ECE453Fall2010Notes6[1] - Fall 2010 ECE 453 Lecture Notes...

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Unformatted text preview: Fall 2010 ECE 453 Lecture Notes #6 (Final) For Purdue ECE 453 students ONLY NOT FOR CIRCULATION ECE 453 Lecture Notes#6 (Final) Excerpted from (LNE) Lessons from nanoelectronics: A new perspective on transport 1. The bottom-up approach 4 Introductory concepts 2. Why electrons flow 6 3. The elastic resistor 10 4. The new Ohm's law 14 Notes #1 5. Where is the resistance? 19 ***************************************************************** 6. Transverse modes 27 7. Drude formula 33 8. Kubo formula 38 Notes # 2 9. How realistic is an elastic resistor? 41 ***************************************************************** Semiclassical and quantum transport 10. Beyond low bias: The nanotransistor 44 Notes#3 11. Semiclassical Transport and the Scf method 50 ***************************************************************** 12. Resistance and uncertainty 56 13. Quantum Transport: Schrodinger to NEGF 63 Notes#4 14. Resonant tunneling and Anderson localization 68 ***************************************************************** 15. Coulomb blockade and Mott transition 72 16. Hall effect / QHE 78 Beyond voltages and currents 17. Thermoelectricity 83 Notes#5 18. Heat flow 88 ***************************************************************** 19. Spin flow 92 20. Spin transistor 97 Notes#6 21. Electronic Maxwell's demon 103 ***************************************************************** 22. Physics in a grain of sand 111 Supriyo Datta, [email protected] Purdue University World Scientific (2011), to be published Lessons from nanoelectronics: Copyright S. Datta [email protected] All Rights Reserved 92 19. Spin flow So far we have treated spin as part of a "degeneracy factor, g" (see Eqs.(6.10), (6.11)), the idea being that electronic states always come in pairs, one corresponding to each spin. It is a if we have two sets of channels, which we could call up spin and down spin, or more colorfully, red and blue as shown in Fig.19.1. Ordinarily they are identical and we can calculate the conductance due to one and remember to multiply by two. But in spin valve devices the contacts are magnets that treat the red and blue channels differently leading to an observable and very useful effect. Spin valve We assume that in the channel red and blue have equal density of states, D, but the contacts are magnetic where the majority spin (red) band is shifted down with respect to the minority spin (blue) band as shown in Fig.19.1. This makes it easier for the red electrons to get in and out of the channel so that the characteristic time t 1 for this process is shorter than the corresponding time t 2 for the blue electrons. Assuming the transfer time is interface-limited, it is given by 2t 1 for the red channel and 2t 2 for the blue channel so that the total conductance from Eq.(3.3c) is given by (t 1 < t 2 ) G P = q 2 D 2 1 2 t 1 + 1 2 t 2 !...
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This note was uploaded on 11/29/2010 for the course ECE 453 taught by Professor Supriyodatta during the Spring '10 term at Purdue.

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ECE453Fall2010Notes6[1] - Fall 2010 ECE 453 Lecture Notes...

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