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surface trapping and the ‘‘phone bottleneck’’ turned out to be much less importantcompared to such largely unforeseen problems as nonradiative,multiparticle Auger recombination [16] and interference from photoinducedabsorption (PA) due to carriers trapped at NQD interfaces [17].In this chapter, we analyzed the underlying physics of processes relevantto optical amplification and lasing in strongly confined NQDs with a focus onsub-10-nm CdSe colloidal nanoparticles. Specifically, we discuss the issues ofintraband carrier relaxation, multiparticle interactions, and photoinducedabsorption in the context of NQD optical-gain properties. We also analyzethe effect of NQD sample parameters, such as NQD size, surface passivationquality, matrix–solvent identity, and NQD densities on optical-gain performance.Furthermore, we illustrate lasing action in NQDs using several experimentalexamples in which different cavity configurations (e.g., microringand distributed feedback) were utilized.II.ENERGY STRUCTURES AND INTRABAND RELAXATIONIN NQDsA. Band-Edge Optical TransitionsThis chapter concentrates on sub-10-nm CdSe NQDs that can be fabricated,for example, by organometallic, colloidal methods described in Chapter 1. Inbulk CdSe, the exciton Bohr radius is approximately 5 nm. Therefore, NQDswith sub-10-nm sizes (mean radii, R
function and envelope function momenta) [19]. In the notation for the holestates, the F number is usually shown as a subscript. For example, thenotation for the lowest hole state is 1S 3/2 . The hole states are (2F+1)-folddegenerate. This degeneracy is lifted if the effects of the crystal field in ahexagonal lattice [20], NQD nonspherical shape [21], and e–h-exchangeinteractions [22,23] are taken into account, leading to a ‘‘fine-structure’’ splittingof hole levels [23].Band-edge optical properties of NQDs are dominated by transitionsinvolving the lowest electron 1S state and fine-structure states derived fromthe 1S 3/2 hole level (Fig. 1a). The split-off 1S 3/2 hole states form two groups ofclosely spaced levels separated by the gap that can be as large as tens ofmillielectron volts in small-size dots. The high-energy manifold of hole statesis coupled to the 1S electron state by a strong optical transition observed inabsorption spectra as the lowest 1S absorption maximum. The low-energyhole states are coupled to the 1S(e) state by a much weaker transition thatgives rise to a band-edge PL band. The large, NQD size-dependent gapbetween the high- and low-energy manifolds of hole states (manifolds of‘‘absorbing’’ and ‘‘emitting’’ states, respectively) is observed in opticalspectra as a large Stokes shift between the lowest 1S absorption maximumand a band-edge PL detected under nonresonant excitation (Fig. 1b). Thisshift is often referred to as the ‘‘global’’ Stokes shift, in contrast to the‘‘resonant’’ Stokes shift [24] observed under quasiresonant excitation influorescence line-narrowing experiments (see Chap. 2).B. Electron Intraband RelaxationIn the case of both the optical and electrical pumping of semiconductor gainmedia, nonequilibrium charge carriers are usually injected with energies thatare greater than the material’s energy gap. Therefore, intraband energyrelaxation, leading to the population buildup of the lowest ‘‘emitting’’ transition,is an important process in the sequence of events leading to lightemission and, ultimately, to lasing. To ensure efficient pumping of electron/hole states involved in the ‘‘emitting’’ transition, energy relaxation in bothconduction and valence bands has to be more efficient than carrier recombinationdue to both radiative and nonradiative processes.In bulk II–VI semiconductors, carrier energy relaxation is dominated bythe Fro¨hlich interactions with longitudinal optical (LO) phonons that lead tofast (typically subpicosecond) carrier cooling dynamics [25–27]. In QDs, evenin the regime of weak confinement when the level spacing is only a fewmillielectron volts, the carrier relaxation mediated by interactions withphonons is hindered dramatically because of restrictions imposed by energyand momentum conservation, leading to a phenomenon called a ‘‘phononCopyright 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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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
Page 125 and 126: In crystals for which the function
Page 127 and 128: The respective wave functions areC
Page 129 and 130: passive, as was shown in Ref. 12. T
Page 131 and 132: square of the matrix element of the
Page 133 and 134: where e F = e F ieV and e F F = e x
Page 135 and 136: see that for all nanocrystal shapes
Page 137 and 138: optical recombination of the excito
Page 139 and 140: B. Recombination of the Dark Excito
Page 141 and 142: where x = cos h and f = l B g e H/3
Page 143 and 144: The theory of the polarization memo
Page 145 and 146: Figure 7 The size dependence of the
Page 147 and 148: state would have an infinite lifeti
Page 149 and 150: crystal axis [see Eq. (40)]. As a r
Page 151 and 152: time of the exciton momentum relaxa
Page 153 and 154: One must also account for the influ
Page 155 and 156: observed in one of the first studie
Page 157 and 158: REFERENCES1. Bawendi, M.G.; Wilson,
Page 159 and 160: 4Intraband Spectroscopyand Dynamics
Page 161 and 162: The solid line in Fig. 1 shows the
Page 163 and 164: Figure 2 FTIR spectra of n-type CdS
Page 165 and 166: of the center frequency. The experi
Page 167 and 168: limit given by radiative relaxation
Page 169 and 170: from a long lifetime due to the pho
Page 171 and 172: are two natural approaches to study
Page 173 and 174: 32. Inoshita, T.; Sakaki, H. Physic
Page 175: continuous spectral tunability over
Page 179 and 180: ottleneck’’ [14,28]. Further re
Page 181 and 182: in NQDs is dominated by nonphonon e
Page 183 and 184: Figure 4 Dynamics of the IR postpum
Page 185 and 186: Figure 5 (a) Time-resolved PL spect
Page 187 and 188: Figure 6 (a) The time delay of the
Page 189 and 190: and due to Auger-type e-h interacti
Page 191 and 192: Figure 9 Dynamics of the 1S bleachi
Page 193 and 194: significantly greater than the fast
Page 195 and 196: Figure 11 (a) Pump-intensity-depend
Page 197 and 198: NQD size. For small NQD sizes (R =
Page 199 and 200: Figure 14 Nonlinear absorption/gain
Page 201 and 202: sorption change associated with a s
Page 203 and 204: where n h em is the hole ‘‘emit
Page 205 and 206: ultrafast (subpicosecond to picosec
Page 207 and 208: Figure 18 Schematic of transitions
Page 209 and 210: Figure 19 Dynamics of pump-induced
Page 211 and 212: where n i (i=1, 2 . . . , N ) is th
Page 213 and 214: Figure 21 (a) Two-e-h-pair (biexcit
Page 215 and 216: the volume fraction (filling factor
Page 217 and 218: intensity dependence of this peak (
Page 219 and 220: Copyright 2004 by Marcel Dekker, In
Page 221 and 222: can contribute to the saturation of
Page 223 and 224: Copyright 2004 by Marcel Dekker, In
Page 225 and 226: 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
Page 257 and 258:
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
Page 307 and 308:
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/
Page 333 and 334:
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.
Page 341 and 342:
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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Page 359 and 360:
Page 361 and 362:
C. Efficient Anti-Stokes Photolumin
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Because HF treatment has been shown
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intensity of the PL when it is on a
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eV stems from recombining carriers
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Figure 16 Model to explain two-colo
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although this term is not rigorousl
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10 ps (about an order of magnitude
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electron relaxation is inhibited an
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Page 381 and 382:
QDs, the nature of the QD capping s
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QD solution. For an interdot distan
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emission spectra of the two individ
Page 387 and 388:
Figure 23 Change of the PL intensit
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(viz. the absorbed light intensity)
Page 391 and 392:
Figure 25Impact ionization in QDs.m
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prevent electron-hole recombination
Page 395 and 396:
36. Miller, R.D.J.; McLendon, G.; N
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91. Vurgaftman, I.; Singh, J. Appl.
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139. Mićić, O.I.; Ahrenkiel, S.P.
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10Synthesis and Fabrication of Meta
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Figure 2 (A-C) Progression of HR-TE
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Figure 3 Schematic for gold nanocry
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Nanocrystal growth can occur by two
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on the other hand, provide an ensem
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Figure 6 (a) SAXS patterns for disp
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Figure 8 The gold nanocrystal film
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of the stabilizing ligand, and the
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successfully modeled the 2D island
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2. Steric Stabilization and a Soft
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are fully extended. Moving away fro
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Figure 11 High-resolution SEM image
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Figure 13 (A) Transmission electron
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function of the density of localize
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Figure 15 High-resolution SEM image
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thiol-capped nanocrystals [2]. The
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41. Ackerson, B.J. Nature 1993, 365
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with the effect of the particle com
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Figure 1a shows the surface plasmon
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Figure 2 (a) Ultraviolet-visible ab
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agents [34]. The short-wavelength b
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Figure 4 (a) Plot of the plasmon ab
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the framework of traditional Mie’
Page 447 and 448:
show that effects due to the surrou
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is located at the position of the g
Page 451 and 452:
Page 453 and 454:
Figure 8 Ultraviolet-visible absorp
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laser pulses while being mixed in t
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Figure 10 shows HR-TEM images of go
Page 459 and 460:
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final irradiation product. At the s
Page 463 and 464:
following the laser excitation appe
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36. Papavassiliou, G.C. Prog. Solid
Page 467 and 468:
particles to expand. Because the he
Page 469 and 470:
was frequency doubled in a 1-mm B-
Page 471 and 472:
Figure 2 Frequency of the acoustic
Page 473 and 474:
Figure 3 Change in radius (DR/R) ve
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In this model, the electrons couple
Page 477 and 478:
Figure 5 Transient bleach data for
Page 479 and 480:
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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