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Quantum Mechanics: Landauer's Formula
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| Contributor(s) | Dragica Vasileska Arizona State University Gerhard Klimeck Purdue University, West Lafayette |
|---|---|
| Abstract | When a metallic nanojunction between two macroscopic electrodes is connected to a battery, electrical current flows across it. The battery provides, and maintains, the charge imbalance between the electrode surfaces needed to sustain steady-state conduction in the junction. This static non-equilibrium problem is usually described according to the Landauer picture. In this picture, the junction is connected to a pair of defect-free metallic leads, each of which is connected to its own distant infinite heat-particle reservoir. The pair of reservoirs represents the battery. Each reservoir injects electrons into its respective lead with the electrochemical potential appropriate to the bulk of that reservoir. Each injected electron then travels undisturbed down the respective lead to the junction, where it is scattered and is transmitted, with a finite probability, into the other lead. From there it flows, without further disturbance, into the other reservoir. The reservoirs are conceptual constructs which allow us to map the transport problem onto a truly stationary scattering one, in which the time derivative of the total current, and of all other local physical properties of the system, is zero. By doing so, however, we arbitrarily enforce a specific steady state whose microscopic nature is not, in reality, known a priori. The Landauer construct is highly plausible in the case of non-interacting lectrons. In the material provided below, we first discuss the concepts of diffusive vs. ballistic transport, then we show the derivation of the Landauer and Landauer-Buttiker formulas, we give a link to a resonant tunneling diode solver and we also provide homework assignments regarding simulation of resonant tunneling diodes. |
| Sponsored by | NSF |
| Cite this work | If you reference this work in a publication, please cite as follows: |
| Date posted | 09 Jul, 2008 |
| Type | Series |
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Resonant Tunneling Diode Simulator
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Usage Stats Overall Period: Updated 20 Nov, 2008 Users: 813 Jobs: 24751 Avg. exec. time: 6 secs Reviews & Citations Google/IEEE: updated 24 Apr, 2008 Avg. Review: Citations: 3
813 users, detailed statistics
10 Oct. 2005 | Tools | Contributor(s): Michael McLennan
Simulate 1D resonant tunneling devices and other heterostructures via ballistic quantum transport
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Homework for Resonant Tunneling Diodes
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Usage Stats Last 12 Months: updated 01 Nov, 2008 Users: 415 Reviews & Citations Google/IEEE Avg. Review: Citations: 0
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06 Jan. 2006 | Teaching Materials | Contributor(s): H.-S. Philip Wong
This homework assignment was created by H.-S. Philip Wong for EE 218 "Introduction to Nanoelectronics and Nanotechnology" (Stanford University). It includes a couple of simple "warm up" exercises and two design problems, intended to teach students the electronic properties of resonant tunneling …
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Slides: Landauer's formula derivation
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Usage Stats Last 12 Months: updated 01 Nov, 2008 Users: 61 Reviews & Citations Google/IEEE Avg. Review: Citations: 0
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09 Jul. 2008 | Teaching Materials | Contributor(s): Dragica Vasileska
www.eas.asu.edu/~vasileskNSF
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Reading Material: Landauer's formula
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Usage Stats Last 12 Months: updated 01 Nov, 2008 Users: 41 Reviews & Citations Google/IEEE Avg. Review: Citations: 0
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09 Jul. 2008 | Teaching Materials | Contributor(s): Dragica Vasileska
www.eas.asu.edu/~vasileskNSF
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Slides: Diffusive vs. ballistic transport
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Usage Stats Last 12 Months: updated 01 Nov, 2008 Users: 25 Reviews & Citations Google/IEEE Avg. Review: Citations: 0
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09 Jul. 2008 | Teaching Materials | Contributor(s): Dragica Vasileska
www.eas.asu.edu/~vasilesk
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Slides: Buttiker formula derivation
- This resource has a 6.4 Ranking
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Ranking is calculated from a formula comprised of user reviews and usage statistics. Learn more ›
Usage Stats Last 12 Months: updated 01 Nov, 2008 Users: 25 Reviews & Citations Google/IEEE Avg. Review: Citations: 0
25 users
09 Jul. 2008 | Teaching Materials | Contributor(s): Dragica Vasileska
www.eas.asu.edu/~vasileskNSF
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5.3 Ranking Series
Part of: Quantum Mechanics for Engineers
Quantum Mechanics for Engineers
Type Series Contributor(s) Dragica Vasileska, Gerhard Klimeck, David K. Ferry Date 14 Jul, 2008 Avg. Rating (0) Rate this This course will introduce the students to the basic concepts and postulates of quantum mechanics. Examples will include simple systems such as particle in an infinite and finite well, 1D and 2D harmonic oscillator and tunneling. Numerous approximation techniques, such as WKB method, time-dependent …
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