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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 20, 05 Nov 13. Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical 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 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  3. sp1 hybridization • Use orthonormality • sp2 hybridization: • Get help from directions • Use orthonormality VM Ayres, ECE802-604, F13

  4. sp2 hybridization: 1 VM Ayres, ECE802-604, F13

  5. sp2 hybridization: 1 Example: how many valence (bonding) electrons do you get in: sp1 hybridization? sp2 hybridization? VM Ayres, ECE802-604, F13

  6. sp2 hybridization: Answer: sp = sp1 hybridization: 2e- per C: linear bonding sp2 hybridization: 3e- per C: trigonal bonding sp sp sp sp sp2 sp2 sp2 VM Ayres, ECE802-604, F13

  7. sp2 hybridization: VM Ayres, ECE802-604, F13

  8. sp2 hybridization: VM Ayres, ECE802-604, F13

  9. sp2 hybridization: VM Ayres, ECE802-604, F13

  10. sp2 hybridization: VM Ayres, ECE802-604, F13

  11. sp2 hybridization: VM Ayres, ECE802-604, F13

  12. sp2 hybridization: VM Ayres, ECE802-604, F13

  13. sp2 hybridization: VM Ayres, ECE802-604, F13

  14. sp2 hybridization: VM Ayres, ECE802-604, F13

  15. sp2 hybridization: VM Ayres, ECE802-604, F13

  16. sp2 hybridization: VM Ayres, ECE802-604, F13

  17. sp2 hybridization: VM Ayres, ECE802-604, F13

  18. sp2 hybridization: VM Ayres, ECE802-604, F13

  19. sp2 hybridization: VM Ayres, ECE802-604, F13

  20. sp2 hybridization: VM Ayres, ECE802-604, F13

  21. sp2 hybridization: VM Ayres, ECE802-604, F13

  22. sp2 hybridization: VM Ayres, ECE802-604, F13

  23. sp2 hybridization: VM Ayres, ECE802-604, F13

  24. sp2 hybridization: VM Ayres, ECE802-604, F13

  25. sp2 hybridization: VM Ayres, ECE802-604, F13

  26. sp2 hybridization: VM Ayres, ECE802-604, F13

  27. VM Ayres, ECE802-604, F13

  28. sp2 hybridization: VM Ayres, ECE802-604, F13

  29. sp2 hybridization: VM Ayres, ECE802-604, F13

  30. sp2 hybridization: VM Ayres, ECE802-604, F13

  31. sp2 hybridization: VM Ayres, ECE802-604, F13

  32. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  33. VM Ayres, ECE802-604, F13

  34. Expect: 180º Get: 180º F VM Ayres, ECE802-604, F13

  35. Expect: 90º Get: 104.5º “Explanation”: Mutual repulsion of the H atoms “Plausible”: H2S, H2Se = 92º, 90º Greater separation of H around larger S and Se atoms H O H VM Ayres, ECE802-604, F13

  36. Expect: 90º pyramid Get: 107.5º pyramid “Explanation”: Mutual repulsion of the H atoms “Plausible”: H3P, H3As = 92º, 90º Greater separation of H around larger P and As atoms H H N H VM Ayres, ECE802-604, F13

  37. Expect: 90º CH2, like H2O H C H VM Ayres, ECE802-604, F13

  38. Expect: 90º CH2, like H2O Get: CH4 tetrahedron CH4 is impossible in this p-orbital picture. H C H VM Ayres, ECE802-604, F13

  39. sp3 Hybrid orbital picture VM Ayres, ECE802-604, F13

  40. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  41. sp3: • Diamond • methane • alkane VM Ayres, ECE802-604, F13

  42. sp2: • Benzene • Graphene • CNT (curvature) • fullerene (curvature) • Polyacetylene: non-trigonal: linear VM Ayres, ECE802-604, F13

  43. Division of structural and electronic properties in linear sp1 that makes both effective: VM Ayres, ECE802-604, F13

  44. Diamond sp3: no division. Great structural strength but wide bandgap electronic properties VM Ayres, ECE802-604, F13

  45. Division of structural and electronic properties in trigonal sp2 makes both effective: All Structure: s-bonds Electronic: p-bonds VM Ayres, ECE802-604, F13

  46. 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

  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. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure: 1st: polyacetylene 2nd:graphene: R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  49. Game plan: E VM Ayres, ECE802-604, F13

  50. Rules for finding the electronic structure (p. 21): 1 Find Unit cell “a” 2 Find k: 3 Find H and S elements Det [H – SI] =0 4 Solve for E(k) VM Ayres, ECE802-604, F13

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