Anisotropic Origins of Localized Surface Plasmon ... - ACS Publications

Article Cite This: Chem. Mater. XXXX, XXX, XXX−XXX

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Anisotropic Origins of Localized Surface Plasmon Resonance in n‑Type Anatase TiO2 Nanocrystals Clayton J. Dahlman,†,‡ Ankit Agrawal,† Corey M. Staller,† Jacob Adair,† and Delia J. Milliron*,† †

McKetta Department of Chemical Engineering, 200 E. Dean Keeton Street, The University of Texas at Austin, Austin, Texas 78712, United States ‡ Materials Department, University of California, Santa Barbara, Engineering II Building 1355, Santa Barbara, California 93106-5050, United States Chem. Mater. Downloaded from pubs.acs.org by UNIV DE BARCELONA on 01/08/19. For personal use only.

S Supporting Information *

ABSTRACT: Colloidal nanocrystals of anatase TiO2 exhibit localized surface plasmon resonance (LSPR) in the mid-infrared upon carrier accumulation through synthetic doping or electrochemical reduction. However, the energy and intensity of LSPR in anatase TiO2 nanocrystals is anomalously low compared to those of other transparent conductive oxides with similar bulk conductivity. Here, the electronic origin of LSPR energy and intensity in TiO2 nanocrystals is quantified by measuring infrared transmittance of dilute dispersions of doped nanocrystals and ex situ charged thin films. Optical modeling of infrared spectra reveals that TiO2 nanocrystals can accommodate carrier concentrations exceeding 1.5 × 1021 cm−3 upon charging, but the large effective mass along the anatase c-axis is found to diminish the infrared absorption of TiO2 nanocrystals. The respective effects of crystalline anisotropy, synthetic doping, and electrochromic charging on LSPR in TiO2 nanocrystals are investigated, revealing promising new avenues to engineer this material for plasmonic applications.

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INTRODUCTION Degenerately doped metal oxide nanocrystals (NCs) have emerged as tunable plasmonic materials that can be integrated into a variety of optoelectronic applications.1 Several semiconducting oxides, such as doped indium oxide and zinc oxide, have been used for plasmonic electrochromic applications including smart window coatings.2 A recent addition to the library of functional plasmonic metal oxides is nanocrystalline anatase TiO2, a wide band gap semiconductor often used with other functional light-absorbing metals, semiconductors, or organic materials as a scaffold, sensitizer, or charge-separating medium.3 Made by colloidal synthesis methods, degenerate Nb-doped TiO2 NCs have been found to show LSPR in the infrared (IR), with peak energies of about 2000−3000 cm−1, which can be tuned by varying the free electron concentration with different substitutional Nb dopant concentrations.4 IR coloration can also be reversibly modulated in mesoporous films of colloidal Nb-doped TiO2 NCs upon electrolytecompensated charging in an electrochemical cell,5,6 depending on applied potential and doping level. The mobility of free electrons in the conduction band of anatase TiO2 is reasonably high considering the large band gap, approaching μ ∼ 20 cm2 V−1 s−1 for single-crystal and thin-film morphologies.7 Intrinsic anatase TiO2 is an n-type semiconductor with room-temperature resistivity of about 0.1 Ωcm and carrier concentration of about 1018 cm−3, as measured in large single crystals.8 The carrier concentration in anatase TiO2 can be increased dramatically through doping, and anatase has attracted attention as a low-cost and high refractive © XXXX American Chemical Society

index replacement for conventional transparent conductive oxides (TCOs) such as Sn-doped In2O3 (ITO), Ga-doped ZnO, and F-doped SnO2.9 Aliovalent cationic doping with Nb5+,10 Ta5+,11 and W6+,12 along with aliovalent anionic doping with F-13and O-vacancy enrichment,14,15 can compensate free carrier concentrations in anatase TiO2 above ne = 1021 cm−3, allowing low room-temperature resistivity approaching ρ ∼ 10−4 Ω-cm.9,16 However, anatase TiO2 has not been studied as a plasmonic NC material to the same extent as other TCOs. Despite the high conductivity of epitaxial Nbdoped anatase thin films, the LSPR observed in earlier studies4,5 occurs at unexpectedly low energy and intensity. The crystal structure of anatase TiO2 is anisotropic, with a tetragonal unit cell (I41/amd ICSD Coll. Code 96946). The conduction band of anatase is composed largely of Ti 3d orbitals, contributing to strong anisotropy in carrier transport through the lattice.17−19 In fact, both free electrons and photoexcited excitons in anatase TiO2 have been found to have highly anisotropic mobilities, leading to some descriptions of the material as a two-dimensional conductor.18 Macroscopic measurements of LSPR in Nb-doped anatase TiO2 NCs sample both the low- and high-mobility lattice directions within an isotropically oriented dispersion or film. Thus, the broadness, low energy, and low peak intensity of observed LSPR peaks measured for films and dispersions of Nb-doped Received: October 25, 2018 Revised: December 19, 2018

A

DOI: 10.1021/acs.chemmater.8b04519 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials

Varian 710-ES ICP). At high Nb-doping content (>10% Nb), the particles became more oblong and polydispersed in shape, so the synthesis was restricted to moderate doping levels.4 FTIR transmission measurements were taken of 1 mg/mL dispersions of TiO2 NCs in tetrachloroethylene (TCE), with 0.01 vol % oleic acid added to stabilize the colloid. Solutions were filtered through 0.45 μm polytetrafluoroethylene syringe filters and measurements were taken soon after the final preparation of the dispersion to avoid precipitation or solvent evaporation. The volume fraction of NCs in solution was measured by ICP-OES for a stock solution of TiO2 NCs dispersed in TCE. Dilutions were prepared of the filtered ∼1 mg/mL TCE NC stock, yielding stable dispersions with concentrations of about 0.025 mg/mL. The filtered dispersions were found to be stable for at least a week, but NC precipitation was apparent for some samples, particularly at lower NC concentrations, after several weeks. Solution FTIR spectra were taken with a 1 mm path length solution cell with KBr windows and backgrounded to a solution cell filled with neat TCE. All FTIR measurements were conducted with a Bruker Vertex 70 FTIR using a tungsten lamp and a deuterated triglycine sulfate detector. Conductive TiO2 NC films were produced by spin coating colloidal NC dispersions onto a conductive, yet IR-transparent, substrate. To improve conductivity between TiO2 NCs before film deposition, the insulating oleic acid ligands of the as-synthesized and washed NC dispersions were exchanged with more conductive capping agents (i.e., coordinated BF4−) through the process first described by Dong et al.25 Oleic acid-capped NC dispersions in hexane were mixed with an equal volume of dimethylformamide (DMF), and a few mg/mL of NOBF4 were added to the mixture. The solutions were capped and sonicated for an hour, resulting in transfer of the NCs to the polar DMF phase. To remove residual organics, these ligand-exchanged NCs were washed repeatedly (at least three times) by adding toluene, precipitating the NCs through centrifugation, and redispersing the NCs in DMF. The washed particles were finally redispersed in a 1:4 DMF:acetonitrile solvent at a NC loading of 50 mg/mL. A moderately IR-transparent, conductive substrate was created by thermally evaporating a thin ∼1 nm wetting layer of chromium followed by a ∼13 nm layer of gold onto an undoped, double-sided polished silicon substrate. At this gold thickness, the films are about 10% transmissive in the near-IR, with decreasing transparency at lower energies (Figure S13a, Supporting Information). The gold thickness was estimated during thermal evaporation and measured by modeling the IR transmittance of a Cr−Au-coated Si substrate, as shown in Figure S13b. IR transparency and substrate conductivity for electrochemical charging are competing goals because a conductive substrate will generally reflect IR light. Thirteen nanometers was the thinnest coating that could be achieved without dramatic decreases in substrate durability and conductivity due to islanding effects that fragment percolation across the substrate.26 Conductive TiO2 NC films were produced by spin coating the NOBF4-treated, ligand-exchanged TiO2 NCs onto Cr−Au-coated Si substrates. The films were annealed at 300 °C for 30 min in argon to remove residual organics and reduce contact resistance between the NCs. These annealing conditions retain the anatase phase of TiO2 without inducing particle sintering.5 Films processed with lower annealing temperatures, or using postdeposition ligand-exchange methods such as immersion in a formic acid solution to remove insulating oleic acid from deposited NC films,21 showed lower film conductivities and poor reproducibility in measured charge capacity upon charging and discharging. The thickness of each film was varied from 190 to 433 nm, as measured by profilometry, to maintain similar absorbance values, and minimize systematic errors due to sensitivity limits of the FTIR detector, during charging experiments of each film. The final film morphology is observed in top-down and crosssectional scanning electron microscopy (SEM) images in Figure 2e and Figure S8, and raw transmittance spectra of each layer are shown in Figure S13a. The crystal structures of TiO2 NCs, across a doping range of 0− 20% Nb doping, were measured by grazing-incidence wide-angle Xray scattering at beamline 11-3 of the Stanford Synchrotron Radiation

TiO2 NCs may be due to the electronic anisotropy of the particles. In this article, we quantify the electronic origins of the LSPR in degenerate anatase TiO2 NCs based on optical measurements and relate these properties to the material’s anisotropic crystal structure. Measurements of electronic properties in NCs are complicated by barriers to moving electrons between particles. Traditional thin film measurements such as Hall resistivity are difficult to interpret in NC samples and optical conductivity can serve as a surrogate to assess free carrier properties in these materials. The amplitude, energy, and peak profile of LSPR can be used to characterize free carrier properties without a contacting electrical connection. In fact, LSPR absorption is particularly well-suited for analysis of carrier properties in semiconducting NCs. These materials have low intrinsic carrier concentrations (ne < 1020), so the relative changes in carrier concentrationby charging, doping, or other meansare more significant than traditional plasmonic materials such as gold or silver. However, measurements of mid-IR LSPR in weaker absorbers such as TiO2 NCs are complicated by the experimental challenges of accurately measuring broad Fourier transform infrared (FTIR) spectra of reduced NCs. Attempts to change the Fermi level through electrochemical charging methods can destabilize solvent dispersions of NCs. Schimpf et al. have demonstrated methods to measure the free carrier concentration in doped ZnO NCs in solution through the LSPR response, by UV photoexcitation of a dispersion of NCs in the presence of a hole scavenger to stabilize photoexcited electrons, followed by chemical titration using oxidants to quantitatively remove those conduction band electrons.20 This method allows for precise measurements of charge transfer in dispersed NCs, but requires highly stable colloidal dispersions that will not agglomerate or precipitate during charging. A complementary approach is to measure IR transmission through thin layers of mesoporous NC assemblies, and dynamically modulate carrier concentrations by electrochemical charging. This approach has been used to study the electrochromic response of plasmonic NC films such as ITO,21 along with sandwich cells that incorporate Nb-doped TiO2 as an active electrochromic layer.6 However, the electrolyte and experimental apparatus must be carefully designed to avoid convoluting optical losses from the electrolyte, substrate, and counter electrode. Previous attempts to use the optical response of nanocrystalline TiO2 films to characterize free carrier properties have relied on modulation in the visible and near-IR,22 but these measurements neglect the wealth of information that the full LSPR peak profile, which extends well into the mid-IR, can provide. Furthermore, optical measurements of mesoporous thin films are complicated by effective medium interactions, dipole−dipole coupling between particles, and damping due to film conductivity effects.23,24 To this end, this article develops a systematic means to characterize the infrared LSPR response of anatase TiO2 NCs, both in dilute dispersions and upon charging in thin film electrodes, to measure the dependence of free carrier properties on synthetic and electrochemical reduction.

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EXPERIMENTAL SECTION

Undoped and Nb-doped TiO2 NCs were synthesized following the procedures of Dahlman et al.5 Nb-doping content was calculated as the percentage of Ti sites occupied by Nb, and measured by inductively coupled plasma-optical emission spectroscopy (ICP-OES, B


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Figure 1. Solution FTIR spectra of TiO2 dispersions. (a) Optical density measured by transmission mode FTIR of 1 mg/mL solutions of oleic acidcapped TiO2 NCs dispersed in TCE. (b) Drude parameters for TiO2 extracted from fits of the FTIR spectra shown in (a). The error bars shown represent a 95% confidence interval for the fitted parameters. (c) Simulated extinction of an ensemble of NCs aligned with incident light polarized along the high-mobility basal plane (E⃗ ⊥ c⃗) and low-mobility c axis (E⃗ ∥ c⃗), as illustrated in (d) a schematic showing the unit cell of anatase TiO2 (I41/amd ICSD Coll. Code 96946). Simulated spectra in (c) were obtained using COMSOL, as described in the Supporting Information (Figure S6 and S7c). Laboratory (SSRL). The beamline energy was 12.7 keV and a Mar345 image plate detector was used. The sample-to-detector distance (∼150 mm) was calibrated with a standard sample of lanthanum hexaboride (LaB6) using the Nika software suite.27 NC films were prepared in the same manner as the conductive TiO2 NC films described above, by spin coating NOBF4-treated NC dispersions onto Cr−Au-coated Si substrates and annealing in argon. A grazing incidence angle of 0.12° was used. Raw images were geometrically corrected using the WAXStools software.28 The anatase crystal structure (I41/amd ICSD Coll. Code 96946) was confirmed for the entire range of Nb doping, as described previously4,5 (Figure S1). For electrochemical testing, the TiO2−Au−Si substrate was used as the working electrode, and a platinum foil and fritted Ag/Ag+ cell were used as the counter and reference electrodes, respectively. The electrolyte was 0.1 M tetrabutylammonium bis-trifluoromethanesulfonimidate (TBA-TFSI, Aldrich) salt dissolved in propylene carbonate (PC). The reference electrode was a 0.01 M solution of AgNO3 dissolved in the 0.1 M TBA-TFSI in PC electrolyte solution and calibrated to clean Li foil. The active charging area was controlled by sealing the electrochemical cell with a 0.8 cm diameter O-ring pressed onto the electrode surface. The film was charged inside an argon-filled glovebox and current was measured with a Biologic VMP-3 potentiostat. IR transmittance of charged films was measured ex situ by rinsing off the electrolyte with dimethyl carbonate (DMC) and placing the dry film in an O-ring sealed air-free cell capped by the Si substrate on one end and a 2 mm CaF2 window on the other end, mounted on a 5 mm pinhole mount. The sealed path length of the dry ex situ cell, containing argon from loading in the glovebox, was about 1 cm. FTIR transmittance spectra were baselined to the transmittance of the empty air-free cell, CaF2 window, and 5 mm pinhole mount. A schematic of the apparatus is shown in Figure S9. The optical transmittance spectra of charged films were fitted using a transfer matrix model following methods developed by S.J. Byrnes.29 The Scout software package (www.wtheiss.com) was also used for preliminary optical modeling. Details of the fitting procedure are described in the manuscript and Supporting Information.

Simulations of the absorbance of oriented monolayer assemblies of 10 nm cubic TiO2 NCs were performed by solving Maxwell’s equations with COMSOL as described in the Supporting Information. The NCs were oriented with respect to the incident polarized light to compare the LSPR along different crystal axes of the particles, and a range of interparticle separations was tested. The properties of the simulated NCs were estimated based on fitted parameters of the Nb− TiO2 dispersions and films. Parameters and assumptions used for the simulations are included in the Supporting Information (Figure S6).

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RESULTS AND DISCUSSION The electronic and optical properties of dense epitaxial or polycrystalline films of anatase TiO2 are well-characterized.9 However, the LSPR response of anatase TiO2 NCs has only been observed qualitatively, without any attempts to quantify the free carrier transport properties contributing to the LSPR. Here, the LSPR response of dilute TiO2 NC dispersions was measured by dispersing NCs in TCE at concentrations below 1 mg/mL, and measuring FTIR transmittance through a solution cell enclosed by two KBr windows. Figure 1a shows the extinction spectra for 1 mg/mL TiO2 solutions of varying Nb doping. A broad peak is observed around 3000 cm−1 for highly Nb-doped NCs corresponding to an LSPR absorption that scales with NC concentration (Figure S2). The intensity of the LSPR peak increases dramatically with Nb doping, and the peak energy blue-shifts with increasing Nb content. Another broad peak is observed at 3187 cm−1 that can be assigned to the O−H stretch of hydroxyl groups at the NC surface.30,31 The free oleic acid added to maintain a stable NC dispersion contributes several sharp peaks, including 2900 cm−1 (C−H stretch), 1720 cm−1 (CO stretch), and several smaller peaks below 1500 cm−1. C


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calculated an EMA that models anisotropic inclusions in an isotropic host medium.34 The macroscopic dielectric function based on this anisotropic EMA becomes an isotropic scalar if all of the inclusions are randomly oriented:

The optical dielectric response of conductive NCs can be described by a Drude model of free carrier excitation in the particles.1 The Drude model relates the complex dielectric response of free carriers to the plasma frequency, ωp, and the scattering rate, Γ: εD = 1 −

εeff = εh + 3fεh

ωp2

×

ω 2 − i ωΓ

The plasma frequency is dependent on the free electron concentration, ne, and conduction band effective mass, m*, in n-type semiconductors: ωp =

This EMA approaches the standard MG EMA as the inclusion (i.e., NC) dielectric anisotropy vanishes to the isotropic limit and approaches the Mie scattering model as the volume fraction approaches zero. The randomly oriented anisotropic MG EMA was used to model the transmittance of TiO2 NC dispersions in TCE, as shown in Figure 1. Several parameters were constrained to extract reliable properties from the fitted measurements. A dilution series of NC dispersions was prepared from the measured stock solutions to obtain reliable concentrations for FTIR spectra fitting, with NC volume fractions (volume of TiO2/total volume of solution) ranging from 250 to 10 ppm (Figure S2). The anisotropic high-frequency dielectric constants of TiO2 were set as 5.8 in the a direction and 5.4 in the c direction based on literature values.35 The dielectric constant of TCE was set as 2.336 and the path length of the solution was 1 mm. For measurements of the free carrier concentration, the components of the effective mass tensor were defined as 0.5m0 in the a direction (⟨100⟩) and 2.4m0 in the c direction (⟨001⟩) based on measurements by Hirose et al. However, Hirose et al. measured a wide range of effective masses in epitaxial Nb-doped TiO2 for the a direction (0.2− 0.6m0) and c direction (2−6m0) depending on Nb-doping content, likely due to nonparabolicity of the Ti 3d-derived conduction band.17 This uncertainty in the effective masses may contribute significant error in the extracted parameters from the model, and Drude parameter fits directly provide only the ratio ne/m*⟨hkl⟩. However, for the sake of comparison to practical values and evaluation of trends within the current data set, the free carrier concentrations, ne, are fit directly while assuming fixed values of effective mass (m*⟨100⟩ = 0.5m0 and m*⟨001⟩ = 2.4m0) throughout the rest of this article. The fitting parameters for the model were the TiO2 NC free carrier concentration, ne, damping, Γ, and a correction term to modulate the intensity of the hydroxyl O−H stretching peak at 3187 cm−1.30,31 The fits capture well the peak energy, height, and broadening for the highly Nb-doped samples, but are only weakly determined for dilute dispersions, or NCs with low Nb doping (Figure 1, Figures S2 and S4). The fitted Drude parameters for these dispersions are plotted in Figure 1b, and a comparison of the fitted parameters for different dilutions is shown in Figure S4. The carrier concentration increases from unmeasurably low values for the undoped NCs to about 4 × 1020 cm−3 for 6% Nb-doped TiO2. Despite the large uncertainty of the fits for 0% and 2% Nb-doped samples, several clear trends can be observed with increasing Nb doping at higher doping levels. These values reflect doping compensation efficiencies (i.e., activation) of 5−20%, as shown in Figure S5. Interestingly, the doping efficiency increases with Nb-doping content. Damping also increases with Nb doping, suggesting that Nb-dopant defects or electron−electron interactions are major sources of scattering in colloidal anatase TiO2 NCs. Epitaxial thin films of Nb-doped TiO2 can approach 100% doping compensation efficiency up

nee 2 ε0m*

At the dilute limit of conductive spherical nanoparticles in an insulating medium, the resonant energy of LSPR follows the Mie approximation,32,33 which predicts that the LSPR absorption peak energy and amplitude scales with the Drude plasma frequency, ωp. The scalar Drude model of charge transport does not distinguish between different lattice directions. Carrier transport in anatase TiO2 is highly anisotropic because of the tetragonal crystal structure and Ti 3d orbital-derived conduction band. Thus, to accurately describe scattering in this material, the model must incorporate a polarization tensor aligned with the anatase lattice directions. The anisotropic polarizability can be expressed by a diagonal tensor along the a and c axes of the anatase unit cell:17 ij ε⟨100⟩(ω) 0 0 yzz jj zz jj z jj 0 ε⟨100⟩(ω) 0 zzzz ε(ω) = jj jj zz jj z j 0 ε⟨001⟩(ω)zz 0 k {

ij ωp⟨hkl⟩2 yzz zz ε⟨hkl⟩(ω) = ε∞⟨hkl⟩jjjj1 − 2 j ω − i Γω zz k {

ωp⟨hkl⟩ =

(ε⟨100⟩ + 2εh)(ε⟨001⟩ − εh) − 2εh(ε⟨001⟩ − ε⟨100⟩) (1 − f )(ε⟨100⟩ + 2εh)(ε⟨001⟩ + 2εh) + fεh(ε⟨100⟩ + 2ε⟨100⟩ + 6εh)

nee 2 ε0m⟨*hkl⟩

In anatase TiO2, the high-frequency dielectric constant, ε∞, and effective mass, m*, have both been measured to have different values along the a and c lattice directions.17 However, lacking any definitive reason to believe otherwise, the damping parameter is assumed to be isotropic for this study. From these values a scalar Drude dielectric function can be defined for each diagonal element in the polarizability tensor. A macroscopic measurement of transmittance through a dispersion or thin film of TiO2 NCs samples an isotropic mixture of different crystal grain orientations. In both films and dispersions, the measured optical properties will be influenced by interfaces between the NCs and host medium, that is, TCE solvent for dispersions and the chemical environment of mesopores for thin films. NCs are much smaller than the wavelength of light exciting the LSPR, so an effective medium approximation (EMA) can be used to model the optical properties. Mendelsberg et al. have successfully applied an isotropic Maxwell-Garnet (MG) EMA to densely packed films of ITO NCs, which has a cubic unit cell and isotropic electronic properties.24 To extend the MG EMA to anatase TiO2, we follow the approach of Levy and Stroud, who have D


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Figure 2. Transmission FTIR spectra of TiO2 NC films deposited on 13 nm Au-coated Si substrates mounted in a CaF2-enclosed air-free cell. Optical density spectra of (a) 446 nm thick undoped TiO2, (b) 250 nm thick 6% Nb-doped TiO2, and (c) 210 nm thick 11% Nb-doped TiO2 NC films charged to −2 V vs Ag/Ag+ for sequential 2 min intervals of charging. (d) Differential optical density spectra for each charged film, relative to the measured spectrum of the oxidized film for each sample. (e) Cross-sectional SEM of annealed 6% Nb-doped TiO2 NC films deposited on a Cr,Au-coated undoped Si substrate, prior to electrochemical charging. The scale bar is 200 nm, and the inset shows a top-down SEM of the same film.

samples (ne > 1021 cm−3).9,16 For comparison, the plasma frequency, ωp, and optical mobility, μ = e/m*Γ, can be calculated for the high-mobility basal plane (m⟨100⟩ * ∼ 0.5m0) based on these extracted parameters. Along the a direction, 6.6% Nb-doped TiO2 NCs are found to have ωp,⟨100⟩ = 8080 cm−1 and μ⟨100⟩ = 7.6 cm2 V−1 s−1. This derived mobility is comparable to values recorded at room temperature by Hall effect measurements in epitaxial thin films of undoped anatase TiO2 (μ ∼ 10−20 cm2 V−1 s−1).7 The range of tuning of LSPR absorption achieved through synthetic doping is limited by the incorporation of dopant ions in the host lattice. LSPR can also be postsynthetically modulated by charging TiO2 NCs, which may allow for greater accumulated carrier densities than synthetic doping alone.5,6 Multiple approaches have been demonstrated to observe modulation in IR transmittance by charging colloidal metal oxide NCs, including UV photodoping of dispersed NCs in solution.20,37,38 The optical response of photodoped NCs may differ from electrochemically charged NCs because of differences in how the excess electronic charge is compensated. Moreover, in electrochromic films of NCs, the optical response is further modified by particle−particle interactions. Mendelsberg et al. demonstrated a method to extract Drude free-carrier parameters from the transmittance of a mesoporous film of ITO NCs using a multilayer stack optical model and employing a MG EMA.24 This approach is applicable to charged NC films and allows for the correlation of optical properties with electrochemical measurements. However, an in situ measurement of TiO2 NCs in a full electrochromic cell6 is difficult to resolve in the mid-IR range of the LSPR peak because of convoluted optical loss from the electrolyte and counter-electrode absorption and substrate reflectivity. Instead, an air-free ex situ measurement technique was used to probe the LSPR in charged TiO2 NC films within a simpler, more IRtransparent layer stack, as described in the Experimental

to 6% Nb,10 so these results indicate that future synthetic developments may produce doped anatase TiO2 NCs with much higher conductivity than the materials realized up to this point. The role of crystalline anisotropy in the LSPR response is revealed by comparing fits to an isotropic model of the dielectric function. Figure S3a demonstrates that a reasonable fit to the measured volume fractions is infeasible for an isotropic EMA. The only way to simulate these LSPR peaks with an isotropic EMA is to artificially decrease the volume fraction to about 75% of the actual value (Figure S3c). The high-mobility a axes will scatter more of the incident field than the c axis, so the infrared absorption in a NC ensemble will depend on the averaged projections of the incident field on the anatase unit cell orientation for each particle. Inclusions that are oriented with a smaller projection of the incident field along the a axes, that is, with the field primarily along the c axis, will absorb less light than other orientations. Thus, the macroscopic effective medium is expected to show an artificially lowered volume fraction of scattering inclusions, consistent with the observed deviation in optical density. This phenomenon can be illustrated by simulating the absorption of an ensemble of dispersed Nb-doped TiO2 NCs using COMSOL, as described in the Supporting Information (Figure S6). Figure 1c illustrates that particles oriented with a maximal projection of the incident field along the high-mobility a axis (E⃗ ⊥ c⃗) have significantly higher amplitude and energy LSPR absorption than particles oriented with a minimal projection along the a axis (E⃗ ∥ c⃗). Furthermore, the simulated isotropic averaged spectrum has a similar peak energy and broadness to the E⃗ ⊥ c⃗ projection spectrum, but with only about 70% of the amplitude, agreeing well with the results shown in Figure S3. Drude fits of TiO2 NC dispersions reveal that carrier concentrations achieved by Nb doping are nearly an order of magnitude lower than values achieved in conventional thin film E


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Figure 3. (a) Schematic describing the fitting algorithm to extract electronic properties from modeled optical transmittance through charged TiO2 NC films on Au-coated Si substrates. (b) A comparison of measured and fitted optical spectra for oxidized and maximally reduced TiO2 NC films.

Figure 4. Drude carrier properties extracted from optical fits of charged films. Each marker represents a different electrochemical charging state, ) to the total with the bold-edged markers corresponding to oxidized films. (a) Comparison of the optically fitted free carrier concentration (noptical e + ndoping ). The dashed line indicates 100% optical charging accumulated carrier concentration from electrochemical charging and Nb doping (nechem e e = nechem + ndoping ). (b) Plot showing the variations in optically fit carrier concentration for different Nb-doping percentages for NC efficiency (noptical e e e dispersions and thin films. (c) Plot showing the correlation between the optically fit carrier concentration and damping parameter for charged films )1/3, along with a linear fit to all film and dispersion data. and NC dispersions. The inset shows a plot of damping against (noptical e

Supporting Information. The total measured charge accumulation was found to depend strongly on leakage current, so a kinetic model of charging was used to estimate this value. For each charging step, the time-dependent charge was fit to a combined capacitive and diffusive kinetic model, accounting for both the capacitive response of the NC film and the diffusive transport of compensating ions through the electrolyte in the mesoporous film, as described in the Supporting Information (Figures S10 and S11). FTIR transmission spectra for TiO2 NC films with different Nb-doping content are shown in Figure 2 during stepwise ex situ charging at −2 V. Each film shows broad increases in optical density after each charging step, indicating that charge accumulates across sequential steps. Figure 2d reveals that the electrochromic modulation peaks around 2000−6000 cm−1, which is consistent with an increase in the carrier

Section. Figure 2e shows cross-sectional and top-down SEM of the conductive films used for ex situ IR transmission measurements, highlighting the ligand-exchanged TiO2 NC films deposited on a conductive, semitransparent Cr,Au-coated Si substrate. TiO2 NC films were electrochemically charged using a nonintercalating electrolyte in an aprotic solvent (0.1 M TBATFSI in PC) to avoid phase transformations and electron trapping caused by the insertion of small cations such as H+ and Li+.37,39−41 TBA+ is a bulky, nonintercalating cation that can compensate only electrochemical charge by surface capacitance or pseudocapacitive surface reactions.5,39,42,43 Other electrolyte solvents, such as tetraglyme, were found to delaminate the NC films from the substrates during sustained charging. A stepwise charging process was used to access a variety of electrochemical charge states, as described in the F


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concentrations in Nb-doped TiO2 films.16 Higher carrier concentrations in TiO2 NC films may be attributable to the 300 °C in argon annealing conditions used to prepare the films. Furthermore, the NOBF4 ligand-exchange treatment may have induced changes in NC surface states, which can play a dominant role in the distribution, and therefore the concentration, of carriers within semiconductor NCs.45 Electrochromic LSPR modulation is also affected by synthesis and processing conditions. All of the films show more effective modulation in noptical upon doping and charging than the NC e dispersions. However, the role of Nb-doping concentration on charging efficiency (noptical /[nechem + ndoping ]) deviates between e e e electrochromic thin films and dispersed NCs. Nb-doped thin films show less efficient electrochromic charging than undoped films, whereas synthetic doping efficiency apparently increases with higher Nb doping (Figure S5). Previous studies have observed a dependence between Nb-doping content and the total and relative modulations in optical density upon electrochemical charging,6 and these results suggest that synthetic doping and processing conditions may be used to optimize LSPR modulation in TiO2 NCs. The broad LSPR response in doped and charged TiO2 NCs demonstrates that high damping may be a significant constraint restricting functional application of this material, depending on the specific application requirements. Figure 4c shows that damping values determined by optical fitting generally increase with carrier concentration in the charged films, similar to the results for NC dispersions in Figure 1b. Damping can be caused by a variety of sources, such as ionized impurity scattering from aliovalent dopants or oxygen vacancies,46−48 phonon scattering,49 surface scattering,19,30,45 and electron correlation effects,50 or broadening due to NC ensemble heterogeneity and inhomogeneous interparticle damping. However, a simple model can be applied that considers only the expected electron−electron scattering from free carrier transport, to test if any sources of nonideal carrier scattering play a significant role in charged and Nb-doped NCs. A freeelectron model of scattering can be derived from the Fermi velocity, vF, and bulk mean free path, λ, of electrons in anatase TiO2:32

concentration and LSPR absorption around these energies. Transmission spectra of the charged films were fit to a transfer matrix optical model of reflection and transmission across each layer in the film stack, adapted from simulation software created by S.J. Byrnes. A similar model was used by Matsuzaki et al. to simulate optical spectra of epitaxial films of anatase TiO2.44 Mendelsberg et al. followed the same framework to model charged thin films of ITO NCs with the Scout software package (www.wtheiss.com), albeit with an MG EMA to model the NC layer.24 Electronic properties were extracted from the optical spectra through an iterative fitting method, as shown in Figure 3a, and described in more detail in the Supporting Information. The transfer matrix model was adapted to TiO2 NC films by incorporating an anisotropic MG EMA model for the complex dielectric constant of the NC layer, identical to the EMA used for measurements of NC dispersions in TCE (Figure 1). All films show good fits to the layer stack optical simulations across a wide IR spectral range for both reduced and oxidized samples (Figure 3b). Fits also reproduce the differential optical density (ΔOD) of the measured spectra (Figure 2d). In earlier attempts to model the optical properties of ITO NC thin films, Mendelsberg et al. demonstrated that the volume fraction and host dielectric constant are linearly correlated in fits of optical transmittance.24 Both of these parameters were allowed to float during fitting in this study, and a similar linear correlation was observed (Figure S17). A sensitivity analysis of the input parameters on the goodness of fit and extracted carrier concentration is shown in Figure S16, revealing that the extracted fits were insensitive to most input parameters, and yielded only minor uncertainties to parameter variations. Fits of all three films yielded realistic volume fractions of about 85%, and a host dielectric constant between the limits of air (ε = 1) and TiO2 inclusions (ε = 5.4−5.8), as expected. The extracted free carrier parameters from optical fitting enable a direct comparison of the inserted charge (through synthetic doping or electrochemical charging) to apparent values from IR spectra, as shown in Figure 4a. The optically fit carrier concentration, noptical , increases with Nb doping and e electrochemical reduction for all measured samples. Interestingly, Nb doping has a significant effect on both the absolute carrier concentrations reached in charged films and NC dispersions, as well as the modulation in noptical with charging e or doping. Charged films of undoped TiO2 NCs reach only ∼ 3 × 1020 cm−3, while Nb-doped TiO2 NC films exceed noptical e 21 10 cm−3 upon charging, similar to values measured in with epitaxial Nb-doped TiO2 films.9,16 The change in noptical e charging also depends on Nb doping, with the total modulation in noptical ranging from 2.5 × 1020 cm−3 for e undoped TiO2 to 7 × 1020 cm−3 for 11% Nb-doped TiO2. Although the low mobility along the anatase c direction redshifts, broadens, and diminishes the intensity of the observed LSPR peak, these results indicate that anatase TiO2 NC films can support the same dramatic modulation in carrier concentrations observed in epitaxial thin films. Fitted carrier concentrations for TiO2 NCs in dispersions and films are also found to differ, as shown in Figure 4b. Films of both the undoped and 6% Nb-doped TiO2 NCs show higher carrier concentrations, even in their electrochemically oxidized states, than dispersed NCs of the same stoichiometry. Film processing may be responsible for this discrepancy; Nakao et al. observed that annealing conditions, particularly the oxygen partial pressure, can impact free carrier

Γ=

ℏ(3π 2ne)1/3 vF ; vF = λ m*

This scattering model implies that damping increases linearly with ne1/3. The inset of Figure 4c demonstrates this hypothesis, and all of the doped NC dispersion samples and charged film samples follow the same linear trend. The large uncertainty in fitted ne values for low Nb-doping dispersion measurements (Figure 1b) prevents an accurate quantitative determination of carrier-independent scattering sources, particularly at the lowdoping and unbiased limit. However, assuming a constant, isotropic effective mass of m* = 0.5m0 and no other sources of scattering, a linear fit yields a mean free path of 9.6 Å. By this qualitative model, a bulk isotropic mobility of μ = 4.7 cm2/(V s) is estimated for ne = 1021 cm−3, roughly consistent with measured values of thin films as described previously. There are several reasons to expect that this measured mobility is underestimating the bulk carrier mobility in Nb-doped TiO2 NCs. The analysis above ignores the anisotropic crystal structure of anatase TiO2, and there is actually a significant difference between the a and c direction mobilities, as described previously. Also, the small radius of the NCs (r ∼ G


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dispersions and films of Nb-doped TiO2 NCs. We observed that the low effective LSPR energy and intensity can be attributed to the high effective mass along the c axis of anatase TiO 2. Nb doping is observed to induce free carrier concentrations comparable to those observed in thin film measurements of Nb-doped TiO2, although with low doping efficiencies of 10−20%. Much greater modulation of carrier concentration was observed in electrochemically charged thin films of TiO2 NCs, which can reach carrier concentrations above 1.5 × 1021 cm−3 when fully reduced. These results reveal that carrier concentration in anatase TiO2 NCs can be effectively modulated by synthetic and electrochemical means, with mobilities similar to those of thin film samples. Furthermore, the large carrier concentrations achieved in NC thin films suggest that different synthetic or postprocessing techniques may be profitably applied to increase the carrier concentration, and IR LSPR response, of unbiased TiO2 NCs. These results also showcase a comprehensive method to quantify carrier properties in plasmonic semiconductor NCs. A combination of dispersion and thin-film optical measurements of semiconducting colloidal NCs provides complementary information to study defect properties, scattering mechanisms, and other optical behaviors. Appropriate substrate design allows for ex situ transmission IR observations of reduced semiconductor films, which can resolve mid-IR light−matter interactions. The energy, intensity, and broadening of LSPR absorption in conductive NCs is highly sensitive to free carrier properties, so IR optical analytical methods can provide a wealth of information about these materials. These techniques can be used to advance our understanding of electron transport in IR plasmonic nanostructures and rationally design materials with improved mobilities and conductivities. More generally, the role of effective mass anisotropy in determining the IR response ensembles of anatase TiO2 NCs suggests a potential new role for birefringent semiconductors in plasmonics applications. Simulations of degenerate NCs aligned with the high-mobility basal lattice plane parallel and perpendicular to the incident electric field demonstrate that dynamic modulation of IR LSPR could be achieved through stimulated changes in NC orientation within self-assembled architectures, as well as through electronic modulation.

5 nm) is of the same order of magnitude as the fitted mean free path, suggesting that surface scattering may contribute to the observed damping of the LSPR.19,30,45 Nonetheless, the agreement of a simple free-electron model with the observed damping values for both NC films and dispersions across a wide range of Nb doping suggests that electron−electron scattering dominates carrier mobility of Nb-doped and charged TiO2 NCs. Scattering is ultimately limited by the relatively large intrinsic effective mass in anatase TiO2, compared to other semiconducting oxides commonly used in plasmonic or TCO applications, which places an upper bound on the mobilities that can be achieved in this material. Nevertheless, these results confirm that free carrier concentration in TiO2 NCs can be effectively modulated across a wide range of values with comparable bulk mobilities to observed anatase TiO2 thin films. The analysis above indicates that the observed broadness and low peak energy of LSPR absorption in TiO2 NCs can be attributed primarily to crystalline anisotropy and intrinsic scattering rather than ineffective synthetic doping or electrochromic modulation. The NC films and dispersions measured in this study contain randomly oriented ensembles of particles, with the incident electric field projected onto the anatase highmobility a directions and low-mobility c direction with equal weight. However, an ensemble of NCs preferentially aligned along the incident electric field may show more responsive LSPR absorption. Indeed, this scheme may already be experimentally feasible; bottom-up approaches to direct the assembly of colloidal nanoparticles into dense films have produced assemblies with oriented faceting and superlattice order.51 To highlight the optical effects of NC alignment in thin films, simulations of IR absorption in dense ensembles of oriented NCs were performed (Figure S7). A clear difference in LSPR peak intensity and energy is observed between light polarized along the high-mobility basal plane and the lowmobility c axis for dense monolayers with interparticle separations of both 1 and 2 nm. These results are consistent with simulations of dispersed NCs, separated by 30 nm interparticle distances (Figure 1c, Figure S7). Figure S7 reveals that packing density has a nonmonotonic relationship with the peak energy, broadness, and amplitude of LSPR absorption, indicating the convoluting effects of particle morphology and interparticle coupling between adjacent LSPR modes.23,24,52−56 Nonetheless, these results are consistent with the observed sensitivity of the anisotropic MG EMA fits to the NC volume fraction (Figures S16 and S17). More generally, these simulations indicate that the IR optical response of TiO2 NC ensembles can be dramatically targeted and improved for specified applications through oriented self-assembly. Particle orientation thus presents an additional source of IR modulation for birefringent semiconductor NCs, which can complement the effects of synthetic doping or electrochemical charging.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b04519. Grazing-incidence XRD of TiO2 NC films, transmission FTIR spectra of TiO2 NC dispersions and additional comparisons of fitted parameters, details of COMSOL optical transmittance simulations, SEM of TiO2 NC films, additional details of the electrochemical charging apparatus and electrochemical measurements, a description of the thin-film optical transmittance model, tabulated parameters from thin-film fits, and a sensitivity analysis of fitted thin-film optical spectra (PDF)

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CONCLUSIONS AND OUTLOOK Anatase TiO2 is a promising alternative transparent conductive oxide that shows high carrier concentrations and conductivities, comparable to industry standard materials such as ITO. However, Nb-doped anatase TiO2 NCs have anomalously low energy and amplitude LSPR responses despite the high conductivities of conventional Nb-doped anatase TiO2 thin films. We applied an anisotropic MG EMA model of Drude electronic properties to quantitatively model the LSPR of

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Clayton J. Dahlman: 0000-0002-4555-4846 H


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Ankit Agrawal: 0000-0001-7311-7873 Delia J. Milliron: 0000-0002-8737-451X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the National Science Foundation, including NASCENT, an NSF ERC (EEC1160494, C.M.S.), CHE-1609656 (C.J.D., A.A.), and the Welch Foundation (F-1848). Use of SSRL, SLAC National Accelerator Laboratory, was supported by the U.S. Department of Energy (DOE) under Contract No. DE-AC02-76SF00515.

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