hw3
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hw3 [2016/04/06 09:15] – [Landauer to Drude (10 pts)] janet | hw3 [2016/04/16 11:53] – [Landauer to Drude (10 pts)] janet | ||
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====== Homework #3 ====== | ====== Homework #3 ====== | ||
PH 671 - Spring 2016, //Due 5pm on Friday, Week 3// | PH 671 - Spring 2016, //Due 5pm on Friday, Week 3// | ||
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- | **Under construction** | ||
===== 1D Subbands (5 pts) ===== | ===== 1D Subbands (5 pts) ===== | ||
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$$R = {h \over {2{e^2}}}\left( {1 + {{{{\left| {{r_1}} \right|}^2}} \over {{{\left| {{t_1}} \right|}^2}}} + {{{{\left| {{r_2}} \right|}^2}} \over {{{\left| {{t_2}} \right|}^2}}}} \right)$$ | $$R = {h \over {2{e^2}}}\left( {1 + {{{{\left| {{r_1}} \right|}^2}} \over {{{\left| {{t_1}} \right|}^2}}} + {{{{\left| {{r_2}} \right|}^2}} \over {{{\left| {{t_2}} \right|}^2}}}} \right)$$ | ||
- | **b)** Consider a 1d wire where transport is characterized by a inelastic scattering length ${L \over {{\ell _{ph}}}}$. | + | **b)** Consider a 1d wire where transport is characterized by a inelastic scattering length ${L \over {{\ell _{ph}}}}$. |
$$R = {h \over {2{e^2}}}{L \over {{\ell _{ph}}}}$$ | $$R = {h \over {2{e^2}}}{L \over {{\ell _{ph}}}}$$ | ||
- | **c)** Show that the the above result is equivalent to the Drude formula if we assume a free electron dispersion relation | + | **c)** Show that the above result is equivalent to the Drude formula, within a factor of 2, if we assume a free electron dispersion relation |
- | {{: | + | $${\rho _{1d}} = {m \over {{n_{1d}}{e^2}{\tau _{e - ph}}}}$$ |
- | within a factor of 2. τ_phonon | + | ${\tau _{e - ph}}$ is the time between phonon scattering events. ρ< |
===== Field-effect transistor fundamental limits (5 pts) ===== | ===== Field-effect transistor fundamental limits (5 pts) ===== | ||
- | This question explores the "60 mV/decade limit" for the subthreshold | + | This question explores the "60 mV/decade limit" for the sub-threshold |
To reduce the power consumption of microprocessors, | To reduce the power consumption of microprocessors, | ||
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Set up an integral to calculate the number of free electrons in silicon when the chemical potential is 200 meV below the conduction band edge. Do the same thing when the chemical potential is 260 meV below the conduction band edge. What is the ratio of electron densities? (work out the number, not just an expression). | Set up an integral to calculate the number of free electrons in silicon when the chemical potential is 200 meV below the conduction band edge. Do the same thing when the chemical potential is 260 meV below the conduction band edge. What is the ratio of electron densities? (work out the number, not just an expression). | ||
- | | + | *Factoid: The 60 mV/decade limit was beaten in 2004 by a team at IBM using a new type of tunnel diode. See Appenzeller //et al.//, PRL 93, 196805 (2004). |
- | | + | |
===== Journal reading (5 pts) ===== | ===== Journal reading (5 pts) ===== | ||
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Include full bibliographic information (journal name, volume number, page number, article title). Please limit yourself to the following journals (this list can be augmented with class consensus; and you may need to request an interlibrary loan to access some): | Include full bibliographic information (journal name, volume number, page number, article title). Please limit yourself to the following journals (this list can be augmented with class consensus; and you may need to request an interlibrary loan to access some): | ||
*Science | *Science | ||
- | *Nature | + | *Nature; Nature Physics; Nature Communications, |
*Proceedings of the National Academy of Sciences (PNAS) | *Proceedings of the National Academy of Sciences (PNAS) | ||
- | *Nature Physics | ||
*Physical Review Letters | *Physical Review Letters | ||
*Nano Letters | *Nano Letters | ||
*Applied Physics Letters | *Applied Physics Letters | ||
*Physical Review X | *Physical Review X | ||
+ | |||
+ | Articles | ||
+ | * Monte-Carlo simulation of nano-collected current from a silicon sample containing a linear arrangement of uncapped nanocrystals , Mohammed Ledra and Abdelillah El Hdiy J. Appl. Phys. 118, 115705 (2015); | ||
+ | * Picosecond photoresponse in van der Waals heterostructures, | ||
+ | * Determination of band alignment in the single-layer MoS2/WSe2 heterojunction, | ||
+ | * Electron-Phonon Coupling and Energy Flow in a Simple Metal beyond the Two-Temperature Approximation, | ||
+ | * The Valley Hall effect in MoS2 transistors. K. F. Mak et al Science 344, pp. 1489-1492 (2014) DOI: 10.1126/ | ||
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hw3.txt · Last modified: 2020/03/06 09:14 by 127.0.0.1