Quantum transport in nanostructures-I
Prof. Ilari Maasilta
Nanoscience Center, Department of Physics, University of Jyväskylä
YN 215, maasilta@phys.jyu.fi
Fundamentals of nanoscience
8.2.2008
What is quantum transport
• How is current (charge) and energy
transported in devices where
quantum mechanics matters
• In microscopic physics (such as
atoms) the laws of physics, as we
know them now, are governed by
quantum mechanics (QM)
• QM is important also size scales a
bit larger than atoms and molecules
= nanostructures
Fundamentals of nanoscience
8.2.2008
How to study quantum transport?
•
1.
2.
3.
There is no way to learn quantum
transport in 2 lectures…. (let’s go
home?)
learn quantum mechanics+solid state
physics (FYSA230, FYSM300, books)
After that take my course on quantum
transport (FYSM530) or
Study a good book say
Datta, Quantum Transport: Atom to Transistor,
Cambridge 2005
Datta, Electronic Transport in Mesoscopic
Systems, Cambridge 1995
Fundamentals of nanoscience
8.2.2008
Some topics in electric quantum
transport
• Top-down nanofabrication
• Semiconducting low-D devices
• Quantized conductance and fabricated
quantum dots
• Metallic nanostructures; tunnel junctions
• Applications of tunnel junctions etc. in
detectors,SET etc.
Fundamentals of nanoscience
8.2.2008
Nanofabrication
• Either you let Nature self-organize (magic
or sometimes know as chemistry)
• Or you use the physicists method=brute
force. This is how transistor size has
shrunk by many orders of magnitude in
past decades (Moore’s law)
Fundamentals of nanoscience
8.2.2008
Gordon E. Moore (b. 1929)
•
•
•
•
Gordon Earle Moore is the co-founder and
Chairman Emeritus of Intel Corporation and the
author of Moore's Law (published in an article 19
April 1965 in Electronics Magazine).
He received a B.S. degree in Chemistry from the
University of California, Berkeley in 1950 and a
Ph.D. in Chemistry and Physics from the
California Institute of Technology (Caltech) in
1954.
In 2001, Moore and his wife donated $600
million to Caltech
On December 6, 2007, Gordon Moore and his
wife donated $200 million to Caltech and the
University of California for the construction of the
world's largest optical telescope.
Moore is more (for Caltech at least)
Fundamentals of nanoscience
8.2.2008
Lithography
•
•
•
Photolithography: Use UV
light to expose sensitive
resist in certain areas (use
mask). Limited in principle by
the wavelength of light, can
improve with expensive
optics down to 50 nm
Electron-beam lithography:
Write an e-beam resist
directly with an e-gun. Not
limited by the wavelength of
electrons (Å), but by the
resolution of the resist (~10
nm)
We have both at NSC
Fundamentals of nanoscience
8.2.2008
Example:
Self-supporting (hanging) metallic lines ~200 nm wide (= nanomechanics)
Fundamentals of nanoscience
8.2.2008
Semiconducting low-D structures
•
•
•
•
2D electron gas
1D electron gas
0D electron gas!
-1D electron gas is hard to fathom…
Fundamentals of nanoscience
8.2.2008
2D electron gas-I
• Used commercially in
High Electron Mobility
Transistor (HEMT),
Fujitsu etc.
• Less scattering=higher
mobility=faster operation
(up to 600 GHz) =>
needed in satellite
communcations, radar
etc. microwave
applications
Fundamentals of nanoscience
8.2.2008
2D electron gas-II
•
•
•
Condensed matter physicists love
2D electron gas (I did my PhD on
it..) because of Quantum Hall
effect (2 Nobel prizes,
integer+fractional)
QHE is a new highly correlated
state of ”matter” in high magnetic
fields, where weird phenomena
take place (for example quantized
non-integer charge!)
Don’t believe particle physicists if
they say that they can explain
everything with quarks and
leptons= ”fundamental” particles. A
piece of semiconductor can have
it’s own fundamental particles!!!
Fundamentals of nanoscience
8.2.2008
1D electron gas
• Known as a quantum wire
(2D gas can be made
from a quantum well)
• Carbon nanotubes,
semiconducting
nanowires,
semiconductor
heterostructure
nanowires
• Intense active research,
not too many applications
yet
Fundamentals of nanoscience
8.2.2008
Transport in 1D systems-I
• Usual piece of metal
obeys Ohm’s law
(this is something even a
biologist should
remember from high
school…)
Notion of resistance, which
depends on material
dimensions and a
material parameter,
resistivity ρ
I =V
R
, V = RI
R = ρL / A
Fundamentals of nanoscience
8.2.2008
1D transport-II
• In quantum limit-shockingly- Ohm’s law doesn’t
work!
• Sorry Ohm, but your law is not a law of nature…
• It requires a lot of scattering, so that a
continuous model works (scattering length is
microscopic ~ 1nm)
• Quantum wires etc can be made so pure that
nothing disturbs the electron inside the
nanosample = coherent and/or ballistic transport
(in analogy with usual waves)
Fundamentals of nanoscience
8.2.2008
1D transport -III
• A new ”law” by Rolf
Landauer IBM (19271999):
• Each 1D channel
conducts exactly G0
• This is the maximum
conducting capacity
• Conductance can be
lowered by introducing
scatterers
2e 2
G0 =
= (12.906404kΩ) −1
h
The measurement of G0 via Quantum Hall
effect is more accurate (10-8)
than the direct measurements of e and h.
Therefore metrological labs agreed on a value
by convention.
Fundamentals of nanoscience
8.2.2008
1D transport
2
• If there is a scatterer with
transmission probability T, then
• Why is there resistance at all????
(No dissipation inside nanostructure)
• Resistance arises because the 1D
channel must be contacted with
the outside world to be able to
conduct (contact with
leads+battery) The energy is
disspated in the contacts, so 1/G0
is a contact resistance
Fundamentals of nanoscience
2e
G=
T
h
Van Wees 8.2.2008
et al. Phys. Rev. Lett. 60, 848 - 850 (1988)
0D transport
•
•
•
As mentioned by prof.
Manninen, it is possible to
engineer devices where
electron states are fully
quantized (discrete), like
”artificial atoms”-also known
as quantum dots.
0D means that the electron
inside the dot has no
freedom to move
But you can still couple
current through it, it can be
weakly coupled to leads by
tunnel barriers (T very small)
Fundamentals of nanoscience
8.2.2008
Tunneling
• Quantum mechanical
tunneling is a process
where particles
(electrons) can travel
through classically
prohibited areas!
• ”Walking through
doors”
• In practice the barrier
has to be of thickness
1-100 nm for electrons
depending on the
barrier height
Fundamentals of nanoscience
8.2.2008
Conductance through a quantum
dot
Fundamentals of nanoscience
8.2.2008
Metallic nanostructures
• You can also make intersting nanostructure devices from
metals,but with a typical metal there are no low-D effects
(electron wavelength is ~ 1 nm instead of ~100 nm in
semiconductors)
• Also, metals can become superconducting (= zero
resistance for current flow) at low enough temperatures,
typically < 10 K
• In the superconducting state, we again have new
”quasiparticles”, Cooper pairs, which consist of pairs of
two electrons (charge 2e).
• These Cooper pairs ”condense” into a collective state,
which is coherent across marcoscopic distances => no
scattering, no resistance
Fundamentals of nanoscience
8.2.2008
Resistance (Ω)
A superconducting Nb bridge
40
35
30
25
20
15
10
5
0
-5
4
A sub-mm radiation detector
5
6
7
8
9 10
Temperature (K)
11
12
M. Nevala, K. Kinnunen, I. Maasilta,
unpublished
Fundamentals of nanoscience
8.2.2008
A superconducting junction
6
4
N
S
I (mA)
2
S
0
T = 4.2 K
T = 4.7 K
T = 5.1 K
T = 5.9 K
T = 6.8 K
T = 7.6 K
T = 8.7 K
T = 11.0 K
-2
-4
Normal metal layer 10 nm thick
-6
-0.10
-0.05
0.00
0.05
0.10
V (mV)
M. Nevala, I. Maasilta unpublished
The resistance of the normal metal does not show at all for currents below
certain value (critical current), here ~ 3.5 mA at 4.2 K
(No voltage drop !!!) This is the supercurrent, which is carried by
Cooper pairs only
Fundamentals of nanoscience
8.2.2008
SNS Josephson junctions
director of the Mind-Matter Unification Project
I = I c sin φ
Brian Josephson
Nobel in 1973 "for his theoretical predictions of the
properties of a supercurrent through a tunnel barrier,
in particular those phenomena which are generally
known as the Josephson effects"
Fundamentals of nanoscience
8.2.2008
Applications of Josephson
junctions
• Can be used for ultra-high frequency
digital electronics
COOL...
FAST...
RELIABLE...
RAPID
Typical speed of RSFQ devices fabricated using an obsolete 3.5um technology
is close to 100GHz (20GHz clock).
The ultimate speed of an RSFQ device ever measured experimentally is 770GHz.
The Intel® Core™2 Extreme processor QX9650 running at 3.0 GHz
Fundamentals of nanoscience
8.2.2008
Commercial applications in the
works ?
+
2nd Stage: 1W @ 4.2K
1st Stage: 40W @ 45K
Minimum Temperature: 0W @ 2.8K
Type: Pulse Tube
Cooling: liquid
=?
Fundamentals of nanoscience
8.2.2008
Single electron transistor
charge variations of 2 x10-6 e can be detected in a measurement period of just one
second and with a bandwidth of several hundred megahertz.
Fundamentals of nanoscience
8.2.2008
Summary of part I
• Classical laws of conduction do not work if
devices are in the nanoscale
• Need quantum mechanics
• Quantum transport can be utilized for
novel devices such as ultrasensitive
radiation detectors (more on that next
time), ultrafast electronics and
ultrasensitive electrometry
Fundamentals of nanoscience
8.2.2008