1 / 42

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)

daquan-west
Télécharger la présentation

Transport in nanostructures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related