Letter pubs.acs.org/NanoLett
Direct Mapping of Hot-Electron Relaxation and Multiplication Dynamics in PbSe Quantum Dots L. Miaja-Avila,†,‡ J. R. Tritsch,† A. Wolcott,§ W.-L. Chan, C. A. Nelson, and X.-Y. Zhu* Department of Chemistry and Biochemistry, University of Texas, Austin, Texas 78712, United States S Supporting Information *
ABSTRACT: How hot electrons relax in semiconductor quantum dots is of critical importance to many potential applications, such as solar energy conversion, light emission, and photon detection. A quantitative answer to this question has not been possible due in part to limitations of current experimental techniques in probing hot electron populations. Here we use femtosecond time-resolved twophoton photoemission spectroscopy to carry out a complete mapping in time- and energy-domains of hot electron relaxation and multiexciton generation (MEG) dynamics in lead selenide quantum dots functionalized with 1,2-ethanedithiols. We find a linear scaling law between the hot electron relaxation rate and its energy above the conduction band minimum. There is no evidence of MEG from intraband hot electron relaxation for excitation photon energy as high as three times the bandgap (3Eg). Rather, MEG occurs in this system only from interband hot electron transitions at sufficiently high photon energies (∼4Eg). KEYWORDS: Hot electrons, quantum dots, multiexciton generation, carrier multiplication excitation. Here, we show the realization of this “ideal” experiment using femtosecond time-resolved two-photon photoelectron spectroscopy (TR-2PPE) and the model system of lead selenide (PbSe) QD thin films. We choose PbSe QDs because of extensive research on MEG in this system.19−21,23,28,30 A schematic representation of TR-2PPE is shown in Figure 1. A pump laser pulse (hν1) creates a hot electron−hole pair; after a controlled time-delay, a probe laser pulse (hν2) ejects the excited electron, which is detected by an electron energy analyzer. Because the photoemission cross section is relatively insensitive to hot electron energy, the TR-2PPE spectrum represents the energy and population of hot electrons at each pump−probe delay (td), thus providing a complete mapping in time and energy domains of electron relaxation dynamics.31−33 Panels a−c in Figure 2 show gray scale plots of TR-2PPE spectra for a PbSe QD thin film with 1,2-ethanedithiol (EDT) capping molecules34 and an optical gap of Eg = 0.70 eV (see Supporting Information Figure S1). Each spectrum shows hot electron population as they relax in energy with td. The initial hot electron energy increases with hν1 and the excess photon energy is distributed nearly equally between the valence and the conduction band. The electron kinetic at each hν1 decreases monotonically to the bottom of the conduction band (1Se) with increasing td; Note that the 1Pe level (∼0.1 eV above 1Se) is barely resolved in absorption spectrum (Supporting Information Figure S1) and cannot be resolved in TR-2PPE measurement.
H
ot electron relaxation in semiconductor quantum dots (QDs) has been a subject of considerable interest due in a major part to potential applications in optoelectronics.1−5 Early considerations of electronic quantization have led to the proposal of slowed electron−phonon scattering in QDs,6 but experiments have revealed ultrafast hot electron relaxation times in colloidal II−VI7−9 and IV−VI10−13 QDs. This ultrafast relaxation has been attributed to an Auger-like mechanism14 in which the excess electron energy is transferred to that of a hole.15−17 The hot hole in the valence band with greater density-of-states (DOS) then relaxes efficiently via phonon emission. Indeed, much longer hot electron lifetimes become possible when the Auger mechanism and an additional energy transfer to molecular vibrations are both minimized in core− shell QDs.18 The dynamics of hot electrons significantly above the conduction band minimum (CBM = E1S) are particularly important to multiexciton generation (MEG) in which the excess energy of the electron (hole) is used to generate multiple electron−hole pairs.19−23 Multiexciton generation may find applications in highly efficient solar cells24 and photodetectors.25 While enhanced Coulomb interactions in nanoconfined systems26 are believed to lead to efficient MEG in QDs,19,20 there are also evidences that highly excited electron/ holes in QDs behave essentially bulklike.27−29 A major obstacle to the quantitative understanding of MEG has been the limitation of commonly used absorption and fluorescence techniques that rely on distinct spectroscopic signatures existing only for the two lowest excited electron states (1Se and 1Pe).8,18−23 Ideally, one would like to determine the relaxation rates of all excited electrons with energies ranging from the CBM to the highest level accessed by optical © 2012 American Chemical Society
Received: December 20, 2011 Revised: February 12, 2012 Published: February 15, 2012 1588
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phonon scattering and Auger e−h energy transfer. In the phonon mechanism, Γ is proportional to the electron density of states (DOS), which in the parabolic approximation is DOSe ∝ (Ee − ECBM)0.5. While on the surface, this prediction disagrees with the linear scaling law, but deviation from the parabolic band is expected at electron energies high above the CBM. This may bring expectations from the phonon mechanism closer to experimental data. In the Auger mechanism, Γ is proportional to both DOSe and that of the hole (DOSh). If we assume symmetric conduction/valence bands and correlated hot electron/hole cooling in the excitonic state, we can approximate the hot electron relaxation rate as Γ ∝ (Ee − ECBM)0.5 (EVBM − Eh)0.5 ≈ (Ee − ECBM), where EVBM is the valence band maximum. The Auger mechanism suggested previously15−17 seems to agree with our experimental results. However, the DOS far above (below) the CBM (VBM) is hardly parabolic and a linear scaling law is not proof for an Auger mechanism. Thus, a quantitative interpretation of the linear scaling requires a high-level theoretical investigation, which must take into account a realistic description of band structure far above the conduction band minimum and an accurate treatment of the many-body scattering problem for hot electrons. Such a theory is beyond the scope of the present study. TR-2PPE spectra in Figure 2 show no evidence of MEG for hν1 as high as 2.2 eV (>3Eg). In MEG, the excess energy in a hot electron (hole) should decrease by a quantized amount (∼Eg) to create a new electron−hole pair at the band edges. This is not observed in 2PPE spectra. Primarily, there is an absence of population near the CBM on the short time scale (4Eg), we find direct evidence of MEG. Unlike the simple spectral feature attributed to intraband relaxation at lower hν1, the spectrum with hν1 = 2.85 eV (Figure 3a) shows rich features at both positive and negative time-delays. For td < 0, there is constant photoelectron signal at E − E1S ∼ 0.1−0.2 eV (feature C), indicating photoexcitation and ionization by the same laser pulse (hν1 = 2.85 eV). As expected, this constant spectral feature persists when we block the probe laser beam (hν2). This feature is much enhanced near td = 0 (feature B in Figure 3a on the negative td side) when there is overlap between pump and probe laser pulses. We assign this spectral feature to the photoexcitation of a resonant hot electron state above the first conduction band, as schematically shown in Figure 4a. This resonant state can be populated by either hν1 = 2.85 eV or hν2 = 4.28 eV via different initial states. Further support for this interpretation can be found near td = 0 on the positive side. Photoexcitation by hν1 = 2.85 eV and ionization by hν2 = 4.28 eV leads to a short-lived peak (feature A), which is ∼1.3 eV above spectral features B or C. Since the energy difference between A and B corresponds to the difference in photon energy (hν2 − hν1), these two peaks come from the same hot electron state (Figure 4a). In bulk PbSe, the first conduction band is at the L point and in the same momentum space there is a second conduction band at ∼1.4 eV above the bottom of the first conduction band.35 This agrees with the energetic position of the hot electron resonance (E − E1S ∼ 1.4 eV). We remove the constant background (C) in 2PPE spectra due to two-photon photoemission from the pump laser pulse
Figure 1. Probing hot electron dynamics in QDs by TR-2PPE. EF and EV: Fermi and vacuum levels. The pump (hν1) and probe (hν2) laser pulses are time delayed (td).
Figure 2. Gray-scale plots of TR-2PPE spectra with three different excitation photon energies: (a) hν1 = 1.40, (b) hν1 = 1.80, and (c) hν1 = 2.20 eV. The probe photon energy is hν2 = 4.28 eV in all experiments. Panel (d) compares mean electron energy from experiments (symbols) with simulations based on electron relaxation rate of Γ ∝ (Ee − ECBM) (solid curves) and Γ ∝ (Ee − ECBM)0.5 (dashed curves).
The energy decay rate, that is, the negative slope in each spectrum in Figure 2a−c, decreases as the electron energy decreases. We carry out analysis using a cascading model in which an electron at a higher energy level can decay into a lower level with an energy-dependent relaxation rate, Γ (see Supporting Information). We find the best fit with a linear scaling law in the relaxation rate with electron energy, Γ ∝ (Ee − ECBM). Figure 2d shows the excellent agreement between the experimental values of mean electron energy ⟨Ee − ECBM⟩ (symbols) from TR-2PPE spectra with simulations based on Γ ∝ (Ee − ECBM) (solid curves). For comparison, simulations from Γ ∝ (Ee − ECBM)0.5 (dashed curved) deviate significantly from experimental data. To understand the linear scaling law discovered here, we consider two mechanisms for intraband electron relaxation: 1589
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shows clearly a change in decay rate (slope) as A becomes D. The ultrafast decay in electron energy also leads to an increase in photoemission intensity: the intensity of peak D is ∼110% of that of peak A. We take the quantized loss of hot electron energy and the corresponding increase in electron population as direct evidence for MEG, following which we see only slower energy relaxation due to intraband relaxation. To ensure that our measurements are in the single excitation region, we show the independence of hot electron dynamics on excitation laser fluence over two-orders of magnitude, Figure 3d. The observed MEG process is summarized in Figure 4 (td > 0). Absorption of hν1 = 2.85 eV excites a hot electron to the second conduction band. This is followed by interband transition to the lower conduction band and the concurrent excitation of a second electron-hole pair, that is, MEG. Compared to the commonly assumed intraband mechanism, the interband MEG process permits easier matching of energy and momentum simultaneously. We use band structure in this discussion as highly excited electrons in QDs are not subject to quantum confinement and are essentially bulklike.27 The estimated MEG yield of ∼1.1 exciton per photon at hν1 = 2.85 eV is similar to the reported MEG yield in bulk PbSe.28 Beard and co-workers reported the absence of significant MEG yield in EDT treated PbSe QDs but significant MEG yield with other chemical treatments,36 particularly a unique combination of EDT and hydrazine treatment.21 We have attempted TR2PPE measurements on PbSe QD films with other chemical treatments (hydrazine, ethanol, methylamine, EDT/hydrazine, etc.); unfortunately, these samples were too unstable under vacuum conditions to allow for unambiguous TR-2PPE measurements. Note that the TR-2PPE technique tracks the excited electron by ionizing the excitonic state (by hν2).37 There is little information on the excited hole besides the exciton binding energy. In summary, we apply time-resolved 2PPE spectroscopy to directly determine hot electron relaxation and multiplication dynamics in EDT passivated PbSe QDs. We find a linear scaling law between hot electron relaxation rate and its energy above the conduction band minimum. We show the absence of MEG from intraband hot electron relaxation for excitation photon energy as high as 3Eg but a low MEG yield (∼1.1 exciton per photon) from interband hot electron transitions at sufficiently high photon energies (∼ 4Eg) in this system. Methods. Details on sample preparation and TR-2PPE experiments can be found in the Supporting Information. Briefly, we prepare PbSe QD thin films in an inert N2 environment by controlled dip-coating of a gold surface in a solution of oleic acid functionalized QDs. The film is then treated in a solution of 1,2-ethanedithiol (EDT) to remove and replace the insulating oleic acid molecules. The EDT functionalized PbSe QD thin film sample is transferred under inert atmosphere into an ultrahigh vacuum chamber (1 × 10−10 Torr) for TR-2PPE measurements. Pump and probe pulses are generated with a femtosecond Ti:Sapphire laser system (Coherent Mira-OPO, 76 mHz). After variable optical-delay (td), the pump and probe laser pulses (temporal width ≤100 fs) are spatially overlapped and focused (∼100 μm2 spot size) onto the sample. The pulse energy density is below 0.01 mJ/cm2 for both pump and probe beams, corresponding to an average photoexcitation of ≪0.1 electron−hole pair per quantum dot per laser pulse. The photoemitted electrons are detected through a hemispherical electron energy analyzer (VG-Scienta R3000). The optical absorption spectrum of the EDT
Figure 3. (a) Pseudocolor representation of TR-2PPE spectra for PbSe QD films at an excitation photon energy of hν1 = 2.85 eV and a probe photon energy of hν2 = 4.28 eV. (b) The same data as in (a) with the spectral feature at negative time delays subtracted. (c) Mean kinetic energy of the photoelectrons as a function of pump−probe delays obtained from panel (b). (d) Mean kinetic energy of the photoelectrons as a function of (positive) pump−probe delays for the indicated pump laser pulse fluences (6 × 1013 to 5.6 × 1015 photons/ cm2).
Figure 4. Schematic illustration of the TR-2PPE process at different pump−probe delays: td ≤ 0 (left) and td > 0 (right). The photoelectron signals (A, B, C, D) corresponding to spectral features in Figure 3 are indicated.
only by subtracting the spectrum at each td by an averaged spectrum at long negative time delays. The result is shown in Figure 3b, which clearly reveals the short-lived resonant features of A and B on two sides of td = 0. For td > 0, the decay of the initially excited hot electrons is not monotonous. Rather, the hot electron from the resonant state first decays with an ultrafast lifetime of ∼100 fs in nearly a quantum step to give spectral feature D at ∼0.9 eV below peak A. The quantized energy relaxation step is most obvious in the discontinuity in the photoelectron intensity between A and D; this is in stark contrast to the continuous hot electron relaxation attributed to the cascading intraband mechanism at lower exciting photon energies (see Figure 2). The change in relaxation dynamics is also obvious in Figure 3c (mean kinetic energy vs td), which 1590
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functionalized PbSe QD film shows a first exciton transition at Eg = 0.70 ± 0.02 eV (Figure S1 in Supporting Information). We use excitation photon energies in the range of 2−4Eg (hν1 = 1.40−2.85 eV).
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ASSOCIATED CONTENT
S Supporting Information *
Materials and methods, Figures S1−S5. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Addresses ‡
Quantum Electronics and Photonics Division, NIST, Boulder, CO 80305, United States. § Columbia University, Department of Chemistry, New York, NY 10027, United States. Author Contributions †
These two authors contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Department of Energy under Grant ER46673 DE-SC0001928. Partial support by the Welch Foundation under Grant F-1726 and the Southwest Academy of Nanotechnology (SWAN) are also acknowledged. C.A.N. acknowledges Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF, made possible in part by the American Recovery and Reinvestment Act of 2009) administered by ORISE-ORAU under contract number DEAC05-06OR23100. A.W. acknowledges support by an ACC-F award through the National Science Foundation (CHE No. 0937032).
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