prof. ilari maasilta nanoscience center, department of physics, … · 2016-06-01 · fundamentals...

Fundamentals of nanoscience 8.2.2008

Quantum transport in nanostructures-I

Prof. Ilari MaasiltaNanoscience Center, Department of Physics, University of Jyväskylä

YN 215, [email protected]


What is quantum transport• How is current (charge) and energy

transported in devices wherequantum mechanics matters

• In microscopic physics (such as atoms) the laws of physics, as weknow them now, are governed byquantum mechanics (QM)

• QM is important also size scales a bit larger than atoms and molecules= nanostructures


How to study quantum transport?

• There is no way to learn quantumtransport in 2 lectures…. (let’s gohome?)

1. learn quantum mechanics+solid statephysics (FYSA230, FYSM300, books)

2. After that take my course on quantumtransport (FYSM530) or

3. Study a good book sayDatta, Quantum Transport: Atom to Transistor, Cambridge 2005Datta, Electronic Transport in MesoscopicSystems, Cambridge 1995


Some topics in electric quantumtransport

• 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.


Nanofabrication

• Either you let Nature self-organize (magic or sometimes know as chemistry)

• Or you use the physicists method=bruteforce. This is how transistor size hasshrunk by many orders of magnitude in past decades (Moore’s law)


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)

http://en.wikipedia.org/wiki/Intel_Corporation

http://en.wikipedia.org/wiki/Moore%27s_Law

http://en.wikipedia.org/wiki/April_19





http://en.wikipedia.org/wiki/Chemistry

http://en.wikipedia.org/wiki/University_of_California%2C_Berkeley

http://en.wikipedia.org/wiki/Doctor_of_Philosophy

http://en.wikipedia.org/wiki/Physics

http://en.wikipedia.org/wiki/California_Institute_of_Technology

http://en.wikipedia.org/wiki/Caltech

http://en.wikipedia.org/wiki/University_of_California


Lithography• Photolithography: Use UV

light to expose sensitiveresist in certain areas (usemask). Limited in principle bythe wavelength of light, canimprove with expensiveoptics down to 50 nm

• Electron-beam lithography: Write an e-beam resistdirectly with an e-gun. Notlimited by the wavelength of electrons (Å), but by the resolution of the resist (~10 nm)

• We have both at NSC


Example: Self-supporting (hanging) metallic lines ~200 nm wide (= nanomechanics)


Semiconducting low-D structures

• 2D electron gas• 1D electron gas• 0D electron gas!• -1D electron gas is hard to fathom…


2D electron gas-I• Used commercially in

High Electron MobilityTransistor (HEMT), Fujitsu etc.

• Less scattering=highermobility=faster operation(up to 600 GHz) => needed in satellitecommuncations, radar etc. microwaveapplications


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 correlatedstate of ”matter” in high magneticfields, where weird phenomenatake place (for example quantizednon-integer charge!)

• Don’t believe particle physicists ifthey say that they can explaineverything with quarks and leptons= ”fundamental” particles. A piece of semiconductor can haveit’s own fundamental particles!!!


1D electron gas• Known as a quantum wire

(2D gas can be made from a quantum well)

• Carbon nanotubes, semiconductingnanowires, semiconductorheterostructurenanowires

• Intense active research, not too many applicationsyet


Transport in 1D systems-I• Usual piece of metal

obeys Ohm’s law(this is something even a

biologist shouldremember from highschool…)

Notion of resistance, whichdepends on materialdimensions and a material parameter, resistivity ρ

RIVRVI == ,

ALR /ρ=


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 thatnothing disturbs the electron inside the nanosample = coherent and/or ballistic transport (in analogy with usual waves)


1D transport -III• A new ”law” by Rolf

Landauer IBM (1927-1999):

• Each 1D channelconducts exactly G0

• This is the maximumconducting capacity

• Conductance can belowered by introducingscatterers

12

0 )906404.12(2 −Ω== kheG

The measurement of G0 via Quantum Halleffect is more accurate (10-8)than the direct measurements of e and h. Therefore metrological labs agreed on a valueby convention.


1D transport• If there is a scatterer withtransmission probability T, then

• Why is there resistance at all????(No dissipation inside nanostructure)• Resistance arises because the 1D

channel must be contacted withthe outside world to be able to conduct (contact withleads+battery) The energy is disspated in the contacts, so 1/G0is a contact resistance

TheG

22=

Van Wees et al. Phys. Rev. Lett. 60, 848 - 850 (1988)


0D transport• As mentioned by prof.

Manninen, it is possible to engineer devices whereelectron states are fullyquantized (discrete), like”artificial atoms”-also knownas quantum dots.

• 0D means that the electroninside the dot has no freedom to move

• But you can still couplecurrent through it, it can beweakly coupled to leads bytunnel barriers (T very small)


Tunneling• Quantum mechanical

tunneling is a processwhere particles(electrons) can travelthrough classicallyprohibited areas!

• ”Walking throughdoors”

• In practice the barrierhas to be of thickness1-100 nm for electronsdepending on the barrier height


Conductance through a quantumdot


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 (= zeroresistance 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


A superconducting Nb bridge

4 5 6 7 8 9 10 11 12-505

10152025303540

Res

ista

nce

(Ω)

Temperature (K)

M. Nevala, K. Kinnunen, I. Maasilta,unpublished

A sub-mm radiation detector


A superconducting junction

-0.10 -0.05 0.00 0.05 0.10-6

-4

-2

0

2

4

6

I (m

A)

V (mV)

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

S S

N

Normal metal layer 10 nm thick

The resistance of the normal metal does not show at all for currents belowcertain value (critical current), here ~ 3.5 mA at 4.2 K(No voltage drop !!!) This is the supercurrent, which is carried byCooper pairs only

M. Nevala, I. Maasilta unpublished


SNS Josephson junctions

Brian JosephsonNobel 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"

director of the Mind-Matter Unification Project

φsincII =


Applications of Josephsonjunctions

• Can be used for ultra-high frequencydigital electronics

COOL...FAST...RELIABLE...

RAPIDTypical 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


Commercial applications in the works ?

2nd Stage: 1W @ 4.2K1st Stage: 40W @ 45KMinimum Temperature: 0W @ 2.8KType: Pulse TubeCooling: liquid

+ = ?


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.


Summary of part I

• Classical laws of conduction do not work ifdevices are in the nanoscale

• Need quantum mechanics• Quantum transport can be utilized for

novel devices such as ultrasensitiveradiation detectors (more on that nexttime), ultrafast electronics and ultrasensitive electrometry

prof. ilari maasilta nanoscience center, department of physics, … · 2016-06-01 · fundamentals...

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