quantum dots quantum transport bio-medical...
TRANSCRIPT
![Page 1: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/1.jpg)
Lecture 3
Quantum dotsQuantum transportBio-medical applications
![Page 2: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/2.jpg)
Quantum dots
- definition- production- quantum shells- Wigner crystallization Wigner moleculesg e o ecu es
- Coulomb blocade- spintronics
![Page 3: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/3.jpg)
Quantum dots
Quantum dot is a semiconductor nanostructure that confines motion of electrons (holes, excitons) in a limited 2D space.
2D electron gas at semiconductor interface
EConduction zone
Forbidden zone
Zone structure in semiconductor
Valence zone
Fully filled zone
Forbidden zone
![Page 4: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/4.jpg)
Finally one gets quasi two-dimensional (2D) systemconfining 2-200 electrons
2 2( ) ( )2 x y
mV r x yω ω= +
r
Harmonic confinement
Electrons move at 2Doscillator mean field
New kind of a finite 2D Fermi-system !
2
Various applications:
- It is rather easy to connect QD by tunnel barriers to conductive leads:
- Energy spectrum of QD can be engineered by controlling its size and shape as well as the confinement potential:
electronic and spin transport
nano-electronics
![Page 5: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/5.jpg)
Quantum dots (2): images
Lateral quantum dot at a surfaceVertical quantum dots
gate voltage
bias voltage
to regulate the confinement well
to regulate transport window, …
![Page 6: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/6.jpg)
Quantum dots : physics around
- Quantum shells for electrons:- magic numbers 2, 6, 12, … are magic numbers of 2D oscillator
- Wigner molecules
![Page 7: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/7.jpg)
QD: quantum shells
* 2 2 2conf
1 1V (x,y)= m ω ( x + y )
2δ
δ
parabolic confinement:
deformation (Jahn-Teller effect):
xδ ω= =1δ = circular QD
* 2 2conf x y
1V (x,y)= m (ω x +ω y )
2
2 , ,x y x y
ωω ω ω ω ω δ ωδ
= = =
magic numbers in circular QD:
N=2,6,12,20,24,…
y
δω
= =1δ > elliptic QD
spectrum:1 1 1
[( ) ( ) ]2 2x yE n nδ
δω= + + +hquantum shell number:
0 0,1,2,...x yN n n= + =
shell degeneracy:
0 1N +
![Page 8: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/8.jpg)
Experimental observation of magic numbers in circular QD (Tarucha et al, 1996).
![Page 9: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/9.jpg)
Wigner crystallization
Prediction of Wigner (1934): 3d and 2d electron gas at low densities is crystallized and form a lattice
Coulomb dominates at low densities!
3 14( )
3s srπρ −
=Wigner-Seitz radius sr average distance between electrons
Reason
homogeneous 3d *100s Br a>
homogeneous 2d *37s Br a>
QD *7.5s Br a>
Critical to form Wigner molecules: sr
QD is a good candidate!
2* 0
* 2
(4 )Ba
m eπεε
=h
Effective Bohr radius
* 9.8 nmBa ≈ in GaAs
![Page 10: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/10.jpg)
QD: Wigner molecules
WR =0.95
WR =1.48
QD: 6e
k - dielectric constant
W
0
1R
k ω≈ can be varied through the choice
of material and strength of the confinement
CoulW
trap
VR
V=
By monitoring the circular confinement field,we can make it weaker than Coulomb interaction: Then we have: - strict localization of electronic w.f.
(formation of a Wigner molecule),- spontaneous breaking rotation symmetry ofthe circular confinement field.
WR >1
WR =3.18
C. Yannouleas, U. Landman, PRL, 1999Not still observed in QD …
![Page 11: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/11.jpg)
3D quantum dot CdSe3D quantum dots
3D quantum dots are similar to atomic clusters
High fluorescence in narrow (~30nm)wave range: depends on QD
Fluorescence induced by uv-light in vials containing CdSe QD of different size
UV< 400 nm
IR> 700 nm
Visible light 400-700 nm
400 nm 500 nm 600 nm 700 nm
g psize and structure:
ZnS, CdS, ZnSeCdSe, CdTePbS, PbSe, PbTe
UV
VLIR
GeteroQD
![Page 12: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/12.jpg)
References: quantum dots, spintronics
1) S.M. Reinmann and M. Manninen,"Electronic structure of quantum dots",Rev. Mod. Phys., 74, 1284 (2002).
2) I.Zutic, J. Fabian, S. Das Sarma,"Spintronics: fundamentals and applications", Rev. Mod. Phys., 76, 323 (2004).
3) R. Hanson et al, “Spins in few electron quantum dots”
4) «Нанотехнологии в ближайшем десятилетии», под ред. М.Роко. М.. Мир. 2002.
Spins in few-electron quantum dots ,Rev. Mod. Phys., 79, 1217 (2007).
5) R.G. Nazmitdinov,“Magnetic field and symmetry effects in small quantum dots”,Phys. Part. Nucl. , 40, n.1, 71-92 (2009).
![Page 13: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/13.jpg)
Quantum transport- variety of quantum transport- Landauer equations
![Page 14: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/14.jpg)
Quantum transport
leads
Organic molecule
molecule, cluster 60C
Chain of atomsAu, Ag
Quantum dot
Transport of electrons
- not ohmic law,- fundamental effects(Hall effects),
- wide applications!
Atoms or BEC in optical lattice Atoms or BEC inmulti-well traps Transport of atoms
Quantum dot
Transport of spin
![Page 15: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/15.jpg)
Examples:
Conductance via organic molecule. The contacts are modeled by Au-clusters with 55 atoms each
F. Evers et al, Physica E, 18, 255 (2003).
Typical problem is to determine current-voltagecharacteristics I (V)
V
I
?
Ohmic law I=V/R
Conventional electricity: Quantum transport:
Complicated no-Ohmic laws(resonances, influence of contacts, …)
![Page 16: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/16.jpg)
Low temperature, low bias basic transport features(electrons at the Fermi energy)
Room temperature, high bias practical applications
We will consider
basic transport features!
Mainly planar semi-conductor systems likeGaAs – AlGaAs
(gallium arsenide – aluminium gallium arsenide)
References:- S. Datta, “Electronic transport in mesoscopic systems”,
(Cambridge Univ. Press, Cambridge, 1995)- S. Datta, “Quantum transport: atom to transistor”,
(Cambridge Univ. Press, Cambridge, 2005)
![Page 17: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/17.jpg)
Mesoscopic transport
Ohmic behavior for macroscopic conductors:
1/G W L
Rσ= =
W
L
current
Principle question:How small can we make the dimensions before the ohmic behavior breaks down?
Conductance:
1
U IR
IR U
=
=
Ohmic:
Mesoscopic systems:- larger than microscopic objects (atoms, …),- but not large enough to be ‘ohmic’,- typical dimensions: or
The system demonstrates ‘ohmic’ behavior if
, , ,B D PhaseW L r rλ>>
B
D
Phase
r
r
λ - de Broglie wavelength
- mean free path (the distance that electron travels before its initial momentum is destroyed)
- phase-relaxation length
nm mμ÷ 9 410 10 m− −−
Mesoscopic transport!
![Page 18: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/18.jpg)
Landauer formalism
/G W Lσ=
Ohmic equation Landauer equation
22eG MT
h=
Conductance: 1
GR
= W
L
current
Mesoscopic transport:- Conductance does not depend on the length L.For ballistic conductor has resistance (= interface resistance).
- Conductance depends on W not linearly but in discrete steps(determined by number of transversal modes).
-- conductivity (depends on the material propeties, independent on W and L)
T – transmission probability (probability to transmit electron through the sample) M – number of transversal modes
σ
DL r< CR
![Page 19: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/19.jpg)
Spintronics = spin electronics
Electronics: currents, charges; spin of electrons does not matter.Spintronics: manipulation with spin of electrons; - currents of polarized electrons, non-uniform spin distributions.- unlike electrical charge, “spin charge” is not conservedand depends on several factors: spin-orbital interaction,…
Change of electron spin directionby using its precession in magnetic field:
low energy effort and heating
Si-based microelectronics Spintronics
- low energy effort and heating- prompt ( ~ ps = )- long-living
910 s−
Best perspectives:
- quantum computer- spin field-effect transistor - spin memory, 8 registers
![Page 20: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/20.jpg)
Giant magnetoresistance
- Possibility to change essentiallyelectric resistance by small varyingmagnetic field
- Multilayer structures, e.g. Fe/Cr/Fe, with very thin 3-50 layers (~ 100 nm altogether)
Spin-valve GMR (layers ~ 3nm)
Geterostructures:
- Effect via spins of electrons.Hence
SPINTRONICS!
![Page 21: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/21.jpg)
1) S. Datta, “Electronic transport in mesoscopic systems”,(Cambridge Univ. Press, Cambridge, 1995)
2) S. Datta, “Quantum transport: atom to transistor”, (Cambridge Univ. Press, Cambridge, 2005)
References: quantum transport
![Page 22: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/22.jpg)
Bio-medical applications of nanosystems
![Page 23: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/23.jpg)
Nanoparticles for bio-medical aims (1)
- targeted drug delivery- biomarkers, diagnostics- photo-thermolise
Main applications:
Main candidates:- semiconductor QD CdSe (toxic!)- Au and Ag nanoclusters
using of plasmon
- functionalization- bioconjugate
P.K. Jan et al, “Au nanoparticles taget cancer”,Nanotoday, v.2, 18 (2007)
Problems of traditional sensors(organic dyes):- weak signal- rapid photobleaching- subtle spectra differences for normal and deceased cells
- low possibility to change the plasmonfrequency
Nanoparticles can solve these problems!
![Page 24: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/24.jpg)
Colloidal Au:
- known already in ancient Egypt,- nanoparticles of the size 4-80 nm- biocompatible, notoxic- strong binding affinity- optical cross-section is higher
than for conventional dyes
Nanoparticles for bio-medical aims (2)
4 510 10−y
- the ratio absorption/scattering rises with particle size
- Au nanoparticle ~ 35 nm - anti-EGFR/Au nanoparticle conjugate- light scattering images- microabsoption spectrometry(shift ~ 9nm)
![Page 25: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/25.jpg)
- rapid (~ 1 ps) conversion of absorbed light into heat
- times more effective absorption4 510 10− - 4 min exposition of weak CW laser,visible light 530 nm
Targeted cells: - healthy HaCaT die at 57 W/cm^2- malignant HSC die at 25 W/cm^2- malignant HOC die at 19 W/cm^2
Selective photothermal cancer therapy
malignant HOC die at 19 W/cm 2
Non-targeted cells- survive up to 76 W/cm^2
- infrared irradiation:- diagnostic and therapy in vivu- biological NIR window 650-900 nm,
(maximal transmissivity for hemoglobin and water)
- penetration: few cm.
Transparency window for tissue: 800-1000 nm >> visible light
![Page 26: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/26.jpg)
Silica-core Au-shell nanoparticles Nanorods with different aspect ratio
![Page 27: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/27.jpg)
REFERENCES: BIO-MEDICAL APPLICATIONS
1) Н.Г. Хлебцов, В.А. Богатырев, Л.А. Дыкман, Б.Н. Хлебцов"Золотые наноструктуры с плазмонным резонансом для биомедицинских исследований",Российские нанотехнологии, т.2 (3-4), 2007 (www.nanorf.ru)
2) A.O. Govorov and H.H. Richardson, “Generating heat with metal nanoparticles”NanoToday, 2, n.1, 30 (2007)
3) P.K. Jain et al, ”Au nanoparticles target cancer”,p g ,NanoToday, 2, n.1, 18 (2007)
![Page 28: Quantum dots Quantum transport Bio-medical applicationstheor.jinr.ru/~diastp/winter09/lectures/nesterenko/... · 2009. 1. 28. · Finally one gets quasi two-dimensional (2D) system](https://reader035.vdocuments.site/reader035/viewer/2022081621/611ea3d8eba78e628f6dd432/html5/thumbnails/28.jpg)
Thank you for your attention!