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ECE 802-604: Nanoelectronics

ECE 802-604: Nanoelectronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 26, 02 Dec 13. Carbon Nanotubes and Graphene CNT/Graphene electronic properties sp 2 : electronic structure

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ECE 802-604: Nanoelectronics

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  1. ECE 802-604:Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 26, 02 Dec 13 Carbon Nanotubes and Graphene CNT/Graphene electronic properties sp2: electronic structure 2DEG: E-k relationship/graph for graphene and transport 1DEG: E-k relationship/graph for CNTs and transport Examples Molecular Electronics R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes VM Ayres, ECE802-604, F13

  3. CNT Unit cell in green: Ch = n a1 + m a2 |Ch| = a√n2 + m2 + mn dt = |Ch|/p cos q = a1 • Ch |a1| |Ch| T = t1a1 + t2a2 t1 = (2m + n)/ dR t2 = - (2n + m) /dR dR = the greatest common divisor of 2m + n and 2n+ m |T| = √ 3(m2 + n2+nm)/dR = √ 3|Ch|/dR N = | T X Ch | | a1xa2 | = 2(m2 + n2+nm)/dR VM Ayres, ECE802-604, F13

  4. Example: is Ch for the armchair CNT at right angles to Ch for the zigzag CNT? VM Ayres, ECE802-604, F13

  5. Example: is Ch for the armchair CNT at right angles to Ch for the zigzag CNT? Answer: No. It’s at an angle. HW: evaluate the angle. VM Ayres, ECE802-604, F13

  6. If this is the specified unit vector system, then armchair Ch is at the chiral angle and zigzag: Ch in a1 direction . a1 VM Ayres, ECE802-604, F13

  7. Example: for the paper cutout, is Ch for the armchair CNT at right angles to Ch for the zigzag CNT? VM Ayres, ECE802-604, F13

  8. Example: for the paper cutout, is Ch for the armchair CNT at right angles to Ch for the zigzag CNT? Answer. No. Answer doesn’t change. VM Ayres, ECE802-604, F13

  9. Example: for the paper cutout, number and create the largest possible zigzag CNT VM Ayres, ECE802-604, F13

  10. Example: for the paper cutout, number and create the largest possible zigzag CNT Answer: (5,0). HW: evaluate T and cut out the proper Unit cell length. VM Ayres, ECE802-604, F13

  11. Example: for the paper cutout, number and create the largest possible armchair CNT VM Ayres, ECE802-604, F13

  12. Example: for the paper cutout, number and create the largest possible armchair CNT Answer: (3,3). HW: evaluate T and cut out the proper Unit cell length. VM Ayres, ECE802-604, F13

  13. Example: Unit vectors a1 and a2 are not pointing in the same directions in (a) and (b). What is the goal of each arrangement? ARMCHAIR: ZIGZAG: VM Ayres, ECE802-604, F13

  14. Example: Unit vectors a1 and a2 are not pointing in the same directions in (a) and (b). What is the goal of each arrangement? Answer: ARMCHAIR: ZIGZAG: VM Ayres, ECE802-604, F13

  15. Lec 24: Graphene: the 6 equivalent K-points Bottom of the conduction band the 6 equivalent K-points metallic E ky kx This factor slices the graphene Eg2D VM Ayres, ECE802-604, F13

  16. Lec 24: At a K- point = metallic: Condition: Armchair (n,n) are always metallic VM Ayres, ECE802-604, F13

  17. Lec 24: At a K- point = metallic: Condition: Example: Prove this condition. First: identify the Unit vector system being used. VM Ayres, ECE802-604, F13

  18. Answer: First: identify the Unit vector system being used. ARMCHAIR: VM Ayres, ECE802-604, F13

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  24. Ch = n a1 + m a2 |Ch| = a√n2 + m2 + mn cos q = a1 • Ch |a1| |Ch| For HW: VM Ayres, ECE802-604, F13

  25. For HW: Find K1 in this system. Show |K1| = 2p / |Ch| VM Ayres, ECE802-604, F13

  26. Lec 06: VM Ayres, ECE802-604, F13

  27. Lec 24: What you can do with an E-k diagram: Answer: VM Ayres, ECE802-604, F13

  28. 1DEG CNT: VM Ayres, ECE802-604, F13 Conduction energy levels

  29. Lec 24: Consider an (n, n) armchair CNT. This is where the periodic boundary condition on kX comes from in: That leaves just kY as open, MD calls it just k. VM Ayres, ECE802-604, F13

  30. Linearize graphene dependence around the K-point VM Ayres, ECE802-604, F13

  31. Lecture 26, 02 Dec 13 • Molecular Electronics: • Why not polyacetylene? or any conjugated “ene”? • Examples of possibilities • Actual performance • Electronic (p) structure brief review • Mechanical (s) structure brief review • New: bond alteration structure • Electronic result of bond alteration structure • Qualitative VM Ayres, ECE802-604, F13

  32. CNTs: Electronic structure Armchair (n,n) Zigzag (3n,0) Armchair (≠3n,0) VM Ayres, ECE802-604, F13

  33. CNTs: Electronic device VM Ayres, ECE802-604, F13

  34. Graphene: Electronic structure VM Ayres, ECE802-604, F13

  35. Graphene: Electronic device VM Ayres, ECE802-604, F13

  36. Polyacetylene: Electronic structure VM Ayres, ECE802-604, F13

  37. Polyacetylene: Electronic device VM Ayres, ECE802-604, F13

  38. Polyphenylene: Electronic structure: VM Ayres, ECE802-604, F13

  39. Polyphenylene: Electronic device VM Ayres, ECE802-604, F13

  40. VM Ayres, ECE802-604, F13

  41. VM Ayres, ECE802-604, F13

  42. If it looked the same in 2008 as in 1992, there are some problems that people are still trying to solve! VM Ayres, ECE802-604, F13

  43. Expected performance: Polyphenylene and Polyactetylene • Quasi-ballistic like graphene and SWCNTs Actual performance: Polyphenylene and Polyactetylene • Slow • Variable VM Ayres, ECE802-604, F13

  44. Factors that affect transport: • Availability of electrons AND empty states to take them • Scattering: • Particle-like: Lf < Lm < L • Wavelike (ballistic): L < Lm < Lf • Electrons in a 2D or 1D structure are wavelike and therefore should have limited scattering • Transport mechanism: • Diffusion • Tunnelling • Ballistic (Plasmon) • Charge transfer • Soliton (Polaron) • Exciton • Hopping • Injection (Contacts) VM Ayres, ECE802-604, F13

  45. Lecture 27, 03 Dec 13 • Molecular Electronics: • Why not polyacetylene? or any conjugated “ene”? • Examples of possibilities • Actual performance • Electronic (p) structure brief review • Mechanical (s) structure brief review • New: bond alteration structure • Electronic result of bond alteration structure • Qualitative • Quantitative • Solitons (polarons): Su-Schreiffer-Heeger (SSH) model VM Ayres, ECE802-604, F13

  46. Division of structural and electronic properties in sp2 makes both good: -C=C- Structure: s-bonds Electronic: p-bonds VM Ayres, ECE802-604, F13

  47. Structure: s-bonds Electronic: p-bonds p* -conduction band e- ECE, PHY -anti-bonding e- CHM Electronic: Delocalized p e- p -valence band e- ECE, PHY -bonding e- CHM VM Ayres, ECE802-604, F13

  48. Division of structural and electronic properties in sp2 makes both good: -C=C- Structure: s-bonds MECHANICAL Electronic: p-bonds ELECTRICAL VM Ayres, ECE802-604, F13

  49. Lecture 26, 02 Dec 13 • Molecular Electronics: • Why not polyacetylene? or any conjugated “ene”? • Examples of possibilities • Actual performance • Electronic (p) structure brief review • Mechanical (s) structure brief review • New: bond alteration structure • Electronic result of bond alteration structure • Qualitative • Quantitative • Solitons (polarons): Su-Schreiffer-Heeger (SSH) model VM Ayres, ECE802-604, F13

  50. H H H H “A” c c c c c c c “B” H H H -a +a Review: Polyacetylene: HAA types: c c H H VM Ayres, ECE802-604, F13

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