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Similar expressions are used for tunneling off the dot, G i (n), where n is thenumber of excess electrons on the QD. T i (E) is the tunneling matrix elementacross junction i. We do not explicitly calculate T i (E) but, rather, assign eachjunction with a phenomenological ‘‘tunneling resistance’’ parameter [7], R ifT i (E) 1 . We take into account the dependence of T i (E) on applied bias due tothe reduction of the average tunneling barrier height using the WKB approximation[73,74]. The tunneling resistances thus determine the averagetunneling rate between the two junctions, R 1 /R 2 = G 2 /G 1 . D i and D d are thedensity of states in the electrode and the dot, respectively, E i and E d are thecorresponding Fermi levels whose relative positions after tunneling, [E d (n F 1)E i (n)], depend on n, C 1 , C 2 , and the level spectrum, and f(E) is the Fermifunction. The condition for resonant tunneling is the lineup of the Fermilevel of the dot after tunneling (on or off the dot), with the Fermi level of theouter electrode before tunneling. D d is taken to be proportional to a set ofbroadened discrete levels corresponding to the positions of the discrete energylevels.First, one determines the probability distribution of n, P(n), from thecondition that at steady state, the net transition rate between two adjacent QDcharging states is zero [56]:PðnÞ½G þ i ðnÞ þ Gþ 2 ðnÞŠ ¼ Pðn þ 1Þ½G i ðn þ 1Þ þ G 2 ðn þ 1ÞŠ : ð3ÞThe tunneling current is then calculated self-consistently fromIðVÞ ¼ e X nPðnÞ½G þ 2 ðnÞG 2 ðnÞŠ ¼ e X nPðnÞ½G 1 ðnÞ G þ 1 ðnÞŠ ð4ÞAs a working example for the purpose of our explanation, we assumethat our QD has a bandgap E g =1 eV, with two discrete states in the VB andCB. The ground states are twofold spin degenerate, whereas the excited stateshave a fourfold degeneracy (including spin). The spacings between the states,D VB and D CB , are 0.3 and 0.4 eV for the VB and CB, respectively. In thepresent simulation, for simplicity, we did not allow for simultaneous tunnelingthrough the VB and CB states. The I–V curves are calculated as describedearlier, and the tunneling conductance curves (dI/dV versus V), are obtainedby differentiation.We present in Fig. 3 several limiting situations, where the relevantfactors to describe the junction asymmetry are the ratios C 1 /C 2 and R 1 /R 2 . Inall of the curves, the current in the bandgap region around zero bias is suppressed.However, considerable differences can be seen in the peak structureafter the onset of the tunneling current. In Figs. 3a and 3b, C 1 /C 2 = 0.1 and,therefore, most of the bias drops at junction 1. In Fig. 3a, R 1 /R 2 = 0.1, and thecalculated dI/dV curve exhibits resonant tunneling accompanied by single-Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
electron charging. In both positive and negative bias, a doublet of peaks isobserved at the onset of the current. The doublet corresponds to charging ofthe first CB and VB states, respectively. This can be clearly discerned from therepresentation of P(n) versus bias shown (in gray scale) above the dI/dVcurves. The intradoublet spacing corresponds to the single-electron chargingenergy, E c , and the spacing between the first VB and CB peaks is nearly E g +E c , up to a small correction due to the voltage division. At higher positive bias(V B > 1 V), peaks arising from tunneling through the fourfold degenerateexcited CB state are seen. The first small peak corresponds to a situationwhere the most probable n is still 2, but the second electron tunnels throughthe excited state, rather than the ground state. The magnitude of this peak isreduced when the ratio R 1 /R 2 is decreased. The spacing between the secondand third peaks is the interlevel spacing modified slightly by voltage division.The following fourfold multiplet corresponds to sequential addition ofelectrons to the excited state, with intramultiplet spacing corresponding toE c . Similar behavior is observed in the negative bias side, with tunnelingthrough the VB states.A very different peak structure is seen for the opposite situation whereR 1 /R 2 = 50 (Fig. 3b). Here, charging effects are nearly suppressed; only a hintof the second peak in the doublets can be seen. The next large peak, at V Bf1 V corresponds to tunneling through the excited state, with the spacing to thefirst large peak equal to the interlevel separation. The most probable n isessentially zero [see the distribution P(n)], reflecting the situation that (atpositive bias) an electron that tunnels onto a CB state through J 1 rapidlyescapes through J 2 . Again, the negative bias side corresponds to similarbehavior for tunneling through the VB states.The cases where C 1 /C 2 = 0.5 are shown in Figs. 3c and 3d, with R 1 /R 2corresponding to the same ratios as in Figs. 3a and 3b, respectively. The abovediscussion holds also for both these cases, where charging effects can beclearly observed in Fig 3c, where R 1 /R 2 = 0.1, and are nearly suppressed inthe opposite case (Fig. 3d). However, the peak spacing becomes larger due tothe enhanced effect of voltage division [Eq. (1)].III.CORRELATION BETWEEN OPTICAL AND TUNNELINGSPECTRA OF InAs NANOCRYSTAL QDsThe first detailed investigation employing a combined optical-tunneling approachwas performed by us on InAs nanocrystal QDs [12]. InAs is an almostideal system for such a study. It belongs to the family of tetrahedral semiconductors,and colloidal techniques allow for the preparation of nanocrystalsthat are nearly spherically shaped, over a broad range of sizes withCopyright 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
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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
Page 261 and 262: dominates, the mobility is often fi
Page 263 and 264: where the constant A and the temper
Page 265 and 266: components of modulation which are
Page 267 and 268: nanocrystals [41], understanding ph
Page 269 and 270: and ionization potential through tw
Page 271 and 272: quantum dots. Furthermore, because
Page 273 and 274: For many applications, a host mater
Page 275 and 276: form blends with morphologies that
Page 277 and 278: Figure 11 Photoluminescence efficie
Page 279 and 280: Figure 12 (a) Room-temperature PIA
Page 281 and 282: discussed briefly in Section IV. Ch
Page 283 and 284: dithiolates to thiol-terminated DNA
Page 285 and 286: Films of passivated CdSe nanocrysta
Page 287 and 288: Figure 16 Photocurrent action spect
Page 289 and 290: decay with stretched exponential ki
Page 291 and 292: siderably larger than might be esti
Page 293 and 294: dispersing CdSe nanocrystal chromop
Page 295 and 296: memory and charge storage effects [
Page 297 and 298: all) of the optically excited elect
Page 299 and 300: composites of nanocrystals and conj
Page 301 and 302: 55. Asbury, J.B.; Hao, E.C.; Wang,
Page 303 and 304: 108. Morgan, N.Y.; Leatherdale, C.A
Page 305 and 306: The approaches to fabrication of se
Page 307 and 308: Figure 1 Experimental realization o
Page 309 and 310: Due to this voltage division, the m
Page 311: Figure 3 Simulated tunneling spectr
Page 315 and 316: Figure 5 shows the typical features
Page 317 and 318: Figure 7 Map of levels for InAs nan
Page 319 and 320: Figure 8 Scanning electron microsco
Page 321 and 322: D CB = 0.31 eV is thus obtained. On
Page 323 and 324: Figure 11 Correlation of optical an
Page 325 and 326: atomistic approach based on pseudop
Page 327 and 328: charging indicated that the tunneli
Page 329 and 330: capacitance values were also kept t
Page 331 and 332: could not be detected in the QD/DT/
Page 333 and 334: Figure 18 Tunneling conductanceF sp
Page 335 and 336: data in the inset of Fig. 19 repres
Page 337 and 338: corresponding to the s-like wave fu
Page 339 and 340: 7. Grabert, H.; Devoret, M.H., Eds.
Page 341 and 342: 66. Su, B.; Goldman, V.J.; Cunningh
Page 343 and 344: dimensional confinement are created
Page 345 and 346: Figure 1 Transmission electron micr
Page 347 and 348: The room-temperature absorption and
Page 349 and 350: narrower in samples with larger mea
Page 351 and 352: GaInP 2 QDs from a plot of the squa
Page 353 and 354: crystal, indicating lattice-matched
Page 355 and 356: Figure 5 Evolution of Stranski-Kras
Page 357 and 358: Figure 7 Photoluminescence spectra
Page 359 and 360: Figure 8 Photoluminescence spectra
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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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
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Figure 23 Change of the PL intensit
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(viz. the absorbed light intensity)
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Figure 25Impact ionization in QDs.m
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prevent electron-hole recombination
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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’
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show that effects due to the surrou
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is located at the position of the g
Page 451 and 452:
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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
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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
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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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