hw3
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hw3 [2016/04/06 09:09] – janet | hw3 [2016/04/06 09:31] – [Homework #3] 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 | + | **b)** Consider a 1d wire where transport is characterized by a inelastic scattering length |
- | {{: | + | $$R = {h \over {2{e^2}}}{L \over {{\ell _{ph}}}}$$ |
- | **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 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). |
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===== Journal reading (5 pts) ===== | ===== Journal reading (5 pts) ===== |
hw3.txt · Last modified: 2020/03/06 09:14 by 127.0.0.1