Direct Measurement of Single CdSe Nanowire Extinction Polarization

Letter pubs.acs.org/JPCL

Direct Measurement of Single CdSe Nanowire Extinction Polarization Anisotropies Matthew P. McDonald, Felix Vietmeyer, and Masaru Kuno* Department of Chemistry and Biochemistry, University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States S Supporting Information *

ABSTRACT: The origin of sizable absorption polarization anisotropies (ρabs) in onedimensional (1D) semiconductor nanowires (NWs) has been debated. Invoked explanations employ either classical or quantum mechanical origins, where the classical approach suggests dielectric constant mismatches between the NW and its surrounding environment as the predominant source of observed polarization sensitivities. At the same time, the confinement-influenced mixing of states suggests a sizable contribution from polarization-sensitive transition selection rules. Sufficient evidence exists in the literature to support either claim. However, in all cases, these observations stem from excitation polarization anisotropy (ρexc) studies, which only indirectly measure ρabs. In this manuscript, we directly measure the band edge extinction polarization anisotropies (ρext) of individual CdSe NWs using single NW extinction spectroscopy. Observed polarization anisotropies possess distinct spectral features and wavelength dependencies that correlate well with theoretical transition selection rules derived from a six-band k·p theory used to model the electronic structure of CdSe NWs. SECTION: Spectroscopy, Photochemistry, and Excited States

T

As an illustration, individual solution synthesized CdSe NWs exhibit measured ρexc-values on the order of ρexc ∼ 0.90 throughout the visible (488, 532, and 625 nm) for wires with radii (a) of a ∼ 3 nm.2 This is also the case with a ∼ 7.5 nm InP NWs.4 Solution−liquid−solid (SLS) synthesized CdSe NWs are well-studied 1D systems, with an abundance of work on their optical properties.14 This includes studies that conduct ensemble/single NW transient differential absorption, ensemble/single NW absorption/emission, and single NW polarization-dependent emission/excitation spectroscopies.14,15 The probed wires typically possess radii of a ∼ 2−10 nm and lengths up to 10 μm.16 Carrier confinement (associated bulk exciton Bohr radius aB = 5.6 nm) leads to discrete transitions in their optical spectra.14,17−19 These transitions are thought to be excitonic, as evidenced by recent single wire extinction measurements.19 We therefore expect that the transition moments of these resonances should exhibit sizable excitation polarization sensitivities, leading to frequency-dependent ρexc variations.8,10,12 Although absorption polarization anisotropies of 1D nanostructures such as CdSe and other NW systems have previously been probed, a direct determination of ρabs has never been achieved for any 1D material. This is due to the difficulty of measuring the absorption of single nanostructures given their

he optical properties of one-dimensional (1D) semiconductor nanostructures, such as nanowires (NWs), display intrinsic polarization anisotropies.1−7 This phenomenon can be explained by invoking either a classical dielectric contrast argument,1,2,4 or transition selection rules induced by confinement-influenced valence band mixing.8−11 Both approaches are well represented in the literature, where single 1D nanostructure excitation (ρexc ) and emission (ρem ) polarization anisotropies range from 0.412 to 0.964 [ρexc(em) = [I∥exc(em) − I⊥exc(em)]/[I∥exc(em) + I⊥exc(em)]; I∥exc(em) and I⊥exc(em) are the emission intensities for parallel or perpendicularly polarized excitation (emission)]. The classical approach is derived by modeling the NW as a dielectric cylinder subjected to an external electric field, E0. Solving for the NW’s internal field results in E∥NW = E0, and E⊥NW = [2εm/(ε + εm)]E0, where ε (εm) is the dielectric constant of the NW (surrounding medium).13 When defined in terms of I∥ = |E∥NW|2 and I⊥ = |E⊥NW|2, the polarization anisotropy is ρ = (|ε + εm|2 − 4|εm|2)/(|ε + εm|2 + 4|εm|2). Predicted anisotropies for semiconductor NWs are ρ ∼ 0.9 throughout the visible using εm = 1 (air) and nominal frequency-dependent ε-values for bulk semiconductors.2 What’s most notable, though, is that calculated ρ spectra are relatively featureless and show no significant wavelength dependencies.1,2 This is not expected in confined systems, where different electronic transitions likely possess specific polarization sensitivities. To date, nearly all acquired ρexc anisotropy spectra have been featureless1,2,4 with the exception of InGaAs quantum well wires (QWWs) at low temperature.12 © 2012 American Chemical Society

Received: June 22, 2012 Accepted: July 24, 2012 Published: July 24, 2012 2215

dx.doi.org/10.1021/jz3008112 | J. Phys. Chem. Lett. 2012, 3, 2215−2220

The Journal of Physical Chemistry Letters

Letter

Figure 1. (a) Parallel (blue open circles) and perpendicular (red open triangles) extinction spectra of a single a ∼ 4 nm CdSe NW. The perpendicular spectrum is scaled by a factor of 3 for clarity. Solid and dashed black lines are Gaussian fits to the extinction data. Greek letters label the observed resonances. (b) Excited state progression of extracted peak positions plotted as offsets from the first excited state (α∥(⊥)). The bold symbols correspond to α∥ (open black circles), α⊥ (filled black circles), β∥ (red crosses), β⊥ (black crosses), γ∥ (open blue triangles), η⊥ (filled black diamonds), δ∥ (open green squares), and δ⊥ (filled green squares). Previously acquired data (light gray symbols) from refs 14 and 19 are shown underneath. Note for the largest size shown, the narrow spacing between α and β makes it difficult to resolve β∥. An additional high energy state ζ (green star) is also resolved.

Figure 2. (a) Representative ρext spectra for several different individual CdSe NWs. (b) Model predictions (dotted, dashed, and solid black lines) graphed as offsets from the first excited state (α, 1Σ1/21Σe) to account for uncertainties in NW radii. The symbols α (black open circles), β (red crosses), and δ (green open squares) display average σ∥ext and σ⊥ext peak energies extracted from Gaussian fits of many single NW extinction spectra and correspond to maxima and minima in ρext spectra. Additionally, extracted γ (blue open triangles) and η (pink solid diamonds) energies are plotted as offsets from α. The data points are labeled with the same Greek letters used in Figure 1.

Utilizing this technique, we have directly probed the extinction polarization anisotropy [ρext = (σ∥ext − σ⊥ext)/(σ∥ext + σ⊥ext)] of individual confined CdSe NWs by measuring their parallel and perpendicular extinction spectra. Figure 1a shows the extinction spectrum of a single a ∼ 4 nm CdSe NW under both parallel (open blue circles) and perpendicularly (open red triangles, scaled by a factor of 3 for clarity) polarized excitation. All polarizations are defined relative to the NW growth axis. The provided radius is a rough estimate based on a sizing curve assembled from ensemble literature data.19 Clear resonances are apparent in both the parallel and perpendicular spectra, with features labeled α∥(⊥), β∥(⊥), γ∥, η⊥, and δ∥(⊥). Employed superscripts refer to features seen under parallel (∥) or perpendicular (⊥) excitation. The observed

small absorption cross sections. For example, NW extinction cross sections are on the order of σ∥ext ∼ 10−11 and σ⊥ext ∼ 10−12 cm2 μm−1 for parallel and perpendicularly polarized light.20 This means that, at best, only ∼0.1−0.01% of a transmitted beam’s power is extinguished by the NW, making such measurements inherently difficult.19 We have recently developed a modulation spectroscopy technique that allows us to directly measure the extinction of single a = 2.5−5 nm NWs.19 Extinction in this size regime is primarily due to absorption, since scattering accounts for only ∼5% of the extinguished light.21 Experimental details about the measurement can be found in the Experimental Methods section, the Supporting Information (SI), and refs 14 and 19. 2216



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explain their excitonic origin.14,19,22 In the model, electron wave functions take the form

transitions are likely excitonic based on our previous study into the excited state progression of individual confined CdSe NWs.19 They can be modeled and assigned using results from a 6-band k·p model first developed by Efros and Shabaev for CdSe nanorods.22 Notably, the model accounts for enhanced exciton binding energies as well as electron/hole selfinteractions with mirror charges. This leads to good agreement between experiment and theory as seen in Figure 1b. Namely, previously acquired single wire transitions (α, β, γ, and δ) using parallel polarized light are shown as light gray symbols.14,19 Their energies have been plotted as offsets from α to avoid ambiguities stemming from NW size estimates. On top are theory predictions (black lines) where solid lines indicate strong transitions, dashed lines indicate intermediate strength transitions, and dotted lines denote weak transitions. Obtained α∥(⊥), β∥(⊥), γ∥, η⊥, and δ∥(⊥) energies for different NW sizes are also shown in Figure 1b (dark symbols). As with the older data, extracted energies are plotted as offsets relative to α∥(⊥). The new and old parallel extinction data coincide within a standard error of ∼3%. In addition, we see that α∥ = α⊥, β∥ = β⊥, and δ∥ = δ⊥ in terms of their peak energies (SI, Figure S1). This suggests that they represent the same excited states. However, they differ in their relative transition strengths, as discussed below. We also find that γ and η likely originate from two distinct transitions given that they possess different peak energies and polarization sensitivities (SI, Figure S1). Several things should be noted in Figure 1a. First, σ⊥ext is smaller than σ∥ext. Approximate values are σ⊥ext ∼ 3 × 10−12, and σ∥ext ∼ 4 × 10−11 cm2 μm−1 at α, which correspond well with theoretical predictions showing σ⊥ext ∼ 10−13−10−12 and σ∥ext ∼ 10−12−10−11 cm2 μm−1.20 As a consequence, the perpendicular spectrum has been scaled by a factor of 3 for clarity. Next, the relative oscillator strengths of α, β, γ, η, and δ differ. In particular, α∥ is more intense than β∥. Conversely, β⊥ is larger than α⊥ in the perpendicular spectrum. A similar trend follows for the next two transitions, γ and η, where γ dominates in the parallel spectrum while the reverse is true in the perpendicular spectrum. Given these observed differences between α∥/α⊥ and β∥/β⊥, it is clear that their corresponding transitions exhibit sizable polarization sensitivities. A ρext anisotropy spectrum constructed using σ∥ext and σ⊥ext is shown in Figure 2a (stars) for the a ∼ 4 nm NW first seen in Figure 1a. ρext spectra for other representative NW sizes are also shown. In all cases, there is a clear maximum in the extinction anisotropy at α (ρext∼0.86), followed by a minimum at β (ρext∼0.61). The trend repeats itself for the next two transitions, γ and η, where ρext rises to a local maximum (∼0.76) and then falls to a minimum (∼0.61). These oscillations in ρext unambiguously illustrate the differing polarization dependencies of α, β, γ, η, and δ in CdSe NWs. This is the first time ρext, as well as structure in the ρext spectrum, has been resolved in any NW system. Figure 2b shows average peak energies extracted from Gaussian fits of σ∥ext and σ⊥ext. These data points are plotted as offsets from α and correspond to extrema in the ρext spectra (Figure 2a). Specifically, ρext maxima correspond to α, γ, and δ, while ρext minima align with β and η. Note that a ρext maximum (minimum) occurs if a transition is preferentially excited using parallel (perpendicularly) polarized light. To quantify model anisotropies, we now evaluate relevant transition selection rules for α, β, γ, η, and δ. This can be done using results from the earlier six-band k·p model first invoked to

u±c 1/2

⎛ αn , |m | ⎞ J|m |⎜ e e ρ⎟eimeϕ ⎠ π aJ ′|me| (αne , |me|) e ⎝ a

Ψ ene , |me| =

(1)

where ne is a quantum number representing the electron’s energy level, me is the state’s angular momentum projection onto the NW growth axis (z-axis), uc+1/2 = |S↑⟩ and uc−1/2 = |S↓⟩ are associated conduction band Bloch functions, J|me| is the |me|th ordered Bessel function of the first kind, J′|me| is its first derivative, αne,|me| is the neth zero of the |me|th order Bessel function, and ρ (ϕ) is the radial distance (azimuthal angle) in cylindrical coordinates. Associated eigenenergies are Ene,|me| = (ℏ2αn2e,|me|)/(m*(Ene,|me|)2a2), where m*(Ene,|me|) = m0/(1 + 2f + Ep/3{[2/(Ene,|me| + Eg)] + [1/(Ene,|me| + Eg + Δ)]}) is the electron’s effective mass, m0 is the free electron mass, Ep = 19.0 eV and f = −1.035 are valence band/remote band warping terms, Δ = 0.420 eV is the spin−orbit splitting,22 and Eg = 1.74 eV is the bulk CdSe band gap (293 K). Hole wave functions are similarly written as linear combinations of heavy hole (HH), light hole (LH), and splitoff hole (SOH) states +3/2 z

v χj3/2 (ρ) ·ei(jz − Jz )ϕ·u3/2, J −J

∑

Ψj =

z

z

z

Jz =−3/2 +1/2

v χj1/2 (ρ) ·ei(jz − Jz )ϕ·u1/2, J −J

∑

+

z

Jz =−1/2

z

z

(2)

In eq 2, jz is the total angular momentum projection onto the NW z axis [jz = mh + Jz, where mh (Jz) is the envelope (Bloch) angular momentum projection],19 and χJjz−Jz(ρ)·ei(jz−Jz)ϕ are envelope functions.22 The terms uvJ,Jz are valence band Bloch functions that take the form uvJ,Jz = |J,Jz⟩, with J being the angular momentum. Given HH: J = 3/2, Jz= ± 3/2; LH: J = 3/2, Jz= ± 1/2; SOH: J = 1/2, Jz= ± 1/2,23 we have 1 1 , 2 2

=

1 [(X + iY ) ↓ +Z ↑ ] 3

1 1 ,− 2 2

=

i [−(X − iY ) ↑ +Z ↓ ] 3

3 1 , 2 2

=

i [(X + iY ) ↓ −2Z ↑ ] 6

3 1 ,− 2 2

1 [(X − iY ) ↑ +2Z ↓ ] 6

=

3 3 , 2 2

=

3 3 ,− 2 2

=

1 (X + iY )↑ 2 i (X − iY )↓ 2

(3)

This leads to 2217


The Journal of Physical Chemistry Letters ±, j

Ψ±j (ρ , ϕ) = R1 z(ρ)Φ1±(ϕ) z

3 3 ,∓ 2 2

3 1 ,± 2 2 ±, j

Letter

radial portion of the electron’s wave function. Note that attenuation of the incident light’s electric field due to dielectric 2 contrast is explicitly taken into account by |E∥(⊥) NW | . Thus, both dielectric contrast and intrinsic polarization sensitivities are naturally accounted for. Additionally, each term within the absolute value in eq 4 is governed by a strict envelope angular momentum selection rule, requiring mh = me.10,26 The derivation of eq 4 is available in the SI. We illustrate what results for 1Σ1/21Σe. In this case, the hole + wave function is Ψ1/2 (ρ,ϕ) = R1+,1/2 (ρ)Φ 1+(ϕ)|3/2, 1/ +,1/2 + 2⟩+R2 (ρ)Φ2 (ϕ)|3/2, −3/2⟩+R+,1/2 (ρ)Φ+3 (ϕ)|1/2, 1/2⟩. For 3 parallel polarization, ê·p̂ = p̂z and eq 4 becomes

±, j

+ R 2 z(ρ)Φ±2 (ϕ)

+ R3 z(ρ)Φ±3 (ϕ)

1 1 ,± 2 2

where the superscript ± on Ψjz denotes the upper/lower 3 × 3 ±,j ±,j sub-block of a simplified 6 × 6 Hamiltonian.14 R1 z(ρ), R2 z(ρ), ±,jz ± ± ± R3 (ρ) [Φ1 (ϕ), Φ2 (ϕ), Φ3 (ϕ)] are the radial [angular] portions of the wave function’s envelope (see SI for more information).22 In keeping with the nomenclature used in ref 22, electron states are labeled neΛe where ne indexes the electron energy level, and Λe represents the absolute value of me, such that |me| = 0, 1, 2, ... corresponds to Λe = Σ, Π, Δ,... Hole states are similarly denoted nhΛjz, where nh is the hole’s energy index and Λ stands for the smallest value of |mh| = |jz − Jz| in eq 2. The first optical transition in Figure 1b is therefore 1Σ1/21Σe, where the hole/electron wave functions are Ψ+1/2/Ψe1,0 and correspond to nh = 1, jz = 1/2, |1/2 − Jz| = 0 (1Σ1/2) and ne = 1, |me| = 0 (1Σe). In the special case of jz = 1/2 and |mh| = |1/2 − Jz| = 1 LH (i.e., Ψ−1/2), resulting hole states are labeled nhΠHH jz , nhΠjz , and SOH nhΠjz . Having assessed that the first maximum in the ρext spectra (α) corresponds to the 1Σ1/21Σe transition, this suggests that it (1Σ1/21Σe) must possess a strong parallel absorption polarization dependence. Likewise, given β’s correspondence to 1Σ 3/2 1Σ e, its ρext minimum suggests that 1Σ 3/2 1Σ e is preferentially excited with perpendicularly polarized light. The other transitions, γ (open blue triangles), η (filled black diamonds), and δ (open and filled green squares), are loosely LH assigned to 1ΠHH 1/2 1Πe, 1Π5/21Πe, and 1Π1/21Πe. They are experimentally observed to have parallel, perpendicular and parallel polarization dependencies. γ could also be caused by 1Π3/21Πe due to its proximity to 1ΠHH 1/2 1Πe and its parallel polarization dependence (SI). Overall, we find that transitions involving Σ1/2 or Π1/2 hole states possess parallel polarization dependencies. Conversely, transitions involving Σ3/2 and Π5/2 hole states are preferentially excited with perpendicularly polarized light. To assess whether these experimental anisotropy trends are predicted by theory, we evaluate the associated squared transition matrix element for 1Σ1/21Σe, 1Σ3/21Σe, 1ΠHH 1/2 1Πe, etc., where |Mjz± |2 ∼ |⟨Ψne e,|me||(ê·p̂)|Ψjz± ⟩|2. Specifically, eqs 2 and 3 lead to M j±, (⊥) z

2

≅

(⊥) E NW

ω2

2

+, M1/2 ≅

3 3 ±, j ,∓ ⟨R nee , |me|(ρ)|R 2 z(ρ)⟩ 2 2

+

1 1 ±, j ⟨R nee , |me|(ρ)|R3 z(ρ)⟩ S (ê·p̂ ) , ± 2 2

2

(4) ± ,∥ 2

3 1 e , (ρ) R1+,1/2(ρ)⟩ ⟨R1,0 2 2

S pẑ

1 1 e , (ρ) R3+,1/2(ρ)⟩ ⟨R1,0 2 2

2

2 2 2 2 Substitution of eq 3 into eq 5 results in |M+,∥ 1/2| ≅ (|E0| |Kp| 4π / 2 e e ω2)[(2/3)|⟨R1,0 (ρ)|R1+,1/2(ρ)⟩|2 + (1/3)|⟨R1,0 (ρ)|R+,1/2 (ρ)⟩| ], 3 10,25,27 where Kp is the Kane matrix element. The corresponding perpendicular polarization transition matrix element can be 2 2 calculated in an identical manner, resulting in |M+,⊥ 1/2 | ≅ (|E0| | e e K p|2 4π 2/ω2 )[(1/6)|⟨R1,0 (ρ)|R1+,1/2(ρ)⟩|2 + (1/3)|⟨R1,0 (ρ)| R+,1/2 (ρ)⟩|2][(2εm)/(ε + εm)]2. 3 Using ρext in terms of |M±,∥(⊥) |2, E∥NW and E⊥NW, [i.e., ρext = (| jz 2 ±,⊥ 2 ±,∥ 2 ±,⊥ 2 M±,∥ jz | −|Mjz | )/(|Mjz | + |Mjz | )], the predicted 1Σ1/21Σe polarization anisotropy is then ρext = 0.961 for a a = 4.0 nm CdSe NW. This is in good agreement with the experimental ρext = 0.86 maximum at α for the a = 4 nm NW in Figure 2. The predicted anisotropy is (very) slightly size dependent and varies from ρext = 0.9610−0.9611 when a → 2−6 nm (SI, Figure S2). Therefore, no significant size dependence is predicted for the NW size regime investigated (the average experimental ρext for all NW sizes studied is ρext = 0.86 ± 0.07, red triangle, Figure 3). Note that, without taking into account the attenuation of ⊥ ENW due to dielectric contrast, the predicted 1Σ1/21Σe extinction anisotropy is only ρext ∼ 0.6. This value is significantly smaller than what is seen experimentally. Clearly, dielectric contrast effects are important in determining the overall magnitude of ρext in solution-based NWs (Supporting Information, Table 1). By contrast, in low-temperature ρexc studies involving InGaAs QWWs embedded in InP and GaAs, the lack of a sizable dielectric mismatch between the wires and their immediate surroundings reveals similarly suppressed anisotropies.12 An identical analysis can be conducted for 1Σ3/21Σe. In this 2 case, ρext completely depends on |3/2, 3/2⟩, such that |M−,∥ 3/2| = e 0 and |M 3−,/ 2⊥ | 2 ≅ (|E 0 | 2 |K p | 2 4π 2 /ω 2 )[(1/2)|⟨R 1,0 (ρ)| R−,3/2 (ρ)⟩|2[(2εm)/(ε + εm)]2]. Consequently, the predicted 2 anisotropy is ρext = −1 and has no a dependence. Even though this ρext reversal is evident in Figure 2, its average magnitude is only ρext = 0.62 ± 0.05 (black star, Figure 3) for all NW sizes (Δρext ∼ −0.25 from 1Σ1/21Σe to 1Σ3/21Σe). This may be due to limitations of the effective mass theory as well as overlapping absorption from nearby states. HH Analyses of 1Π1/2 1Πe and 1Π5/21Πe show that their predicted polarization anisotropies are ρext = 0.961, and ρext = −1, respectively (Figure S2, SI). The model therefore predicts a HH ρext maximum at 1Π1/2 1Πe followed by a minimum at

3 1 ±, j ,± ⟨R nee , |me|(ρ)|R1 z(ρ)⟩ 2 2

S (ê·p̂ )

4π 2 S pẑ

(5)

4π 2

+

ω2

2

+

2

S (ê·p̂ )

E NW

± ,⊥ 2

for the parallel (|Mjz | ) and perpendicularly (|Mjz | ) polarized cases.10,12,24 In the expression, ω is the angular frequency, ê is the unit polarization vector of the optical electric field, p̂ is the momentum operator,10,25 and Rene,|me|(ρ) is the 2218



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In conclusion, the absorption polarization anisotropies of individual solution grown CdSe NWs have been measured for the first time by way of single particle extinction spectroscopy. Obtained ρext spectra show distinct wavelength dependencies that have previously been unseen. These spectral features originate from differing transition matrix elements for optical transitions caused by the 1D confinement-influenced mixing of valence band states. At the same time, the magnitude of these anisotropies suggests a significant contribution from dielectric contrast effects. When considered jointly, both explain the observed structure in the anisotropy as well as their magnitudes. This provides insight into the electronic transitions that dominate the optical properties of individual CdSe NWs and further elucidates their absorption polarization sensitivities.

■

EXPERIMENTAL METHODS Highly crystalline, straight CdSe NWs were produced using SLS growth.16 A typical reaction for a∼2.5 nm NWs follows: CdO (25 mg, 0.19 mmol), myristic acid (0.662 g, 2.9 mmol), and trioctylphosphine oxide (0.5 g, 1.3 mmol) are mixed together in a three neck flask. After heating/degassing this mixture at 100 °C for 50 min, its temperature is raised to 250 °C under nitrogen. Upon stabilizing, a solution 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 injected into the reaction vessel. After 2 min of growth, the reaction is quenched by rapidly cooling the solution. The resulting product is then washed ∼3 times with a 70:30 toluene:methanol mixture and stored in toluene. Single-particle extinction spectra are obtained using a sample modulation approach, in which single NWs are modulated in and out of a diffraction limited laser spot. The sample is prepared from dilute NW suspensions drop-cast onto glass microscope coverslips that have been cleaned with methanol and briefly flamed. The coverslip is mounted on a single axis open-loop piezo stage (Nanonics) using microscope immersion oil. Sample modulation is subsequently accomplished by feeding the 750 Hz sine output of a function generator (Rigol) into the piezo stage. Tunable excitation (480−800 nm) is produced by dispersing a white light supercontinuum laser (Fianium) with a prism. Wavelength selection is accomplished by rotating the prism and is automated through home-written software. A power control module (BEOC) stabilizes the source. The polarization of the excitation source is controlled with a sheet polarizer. For perpendicularly polarized extinction measurements, a λ/2 waveplate is placed prior to the sheet polarizer. The source is then split with a 70/30 beam splitter into a reference and a signal beam. The reference beam is focused onto the reference input of an autobalanced photodiode (Nirvana 2007) while the signal beam is focused using a high NA objective (Nikon, 60x, 0.95NA) onto the sample. Transmitted light is collected with a second objective (Zeiss, 100×, 0.75NA) collinear to the first and is then focused onto the signal channel of the autobalanced photodiode. As the NW is modulated in and out of the diffraction limited laser spot, the change in transmitted intensity due to extinction is detected using a lock-in. The resulting data is then processed and analyzed using home written software. A typical extinction measurement takes ∼6 min per spectrum. A representative schematic of the optical setup is shown in the Supporting Information. Additional experimental details can be found in refs 14 and 19. We note that the NW’s emission is not

Figure 3. Average values for observed ρext extrema for several single NW traces. The symbols correspond to the 1Σ1/21Σe (α, red triangle), 1Σ3/21Σe (β, black star), 1ΠHH 1/2 1Πe (γ, blue circle), 1Π5/21Πe (η, purple square), and 1ΠLH 1/21Πe (δ, pink diamond) transitions. They are plotted relative to an arbitrary x-axis (not the wavelength axis). This is rationalized by their insensitivity to size, as predicted by theory and shown in Figure S2 (SI). Inlayed across the data is the ρext spectrum of a single a ∼ 4.6 nm NW (black dots/black dashed line).

1Π5/21Πe. In Figure 3, γ (blue circle) and η (purple square) qualitatively follow this max−min trend, where average ρext magnitudes are ρext = 0.76 ± 0.06 and ρext = 0.68 ± 0.06, respectively. These experimental transitions (γ and η) are therefore tentatively assigned to 1ΠHH 1/2 1Πe and 1Π5/21Πe. However, 1Π3/21Πe is in close proximity to 1ΠHH 1/2 1Πe and has a parallel polarization dependence (ρext = 0.961), meaning that γ could be a mixture of both states. δ is loosely assigned to 1ΠLH 1/21Πe since its observed experimental ρext maximum (ρext ∼ 0.79) qualitatively agrees with the theory’s predicted maximum (ρext = 0.958). Alternatively, it could be the slightly higher energy state (2Σ3/21Δe) which is also predicted to have a parallel polarization dependence (ρext = 0.961). Previously reported excitation polarization anisotropy spectra of CdSe NWs have shown little or no structure.1,2 In one case involving narrow radii (a ∼ 3.3 nm) CdSe NWs,2 only three excitation energies were monitored. None were at the band edge. In a second study,1 bulk-like (a ∼ 12 nm) CdSe NWs were studied. NWs in this size regime possess relatively featureless19 absorption spectra due to the close spacing of states, making spectral ρext variations difficult to resolve. The results of both studies therefore contrast with the structured ρext spectra seen in Figures 2a and 3. Note that intrinsic ρexc and ρext discrepancies can also occur due to the fact that ρexc measurements rely on probing the NW’s emission as opposed to its absorption. The excitation experiment therefore implicitly assumes that NW quantum yields (QYs) remain independent of excitation intensity (Iexc). We have previously seen that NW QYs can vary with Iexc, resulting in variable QYs.14 This is tied to absorption saturation effects in the optical spectra of individual CdSe NWs19 and can lead to qualitative and quantitative ρexc and ρext differences. In fact, we find that ρext spectra of CdSe NWs probed at high excitation intensities (∼500 W/cm2 at 650 nm) show large deviations from those acquired at lower intensities (∼40 W/ cm2 at 650 nm)[SI, Figure S3]. This suggests that many-body effects can dramatically alter band-edge excitation/extinction polarization anisotropies.28 2219



Letter

(9) Maslov, A. V.; Ning, C. Z. Radius-Dependent Polarization Anisotropy in Semiconductor Nanowires. Phys. Rev. B 2005, 72, 161310−1−161310−4. (10) Sercel, P. C.; Vahala, K. J. Polarization Dependence of Optical Absorption and Emission in Quantum Wires. Phys. Rev. B 1991, 44, 5681−5691. (11) Akiyama, H.; Someya, T.; Sakaki, H. Optical Anisotropy in 5nm-Scale T-Shaped Quantum Wires Fabricated by the Cleaved-Edge Overgrowth Method. Phys. Rev. B 1996, 53, R4229−R4232. (12) Ils, P.; Gréus, C.; Forchel, A.; Kulakovskii, V. D.; Gippius, N. A.; Tikhodeev, S. G. Linear Polarization of Photoluminescence Emission and Absorption in Quantum-Well Wire Structures: Experiment and Theory. Phys. Rev. B 1995, 51, 4272−4277. (13) Landau, L. D.; Lifshitz, E. M.; Pitaevskii, L. P. Electrodynamics of Continuous Media; Pergamon: Oxford, U.K., 1984; pp 34−42. (14) Vietmeyer, F.; McDonald, M. P.; Kuno, M. Single Nanowire Microscopy and Spectroscopy. J. Phys. Chem. C 2012, 116, 12379− 12396. (15) Carey, C. R.; Yu, Y.; Kuno, M.; Hartland, G. V. Ultrafast Transient Absorption Measurements of Charge Carrier Dynamics in Single II−VI Nanowires. J. Phys. Chem. C 2009, 113, 19077−19081. (16) Kuno, M. An Overview of Solution-Based Semiconductor Nanowires: Synthesis and Optical Studies. Phys. Chem. Chem. Phys. 2008, 10, 620−639. (17) Puthussery, J.; Kosel, T. H.; Kuno, M. Facile Synthesis and Size Control of II−VI Nanowires Using Bismuth Salts. Small 2009, 5, 1112−1116. (18) Wang, F.; Buhro, W. E. An Easy Shortcut Synthesis of SizeControlled Bismuth Nanoparticles and Their Use in the SLS Growth of High Quality Colloidal Cadmium Selenide Quantum Wires. Small 2010, 6, 573−581. (19) Giblin, J.; Vietmeyer, F.; McDonald, M. P.; Kuno, M. Single Nanowire Extinction Spectroscopy. Nano Lett. 2011, 11, 3307−3311. (20) Giblin, J.; Kuno, M. Nanostructure Absorption: A Comparative Study of Nanowire and Colloidal Quantum Dot Absorption Cross Sections. J. Phys. Chem. Lett. 2010, 1, 3340−3348. (21) Protasenko, V.; Bacinello, D.; Kuno, M. Experimental Determination of the Absorption Cross-Section and Molar Extinction Coefficient of CdSe and CdTe Nanowires. J. Phys. Chem. B 2006, 110, 25322−25331. (22) Shabaev, A.; Efros, A. L. 1D Exciton Spectroscopy of Semiconductor Nanorods. Nano Lett. 2004, 4, 1821−1825. (23) Efros, A. L.; Rosen, M. The Electronic Structure of Semiconductor Nanocrystals. Annu. Rev. Mater. Sci. 2000, 30, 475− 521. (24) Bockelmann, U.; Bastard, G. Interband Absorption in Quantum Wires. I. Zero-Magnetic-Field Case. Phys. Rev. B 1992, 45, 1688−1699. (25) Schade, L.; Schwarz, U. T.; Wernicke, T.; Weyers, M.; Kneissl, M. Impact of Band Structure and Transition Matrix Elements on Polarization Properties of the Photoluminescence of Semipolar and Nonpolar InGaN Quantum Wells. Phys. Status Solidi B 2011, 248, 638−646. (26) Tadić, M.; Mlinar, V.; Peeters, F. M. Multiband k·p Calculation of Exciton Diamagnetic Shift in InP/InGaP Self-Assembled Quantum Dots. Physica E 2005, 26, 212−216. (27) Kane, E. O. Band Structure of Indium Antimonide. J. Phys. Chem. Solids 1957, 1, 249−261. (28) Califano, M.; Franceschetti, A.; Zunger, A. Lifetime and Polarization of the Radiative Decay of Excitons, Biexcitons, and Trions in CdSe Nanocrystal Quantum Dots. Phys. Rev. B 2007, 75, 1154011−115401-7.

prevented from being detected along with the transmitted light. However, the expected error in the extinction due to simultaneously detecting emission is ∼0.01% (see SI for analysis). Single, straight NWs that are oriented with their long axis parallel to the excitation source are found by wide field photoluminescence imaging according to previously published methods.19 The absorption signal is maximized (minimized) to ensure that the polarization of the excitation source is parallel (perpendicular) to the NW’s long axis.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental details about the measurement; comparison of peak energies for α∥ and α⊥, β∥ and β⊥, γ and η, and δ∥ and δ⊥; k·p theory and derivation of square transition matrix elements; plots of theoretical ρext versus a predictions for 1Σ1/21Σe, LH 1ΠHH 1/2 1Πe, 1Π3/21Πe, 1Π1/21Πe, and 2Σ3/21Δe; table of ρext values with and without dielectric contrast; power-dependent extinction spectra and corresponding ρext spectra; error analysis of emission contributions to the extinction. 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]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.K. acknowledges support from the NSF CAREER program (CHE-0547784). We also thank Dr. Jay Giblin for helpful discussions.

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REFERENCES

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Direct Measurement of Single CdSe Nanowire Extinction Polarization

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