ECE453Fall2010Notes2[1]

ECE453Fall2010Notes2[1] - Fall 2010 ECE 453 Lecture Notes...

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Fall 2010 ECE 453 Lecture Notes #2 ForPurdueECE453studentsONLY NOTFORCIRCULATION ECE 453 Lecture Notes#2 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 11. Semiclassical Transport and the Scf method xx 12. Resistance and uncertainty xx 13. Quantum Transport: Schrodinger to NEGF xx 14. Resonant tunneling and Anderson localization xx 15. Coulomb blockade and Mott transition xx 16. Hall effect / QHE xx Beyond voltages and currents 17. Thermoelectricity xx 18. Heat flow xx 19. Spin flow xx 20. Spin transistor xx 21. Electronic Maxwell's demon xx 22. Physics in a grain of sand xx Supriyo Datta, [email protected] Purdue University World Scientific (2011), to be published
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A new perspective on transport Copyright S.Datta [email protected] All Rights Reserved 27 6. Transverse modes As we saw in Chapter 4, a key new concept whose importance has only been appreciated since the seminal experiments on ballistic conductors, is the number of modes (see Eq.(4.9)): M ( E ) K v 2 h D ( E ) v ( E ) L (6.1) where K v is a numerical factor that comes from averaging over the angular distribution of velocities (Exercise 4.2): K ν = 1, 2 π , 1 2 in one, two and three dimensions We also explained how this quantity can be viewed as the number of independent current carrying channels and estimated from the standard experimental quantities, namely resistivity and mean free path. So far we have kept our discussion general in terms of the density of states, D(E) and the velocity, v(E) without adopting any specific models. These concepts are generally applicable even to amorphous materials and molecular conductors. A vast amount of literature both in condensed matter physics and in solid state devices, however, is devoted to crystalline solids with a periodic arrangement of atoms because of the major role they have played from both basic and applied points of view. For such materials, the concept of "bandstructure" leads to a very useful model that can be used to calculate D(E), v(E) and hence M(E). That is what we will do in this Chapter. E(p) or E(k) relations for crystalline solids The general principle for calculating D(E) is to start from the Schrodinger equation treating the electron as a wave confined to the solid. Confined waves (like a guitar string) have resonant "frequencies" and these are basically the allowed energy levels. By counting the number of energy levels in a range E to E+dE, we obtain the density of states D(E).
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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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ECE453Fall2010Notes2[1] - Fall 2010 ECE 453 Lecture Notes...

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