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--- hw3 [2016/04/06 09:21] – [Landauer to Drude (10 pts)] janet
+++ hw3 [2020/03/06 09:14] (current) – external edit 127.0.0.1
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 ====== Homework #3  ======
 PH 671 - Spring 2016, //Due 5pm on Friday, Week 3//
-**Under construction**
 ===== 1D Subbands (5 pts) =====
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 $$R = {h \over {2{e^2}}}{L \over {{\ell _{ph}}}}$$
-**c)** Show that the the above result is equivalent to the Drude formula, within a factor of 2, if we assume a free electron dispersion relation $E = {{{\hbar ^2}{k^2}} \over {2m}}$.
+**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 $E = {{{\hbar ^2}{k^2}} \over {2m}}$.
 $${\rho _{1d}} = {m \over {{n_{1d}}{e^2}{\tau _{e - ph}}}}$$
-${\tau _{e - ph}}$ is the time between phonon scattering events. ρ_1D is one-dimensional resistivity (units Ωm^-1).
+${\tau _{e - ph}}$ is the time between phonon scattering events. ρ<sub>1d</sub> is one-dimensional resistivity (units Ωm<sup>-1</sup>).
 ===== Field-effect transistor fundamental limits (5 pts) =====
-This question explores the "60 mV/decade limit" for the subthreshold slope of field-effect transistors.
+This question explores the "60 mV/decade limit" for the sub-threshold slope of field-effect transistors.
 To reduce the power consumption of microprocessors, transistors should switch off completely (infinite resistance) by application of a minimal voltage. This is not possible at room temperature. For a [[http://en.wikipedia.org/wiki/MOSFET|standard transistor design]], it takes at least 60 mV of gate voltage to increase the channel resistance by a factor of 10 (factor 10 = one decade).
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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).
-  *Note: On page 572 of A&M is a section called "Number of carriers in thermal equilibrium".
+  *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).
-  *Factoid: The 60 mV/decade limit was beaten in 2004 by a team at IBM ({{:2004-prl_band-to-band_tunneling.pdf|pdf}}) using a new type of tunnel diode.
 ===== 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):
   *Science
-  *Nature
+  *Nature; Nature Physics; Nature Communications,
   *Proceedings of the National Academy of Sciences (PNAS)
-  *Nature Physics
   *Physical Review Letters
   *Nano Letters
   *Applied Physics Letters
   *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, M. Massicotte et al. Nature Nanotechnology 11, 42–46 (2016) doi:10.1038/nnano.2015.227.
+  * Determination of band alignment in the single-layer MoS2/WSe2 heterojunction,  Ming-Hui Chiu, et al., Nature Communications 6, 7666, doi:10.1038/ncomms8666
+  * Electron-Phonon Coupling and Energy Flow in a Simple Metal beyond the Two-Temperature Approximation, Lutz Waldecker, Roman Bertoni, Ralph Ernstorfer, and Jan Vorberger, PHYSICAL REVIEW X 6, 021003; (2016)
+  * The Valley Hall effect in MoS2 transistors. K. F. Mak et al Science 344, pp. 1489-1492 (2014) DOI: 10.1126/science.1250140