Contents 2 Types of QDs Metal clusters. Electronic properties
Fullerenes Synthetic nanocrystals. Self-assembled QDs. QDs produced
from heterostructures and lithografic etching Optical properties
Coulomb blockade and single electron devices Summary
Slide 3
Types of QDs Synthetic nanocrystals Self-assembled QDs QDs
produced from heterostructures and lithographic etching Clusters of
atoms grown from vapour-phase condensation increasing size
Fullerenes 3
Slide 4
Metal clusters. Electronic properties Clusters of atoms grown
from vapour-phase condensation Metal cluster superatoms Nucleus
Metal Cluster Atom Hydrogen (Z=1)Lead (Z=82) 4
Slide 5
Shell-structures Metal clusters. Electronic properties closed
shells of 2, 8, 20, 40, 58, 92, 138... electrons, sizes specially
stables magic numbers of atomic clusters valence electrons in a
spherical box Parabolic (harmonic osc.) V r 2 square well shell
structure of nuclei 5
Slide 6
Metal clusters. Electronic properties Jellium (sphere) model
Electron spill-out 6
Slide 7
Magic numbers of alkali metal atom clusters ion-mass
spectrometer Fig 8.11 Supersonic beams produced by mixing the metal
vapour with an inert carrier gas and ejecting the mixture through a
nozzle Metal clusters. Electronic properties 7
Slide 8
Spherical shell closing N=1430 atoms complete icosahedral
clusters (e.g. Al 13 ) N=25000 atoms..... bulk material Metal
clusters. Electronic properties 8
Slide 9
Photoabsorption cross section of two potasim cluster ions
Plasmon resonances Measured and calculated plasma resonances of
potasim cluster ions Metal clusters. Electronic properties 9
Slide 10
Fullerenes C 60 (next chapter) 10
Slide 11
Synthetic nanocrystals. Obtained by chemical methods.
Precipitates in colloids. Nanocrystals in insulating matrix, e. g.,
CdS, CdSe in glassy matrix, CuCl in NaCl crystals, Si, Ge... Size
control (~1nm-> ~200nm) 11
Slide 12
From the chemical point of view, QDs are molecular agregates.
Cd 32 S 55 is a piece of CdS lattice (zincblende) Synthetic
nanoparticles interesting because of optical properties. Reducing
the size the gap changes, Higher fusion temperatures, estructural
changes... e.g. the gap of CdSe can be tuned from red (1.7eV) to
green (2.4 eV) when the particle diameter is reduced from 200 nm to
2 nm Aplications: lasers, LEDS, biosensors.... TEM image of
wurtzite (hexagonal) Cd Se nanocrystals - Semiconductor Clusters,
Nanocrystals and Quantum Dots, A. Paul Alisavatos, Science 271, 933
(1996) - Perspectives of the Physical Chemistry of Semiconductor
Nanocrystals, A. Paul Alisavatos, J. Phys. Chem. 100, 13226 (1996)
Synthetic nanocrystals. 12
Slide 13
Synthetic nanocrystals. Higher fusion temperatures Fluorescence
of semiconductor nanocrystals 13
Slide 14
Self-assembled QDs. Obtained by deposition with MBE on
semiconductor material of wider gap (e.g. In on Ga As). Nucleation
islands (In x Ga 1-x As) form spontaneously. QDs are obtained when
these islands are covered with an epitaxial layer of a second
semiconductor of wider gap. 14
Slide 15
- Self-assembling of nanocrystals fcc superlattice of CdSe
nanocrystals of 48 in diameter - Opal: naturally occurring
colloidal crystal of silica particles Interaction between QDs in
supperlattice red-shift in optical absorption with respect to
isolated nanocrystal Self-assembled QDs. 15
Slide 16
Self-assembled QDs. 16
Slide 17
Applications Optical and optoelectronical devices M. Bayer et
al., Nature 405, 923 (2000) It is possible to create on individual
exciton in a QD, by optical excitation. The study of the light
emitted after the e-hole recombination provides information about
the structure of the QD. Application: new lasers. Quantum rings
Optical and optoelectronical devices Computation, quantum
information P. Michler et al., Science 290, 2282, 2000 Combinig QDs
with light cavities it is possible to perform quantum optics
experiments, where emission is due to oneindividual photon.
Applications : information and quantum computing A. Lorke et al.,
Phys Rev. Lett. 84, 2223 (2001) The energies of a quantum ring
depend on the external magnetic field due to flux.crossing the ring
Self-assembled QDs. 17
Slide 18
QDs produced from heterostructures and lithografic etching
Lithographic etching Reed et al., PRL 60, 535 (1988) Obtained from
GaAs/AlGAAs heterostructures, whre a 2D electron gas has been
formed. Lateral (in the plane of the 2D electron gas) QDs are
produced by lithographic etching. Also vertical QDs are produced bt
MBE growth in the direction perpendicular to the electron
confinement plane. Size: 10-20 nm to ms 18
Slide 19
Vertical quantum dots QDs produced from heterostructures and
lithografic etching 19
Slide 20
Vertical QDs from lithographic etching: different shapes QDs
produced from heterostructures and lithografic etching 20
Slide 21
QDs produced from heterostructures and lithografic etching
21
Slide 22
QDs obtained by lithography Double QDs QDs produced from
heterostructures and lithografic etching 22
Slide 23
Optical properties Assume spherical QDs... 1)Weak- confinement
regime R Mott-Wannier exciton radius Reduced mass for e - -hole
bound state Exciton binding energy Exciton mass for center-of-mass
motion dielectric constant of semiconductor 23
2)Strong- confinement regime weak e - -hole correlation e - and
hole levels particle-in-a-box model: e.g. s-sate Optical properties
25
Slide 26
blue shift in absorption e - -hole pair 1s-state (n=1) e -
-hole interaction inside sphere remanent of exciton interactions
due to quantum confinement effects Optical properties 26
Slide 27
CdS in glass strong confinement CuCl in NaCl weak confinement
theory R 30 29 77 Blue shift of energy gap Optical properties
27
Slide 28
Optical absorption intensity, CdS in glass blue shift R= 5nm
1.7 nm Enhanced exciton effects (subbands) Optical properties
28
Slide 29
Radiative interband transitions e.g. bulk Si in indirect-
band-gap semiconductors low intensity porous Si: - etching isolated
Si-columns substrate surface k not a good quantum number direct
transitions without phonon allowed Photoluminiscence,
electroluminiscence direct- band-gap semiconductor Optical
properties 29
Slide 30
indirect- band-gap direct transitions phonon Optical properties
30
Slide 31
Coulomb blockade Single electron transistors (SETs) Diferencial
conductance vs. V gate Peaks corresponding to one electron addition
Coulomb blockade model Electron non-coherent tunnelling Coulomb
blockade and single electron devices 31
Slide 32
Coulomb blockade and single electron devices Different modes to
confine electrons in QDs Coplanar metal QD Etched vertical QD
(mesa) Potential Lateral GaAs QD insulator QD GaAs Al x Ga 1-x As
Source GaAs Gate Electrons at interface
Slide 33
Differencial conductance vs. gate voltage Coulomb blockade and
single electron devices
Slide 34
Coulomb blockade model Adding 1 e- E=e 2 /2C, C=capacity
between dot and surrounding threshold energy above E F for current
flow - If k B T < e 2 /2C no current, Coulomb blockade only
evident at very low T
Slide 35
But a current can be made to flow varying Vg voltage E=QV g + Q
2 /2C parabola with min. at Q 0 =-CV g, but charge is quantized
Q=Ne exact for metallic QDs, 10 7 electrons, extra charge on
surface Q 2 /2C exact Approximative for semiconductor QDs, N <
50 electrons, confinement of electron wave function espatial size
quantization discrete energy spectrum Coulomb blockade and single
electron devices 35
Slide 36
Coulomb blockade and single electron devices V g =Ne/C
E(N+1)-E(N)= e 2 /2C V g =(N+1/2)e/C E(N+1)=E(N) electron-hole
tunneling gap e 2 /C E=QV g + Q 2 /2C 36
Slide 37
Electron transport controlled e - by e - single electron
transistor Coulomb blockade and single electron devices 37
Slide 38
A single electron transistor made from a CdSe nanocrystal, D.L.
Klein et al, Nature 389, 699 (1997) It is possible to add electrons
one by one into the nanocrystal Distance between electrodes: 10 nm
The particle (d=5.5 nm) is joined to the contacts by hexanoditiol
molecules, which form tunel barriers of 1.2 nm between particle and
leads. Coulomb blockade and single electron devices 38
Slide 39
Coulomb blockade and single electron devices Double QD 39
Slide 40
Coulomb blockade and single electron devices Coulomb blockade
and Kondo effect 40
Slide 41
Coulomb blockade and single electron devices What is the Kondo
effect? The Kondo physics appears at very low T, when there is a
quantum impurity (with charge and spin freedom) coupled to the
Fermi sea itinerant electrons by tunnel effect. The virtual tunnel
effect processes, together with the strong Coulomb repulsion, give
rise to non-trivial physical effects, effective spin-flip
originating the Kondo effect. + spin-flip The Kondo effect appears
in the DOS of the impurity, as a sharp p resonance placed at the
fermi level of the itinerant electrons at T