hw2
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hw2 [2016/03/31 16:37] – [Velocity and effective mass (5 pts)] janet | hw2 [2020/03/06 09:14] (current) – external edit 127.0.0.1 | ||
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====== Homework #2 ====== | ====== Homework #2 ====== | ||
PH 671 - Spring 2016, //Due 5pm on Friday, Week 2// | PH 671 - Spring 2016, //Due 5pm on Friday, Week 2// | ||
- | |||
- | **Under construction - will remove when ready** | ||
===== Journal reading (5 pts) ===== | ===== Journal reading (5 pts) ===== | ||
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===== Velocity and effective mass (5 pts) ===== | ===== Velocity and effective mass (5 pts) ===== | ||
- | Begin with semiclassical equations for electrons | + | Electrons |
- | $\vec v\left( {\vec k} \right) = {1 \over \hbar }{\nabla _k}E$ and | + | $\vec v\left( {\vec k} \right) = {1 \over \hbar }{\nabla _k}E$ and ${m^*} = {{{\hbar ^2}} \over {\nabla _k^2E}}$. |
- | $$m* = {{{\hbar ^2}} \mathord{\left/ | + | |
- | | + | |
- | \kern-\nulldelimiterspace} {\nabla _k^2E}}$$ | + | |
===== Boltzmann transport equation (15 pts) ===== | ===== Boltzmann transport equation (15 pts) ===== | ||
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Estimate the energy in eV of the highest frequency phonon in graphene (this phonon mode will show up in many types of experiments, | Estimate the energy in eV of the highest frequency phonon in graphene (this phonon mode will show up in many types of experiments, | ||
*Treat the graphene lattice as square grid. | *Treat the graphene lattice as square grid. | ||
- | *Choose an interatomic spacing that gives the correct area per unit mass for graphene, i.e. 1500 m< | + | *Choose an interatomic spacing that gives the correct area per unit mass for graphene, i.e. 1500 m< |
- | *You can check your answer by reading this {{:2000-prl_current_saturation_in_cnt.pdf|Phys. Rev. Lett. paper}}, where the authors observe that a phonon with energy 160 meV is responsible for current | + | *You can check your answer by reading this [[http:// |
+ | |||
+ | ===== Articles ==== | ||
+ | * // | ||
+ | * //Current oscillations as a manifestation of spatio-temporal inhomogeneity of temperature distribution in vanadium dioxide films at semiconductor-metal phase transition//, | ||
+ | * //Zener Tunneling and Photocurrent Generation in Quasi-Metallic Carbon Nanotube pn-Device// | ||
+ | * //Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube p−i−n Photodiodes//, | ||
+ | * //Transient Absorption and Photocurrent Microscopy Show That Hot Electron Supercollisions Describe the Rate-Limiting Relaxation Step in Graphene//, Graham et al., Nano Lett., 2013, 13 (11), pp 5497–5502; |
hw2.1459467476.txt.gz · Last modified: 2020/03/06 09:14 (external edit)