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Single Nanowire Extinction Spectroscopy Jay Giblin, Felix Vietmeyer, Matthew P. McDonald, and Masaru Kuno* Department of Chemistry and Biochemistry, University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
bS Supporting Information ABSTRACT: Here we show the first direct extinction spectra of single one-dimensional (1D) semiconductor nanostructures obtained at room temperature utilizing a spatial modulation approach.1 For these materials, ensemble averaging in conventional extinction spectroscopy has limited our understanding of the interplay between carrier confinement and their electrostatic interactions.2 4 By probing individual CdSe nanowires (NWs), we have identified and assigned size-dependent exciton transitions occurring across the visible. In turn, we have revealed the existence of room temperature 1D excitons in the narrowest NWs. KEYWORDS: CdSe nanowires, six-band effective mass model, spatial modulation, single molecule detection, dielectric contrast, excitons
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o properly describe the optical properties of low-dimensional semiconductors, both carrier confinement effects and their electrostatic interactions must be taken into account. The latter include the direct Coulomb interaction between the electron and hole, self-interactions with image charges (dielectric confinement), and indirect interactions with oppositely signed images.5 11 In one-dimensional (1D) systems, the Coulomb attraction can transfer a significant amount of oscillator strength to excitonic transitions, suppressing the appearance of Van Hove singularities in the extinction.12,13 Furthermore, this effect is enhanced by strong dielectric contrast, leading to 1D excitons with binding energies exceeding 100 meV.9 11 This suggests that the room-temperature optical extinction of colloidal NWs should be dominated by 1D exciton resonances. To date, the identification of such 1D transitions in ensemble NW spectra has been plagued by heterogeneous broadening from unavoidable size distributions. Heterogeneous broadening can be overcome by examining single wires. Measuring the extinction of single entities can be approached indirectly or directly. Indirect techniques include photoluminescence excitation spectroscopy14,15 and photothermal heterodyne imaging.16 Direct techniques include autobalanced photodetection17 and spatial modulation.1,18,19 In all cases, determining the absorption of single nanoparticles is inherently difficult because of their small extinction cross sections (σext). To illustrate, experimentally measured CdSe NW σext-values range from 10 12 to 10 10 cm2 μm 1.20 As such, the power of a laser focused to a diffraction-limited spot on a single NW decreases by only ∼0.01 1% due to NW extinction. In what follows, we present the first single particle extinction spectra of nonmetal nanomaterials with σext-values as small as ∼1.1 10 11 cm2 μm 1. Within the NW size regime studied, the major contribution to σext is absorption since based on prior NW scattering calculations,21 scattering accounts for less than 5% of σext-values. For completeness though, we refer to σext rather than σabs in what follows. As shown in Figure 1a, two microscope objectives are used; one to focus the output of a tunable laser onto the sample and one to collect the transmitted light. A piezo stage varies the nanowire’s position sinusoidally relative to the r 2011 American Chemical Society
laser spot while modulated transmitted light is detected with an autobalanced photodiode coupled to a lock-in amplifier. Single wire extinction spectra are taken using light polarized parallel to the wire’s growth axis. Figure 1b illustrates structure that emerges in the extinction spectra of single CdSe NWs (a ∼ 3.7 nm). Namely, three distinct peaks labeled R, γ, and δ are apparent. Note that the plot’s y-axis has σext units (cm2 μm 1), illustrating the ability of the spatial modulation technique to quantitatively determine a wire’s extinction cross section across the visible.1,22 For comparison purposes, the extinction spectrum of the corresponding ensemble is shown using a solid red line. It is apparent that the γ transition is hidden in the ensemble spectrum while R and δ correspond to the broadened features at ∼1.8 and ∼2.0 eV, respectively. For both extinction and emission, the range of peak positions found in our single NW spectra corresponds well with the inhomogeneous linewidths typically found in ensemble measurements.23,24 This illustrates the innate ability of single particle measurements to dramatically improve the resolution of extinction experiments by eliminating inhomogeneous broadening and simultaneously opens the door to more quantitative studies. Using three NW ensembles with mean radii (Æaæ) of 2.5, 3.7, and 5.0 nm, we reveal in Figure 2 the size-dependent extinction spectra of single CdSe NWs. For each trace, approximate sizing is provided by comparing the spectral peak of its first optical transition to a sizing curve assembled from ensemble literature data23,24,3 (Supporting Information Figure S1). Spectral shifts of 60 170 (27 155) meV in the R (emission) position relative to CdSe’s bulk bandgap (Eg = 1.74 eV at 300 K) are observed between the largest (a ∼ 5.0 nm) and smallest (a ∼ 2.6 nm) wires. Both the extinction and the emission spectra (inset) blueshift with decreasing size, suggesting the influence of confinement effects. To better quantify the size-dependent progression of excited states, single wire extinction spectra are fit to a sum of Gaussians. Received: May 18, 2011 Revised: July 15, 2011 Published: July 19, 2011 3307
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Figure 2. Size-dependent progression of single CdSe NW extinction spectra (offset for clarity). The inset shows the corresponding emission peak position as a function of NW radius.
Figure 1. (a) Schematic outlining the spatial modulation spectroscopy approach along with a high-resolution TEM image of an individual CdSe nanowire. (b) Extinction spectrum of a single CdSe NW (open circles) with three clear transitions labeled R, γ, and δ. The underlying dashed line is obtained by fitting the data to a sum of Gaussians. The wire’s corresponding emission spectrum is shown by the dash double dotted curve. For comparison purposes, the associated ensemble extinction spectrum (Æaæ ∼ 2.5 nm) is shown (solid line) along with its emission spectrum (dashed-dotted line).
This enables us to extract R, γ, and δ peak positions as illustrated in Figure 3a,b for two distinct NW sizes. The accompanying dashed lines are individual Gaussian components of the resulting fit (solid line). During the course of the fitting, a second feature appears to the blue of R, which we label β. Though not immediately apparent in most single wire spectra, it can be discerned as a slight, high energy, shoulder to R in the a ∼ 3.4 nm spectrum (Figure 2). An additional spectrum illustrating this can be found in the Supporting Information (Figure S2). In the largest wires, a fourth state (ζ) emerges at energies near 2.3 eV. This can readily be seen in the a ∼ 5.0 nm spectrum of Figure 2. In all cases, we observe a systematic increase in overall nanowire absorption to the blue that is likely caused by unresolved transitions. Furthermore, a Gaussian fit to the corresponding emission of each wire (insets) reveals a clear, single NW Stokes shift, enabling us to plot its size dependence. Figure 3c summarizes the extracted excited state size progression. We have chosen to plot energy offsets relative to R in order to remove uncertainties in the NW sizing. It is important to note
that all transitions (i.e., β, γ, δ, and ζ, as well as the emission) blueshift with increasing R energy. For the emission, this is consistent with ensemble Stokes shifts of 48 (Figure 1b), 39, and 21 meV in the a ∼ 2.5 nm, a ∼ 3.7 nm, and a ∼ 5.0 nm ensembles used here. It is also consistent with size-dependent ensemble emission Stokes shifts seen in PbSe NWs.25 To identify the origin of these transitions and to elucidate their free carrier versus excitonic nature, Figure 3c provides model predictions. Our analysis is based on calculations first developed by Shabaev and Efros to describe the linear absorption of CdSe nanorods.10 Briefly, electron and hole energy levels are determined within a six-band effective mass model. Each electron state is characterized by the quantum number m, which is the z-projection of the carrier’s envelope angular momentum onto the NW growth axis. Hole quantum states are similarly distinguished by the projection of their total angular momentum onto the NW growth axis, jz = m + Jz, where Jz is the z-projection of the Bloch angular momentum. The calculated transition energies and transition probabilities (K)10,27 permit us to identify the various observed resonances. Without taking Coulombic effects into account, the free carrier transitions predicted by the k 3 p model agree poorly with our experimentally derived R, β, γ, δ, and ζ energies.22 This has also been observed when explaining discrepancies between the optical and transport gaps in CdSe nanorods.10 As a consequence, our theoretical energies must be modified to account for the enhanced 1D exciton binding energy as well as additional electron/hole self-image interactions. In turn, we obtain good agreement between experiment and theory as illustrated below. Additional details of the calculations, as well as K-values, plots of the electron and hole energy levels, sizedependent 1D exciton binding energies, and total self-image interaction contributions can be found in the Supporting Information, Table 1 and Figures S3 S5, respectively. We note that the employed model is based on a zinc-blende crystal structure whereas prior studies have shown that solution-grown CdSe NWs possess intrawire zinc-blend/wurtzite phase admixtures.28,29 Adopting the notation introduced by Shabaev and Efros, we make the following excitonic assignments. First, R is attributed to the 1Σ1/21Σe transition. A second feature just to the blue of it, labeled β, likely corresponds to the 1Σ3/21Σe transition or the much weaker 2Σ1/21Σe transition. A third resonance, γ, is assigned 3308
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Figure 4. Increase of the CdSe NW photoluminescence intensity with increasing excitation intensity. The smallest radius NWs (a ∼ 3.5 nm, black circles) show a linear trend, larger wires (a ∼ 4.2 nm, solid red triangles) display an intermediate trend, while very large radius (a ∼ 11.5 nm, blue crosses) nanowires exhibit near-quadratic growth. For comparison purposes, the dashed lines represent the limiting linear (s = 1) and quadratic (s = 2) cases, where s denotes the growth order.
Figure 3. Single NW extinction spectra (blue open symbols) of (a) a ∼ 4.5 nm and (b) a ∼ 5.0 nm wires fit to a sum of Gaussians (dashed lines). The solid line is the resulting fit. Corresponding insets show the accompanying emission Gaussian fit. (c) Excited state transition energies plotted relative to the energy of the first excited state (R). The solid (dotted) lines represent the strongest (weakest) predicted transitions derived from a six-band model including electrostatic interactions. Dashed lines denote transitions with intermediate strength. The solid symbols represent transitions extracted from current and prior ensemble transient absorption data.26
to 1Πh.h. 1/21Πe, which is the next prominent transition based on calculated K-values. The predicted 1Πl.h. 1/21Πe transition is not observed, possibly due to its proximity to the more dominant /K1Πl.h. ∼ 4). Where applic1Πh.h. 1/21Πe resonance (K1Πh.h. 1/21Πe 1/21Πe able, the superscripts h.h. and l.h. denote transitions from uncoupled heavy hole and light hole energy levels. See the Supporting Information for more information. At present, a definitive assignment of δ is not possible due to the dense manifold of predicted exciton states as well as possible free carrier contributions. Namely, in this spectral range, the strongest exciton transitions, based on calculated K-values, are 2Σ1/22Σe followed by 2Σ1/21Δe (K2∑1/22∑e /K2∑1/21Δe ∼ 2). Additional 1Σ1/22Σe and 1Σ1/21Δe transitions exist, but are significantly weaker (Figure 3c and Table 1 of the Supporting Information). In the absence of additional data, ζ has tentatively been assigned to the uncoupled split off transition, 1Πs.o. 1/21Πe. Predicted energies for all transitions are drawn as solid/dashed/dotted lines in Figure 3c. While the theory is not exact, the solid/dashed lines capture the overall trends of the excitonic features observed.
The aforementioned agreement between experiment and theory, especially in the case of R, β, and γ, strongly suggest that they are excitonic in nature. We are, however, motivated to further confirm these assignments through an independent study, especially since we have previously found that free carrier characteristics dominate the optical response of large radius (a ∼ 11.5 nm) CdSe NWs.30 Specifically, we have been able to distinguish free carrier versus excitonic behavior by monitoring a NW’s photoluminescence intensity (Iem) as a function of excitation intensity (Iexc). A distinction between the two can be made because bimolecular free electron and hole recombination causes emission intensities to grow quadratically with increasing photogenerated carrier density. In contrast, excitonic emission should exhibit a linear Iexc dependence.31 Figure 4 shows that when such experiments are repeated in the current study for large radius (a ∼ 11.5 nm) NWs, near-quadratic emission growth is observed when exciting their band edges (i.e., their R transition). This is shown by the crosses in Figure 4 which lie near the s = 2 quadratic limit (upper dashed line). When the measurement is repeated for narrow radius (a ∼ 3.5) NWs by exciting them on resonance at R, approximate linear behavior is observed (open circles). A slight sublinear growth occurs due to partial saturation of R, as will be discussed shortly. Analogous behavior is seen when exciting γ. The apparent contrast between thick (a ∼ 11.5 nm) and thin (a ∼ 3.5 nm) specimens therefore suggests that the latter exhibit excitonic behavior, corroborating our prior theoretical assignments. This leads us to conclude that carrier recombination processes in narrow radii CdSe NWs are predominantly excitonic. Interestingly, Figure 4 shows mixed behavior in intermediate radii NWs (a ∼ 4.2, red triangles). Their emission intensity grows superlinearly, though at a noticeably slower rate than the thick (a ∼ 11.5 nm) wires. This suggests that while the extinction properties of intermediate and narrower wires are dominated by excitonic resonances, free carrier recombination mechanisms emerge in thicker wires due to exciton ionization. The observed trend can be explained by size-dependent exciton binding energies. Namely, in narrow radii wires, exciton binding energies are much larger than kT. For larger wires, binding energies are smaller due to decreases in dielectric contrast and can lead to 3309
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Figure 5. Intensity-dependent single NW (a ∼ 4.5 nm) extinction spectra. The solid blue line illustrates the low laser intensity spectrum while the dashed red line corresponds to the high intensity case. Underneath the break is a difference spectrum, highlighting R, γ, and δ nonlinearities. (b) Plot of measured σext-values at R, γ, and δ as a function of excitation intensity. The inset shows fractional (f) R, γ, and δ σext-values as a function of Iexc.
exciton dissociation. In between, a general proclivity exists for exciton ionization and is supported by the same theoretical model used earlier in Figure 3c. Specifically, calculated binding energies in the thinnest wires (a ∼ 3.5 nm) exceed 300 meV while in the largest wires (a ∼ 11.5 nm), Ebind-values decrease to ∼100 meV. A plot depicting predicted Ebind size-dependences can be found in the Supporting Information (Figure S5) and suggests that the transition from the linear/sublinear to superlinear emission response arises from the size-dependent balance between excitonic and free carrier behavior in 1D systems, which, in turn stems from the interplay between carrier- and dielectric-confinement effects. Nonlinear effects also manifest themselves in our direct absorption experiments. Namely, the apparent sublinear growth of Iem versus Iexc in narrow radii NWs (Figure 4 a ∼ 3.5 nm, open circles) shows up as partial saturation of R, γ, and δ at modest to high excitation intensities. To illustrate, Figure 5a shows the extinction spectrum of an a ∼ 4.5 nm NW at low excitation intensity (solid blue line). Under these conditions, the wire exhibits the same excited state progression/lineshapes seen earlier in Figure 2. However, when Iexc becomes large, all three transitions begin to saturate (Figure 5a, dashed red line).32 Their nonlinear response is best seen by taking the difference between the low and high intensity spectrum, revealing a clear drop in
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oscillator strength for R, γ, and δ. The absolute and fractional (f) decrease of σext for all three transitions are shown in Figure 5b and in the accompanying inset, as functions of Iexc. It is clear that R exhibits a stronger nonlinear response than γ and δ. The origin of these optical nonlinearities is complex and arises from manybody effects involving phase space filling, exciton screening, and band gap renormalization.13,33,34 All strongly affect single particle energies/wave functions as well as the strength of electron hole Coulomb interactions. These single wire saturation measurements suggest tantalizing prospects of utilizing 1D excitonic nanostructures as optical switches and logic elements based on absorptive bistability. A detailed analysis of such single wire optical nonlinearities is therefore left for future studies where systematic changes in confinement strength as well as 1D exciton binding energies can be investigated through variations in NW size and local dielectric environment. Toward this end, the Supporting Information illustrates preliminary results of dielectric environment influences on exciton binding energies (Supporting Information Figure S7). Our single nanowire extinction spectroscopy has revealed excitonic physics, otherwise lost in ensemble measurements. Using spatial modulation spectroscopy, we have demonstrated for the first time pronounced 1D exciton resonances in the room-temperature extinction spectra of individual colloidal CdSe NWs. Assignment of these transitions to 1D excitons is supported by their remarkable agreement to results of a six-band model that encompasses the confinement of carriers and explicitly includes their electrostatic interactions. This clearly highlights the need to properly account for dielectric contrast in nanostructures beyond 0D systems, where perturbative contributions have sufficed due to symmetry and strong carrier confinement effects. Materials and Methods. Nanowire Synthesis. Three CdSe NW ensembles with mean radii of ∼2.5, ∼3.7, and ∼5.0 nm were prepared using solution liquid solid growth. These radii are only approximate and were determined by comparing the peak of an ensemble’s first optical transition to a sizing curve assembled from ensemble literature data. A typical reaction for Æaæ ∼ 2.5 nm wires consists of mixing CdO (25 mg, 0.19 mmol), myristic acid (0.662 g, 2.9 mmol), and trioctylphosphine oxide (0.5 g, 1.3 mmol) in a three-neck flask. The mixture is then heated/degassed at 100 C for 50 min. Next, the temperature of the reaction mixture is raised to 250 C under nitrogen. Around 220 C the mixture turns clear. Once the temperature stabilizes, an injection solution consisting of 1 M TOPSe (25 μL, 25 μmol), 0.2 mL of TOP, and 1 mM BiCl3 in acetone (25 μL, 2.5 10 8 mol) is introduced. The reaction mixture is heated for 1 min before being quickly cooled to room temperature using an external acetone wash. The reaction mixture is then diluted with toluene to prevent TOPO from solidifying. NWs are precipitated from solution by adding methanol and centrifuging the resulting suspension. Recovered wires are washed four additional times with a 70:30 toluene/ methanol mixture. The NWs are stored in toluene and are sized using a JEOL 2010 TEM (see Supporting Information Figures 8 10). As made wires generally possess straight morphologies and are highly crystalline. Detailed information about the NW synthesis as well as structural studies showing the presence of zinc-blende/wurtzite phase admixtures can be found in refs 28 and 29. In parallel, the ensemble linear absorption of the three samples demonstrate clear blue shifts in their extinction onset with decreasing radius. This is accompanied by a corresponding blue shift of their photoluminescence (Supporting Information Figure S11). Single NW Extinction Measurements. NW optical samples were prepared by drop-casting dilute NW suspensions onto (flamed) 3310
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Nano Letters glass microscope coverslips. Single NW extinction spectra were then obtained on a home-built system assembled using a commercial inverted microscope (Nikon TE2000-U). A protocol for identifying individual wires has been provided in the Supporting Information. The excitation source is the output of a supercontinuum laser (Fianium SC450) dispersed by a home-built double prism monochromator. To control the polarization at the sample, the monochromator’s collimated output is passed through a sheet polarizer prior to the back of the microscope. The beam is then focused to a near diffraction-limited spot with a microscope objective (Nikon, 0.95 N.A.). To determine the actual size of the excitation spot, images were taken with a CCD camera (DVC). The spot’s line profile was then extracted using ImageJ and was subsequently fit with a Gaussian to estimate its 1/e2 value. NWs are situated using a manual X Y micrometer stage (Semprex) coupled to a closed-loop, three-axis piezo positioner (Physik Instrumente, P-527.3CD). The single NW position is modulated at 500 Hz using the sine output of a function generator (Tektronix AFG3022) with a second piezoelectric stage (Nanonics) stacked on top of the first. Any transmitted light is collected using a second objective (Zeiss, 0.75 NA) and is detected with an autobalanced photodiode (New Focus, Nirvana 2007). There are three BNC output channels on the Nirvana 2007: a linear output, a signal monitor, and a log output. The photodiode’s linear output is fed into a lock-in amplifier (SRS, SR830) and the signal monitor is read using a digital multimeter (Keithly, 2000). Extinction scans are automated through home written software. A detailed schematic of the experimental setup can be found in the Supporting Information (Figures S12 and S13). Single Nanowire Photoluminescence Measurements. Single NW photoluminescence spectra were obtained on the same home-built system described above. The only difference is that NWs are wide-field illuminated with a 532 nm diode laser (Power Technology Inc.). This is accomplished by inserting a 400 mm focal length achromat prior to the first objective’s back aperture. An ∼12 μm excitation radius is obtained, defined by its 1/e2 radius (ω). A typical excitation intensity [(2P)/(πω2)] is 400 W/cm2. NW emission is collected using the same microscope objective as the excitation and is passed through a 570 nm long pass filter (Chroma) before being imaged with a CCD/imaging spectrometer combination (DVC/Acton).
’ ASSOCIATED CONTENT
bS
Supporting Information. How to determine σext from the measured lock-in voltage. NW sizing curves. An additional single NW extinction spectrum fit to a sum of Gaussians. Theory and calculations. TEM characterization and sizing of NWs. Ensemble NW extinction and PL spectra. Protocol for identifying individual nanowires. Detailed experimental diagram of the spatial modulation setup. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank A. L. Efros, A. Shabaev, A. C. Bartnik, and P. Frantsuzov for fruitful discussions. We also thank G. V. Hartland for use of a
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SR-830 Lock-In Amplifier and for critically reviewing the manuscript. M.K. acknowledges financial support from the NSF CAREER program (CHE-0547784). Partial funding from the Notre Dame Radiation Laboratory and the DOE Office of Basic Energy Sciences is acknowledged. M.K. is a Cottrell Scholar of Research Corporation.
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