Transcript Document 7445727

Transport in nanostructures
M. P. Anantram
( [email protected] )
Center for Nanotechnology
NASA Ames Research Center, Moffett Field, California
5/23/2016
1
Outline
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Transport: What is physically different?
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Applications
- Resonant Tunneling Diodes (RTD)
- Carbon Nanotubes
- DNA
Trends in Device Miniaturization
Down scaling of
semiconductor technology
Molecular devices
Smaller and Faster Devices
Conventional
- Ultra Small MOSFET
- Interference based devices
- Resonant tunneling diodes
- Single electron transistors
Hybrid
New
- Carbon nanotube
- Molecular diodes
- DNA?
Conventional Methods of Device Modeling
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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
1
T(E)
R(E)
T(E)+R(E)=1
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Electrons behave as waves rather than particles
Schrodinger’s wave equation
Poisson equation still important
Landauer-Buttiker Scattering theory
In this theory,
Current,
I=∫T(E)[f LEFT(E)
f RIGHT(E)]dE
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)
Transport in molecular structures – Interplay between
chemistry and physics
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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
Outline
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Transport: What is physically different?
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Applications
- Resonant Tunneling Diodes (RTD)
- Carbon Nanotubes
- DNA
Resonant Tunneling Diode
GaAs
AlGaAs
+
Typical thickness: tens of Angstrom
1
Transmission
Probability
T(E)
Black – semi-classical
Red - quantum
0
Energy (E)
200meV
What quantum feature
does the peak represent?
Example: Resonant Tunneling Diode
Current
Voltage
• Negative differential resistance
• Peak to valley ratio should be large
Outline
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Transport: What is physically different?
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Applications
- Resonant Tunneling Diodes (RTD)
- Carbon Nanotubes
- DNA
Nanotube Images
Single-wall nanotube
Multi-wall nanotube
Bonard et al, Appl. Phys. A 69 (1999)
Thess et. al, Science (1996)
Quantum conductance experiment
Near perfect quantum wire
Crossed nanotube junction: Inter-tube metalsemiconduction junction, rectifier
Frank et. al, Science 280 (1998)
2
2e
4e
and not
h
h
2
Fuhrer et al, Science (2000)
Work horse of conventional computing
IBM
Wind et. al, Appl. Phys. Lett., May 20, 2002
http://www.research.ibm.com/resources/news/20020520_nano
tubes.shtml
• Logic gates, oscillators, … using many nanotubes
on a single wafer has been demonstrated.
Bent Nanotube or Intra-molecular junction?
Intra-molecular diode?
Cees Dekker, Delft University
Electromechanical Switch?
Tombler et al, Nature 405, 769 (2000)
Mechanism for conductance decrease?
Graphene
r2
Blue box – unit cell of graphene
 a1 & a2 – lattice vectors
 r1, r2 & r3 - bond vectors
 Two atoms per unit cell
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r3
r1
a1
a2
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Applying of Bloch’s theorem:
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E(k ,k )= t 2+t 2+t 2+2t t cos [k (r r )]+2t t cos [k (r r )]+2t t cos [k (r r )]
x
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y
1
2
3
1 2
1
2
2 3
For graphene, symmetry dictates that t1=t2=t3
2
3
3 1
3
1
a1
a2
a1
a2
a1
a2
eikf=eik(f+2p)
Graphene to Nanotube
r2
r3
r1
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Y = eikxx+ikyy (u v)
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  
2
2
2
E(k ,k )= t +t +t +2t t cos [k (r r )]+2t t cos [k (r r )]+2t t cos [k (r r )]
x
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y
1
2
3
1 2
1
2
Example, (6,0) zigzag tube,
2 3
2
3
2π
k =
p
6a
y
0
3 1
3
1
Nanotube wavefunction
Ψ(x, φ) = e χ(x)
Ψ(x, φ) = Ψ(x, φ + 2π)
ikc φ
ikc φ
ikc(φ + 2 π )
e = e
k C = 2πp
2π
k =
p
C
c
c
p - integer
Summary of main electronic properties
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Metallic nanotubes:
n-m = 3*integer
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Semiconducting tubes:
Bandgap a 1/Diameter
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Armchair tubes are truly metallic
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Other metallic tubes have a tiny curvature induced bandgap
zigzag (n,0)
Summary of main electronic properties
zigzag (n,0)
Armchair tubes do not develop a band gap
Summary of main electronic properties
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Metallic nanotubes:
n-m = 3*integer
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Semiconducting tubes:
Bandgap a 1/Diameter
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Armchair tubes are truly metallic
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Other metallic tubes have a tiny curvature induced bandgap
zigzag (n,0)
Shapes in nature
• Nanohorns
• Torus
Armchair nanotube: Bands
Fermi
energy
Close to E=0, only two sub-bands,
At higher energies,
Low bias record (multi-wall nanotube)
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(6.5 kW)
(< 1kW)
(500W)
Can subbands at the higher energies be accessed to drive large
currents through these molecular wires?
Quantum conductance experiment
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Frank et. al, Science 280 (1998)
Frank et. al, Science 280 (1998)
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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
Semiclassical Picture
DENC
Transmission in crossing subband
Bragg refelection
Zener tunneling (non crossing subbands)
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The strength of the two processes are determined by:
Tunneling distance, Barrier height (DENC), Scattering
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DENC a 1/Diameter. So the importance of Zener tunneling
increases with increase in nanotube diameter.
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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)
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The differential conductance is not comparable to the increase in the
number of subbands. (20,20) nanotube – 35 subbands at 3.5eV
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Two classes of experiments with order of magnitude current that differs
by a factor of 5!
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Our ballistic calculations agree with increase in conductance
Summary (Current carrying capacity of nanotubes)
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Nanotubes are the best nanowires, at present!
However, Bragg reflection limits the current carrying capacity of
nanotubes
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Large diameter nanotubes exhibit Zener tunneling
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Conductance much larger than 4e2/h is difficult
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non crossing  non conducting
crossing  conducting
Phys. Rev. B 62, 4837 (2000)
Tombler et. al, Nature 405, 769 (2000)
Upon deformation
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?
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
Bond Length Distribution & Conductance
(12,0) Zigzag
AFM DEFORMATION
BENDING
AFM Deformed versus Stretched
What happens to other chiralities?
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Metallic zigzag nanotubes develop largest bandgap with tensile strain.
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All other chiralities develop bandgap that varies with chirality (n,m).
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Experiments on a sample of metallic tubes will show varying decrease
in conductance.
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Some semiconducting tubes will show an increase in conductance
upon crushing with an AFM tip.
Summary (electromechanical switch)
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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)
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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
AIR
Table Experiment
SiO2
Outline
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Transport: What is physically different?
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Applications
- Resonant Tunneling Diodes (RTD)
- Carbon Nanotubes
- DNA
DNA Conductance
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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.
basepair
Experiments
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Conductivity in DNA has been controversial
Electron transfer experiments (biochemistry) / possible link to
cancer
Transport experiments (physics)
Semiconducting / Insulating
Metallic, No gap
Current
Current
~ 1nA
~ 10nA
Voltage (V)
Porath et. al, Nature (2000)
Voltage 20mV
Fink et. al, Science (1999)
Counter-ions
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Is conduction through the base pair or
backbone? - Basepair
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When DNA is dried, where are the
counter ions?
Crystalline / non crystalline?
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Counter ions significantly modify the
energy levels of the base pairs
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Counter-ion species is also important
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Resistance increases with the length of
the DNA sample (exponential within the
context of simple models)
Counter-ions