453_ClassNotes_1

453_ClassNotes_1 - Lessons from Nanoscience A Lecture Note...

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i Lessons from Nanoscience: A Lecture Note Series Volume 1: Lessons from Nanoelectronics: A New Perspective on Transport Lectures 1-9 Supriyo Datta Purdue University [email protected] August 22, 2011 For more information about the lecture note series, see http://nanohub.org/topics/LessonsfromNanoscience . This DRAFT copy is provided by the author to students enrolled in ECE 453/595 at Purdue University IT SHOULD NOT BE DISTRIBUTED. Copyright World Scientific Publishing Company, 2011
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ii Preface Preface Everyone is familiar with the amazing performance of a modern laptop, powered by a billion-plus nanotransistors, each having an active region that is barely a few hundred atoms long. These lectures, however, are about a less-appreciated by-product of the microelectronics revolution, namely the deeper understanding of current flow, energy exchange and device operation that it has enabled, which forms the basis for what we call the bottom-up approach. I believe these lessons from nanoelectronics should be of broad relevance to the general problems of non-equilibrium statistical mechanics which pervade many different fields. To make these lectures accessible to anyone in any branch of science or engineering, we assume very little background beyond linear algebra and differential equations. We hope to reach those who are not experts in device physics or transport theory and would like to keep it that way. For dedicated graduate students and the experts, I have written extensively in the past. But they too may enjoy these notes taking a fresh look at a familiar subject, emphasizing the insights from mesoscopic physics and nanoelectronics that are of general interest and relevance. I should stress that these are “lecture notes” in unfinished form, and suggestions from readers are very welcome. Readers can view the actual lectures online http://nanohub.org/topics/LessonsfromNanoscience . July 2011
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iii Contents Preface I. The New Ohm’s Law 1. The Bottom-Up Approach 11 2. Why Electrons Flow 15 3. The Elastic Resistor 23 4. How Many Channels? 30 5. Conductivity 35 6. Diffusion Equation for Ballistic Transport 50 7. What about Drift? 62 8. Role of Electrostatics 73 9. Smart Contacts 84 II. Old Topics in New Light 10. Thermoelectricity 92 11. Heat Flow 101 12. Measuring Electrochemical Potential 112 13. Hall Effect 126 14. Spin Valve 139 15. Kubo Formula 153 16. Second Law 160 17. Fuel Value of Information 175 III. Contact-ing Schrodinger 18. The Model 186 19. Non-Equilibrium Green’s Functions (NEGF) 205 20. Can Two Offer Less Resistance than One? 226 21. Quantum of Conductance 235 22. How to Rotate an Electron 244 23. Beyond the Elastic Resistor 261 24. Does NEGF Include “Everything”? 268 25. Spins and Magnets: Quantum and the Classical 277 References 283 Appendices 284
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iv Detailed Contents Detailed Contents Preface Useful Constants I. The New Ohm’s Law 1. The Bottom-Up Approach 11 2. Why Electrons Flow 15 2.1. Two Key Pieces 2.2. Fermi Function 2.3. Non-equilibrium: Two Fermi Functions 2.4. Linear Response 2.5. Difference in “Agenda” Drives Flow 3. The Elastic Resistor 23 3.1. Conductance of an Elastic Resistor
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