ECE453Fall2010Notes4-2[1]

ECE453Fall2010Notes4-2[1] - Fall 2010 ECE 453 Lecture Notes...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Fall 2010 ECE 453 Lecture Notes #4 For Purdue ECE 453 students ONLY NOT FOR CIRCULATION ECE 453 Lecture Notes#4 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 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, datta@purdue.edu Purdue University World Scientific (2011), to be published
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lessons from nanoelectronics: Copyright S. Datta datta@purdue.edu All Rights Reserved 56 12. Resistance and uncertainty In Chapter 4 we saw that the conductance of a short ballistic conductor is given by (q 2 /h)*M, where M is the number of independent conduction channels. What about a really short "molecular" conductor? There cannot be more than a few conduction channels at best, and so we would expect a maximum conductance ~ a few (q 2 /h). Indeed experimentalists have found the conductance of a hydrogen molecule to be ~ 2 (q 2 /h). Would our theoretical treatment predict this? The answer is no. Let me explain why. For something like a hydrogen molecule the energy level diagram should look just like the one-level resistor that we discussed in Section 3 where we obtained the following expression for the conductance G one level q 2 t F T ( 0 ) (same as Eq.(3.2)) This suggests a maximum conductance of ( q 2 / t )*(1/4 kT ) if the energy level sits right on the electrochemical potential μ 0 , dropping down to zero as the level moves away from μ 0 . Clearly this is not the quantized conductance q 2 / h that we are looking for, since there is no reason to expect that 4kT*t < h. After all, kT and t are two independent physical quantities: kT is related to the temperature, while t is the transfer time related to the quality of the contacts if the transit time through the channel is negligible. For any given t, we can always find a temperature below which the conductance would exceed our "maximum." What Eq.(3.2) misses is the broadening of the energy level: Quantum mechanically the process of coupling to a level, effectively spreads it out giving a picture more like the one shown in Fig.6.2. The one-level resistor then effectively becomes a resistor with a density of states, D ~1/ , being the broadening of the energy level. The conductance even for a one-level resistor should then be obtained from the multilevel result G q 2 D / t (see Eq.(3.3c)) which gives G one level q 2 t
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 17

ECE453Fall2010Notes4-2[1] - Fall 2010 ECE 453 Lecture Notes...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online