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ECE 802-604: Nanoelectronics

This lecture covers the physical structure of carbon nanotubes and graphene, including their bond hybridization. It also explores the mechanical and electronic properties of these materials.

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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 19, 31 Oct 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1, sp2, and sp3 sp2: origin of CNT/Graphene mechanical and electronic structures CNT/Graphene electronic properties R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes Imperial College Press, London, 1998. VM Ayres, ECE802-604, F13

  3. Lecture 19, 31 Oct 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure SWCNT endcaps Carbon bond hybridization is versatile : sp1, sp2, and sp3 sp2: origin of mechanical and electronic structures Carbon nanotube/Graphene electronic ‘structure’ R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes Imperial College Press, London, 1998. VM Ayres, ECE802-604, F13

  4. Lec 17: Introduction Buckyball endcaps Many different types of wrapping result in a seamless cylinder. But The particular cylinder wrapping dictates the electronic and mechanical properties. (10,10) (9,0) (7,4) VM Ayres, ECE802-604, F13

  5. Endcaps: ½ stable buckyball: C60 From Wikipedia: C60 is very stable truncated icosahedron 60 vertices with a carbon atom at each vertex and 32 faces 20 hexagons and 12 pentagons where no pentagons share a vertex The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm) http://www.sesres.com/PhysicalProperties.asp C60 mean ball diameter  6.83 Å C60 ball outer diameter  10.18 Å C60 ball inner diameter  3.48 Å http://www.creative-science.org.uk/c60model.html VM Ayres, ECE802-604, F13

  6. Show same idea on a SWCNT: Outer (Van Der Waals) Mean structure dt Inner (repulsion) VM Ayres, ECE802-604, F13

  7. Endcaps: ½ stable buckyball: C60 From Wikipedia: C60 is very stable truncated icosahedron 60 vertices with a carbon atom at each vertex and 32 faces 20 hexagons and 12 pentagons where no pentagons share a vertex The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm) http://www.sesres.com/PhysicalProperties.asp C60 mean ball diameter  6.83 Å C60 ball outer diameter  10.18 Å C60 ball inner diameter  3.48 Å Example: which diameter should you use as an estimate for matching a SWCNT diameter? http://www.creative-science.org.uk/c60model.html VM Ayres, ECE802-604, F13

  8. Endcaps: ½ stable buckyball: C60 From Wikipedia: C60 is very stable truncated icosahedron 60 vertices with a carbon atom at each vertex and 32 faces 20 hexagons and 12 pentagons where no pentagons share a vertex The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm) http://www.sesres.com/PhysicalProperties.asp C60 mean ball diameter  6.83 Å C60 ball outer diameter  10.18 Å C60 ball inner diameter  3.48 Å Example: which diameter should you use as an estimate for matching a SWCNT diameter? Answer http://www.creative-science.org.uk/c60model.html VM Ayres, ECE802-604, F13

  9. Endcaps: ½ stable buckyball: C70 From Wikipedia: C70 is also stable 70 vertices with a carbon atom at each vertex 25 hexagons and 12 pentagons The mean ball diameter is ? LBL: The structure of C70 molecule. Red atoms indicate five hexagons additional to the C60 molecule. VM Ayres, ECE802-604, F13

  10. C60 Guess: C70 Guess: C36 VM Ayres, ECE802-604, F13

  11. Endcaps: ½ stable buckyball: C36 http://www.lbl.gov/tt/techs/lbnl1366.html The above image depicts the D6h isomer of the C36 molecule Piskoti C., Yarger J., Zettl A., "A New Carbon Solid", Letters to Nature, v 393, 1997. XZ Ke, et al, Physics Letters A 255 (1999) 294-300 VM Ayres, ECE802-604, F13

  12. Endcaps: ½ stable buckyball: C20 The smallest possible buckyball is the dodecahedral C20, a shape consisting of 12 pentagonal faces and no hexagonal faces. ~4 angstroms VM Ayres, ECE802-604, F13

  13. Endcaps: ½ stable buckyball: C20  smallest SWCNT inside MWCNT VM Ayres, ECE802-604, F13

  14. Example Problems: • Based on dt ~ 0.4 nm, what ultrasmall SWCNT structures (n.m) are possible? • What types of CNT are they? • What physical issues would be involved in the self-assembly of these SWCNTs? HW04: Find Ch, |Ch |, cosq, q, T, |T |, and N for the smallest SWCNT capped with a C20. VM Ayres, ECE802-604, F13

  15. VM Ayres, ECE802-604, F13

  16. VM Ayres, ECE802-604, F13

  17. VM Ayres, ECE802-604, F13

  18. Lecture 19, 31 Oct 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1, sp2, and sp3 sp2: origin of CNT/Graphene mechanical and electronic structures CNT/Graphene electronic properties R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes Imperial College Press, London, 1998. A. Beiser, Modern Physics, Chapter 13 E. Anderson, Quantum Mechanics, Chapter 7 VM Ayres, ECE802-604, F13

  19. diamond Benzene/graphene/CNTs/buckyballs polyacetylene acetylene alkane VM Ayres, ECE802-604, F13

  20. ~ VM Ayres, ECE802-604, F13

  21. ~ VM Ayres, ECE802-604, F13

  22. These are simulations of e- |y|2 with 1s, 2s, and 2p marked: Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  23. The corresponding y are: 3D in spherical coordinates Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  24. So all of the directional character must come from 2p orbitals: ~ VM Ayres, ECE802-604, F13

  25. Beiser, Modern Physics Boundary surface diagrams s-orbitals are all spherical: no preferred direction p-orbitals are highly directional VM Ayres, ECE802-604, F13

  26. A carbon hybrid orbital comes from combining a 2s and a 2p: VM Ayres, ECE802-604, F13

  27. sp1 (sp) hybridization: • sp1 hybridization • Use orthonormality VM Ayres, ECE802-604, F13

  28. Problem without hybridization: ~ VM Ayres, ECE802-604, F13

  29. sp1 hybridization: ONE ~ VM Ayres, ECE802-604, F13

  30. sp1 hybridization: ONE ~ Warning: watch axes, these directions have real meaning VM Ayres, ECE802-604, F13

  31. sp1 hybridization: ~ Warning: watch axes, these directions have real meaning VM Ayres, ECE802-604, F13

  32. VM Ayres, ECE802-604, F13

  33. sp1 hybridization: VM Ayres, ECE802-604, F13

  34. sp1 hybridization: VM Ayres, ECE802-604, F13

  35. sp1 hybridization: VM Ayres, ECE802-604, F13

  36. sp1 hybridization: VM Ayres, ECE802-604, F13

  37. sp1 hybridization: VM Ayres, ECE802-604, F13

  38. sp1 hybridization: VM Ayres, ECE802-604, F13

  39. sp1 hybridization: Can get the 4th equation for 4 unknowns from the spherical character of the |2s> components: Therefore: VM Ayres, ECE802-604, F13

  40. sp1 hybridization: ~ VM Ayres, ECE802-604, F13

  41. sp1 hybridization: ~ VM Ayres, ECE802-604, F13

  42. sp1 hybridization: ~ VM Ayres, ECE802-604, F13

  43. sp1 hybridization: Therefore acetylene is: ~ VM Ayres, ECE802-604, F13

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