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Transport in nanostructures

Transport in nanostructures. M. P. Anantram ( anant@nas.nasa.gov ) Center for Nanotechnology NASA Ames Research Center, Moffett Field, California. Outline. Transport: What is physically different? Applications - Resonant Tunneling Diodes (RTD)

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Transport in nanostructures

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  1. Transport in nanostructures M. P. Anantram ( anant@nas.nasa.gov ) Center for Nanotechnology NASA Ames Research Center, Moffett Field, California

  2. Outline • Transport: What is physically different? • Applications - Resonant Tunneling Diodes (RTD) - Carbon Nanotubes - DNA

  3. Trends in Device Miniaturization Down scaling of semiconductor technology Molecular devices Smaller and Faster Devices Conventional Hybrid New - Ultra Small MOSFET - Interference based devices - Resonant tunneling diodes - Single electron transistors - Carbon nanotube - Molecular diodes - DNA?

  4. Ballistic Phase-coherent Conventional Methods of Device Modeling • Electrons are waves. de Broglie wavelength of an electron is, h/p, where p is the momentum • Device dimensions are much larger than the electron wave length • Transit time through the device is much larger than the scattering time • Diffusion equation for semiconductors Diffusive

  5. Electrons behave as waves rather than particles • Schrodinger’s wave equation • Poisson equation still important • Landauer-Buttiker Scattering theory • In this theory, Current, T(E) – Transmission probability for an electron to traverse the device at energy E fLEFT(E) – occupancy factor / probability for an electron to be incident from the left contact (Fermi- dirac factor) 1 T(E) R(E) T(E)+R(E)=1

  6. Transport in molecular structures – Interplay between chemistry and physics • Quantum chemistry tools (perform energy minimization) or Molecular Dynamics (MD) are used to find chemically and mechanically stable / preferable structures • Schrodinger equation describes electron flow through the device • Poisson’s equation gives the self-consistent potential profile Chemically & Mechanically Stable Structures Energy Minimization, quantum chemistry (hundred atoms) Molecular Dynamics simulations (millions of atoms) Number of atoms  accuracy Current, Electron Density Schrodinger’s equation / non equilibrium Green’s function Potential (Voltage) Profile Poisson’s equation New Devices

  7. Outline • Transport: What is physically different? • Applications - Resonant Tunneling Diodes (RTD) - Carbon Nanotubes - DNA

  8. GaAs AlGaAs Resonant Tunneling Diode + Typical thickness: tens of Angstrom 1 Transmission Probability T(E) Black – semi-classical Red - quantum What quantum feature does the peak represent? 0 200meV Energy (E)

  9. Example: Resonant Tunneling Diode Current Voltage • Negative differential resistance • Peak to valley ratio should be large

  10. Outline • Transport: What is physically different? • Applications - Resonant Tunneling Diodes (RTD) - Carbon Nanotubes - DNA

  11. Thess et. al, Science (1996) Bonard et al, Appl. Phys. A 69 (1999) Nanotube Images Single-wall nanotube Multi-wall nanotube

  12. and not Quantum conductance experiment Near perfect quantum wire Crossed nanotube junction: Inter-tube metal- semiconduction junction, rectifier Frank et. al, Science 280 (1998) Fuhrer et al, Science (2000)

  13. IBM Wind et. al, Appl. Phys. Lett., May 20, 2002 http://www.research.ibm.com/resources/news/20020520_nanotubes.shtml Work horse of conventional computing • Logic gates, oscillators, … using many nanotubes • on a single wafer has been demonstrated.

  14. Cees Dekker, Delft University Bent Nanotube or Intra-molecular junction? Intra-molecular diode?

  15. Electromechanical Switch? Mechanism for conductance decrease? Tombler et al, Nature 405, 769 (2000)

  16. r2 a1 r3 r1 a2 Graphene • Applying of Bloch’s theorem: • For graphene, symmetry dictates that t1=t2=t3 • Blue box – unit cell of graphene • a1 & a2 – lattice vectors • r1, r2 & r3 - bond vectors • Two atoms per unit cell

  17. a1 a2

  18. a1 a1 a2 a2

  19. r2 r3 r1 Graphene to Nanotube eikf=eik(f+2p) • Y = eikxx+ikyy (u v) • Example, (6,0) zigzag tube,

  20. Nanotube wavefunction p - integer

  21. zigzag (n,0) Summary of main electronic properties • Metallic nanotubes: n-m = 3*integer • Semiconducting tubes: Bandgap a 1/Diameter • Armchair tubes are truly metallic • Other metallic tubes have a tiny curvature induced bandgap

  22. zigzag (n,0) Summary of main electronic properties Armchair tubes do not develop a band gap

  23. zigzag (n,0) Summary of main electronic properties • Metallic nanotubes: n-m = 3*integer • Semiconducting tubes: Bandgap a 1/Diameter • Armchair tubes are truly metallic • Other metallic tubes have a tiny curvature induced bandgap

  24. Shapes in nature • Nanohorns • Torus

  25. Fermi energy Armchair nanotube: Bands • Close to E=0, only two sub-bands, (6.5 kW) • At higher energies, (< 1kW) • Low bias record (multi-wall nanotube) (500W) • Can subbands at the higher energies be accessed to drive large currents through these molecular wires?

  26. Quantum conductance experiment • Frank et. al, Science 280 (1998)

  27. Frank et. al, Science 280 (1998) • E ~ ±120meV, non-crossing bands open • At E~2eV, electrons are injected into about 80 subbands • Yet the conductance is ~ 5 e2/h • VAPPLIED < 200mV, G~2e2/h • VAPPLIED > 200mV, slow increase

  28. Transmission in crossing subband Bragg refelection Zener tunneling (non crossing subbands) Semiclassical Picture • The strength of the two processes are determined by: Tunneling distance, Barrier height (DENC), Scattering • DENCa 1/Diameter. So the importance of Zener tunneling increases with increase in nanotube diameter. DENC

  29. dI/dV 4e2/h for Va < 2DENC (DENC 1.9eV ) • DENC changes with diameter • Effect of diameter on current? 155 mA 25 mA Yao et al, Phys. Rev. Lett (2000) • The differential conductance is not comparable to the increase in the number of subbands. (20,20) nanotube – 35 subbands at 3.5eV • Two classes of experiments with order of magnitude current that differs by a factor of 5! • Our ballistic calculations agree with increase in conductance

  30. noncrossing  non conducting crossing  conducting Summary (Current carrying capacity of nanotubes) • Nanotubes are the best nanowires, at present! • However, Bragg reflection limits the current carrying capacity of nanotubes • Large diameter nanotubes exhibit Zener tunneling • Conductance much larger than 4e2/h is difficult Phys. Rev. B 62, 4837 (2000)

  31. Upon deformation Tombler et. al, Nature 405, 769 (2000) sp2 to sp3 Tombler et al, Nature 405, 769 (2000) Stretching of bonds Opens bandgap in most nanotubes [Phys. Rev. B, vol. 60 (1999)] What is the conductance decrease due to?

  32. Approach 1) AFM Deformation 2) Bending Structure Relaxation Central 150 atoms were relaxed using DFT and the remaining 2000+ atoms were relaxed using a universal force field Density of states and conductance were computed using four orbital tight-binding method with various parametrizations

  33. BENDING (12,0) Zigzag AFM DEFORMATION Bond Length Distribution & Conductance

  34. AFM Deformed versus Stretched

  35. What happens to other chiralities? • Metallic zigzag nanotubes develop largest bandgap with tensile strain. • All other chiralities develop bandgap that varies with chirality (n,m). • Experiments on a sample of metallic tubes will show varying decrease in conductance. • Some semiconducting tubes will show an increase in conductance upon crushing with an AFM tip.

  36. SiO2 AIR Summary (electromechanical switch) • Metallic nanotubes develop a bandgap upon strain. Detalied simulations show that this is a plausible explanation for the recent experiment on electromechanical properties by Tombler et al, Nature (2000) • In contrast, we expect nanotube lying on a table to behave differently. A drastic decrease in conductance is expected to occur only after sp3 type hybridization occurs between the top and bottom of the nanotube. Suspended in air Table Experiment

  37. Outline • Transport: What is physically different? • Applications - Resonant Tunneling Diodes (RTD) - Carbon Nanotubes - DNA

  38. DNA Conductance • Double helix – a backbone & base pairs • Building blocks are the base pairs: A, T, C & G • Example: 10 base pairs per turn, distance of 3.4 Angstroms between base pairs. • Arbitrary sequences possible • A challenge for nanotechnology is controlled / reproducible growth. DNA is an example with some success. However, there are many copies in a solution! • 2D and 3D structures with DNA base pairs as a building block have been demonstrated • Lithography? Not yet.

  39. basepair

  40. Experiments • Conductivity in DNA has been controversial • Electron transfer experiments (biochemistry) / possible link to cancer • Transport experiments (physics)

  41. Semiconducting / Insulating Metallic, No gap Current Current 20mV ~ 10nA ~ 1nA Porath et. al, Nature (2000) Fink et. al, Science (1999) Voltage (V) Voltage

  42. Counter-ions • Is conduction through the base pair or backbone? - Basepair • When DNA is dried, where are the counter ions? • Crystalline / non crystalline? • Counter ions significantly modify the energy levels of the base pairs • Counter-ion species is also important • Resistance increases with the length of the DNA sample (exponential within the context of simple models) Counter-ions

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