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3Fine Structure and PolarizationProperties of Band-Edge Excitonsin Semiconductor NanocrystalsAl. L. EfrosNaval Research Laboratory, Washington, D.C., U.S.A.I. INTRODUCTIONIt has been more than 10 years since the seminal paper of Bawendi et al. [1] onthe resonantly excited photoluminescence (PL) in CdSe nanocrystals (NCs).This first investigation showed that in the case of resonant excitation, the PLfrom CdSe NCs shows a fine structure that is Stokes shifted relative to thelowest absorption band. The fine-structure PL consists of a zero-phonon line(ZPL) and longitudinal optical (LO) phonon satellites. The lifetime of PL atlow temperatures is extremely long, on the order of 1000 ns. All of the majorproperties of the resonant PL in CdSe NCs have been described using thedark/bright-exciton model [2,3].In this chapter, we review the dark/bright-exciton model and summarizethe results of realistic multiband calculations of the band-edge exciton finestructure in quantum dots of semiconductors having a degenerate valenceband. These calculations take into account the effect of the electron–holeexchangeinteraction, nonsphericity of the crystal shape, and the intrinsichexagonal lattice asymmetry. We describe also the effect of an externalmagnetic field on the fine structure, the transition oscillator strengths, andpolarization properties of CdSe NCs. The results of these calculations areused to described unusual polarization properties of CdSe NCs, a size-dependentStokes shift of the resonant PL, a fine structure in absorption, and theCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
formation of a long-lived dark exciton. Particularly strong confirmation ofour model is found in the magnetic field dependence of the dark-exciton decaytime [2], magnetic circular dichroism of CdSe NCs, and the polarization of theCdSe NC PL in a strong magnetic field.The chapter is organized as follows. In Section II, we calculate theenergy structure of the band-edge exciton and obtain selection rules andtransition oscillator strengths. In Section III, the effect of an externalmagnetic field on the fine-level structure and transition oscillator strengthsis discussed. The polarization properties of the NC PL, Stokes shift of theresonant PL, field-induced shortening of the dark-exciton lifetime, magneticcircular dichroism, and PL polarization in strong magnetic fields are consideredwithin the developed theoretical model in Section IV. The results aresummarized and discussed in Section V.II.FINE STRUCTURE OF THE BAND-EDGE EXCITONIN CdSe NANOCRYSTALSA. Band-Edge Quantum-Size LevelsIn semiconductor crystals that are smaller than the bulk exciton Bohr radius,the energy spectrum and the wave functions of electron–hole pairs can beapproximated using the independent quantization of the electron and holemotions (the so-called strong confinement regime [4]). The electron and holequantum confinement energies and their wave functions are found in theframework of the multiband effective mass approximation [5]. The formalprocedure for deriving this method demands that the external potential besufficiently smooth. In the case of nanosize semiconductor crystals, thisrequirement leads to the condition 2a >> a 0 , where a is the crystals radiusand a 0 is the lattice constant. In addition, the effective mass approximationholds only if the typical energies of electrons and holes are close to the bottomof the conduction band and to the top of the valence band, respectively. Inpractice, this means that the quantization energy must be much smaller thanthe energy distance to the next higher (lower)-energy extremum in the conduction(valence) band.In the framework of the effective mass approximation, for sphericallysymmetric NCs having a cubic lattice structure, the first electron quantumsizelevel, 1S e , is doubly degenerate with respect to the spin projection. Thefirst hole quantum-size level, 1S 3/2 , is fourfold degenerate with respect to theprojection (M) of the total angular momentum, K, (M = 3/2, 1/2, 1/2, and3/2) [6,7]. The energies and wave functions of these quantum-size levels canCopyright 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
Page 70 and 71: Figure 30 (a,b) Schematics illustra
Page 72 and 73: Slow, controlled precipitation of h
Page 74 and 75: Figure 34 Schematic illustrating th
Page 76 and 77: Figure 36 Transmission electron mic
Page 78 and 79: achieving biological compatibility
Page 80 and 81: 47. Yu H.; Gibbons P.C.; Kelton K.F
Page 82 and 83: 2Electronic Structure inSemiconduct
Page 84 and 85: Figure 2 (a) Simple model of a nano
Page 88 and 89: electron and hole to be treated as
Page 90 and 91: independently, Eq. (13) is commonly
Page 92: a better description of the bulk ba
Page 95 and 96: investigated. For optical experimen
Page 97 and 98: Figure 4 (a) Absorption (solid line
Page 99 and 100: Figure 6 Normalized PLE scans for s
Page 101 and 102: 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: 69. Gaponenko, S.V.; Woggon, U.; Sa
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 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
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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
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
Page 345 and 346:
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
Page 379 and 380:
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
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
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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
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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
Page 427 and 428:
function of the density of localize
Page 429 and 430:
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
Page 435 and 436:
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
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
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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:
Page 461 and 462:
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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