISBN 978-1-4244-2377-4 [http://arxiv.org/abs/0812.3927]</ref> on the high quality [[Graphene]] field-effect transistor devices. In this paper the Luryi definition of quantum capacitance was used:
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| :<math>D_{Gr} = \frac{aE}{\pi \hbar^2v_F^2}, a = 1 \ </math>
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| :<math>C_{QL} = e^2D_{Gr} = \frac{e^2m^*}{\pi\hbar^2}</math>,
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| where <math>m^* = \frac{E}{v_F^2} = \frac{\hbar}{v_F}\cdot \sqrt{\pi n_{2D}} - \ </math> current carriers cyclotron mass. The authors obtained the linear mirrors dependence of the quantum capacitance on the gate voltage, with the minimal value at the ‘‘Dirac point’’ about (Fig.7):
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| :<math>C_{exp} \approx 4\times 10^{-3}\;\mathrm{F/m^2} \ </math>.
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| In the case of the multi-layer graphene there is the constant value (independent of the gate voltage) of the quantum capacitance, equal to the minimal value of the mono-layer graphene. Further the authors supposed, that in the "ideal case" the quantum capacitance of graphene should have zero value at the Dirac point. This isn’t true. According to Yakymakha (1989),<ref name =Yakym2>Yakymakha O.L.(1989). ''High Temperature Quantum Galvanomagnetic Effects in the Two- Dimensional Inversion Layers of MOSFET's'' (In Russian). Kiev: Vyscha Shkola. p.91. ISBN 5-11-002309-3. [http://eqworld.ipmnet.ru/ru/library/books/Yakimaha1989ru.djvu djvu]</ref> the 2D-system with the particles of two sorts have zone structure with the minimal particles concentration about the intrinsic value:
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| :<math>n_{2D}(T_c) = 3.03\times 10^{14}\;\mathrm{m^{-2}} \ </math>.
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| Using this value for the cyclotron mass, we obtain its minimum value:
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| :<math>m^*(n_{2D}(T_c)) =\frac{2\hbar}{\alpha c}\sqrt{\pi n_{2D}(T_c)} \approx 2.9767\times 10^{-33}\;\mathrm{kg} \ </math>.
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| Then, dimensionless parameter will be approximated as:
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| :<math>\xi = \frac{m^*(n_{2D}(T_c))}{m_0} \approx 3.2677 \times 10^{-3} \ </math>.
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| From above, we can find out the minimal value of the quantum capacitance in graphene:
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| :<math>C_{QL} = \xi C_{Q0} \approx 2.187\times 10^{-3}\;\mathrm{F/m^2} \ </math>.
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| This value is two times lesser than the experimental value. Nothing strange is there. Actually, we used above only one type of current carriers during estimation procedure. However, at the Dirac point in graphene, we have the two type conductivity, due to the quasi-electron and quasi-holes. Therefore, on practice, we have two quantum capacitances due to the quasielectron and quasiholes, connected in the parallel circuit. These two quantum capacitances confirms indirectly the existence of the “[[Electronic band structure|band structure]]” in graphene near the Dirac point with nonzero value of the “[[Band gap|forbidden band]]”.
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://nano.ece.ubc.ca/pub/john04a.pdf D.L. John, L.C. Castro, and D.L. Pulfrey "Quantum Capacitance in Nanoscale Device Modeling" ''Nano Electronics Group Publications''.]
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| *[https://nanohub.org/resources/695/ ECE 453 Lecture 30: Quantum Capacitance]
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| *[http://www.nature.com/nphys/journal/v2/n10/abs/nphys412.html "Measurement of the quantum capacitance of interacting electrons in carbon nanotubes" ''Nature'']
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| {{DEFAULTSORT:Quantum Capacitance}}
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| [[Category:Quantum models]]
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| [[Category:Quantum mechanics]]
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by Nas, is very fitting and the film agrees with it. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. If you are using videos on your site then this is the plugin to use. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting.
Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. Apart from these, you are also required to give some backlinks on other sites as well. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites.
It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. For a much deeper understanding of simple wordpress themes", check out Upon browsing such, you'll be able to know valuable facts. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory.
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