VI' Nanoelectronics

1
Introduction to Nanotechnology
VI. Nanoelectronics M. Meyyappan NASA Ames
Research Center Moffett Field, CA 94035 email
mmeyyappan_at_mail.arc.nasa.gov web
http//www.ipt.arc.nasa.gov
6.1. Transport in nanostructures Guest lecturer
M.P. Anantram
2
Trends in Device Miniaturization
Down scaling of semiconductor technology
Molecular devices
Smaller and Faster Devices
Conventional
New
Hybrid
- Ultra Small MOSFET - Interference based
devices - Resonant tunneling diodes - Single
electron transistors
- Carbon nanotube - Molecular diodes - DNA?
3
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
Ballistic Phase-coherent
4

• Electrons behave as waves rather than particles
• Schrodingers 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)

5
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
• Poissons 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 Schrodingers equation
/ non equilibrium Greens function
Potential (Voltage) Profile Poissons equation
New Devices
6
Resonant Tunneling Diode
7
Example Resonant Tunneling Diode
Current
Voltage

• Negative differential resistance
• Peak to valley ratio should be large

8
Graphene

• Blue box unit cell of graphene
• a1 a2 lattice vectors
• r1, r2 r3 - bond vectors
• Two atoms per unit cell

• Applying of Blochs theorem
• For graphene, symmetry dictates that t1t2t3

9
Graphene
10
Graphene
a1
a1
a2
a2
11
eikfeik(f2p)
Graphene to Nanotube

• Y eikxxikyy (u v)

• Example, (6,0) zigzag tube,

12
Nanotube Wavefunction
p - integer
13
Summary of Main Electronic Properties

• Metallic nanotubes
• n-m 3integer
• Semiconducting tubes
• Bandgap a 1/Diameter
• Armchair tubes are truly metallic
• Other metallic tubes have a tiny curvature
  induced bandgap

14
Summary of Main Electronic Properties
Armchair tubes do not develop a band gap
15
Shapes in Nature

• Nanohorns
• Torus

16
Armchair Nanotube Bands

• Close to E0, only two sub-bands, (6.5 kW)
• At higher energies,
  (lt 1kW)
• Low bias record (multi-wall nanotube)
  (500W)

• Can subbands at the higher energies be accessed
  to drive large currents through these molecular
  wires?

17
Quantum Conductance Experiment

• Frank et. al, Science 280 (1998)

18
Quantum Conductance Experiment (cont.)

• VAPPLIED lt 200mV, G2e2/h
• VAPPLIED gt 200mV, slow increase

• E 120meV, non-crossing bands open
• At E2eV, electrons are injected into about 80
  subbands
• Yet the conductance is 5 e2/h

19
Semiclassical Picture

• The strength of the two processes are determined
  by
• Tunneling distance, Barrier height (DENC),
  Scattering
• DENC a 1/Diameter. So the importance of Zener
  tunneling increases with increase in nanotube
  diameter.

20
Semiclassical Picture (cont.)

• 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

21
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)
22
CNT Conductance Decreases with Deformation
Tombler et. al, Nature 405, 769 (2000) showed
that the conductance of SWNT decreases when
deformed by AFM tip.
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?
23
Model to Explain the Experimental Observation
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
24
Bond Length Distribution Conductance
25
AFM Deformed versus Stretched
26
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.

27
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