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decreased for the majority of NCs and a gradual growth of the maximumallowed polarization degree from 0.625 to 0.75 can occur. Precisely suchbehavior is observed in Fig. 9c, where the low-temperature polarization firstsaturates near f0.6 and then grows slowly to f0.73 at the highest fields.This model [Eq. (61)] provides an excellent fit to the measured PLpolarization data [36], as illustrated in Fig. 10, which displays experimentalresults of NCs of three different sizes (T = 1.45 K) along with results of themodeling for 57-A˚ NCs. Interestingly, all data are roughly equivalent; thisstems from the balancing role played by s nr and the exchange interaction g[see Eq. (51)] both of which decrease with increasing NC size. The best-fitvalues of g ex,2 and s nr are shown in the inset. The extracted exciton g factorsare close to 0.9, which is much smaller than the value calculated for thedark-exciton state.V. DISCUSSION AND CONCLUSIONSWe have shown that the dark/bright-exciton model presented in this chapterdescribes very well many important properties of the band-edge PL in CdSeNCs. The phenomena analyzed here include the fine structure of the PLexcitation spectra, a Stokes shift of the resonant PL, the shortening of theradiative decay time in a magnetic field, the polarization memory effect, thetransition from the circular polarized to the linear polarized PL induced bychanging the NC shape, and PL polarization in strong magnetic fields. Somequantitative disagreements between experimental data and the theory aremainly due to some oversimplifications in the theoretical approach. Forexample, the theory considered here does not take into account the nonparabolicityof the conduction and the valence bands. In small NCs, thenonparabolicity can strongly modify the level structure, the electron–holewave functions, the transition oscillator strength, the overlap integrals, theelectron–hole exchange interactions, g factors, and so forth. All of thesequantities, in principle, can be better described in the framework of a morerigorous approach.The dark/bright-exciton model described in this chapter can also beapplied to NCs with other than CdSe compositions. It was used, for example,to described the size-dependent Stokes shift in InAs NCs [41]. The penetrationof the electron wave function under the barrier was important in InAs NCs forquantitative description of this dependence.After a decade of studies and despite all the success of the dark/brightexcitonmodel, the PL in CdSe NCs still presents several unresolved puzzles.One of the unresolved issues is the temperature-dependent Stokes shiftCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
observed in one of the first studies of small-size CdSe NCs [42,43]. This effectmay be due, for example, to the formation of an exciton–polaron that can be asource of an additional Stokes shift of the luminescence [38]. However, the‘‘polaronic’’ model does not explain the presence of a zero LO phonon line inthe absence of an external magnetic field. This line is strongly activated by thetemperature. The effect of the temperature on the relative intensities of zeroand phonon-assisted lines and PL decay times is very similar to the effect ofan external magnetic field [42,43]. Interaction with paramagnetic defects inthe lattice or surface dangling bonds can also provide an additional mechanismfor the dark-exciton recombination. The spins of these defects cangenerate strong effective internal magnetic fields (potentially several tens oftesla) and induce spin-flip-assisted transitions of the F2 state, enabling thezero-phonon recombination. The electron interaction with these spins canalso lead to the magnetic polaron formation, which may explain the temperature-dependentStokes shift.The electron-dangling bond spin interactions can also explain theunexpected temperature behavior of the dark-exciton g factor [36]. Similarto diluted magnetic semiconductors, the change in g ex in CdSe NCs can beinterpreted as arising from some exchange interaction. We therefore suggestthat temperature-dependent g factors in NCs may be due to the interactions ofuncompensated NC surface spins with photogenerated carriers within theNCs.ACKNOWLEDGMENTSI would like to thank my long-term collaborators A. I. Ekimov, A. Rodina,M. Rosen, M. G. Bawendi, D. Norris, M. Nirmal, K. Kuno, E. Johnston-Halperin, D. D. Awschalom, S. A. Crooker, P. Alivisatos, A. Nozik, and L.Brus for challenging and stimulating discussions which provided strongmotivation for theoretical studies reviewed in this chapter. I also thank M.Nirmal for providing figures. This work was supported by the Office of NavalResearch.APPENDIX: CALCULATION OF THE HOLE g FACTORThe expression for the g factor of a hole localized in a spherically symmetricpotential was obtained by Gel’mont and D’yakonov [29]:g h ¼ 4 5 c 1I 2 þ 8 5 cðI 41 I 2 Þ þ 2j 15 I 2ð62ÞCopyright 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
Page 103 and 104: Figure 10 Theoretically predicted p
Page 105 and 106: Figure 12 Schematics depicting the
Page 107 and 108: Figure 14 Calculated band-edge exci
Page 109 and 110: Figure 15 Absorption (solid line) a
Page 111 and 112: Figure 18 (a) Calculated band-edge
Page 113 and 114: IV.BEYOND CdSeA. Indium Arsenide Na
Page 115 and 116: the six-band Luttinger Hamiltonian.
Page 117 and 118: 11. Norris, D.J.; Efros, Al.L.; Ros
Page 119 and 120: 69. Gaponenko, S.V.; Woggon, U.; Sa
Page 121 and 122: formation of a long-lived dark exci
Page 123 and 124: 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: One must also account for the influ
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 and 176: continuous spectral tunability over
Page 177 and 178: function and envelope function mome
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
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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
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/
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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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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
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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
Page 445 and 446:
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
Page 457 and 458:
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
Page 475 and 476:
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
Page 481 and 482:
that the particles with >80% Au hav
Page 483 and 484:
3. Del Fatti, N.; Valle´e, F.; Fly
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