The World of Carbon Nanotubes

Transcription

1 The World of Carbon Nanotubes Carbon Nanotubes Presentation by Jan Felix Eschermann at JASS05 from March 31st to April 9th,

2 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook unless stated otherwise all information taken from M.S. Dresselhaus, G. Dresselhaus, Ph. Avouris: Carbon Nanotubes. Springer: Berlin, Heidelberg, New York; year

3 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook 3

4 Introduction: History I systematic study of small carbon filaments since 1970s: What is the minimum size of a carbon fibre? (Kubo, 1977) 1991: CNTs discovered by Iijima at NEC Laboratory in Tsukuba, Japan multi wall Nanotubes (MWNT), diameter < 10 nm TEM images of first CNTs. 4

5 Introduction: History II research driven by one-dimensional quantum effects 1992: semiconducting and metallic behavior predicted for single wall nanotubes (SWNT), verified in : first SWNTs (NEC and IBM Almaden Laboratory, CA) more fundamental, important for theoretical studies Structure of chiral single wall CNT (IBM Website) 5

6 Introduction: From Graphene to CNTs chiral vectors C = n a1+m a2 for different CNTs (n,m) 6

7 Introduction: Different Types 7

8 Introduction: Mechanical Properties strongest and most flexible known molecular material 10% higher maximum strain than any other material Young's modulus of 1TPa (~100 time improvement over steel) CNT deformation with an AFM tip [IBM] 8

9 Introduction: Other Properties chemically very stable and functionalizable very light weight high thermal conductivity DNA-array with CNTs [NASA] 9

10 Introduction: Electrical Properties semiconducting or metallic (tunable bandgap) very high conductivity high current densities possible piezoelectric CNT-transistor [IBM] 10

11 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook 11

12 Physics: Band Structure I LCAO (linear combination of atomic orbitals) method: (following an example by Chr. Schönenberger, Uni Basel) two-dimensional sheet of graphite 'graphene' atomic orbitals localized ansatz wavefunction Bloch wave k = exp i k R x R G R G: set of lattice vectors Φ: atomic wavefunctions lattice of graphene 12

13 Physics: Band Structure II linear combination: only π-bands pz orbitals 2 atoms in basis x =b1 1 x b 2 2 x 13

14 Physics: Band Structure II linear combination: only π-bands pz orbitals 2 atoms in basis x =b1 1 x b 2 2 x Hamiltonian: single electron atomic potential 2 p V at x x 2 R H= V at x x 1 R 2 m R G kinetic energy atomic potentials 14

15 Physics: Band Structure II linear combination: only π-bands pz orbitals 2 atoms in basis x =b1 1 x b 2 2 x Hamiltonian: 2 p V at x x 2 R H= V at x x 1 R 2 m R G single electron atomic potential H 1,2 V at x x 2 V at x x 1 R R V at x x 2 1,2 = 1,2 1,2 on site energy R 0 rest of lattice 15

16 Physics: Band Structure II linear combination: only π-bands pz orbitals 2 atoms in basis x =b1 1 x b 2 2 x Hamiltonian: 2 p V at x x 2 R H= V at x x 1 R 2 m R G single electron atomic potential H 1,2 V at x x 2 V at x x 1 R R V at x x 2 1,2 = 1,2 1,2 R 0 ε1,2: ground energy of orbitals set to zero H 1,2= U 1,2 1,2 16

17 Physics: Band Structure III Schrödinger equation: H k =E k k x k = exp i k R R G R solution in k-space!! 17

18 Physics: Band Structure III Schrödinger equation: H k =E k k x k = exp i k R R G R transform into linear system of equations: j U j =E k j 18

19 Physics: Band Structure III Schrödinger equation: H k =E k k x k = exp i k R R G R transform into linear system of equations: j U j =E k j only consider neighboring atoms: * 1 =b1 b exp i k a1 exp i k a2 * 2 U 2 =b1 2 U exp i k a1 exp i k a2 19

20 Physics: Band Structure III Schrödinger equation: x k = exp i k R R H k =E k k G R transform into linear system of equations: j U j =E k j only consider neighboring atoms: * 1 =b1 b exp i k a1 exp i k a2 * 2 U 2 =b1 2 U exp i k a1 exp i k a2 additional assumptions / definitions: 0 = 1* 2 R 1= 1* U 1 2 R k =1 exp i k a1 exp i k a2 20

21 Physics: Band Structure IV Final result: formulation of eigenvalue problem: E k 0 E k 1 b1 0 = * 0 b2 0 E k 1 E k 21

22 Physics: Band Structure IV Final result: formulation of eigenvalue problem: E k 0 E k 1 b1 0 = * 0 b2 0 E k 1 E k condition for non-trivial solution:... =0 22

23 Physics: Band Structure IV Final result: formulation of eigenvalue problem: E k 0 E k 1 b1 0 = * 0 b2 0 E k 1 E k condition for non-trivial solution:... =0 approximation γ0 0: E k =± 3 2 cos k a 1 2 cos k a 2 2 cos k a 2 a 1 23

24 Physics: Bands of Graphene Brillouin zone Band structure of graphene Γ M: ε± (k) = ± const. [5 + 4 cos(2πς)]1/2 M K: ε± (k) = ± const. [3 + 4 cos(2πς/3) - 2 cos(4πς/3) ]1/2 K Γ: ε± (k) = ± const. [3-4 cos(2πς/3) + 2 cos(4πς/3) ]1/2 (0 < ς < 1) 24

25 Physics: From graphene to CNTs periodic boundary condition: Ψ(z, φ) = Ψ(z, φ + 2π) separation ansatz: Ψ(z, φ) = exp(i kc λc(φ)) χ(z) with: C 2 =C =2 p p ℕ k C C line equation in kx,kycoordinates circumference vektor 25

26 Physics: k-vectors I armchair nanotube (n,n): ky kx always metallic!! 26

27 Physics: k-vectors II zigzag nanotube (n,0): ky kx metallic only if n = 3i!! 27

28 Physics: k-vectors III chiral nanotube (n,m): ky kx metallic only if m - n = 3i!! 28

29 Physics: Bands and DOS (a) metallic nanotube (linear dispersion) (b) semiconducting CNT (Eg fewer than 1 ev) 29

30 Physics: Transport Behavior I 1D Transport ballistic (only elastic scattering) geometry independent conduction Landauer formula: 4e G= h 2 Transport through states [Csaba, TUM] 30

31 Physics: Transport Behavior II Metallic CNT vs. Copper resistivity [Ωm]: CNT Cu (CNT: 5nm diameter, 1µm long) max. current densitiy [A/mm²]: CNT Cu ² [Cornell University] 31

32 Physics: Transport Behavior III Semiconducting CNT vs. Si intrinsic hole density [cm-3]: CNT 1020 Si 1010 [Rakitin et al., Brown University, RI] (room temperature) hole mobility [cm²/vs]: CNT p-si 3 10³ [MRS Bulletin (2004)] (NA = 1016 cm-3) 32

33 Physics: Doping with Potassium 33 charge densities in increasingly doped CNT-bundles [Jo, Kim, Lee; Sungkyunkwan University,Korea] 33

34 Physics: LDOS vs. Bending Simulation on bending effects [IBM] 34

35 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook 35

36 Manufacturing: Overview (a) arc discharge (b) laser ablation (c) CVD (chemical vapor deposition) Schematic setups for nanotube growth 36

37 Manufacturing: Arc Discharge setup and parameters high quality good yield cheap MWNT and SWNT BUT: unclean (amorphous C) 37

38 Manufacturing: Laser Ablation setup and parameters good control no electric fields high yield of SWNT BUT: expensive 38

39 Manufacturing: CVD I variety of setups (Univ. of Cambridge, UK) horizontal (most common) vertical (mass production) plasma enhanced (PECVD) 39

40 Manufacturing: CVD II tip- and base-growth in the presence of catalyst (Fe, Co, Ni) 40

41 Manufacturing: CVD III SWNTs and MWNTs patterned growth aligned CNTs batch process cheap and fast 41

42 Manufacturing: Summary Techniques differ in: Types of Nanotubes Catalyst used Yield Purity 42

43 Manufacturing: Purification thermal oxidation annealing micro filtration magnetic separation (catalyst) selective functionalisation 43

44 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook 44

45 Applications: Overview (Prof. Lugli, TUM) 45

46 Applications: Chemical Sensors I FET-structure semiconducting SWCNT depletion / accumulation of carriers CNT based gas-sensor 46

47 Applications: Chemical Sensors II O2, NH3, NO2 high sensitivity (ppm) medical and industrial applications I-V-plots of gas sensors 47

48 Applications: Chemical Sensors III interdigital structure MWNTs impedance measurement MWNT gas sensor [Varghese, Sensors and Actuators (2001)] 48

49 Applications: Chemical Sensors IV Molecular Dynamics simulation of CNT-C6H4 interaction [Lugli, TUM] 49

50 Applications: Nanowire Biosensor principle as chemical sensors CNTs functionalized with Biotin electrochemical gating Si nanowire sensor [Cui et al., Science (2001)] 50

51 Applications: CNT-DNA-Array Nanotube-DNA-Chip [Cassell, NASA (2004)] 51

52 Applications: Electromechanical actuator CNTs in NaCl solution principle: differential charging when voltage applied covalent bonds changed operation: deflection up to 1 cm dynamic up to 15 Hz nanotube cantilever [(Baughman et al., Science (1999)] 52

53 Applications: Deformation Sensor CNT-bridge over trench deformation: weaker π delocalisation lower conductance setup (a,c) and measurement response (b) of a CNT deformation sensor 53

54 Applications: Field Emission CNT - 'light bulb' field emission display [Samsung] 54

55 Applications: Interconnects 55

56 Applications: CNT-MOSFET I schematic and AFM picture of CNFET [IBM] 56

57 Applications: VG-ISD-Diagram intrinsically p-type low currents (na) quite noisy CMOS compatible V-I-plot of CNFET [IBM] 57

58 Applications: CNT-MOSFET II vertical CNFET and circuit architecture [Infineon] 58

59 Applications: n-type CNTs n-type CNTs by annealing (a) / K-doping (b) [IBM] 59

60 Applications: CNT-Inverter [IBM, 2001] 60

61 Outline Introduction Physical Properties Manufacturing Techniques Applications Outlook 61

62 Outlook: Nano-Resonators CNT based NEMS? Silicon resonators 62

63 Outlook: Telescoping CNTs Nanoprobes? (Temperature, DNAHybridisation) Improved field emitters? 63

64 Outlook: Membranes CNT in Si3N4 membrane Nanofluidics? 64

65 Outlook: Molecular Transporters [Stanford] 65

66 Outlook: Y-junctions CNT y-junction and dentrite CNT-Networks? 66

67 Outlook: NASA roadmap I 67

68 Outlook: NASA roadmap II 68

69 The World of Carbon Nanotubes Thank you for your attention!! Спасибо!! Danke für eure Aufmerksamkeit!! 69