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ECE453Fall2010Notes30[1] - Fall 2010 ECE 453 Lecture...

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Fall 2010 ECE 453 Lecture Notes #3 ForPurdueECE453studentsONLY NOTFORCIRCULATION ECE 453 Lecture Notes#3 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 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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Lessons from nanoelectronics: Copyright S. Datta [email protected] All Rights Reserved 44 10. Beyond low bias: The nanotransistor I should state at the outset that this Chapter does not do justice to this important device at the heart of microelectronics. The nanotransistor will be discussed in a separate volume in this series written by Lundstrom, whose model is widely used in the field and forms the basis of our discussion here. Our purpose in this Chapter is simply to use the nanotransistor to illustrate some of the additional factors that need to be considered when dealing with far from equilibrium problems, factors that do not arise in low bias transport. The nanotransistor is a three- terminal device (Fig.10.1), though ideally the current should flow only between the source and drain terminals. The role of the gate terminal is just to control the current as showed in the sketch: The current-drain voltage, I- V D , characteristics are controlled by the gate voltage, V G (see Fig.10.2). The low bias current can be understood based on the principles we have already discussed in connection with the Drude formula (Chapter 7). But currents at high V D involve important new principles and our purpose in this Chapter is to illustrate them. The basic principle underlying an FET is straightforward (see Fig.10.3). A positive gate voltage V G changes the potential in the channel, lowering all the states down in energy. For an n- type conductor this increases the number of available states in the energy window of interest around µ 1 and µ 2 as shown. Of course for a p-type conductor (see Fig.7.2) the reverse would be true leading to a complementary FET (see Fig.0.2) whose conductance variation is just the opposite of what we are discussing. But we will focus here on n-type FET's.
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ECE453Fall2010Notes30[1] - Fall 2010 ECE 453 Lecture...

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