Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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provides a conceptual framework for understanding the disorder–order phasetransition observed for sterically stabilized metal nanocrystals. One couldhypothetically calculate the free energy of the solid and fluid phases,0011XX U i;jF ¼ kT ln@exp@AAkTconfigurationði;j;bondsÞwhere k is Boltzmann’s constant. Because A(r) is either 0 or l,01XU i;jexp@A0 if r V 2R¼kT 1 if r > 2Rði;j;bondsÞand therefore, the free energy depends only on the possible configurations orpacking geometries in the fluid; it depends only on the entropy of the system.At low nanocrystal densities, the disordered fluid can achieve many moreconfigurations than the ordered phase and it is thermodynamically favored.However, at relatively high densities, the solid phase allows the particlesgreater free volume relative to the dense fluid. For example, the fcc latticeexhibits a maximum packing density of 0.74, whereas the disordered phasefreezes into a closest packed glass at a volume fraction of 0.68. The disorder–order phase transition for hard spheres has therefore been termed a disorderavoidingphase transition where the entropic driving force results from anincrease in microscopic disorder that exceeds the macroscopic configurationalentropy loss due to crystallization [40,41]. These considerations alsohold true in two dimensions, even though true long-range order cannot exist.In fact, Gray and co-workers [34,42] found that nanocrystal monolayers canproceed through a fluid–hexatic–hexagonal close-packed (hcp) phase transitionunder the appropriate conditions.Conceptually, an understanding of hard-sphere crystallization is importantfor understanding nanocrystal superlattice formation. However, thenanocrystals are not truly hard spheres and the interparticle interactionenergies can exceed 1/2 kT for particles less than 10 nm in diameter, despitetheir small size [10,33]. In 1995, Ohara et al. revealed that size-dependent vander Waals attractions between particles resulted in the formation of polydisperseaggregates of Au nanocrystals, with the largest particles located on theinterior of the aggregate and progressively smaller particles located on theexterior [43]. The aggregation was reversible and the particles were readilyredispersed with the addition of organic solvent. Molecular dynamics simulationsalso confirmed the importance of the van der Waals attraction on theformation of the aggregates. The interparticle attraction has been found to bevery important to superlattice formation [36,44].Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
2. Steric Stabilization and a Soft RepulsionAttractive van der Waals forces due to dipole-induced dipole interactionsare relatively strong for metal nanocrystals due to the high polarizabilityof the cores, despite their small size and relatively thick organic coating.[For example, dodecanethiol (C 12 thiol) extends approximately 1.5 nm intosolution; therefore, the C 12 -coating surrounding a 5-nm-diameter nanocrystal,for example, occupies 75% of the total volume occupied by the core andligand!] The van der Waals attraction A vdW , between two spheres of equalradius R, separated with a center-to-center distance of d and a Hamakerconstant A [45] isA vdW ¼ A 2R 26 d 2 4R 2 þ 2R2d 2 þ ln d 2 4R 2 d 2The Hamaker constant reflects the strength of the core–core attraction anddepends on the polarizability of the sphere and the dispersing medium. TheHamaker constants for metals interacting across a vacuum have been determined.For example, the tabulated value for bulk silver is A 11 = 2.185 eV[46]. To calculate the Hamaker constant of the nanocrystals dispersed in differentsolvents (denoted as A 131 , where the subscript 1 represents the metaland the subscript 3 represents the solvent), the following relationship can beused:pA 131 cffiffiffiffiffiffiffi pffiffiffiffiffiffiffi 2A 11A 33where A 11 is for the metal interacting across vacuum and A 33 is for the solventinteracting across vacuum. The value for A 33 can be estimated using asimplification of Lifshitz theory [46]:A 33 ¼ 3 4 kT q 3 q 2vacuumþ 3ht eðn 2 3 n 2 vacuump Þ2q 3 þ q vacuum 16 ffiffi2 ðn23þ n 2 vacuum Þ3=2where e is the dielectric constant, n is the refractive index, h is Planck’sconstant, k is Boltzmann’s constant, T is temperature, t e is the maximumelectronic ultraviolet adsorption frequency typically taken to be 3 10 15 s 1 ,and e vacuum = 1 and n vacuum = 1.The typical Hamaker constant for silver in conventional solvents underambient conditions such as hexane is A 131 = 0.91 eV. This is very high,considering, for example, that A for polystyrene in water is 0.087 eV and is0.125 eV for mica in water. Therefore, despite their small nanometer size,values for A vdW can be significant compared to kT.The adsorbed capping ligands provide a short-range steric barrier toparticle aggregation. As two nanocrystal cores capped with stabilizing ligandsCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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Copyright 2004 by Marcel Dekker, In
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This book covers several topics of
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esult, some exciting topics were no
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3. Fine Structure and Polarization
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9. III-V Quantum Dots and Quantum D
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ContributorsUri BaninThe Hebrew Uni
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1‘‘Soft’’ Chemical Synthesi
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structure of energy states leads to
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growth can proceed by Ostwald ripen
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Figure 3 Transmission electron micr
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Figure 4 Temporal evolution of the
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No. 26, are f85% (Fig. 6) [21]. Alt
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tion spectra and broad PL spectra.
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ing surface-to-volume ratio with di
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Figure 8 Photoluminescence spectra
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lattice mismatch. Such a large latt
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match between InAs and ZnS of f11%.
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successfully repeated for up to thr
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Under a different growth regime, on
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Figure 14 Atomic model of the CdSe
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‘‘Teardrop-shaped’’ particl
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Figure 17 High-resolution TEMs of C
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allows isolation of tetrapods in f8
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ligand concentrations yield a reduc
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een determined and quantitatively c
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tion volumes were also shown to be
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synthesis temperatures of z400jC ar
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Figure 23 (a) Photoluminescence spe
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levels (fV1 Mn per NQD). Despite in
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Figure 25 X-ray diffraction pattern
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Figure 27 Transmission electron mic
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An additional factor that strongly
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Figure 30 (a,b) Schematics illustra
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Slow, controlled precipitation of h
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Figure 34 Schematic illustrating th
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Figure 36 Transmission electron mic
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achieving biological compatibility
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47. Yu H.; Gibbons P.C.; Kelton K.F
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2Electronic Structure inSemiconduct
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Figure 2 (a) Simple model of a nano
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electron and hole to be treated as
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independently, Eq. (13) is commonly
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a better description of the bulk ba
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investigated. For optical experimen
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Figure 4 (a) Absorption (solid line
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Figure 6 Normalized PLE scans for s
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Figure 8 A simplistic model for des
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Figure 10 Theoretically predicted p
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Figure 12 Schematics depicting the
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Figure 14 Calculated band-edge exci
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Figure 15 Absorption (solid line) a
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Figure 18 (a) Calculated band-edge
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IV.BEYOND CdSeA. Indium Arsenide Na
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the six-band Luttinger Hamiltonian.
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11. Norris, D.J.; Efros, Al.L.; Ros
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69. Gaponenko, S.V.; Woggon, U.; Sa
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formation of a long-lived dark exci
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where the constant A is determined
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In crystals for which the function
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The respective wave functions areC
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passive, as was shown in Ref. 12. T
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square of the matrix element of the
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where e F = e F ieV and e F F = e x
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see that for all nanocrystal shapes
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optical recombination of the excito
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B. Recombination of the Dark Excito
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where x = cos h and f = l B g e H/3
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The theory of the polarization memo
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Figure 7 The size dependence of the
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state would have an infinite lifeti
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crystal axis [see Eq. (40)]. As a r
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time of the exciton momentum relaxa
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One must also account for the influ
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observed in one of the first studie
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REFERENCES1. Bawendi, M.G.; Wilson,
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4Intraband Spectroscopyand Dynamics
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The solid line in Fig. 1 shows the
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Figure 2 FTIR spectra of n-type CdS
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of the center frequency. The experi
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limit given by radiative relaxation
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from a long lifetime due to the pho
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are two natural approaches to study
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32. Inoshita, T.; Sakaki, H. Physic
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continuous spectral tunability over
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function and envelope function mome
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ottleneck’’ [14,28]. Further re
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in NQDs is dominated by nonphonon e
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Figure 4 Dynamics of the IR postpum
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Figure 5 (a) Time-resolved PL spect
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Figure 6 (a) The time delay of the
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and due to Auger-type e-h interacti
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Figure 9 Dynamics of the 1S bleachi
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significantly greater than the fast
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Figure 11 (a) Pump-intensity-depend
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NQD size. For small NQD sizes (R =
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Figure 14 Nonlinear absorption/gain
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sorption change associated with a s
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where n h em is the hole ‘‘emit
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ultrafast (subpicosecond to picosec
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Figure 18 Schematic of transitions
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Figure 19 Dynamics of pump-induced
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where n i (i=1, 2 . . . , N ) is th
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Figure 21 (a) Two-e-h-pair (biexcit
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the volume fraction (filling factor
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intensity dependence of this peak (
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can contribute to the saturation of
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coupling between ‘‘volume’’
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numerous discussions on the photoph
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53. Kang, K.; Kepner, A.; Gaponenko
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the ‘‘on-off ’’ emission in
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parallel form of data acquisition i
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Figure 3 (a) Spectral time trace of
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transition energies. In fact, these
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distribution (dark line) does not d
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exposure to only room light. In our
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statistics for the off times are in
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230Shimizu and BawendiCopyright 200
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Figure 10 (a) Time trace of a CdSe(
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and excited QD core states to fluct
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arrows indicate the on-time truncat
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W. K. Woo and V. C. Sundar for assi
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size allows the electron affinity a
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II.THEORY OF ELECTRON TRANSFER BETW
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For the specific case of charge tra
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dominates, the mobility is often fi
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where the constant A and the temper
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components of modulation which are
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nanocrystals [41], understanding ph
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and ionization potential through tw
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quantum dots. Furthermore, because
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For many applications, a host mater
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form blends with morphologies that
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Figure 11 Photoluminescence efficie
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Figure 12 (a) Room-temperature PIA
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discussed briefly in Section IV. Ch
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dithiolates to thiol-terminated DNA
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Films of passivated CdSe nanocrysta
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Figure 16 Photocurrent action spect
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decay with stretched exponential ki
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siderably larger than might be esti
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dispersing CdSe nanocrystal chromop
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memory and charge storage effects [
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all) of the optically excited elect
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composites of nanocrystals and conj
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55. Asbury, J.B.; Hao, E.C.; Wang,
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108. Morgan, N.Y.; Leatherdale, C.A
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The approaches to fabrication of se
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Figure 1 Experimental realization o
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Due to this voltage division, the m
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Figure 3 Simulated tunneling spectr
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electron charging. In both positive
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Figure 5 shows the typical features
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Figure 7 Map of levels for InAs nan
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Figure 8 Scanning electron microsco
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D CB = 0.31 eV is thus obtained. On
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Figure 11 Correlation of optical an
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atomistic approach based on pseudop
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charging indicated that the tunneli
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capacitance values were also kept t
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could not be detected in the QD/DT/
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Figure 18 Tunneling conductanceF sp
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data in the inset of Fig. 19 repres
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corresponding to the s-like wave fu
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7. Grabert, H.; Devoret, M.H., Eds.
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66. Su, B.; Goldman, V.J.; Cunningh
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dimensional confinement are created
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Figure 1 Transmission electron micr
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The room-temperature absorption and
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narrower in samples with larger mea
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GaInP 2 QDs from a plot of the squa
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crystal, indicating lattice-matched
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Figure 5 Evolution of Stranski-Kras
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C. Efficient Anti-Stokes Photolumin
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Because HF treatment has been shown
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Page 367 and 368: intensity of the PL when it is on a
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Page 371 and 372: Figure 16 Model to explain two-colo
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Page 375 and 376: 10 ps (about an order of magnitude
Page 377 and 378: electron relaxation is inhibited an
Page 379 and 380: Figure 18 Transmission electron mic
Page 381 and 382: QDs, the nature of the QD capping s
Page 383 and 384: QD solution. For an interdot distan
Page 385 and 386: emission spectra of the two individ
Page 387 and 388: Figure 23 Change of the PL intensit
Page 389 and 390: (viz. the absorbed light intensity)
Page 391 and 392: Figure 25Impact ionization in QDs.m
Page 393 and 394: prevent electron-hole recombination
Page 395 and 396: 36. Miller, R.D.J.; McLendon, G.; N
Page 397 and 398: 91. Vurgaftman, I.; Singh, J. Appl.
Page 399 and 400: 139. Mićić, O.I.; Ahrenkiel, S.P.
Page 401 and 402: 10Synthesis and Fabrication of Meta
Page 403 and 404: Figure 2 (A-C) Progression of HR-TE
Page 405 and 406: Figure 3 Schematic for gold nanocry
Page 407 and 408: Nanocrystal growth can occur by two
Page 409 and 410: on the other hand, provide an ensem
Page 411 and 412: Figure 6 (a) SAXS patterns for disp
Page 413 and 414: Figure 8 The gold nanocrystal film
Page 415 and 416: of the stabilizing ligand, and the
Page 417: successfully modeled the 2D island
Page 421 and 422: are fully extended. Moving away fro
Page 423 and 424: Figure 11 High-resolution SEM image
Page 425 and 426: Figure 13 (A) Transmission electron
Page 427 and 428: function of the density of localize
Page 429 and 430: Figure 15 High-resolution SEM image
Page 431 and 432: thiol-capped nanocrystals [2]. The
Page 433 and 434: 41. Ackerson, B.J. Nature 1993, 365
Page 435 and 436: with the effect of the particle com
Page 437 and 438: Figure 1a shows the surface plasmon
Page 439 and 440: Figure 2 (a) Ultraviolet-visible ab
Page 441 and 442: agents [34]. The short-wavelength b
Page 443 and 444: Figure 4 (a) Plot of the plasmon ab
Page 445 and 446: the framework of traditional Mie’
Page 447 and 448: show that effects due to the surrou
Page 449 and 450: is located at the position of the g
Page 451 and 452: Copyright 2004 by Marcel Dekker, In
Page 453 and 454: Figure 8 Ultraviolet-visible absorp
Page 455 and 456: laser pulses while being mixed in t
Page 457 and 458: Figure 10 shows HR-TEM images of go
Page 459 and 460: Figure 11 Transmission electron mic
Page 461 and 462: final irradiation product. At the s
Page 463 and 464: following the laser excitation appe
Page 465 and 466: 36. Papavassiliou, G.C. Prog. Solid
Page 467 and 468: particles to expand. Because the he
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was frequency doubled in a 1-mm B-
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Figure 2 Frequency of the acoustic
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Figure 3 Change in radius (DR/R) ve
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In this model, the electrons couple
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Figure 5 Transient bleach data for
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Figure 7 (a) Transient bleach data
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that the particles with >80% Au hav
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3. Del Fatti, N.; Valle´e, F.; Fly
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