Localized Charges Control Exciton Energetics and Energy Dissipation

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Localized Charges Control Exciton Energetics and Energy-Dissipation in Doped Carbon Nanotubes Klaus H. Eckstein, Holger Hartleb, Melanie M. Achsnich, Friedrich Schöppler, and Tobias Hertel ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b05543 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 10, 2017

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Localized Charges Control Exciton Energetics and Energy-Dissipation in Doped Carbon Nanotubes Klaus H. Eckstein,

†

Holger Hartleb,

†

Melanie M. Achsnich,

and Tobias Hertel

†Institute

†

Friedrich Schöppler,

†

∗,†,‡

of Physical and Theoretical Chemistry, Julius Maximilian University Würzburg, Germany

‡Röntgen

Research Center for Complex Material Systems, Julius Maximilian University Würzburg, Germany

E-mail: [email protected]

Phone: +49 931 3186300

Abstract Doping by chemical or physical means is key for the development of future semiconductor technologies. Ideally, charge carriers should be able to move freely in a homogeneous environment. Here, we report on evidence suggesting that excess carriers in electrochemically p-doped semiconducting single-wall carbon nanotubes (s-SWNTs) become localized, most likely due to poorly screened Coulomb interactions with counterions in the Helmholtz layer. A quantitative analysis of blue-shift, broadening and asymmetry of the rst exciton absorption band also reveals that doping leads to hard segmentation of s-SWNTs with intrinsic undoped segments being separated by randomly distributed charge puddles approximately 4 nm in width. Light absorption in 1

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these doped segments is associated with the formation of trions, spatially separated from neutral excitons. Acceleration of exciton decay in doped samples is governed by diusive exciton transport and non-radiative decay at charge puddles within 3.2 ps in moderately doped s-SWNTs. The results suggest that conventional band-lling in s-SWNTs breaks down due to inhomogeneous electrochemical doping.

Keywords carbon nanotubes, band-lling, electrochemical doping, carrier localization, exciton connement, exciton transport, energy dissipation

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Most of todays computing and communication technologies would be unthinkable without the functionality provided by semiconductor doping. A prerequisite for providing such functionality is the ability of charges to move freely without being trapped by chemical impurities in the bulk semiconductor or at its interfaces. 1,2 Free carrier motion is also at the heart of technologies based on the manipulation of surplus charges by external elds. Homogeneous doping using substitutional donor or acceptor impurities in conventional semiconductors thus relies on shallow impurity-carrier interaction potentials of only a few tens of meV in depth 3 which ensures that thermal heteroatom ionization is ecient, allowing carriers to become delocalized. The importance of Coulomb interactions between charged impurities and free carriers, however, is enhanced in low-dimensional semiconductors due to both, weaker screening and constraints on wave-functions in reduced dimensionality. 46 The hydrogenic ground state binding energy, for example, increases dramatically as dimensionality is decreased. 6,7 Accordingly, exciton binding energies in quasi 1D s-SWNTs are nearly two orders of magnitude higher than in their three dimensional counterparts. 811 However, the degree to which weak screening aects localization of excess carriers and their interaction with excitons in low-dimensional materials appears not to be as well understood. Electron-hole pair excitations in quantum well (QW) structures, for example, are reported to bind to localized charges forming so-called trion absorption bands. 12,13 Seemingly in contradiction to these results, quantum beats in four wave mixing experiments suggest that trions and excitons in QWs are not spatially separated. 13 In covalently doped s-SWNTs, trion-like emission bands are commonly associated with excitons bound to, or interacting with charges localized at a chemical functionality. 14,15 Similarly, excess carriers in non-covalently or electrochemically doped s-SWNTs are also found to give rise to redshifted trion absorption. 1621 The dynamics of such trion formation and decay has also been studied with reported trion lifetimes of a few picoseconds. 22 However, some reports suggest that excess carriers in these samples are delocalized 23 while the lack of

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a clear temperature-dependence of trion photoluminescence intensities suggests that such excitations are localized. 19 The character of the distribution of excess carriers in non-covalently doped s-SWNTs, homogeneous vs in-homogeneous, is thus still subject of current debate. The work presented here challenges the notion of homogeneous carrier distributions in electrochemically doped s-SWNTs. Instead, doping is found to be inhomogeneous with localized charge puddles readily formed due to poorly screened Coulomb interactions between free carriers in SWNTs and counterions in the Helmholtz layer. Moreover, charge puddles are found to lead to hard segmentation of s-SWNTs and act as conduits for non-radiative exciton decay. These ndings suggest that doping strategies aimed at providing s-SWNTs with highly mobile excess carriers for electronic applications must be able to manage the depth of counterion-induced Coulomb wells.

Results and Discussion Absorption spectra of s-SWNTs are dominated by exciton bands, that arise thanks to characteristically weak electrostatic screening in 1D materials and the associated transfer of oscillator strength from free carrier transitions to bound electron-hole pairs. 5,2426 Dominant exciton bands are clearly seen in the topmost spectrum of Fig. 1a which shows the absorption spectrum of a thin intrinsic (non-doped) nanotube lm made from semiconducting (6,5) SWNTs. The S1 absorption band at 1.24 eV corresponds to the rst and the S2 band at

2.16 eV corresponds to the second subband exciton transition. The broader asymmetric absorption feature at 1.45 eV is attributed to a phonon sideband of the rst exciton. 2729 The electrochemical potential of this lm is controlled by a Pt-mesh working electrode (WE) allowing to reversibly increase or decrease the carrier concentration by electrochemical gate-doping. 21,30 At the potentials applied here, the charge transfer between the WE and the SWNT lm is fully reversible. Thus, the role of the electrolyte is to deliver the electrical eld to the interface between SWNT and WE and thereby to allow a controlled realignment

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a

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S2 S1 + ph moderately doped (+ 0.90 V) +

X1

S1

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H - band

residual S1

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Figure 1: Spectral changes in doped s-SWNT lms. (a) Absorption spectra of an intrinsic, moderately and heavily p-doped (6,5) lm at dierent electrode potentials. Dominant absorption features belong to the rst S1 and second S2 subband exciton. The rst subband exciton becomes more asymmetric, blue shifted, and broadened as doping levels increase. (b) An overview of absorption changes at specic energies.

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of nanotube valence and conduction bands with respect to the Fermi level of the WE. The potential drop at the SWNT-electrolyte interface on the other hand is negligible, due to the accumulation of counterions in the electrochemical double layer and a correspondingly high interface capacitance of approximately 10 fF · µm−1 . 21,30 The center of the spectroelectrochemical window dened by the onset of reduction and oxidation of (6,5) s-SWNTs, seen in Fig. 1b, serves as internal reference facilitating a comparison of redox-potentials for dierent experimental runs and setups. The spectra in the lower part of Fig. 1a were recorded at positive WE potentials of

+0.90 V and +1.10 V, which for an intrinsic band gap of 1.55 eV are expected to lower the electrochemical potential of electrons into the valence band of (6,5) SWNTs. At +0.90 V p-doping is evidenced by the appearance of a trion absorption band X1+ at 1.06 eV and by a decrease of the rst excitons oscillator strength. Trion absorption is associated with the formation of a charged exciton state. 1621,3135 As seen in Fig. 1b the trion band reaches its peak intensity at +0.90 V with a similar behaviour observed at negative potentials. At higher potentials the trion band intensity decreases until it merges with the broad H-band in the heavily doped regime. The latter has previously been found to assume nearly all of the rst subband oscillator strength of the intrinsic system. 21 The transition energies of exciton bands in non-covalently doped SWNTs are typically found to be blue-shifted from a few meV 33,36 up to over 80 meV. 21,37 This has previously been attributed to changes of exciton binding and band gap renormalization in doped sSWNTs 33,36,38 with the tacit assumption that nanotubes are homogeneously doped. Implicitly, exciton and trion bands were thus also assumed to be part of the same electronic manifold. If carrier densities in (6,5) SWNTs at dierent potentials are estimated assuming homogeneous doping within the rigid band model, 21,39 we obtain about 0.6 e · nm−1 for the moderately doped SWNT at +0.90 V and about 0.8 e · nm−1 for the heavily doped (6,5) SWNT at +1.10 V. 21 However, as discussed in detail below, this approach is here called

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into question due to evidence indicating that in-homogeneous carrier distributions dominate both, electrochemical and redox-chemical doping. To better understand how excess charge carries in SWNTs may become localized, we begin by looking at the expected magnitude of carrier interactions with counterions at the SWNT-electrolyte interface (see Fig. 2a). The importance of adsorbed counterions has previously been recognized for redox-chemical p-doping of SWNTs in AuCl3 solution, where contrary to the prevailing belief - the degree of p-doping was found to be correlated with the concentration of adsorbed Cl− counterions rather than the concentration of Au3+ which is reduced by charge transfer from the SWNTs. 40 We stipulate that counterions from the electrolyte may here play a similar role in controlling doping levels due to strong attractive Coulomb interactions with free carriers in SWNTs. The resulting eld-induced chargelocalization can be estimated using the local electrostatic potential surrounding a counterion

V (z) = −e2 /(4π0 (d2 + z 2 )1/2 ), with a homogeneous dielectric constant at counterion distance d from the nanotube axis and at an axial displacement z (see Figs 2a and b). This potential can trap and locally conne excess charges in SWNTs, with the resulting carrier distribution along the SWNT axis being determined by the one-dimensional Schrödinger equation with the Hamiltonian H = −~2 ∇2 /2me + V (z). The eective hole mass of

0.07 me is taken from a chirality corrected tight binding calculation of the (6,5) tube using a nearest neighbour hopping matrix element γ0 = 4.1 eV to reproduce the estimated band gap of 1.55 eV. 21 Two scenarios are considered, one with the counterion located at 0.7 nm from the SWNT center axis (see Fig. 2a) and one with the counterion at 1.5 nm, corresponding to approximate ion distances on bare and on polymer covered SWNTs. The resulting dependence of rst and second eigenstate binding energies and the full width at half maximum ∆ (FWHM) of the corresponding charge distributions are shown in Fig. 2c as a function of the dielectric constant . Dielectric screening is expected to range from = 4, typically used for free SWNTs 27,41 to about 8 for tetrahydrofurane as solvent. For a directly adsorbed counterion, the n = 1

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counterion

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b ✏ V / eV

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| (z)|2 , ✏ = 8 puddle ground state

electrostatic potential

z / nm

c d= 0.7 nm 1.5 nm

n=1 n=2 well depth

✏

Figure 2: Formation of charge puddles. (a) Interaction of carriers in SWNT valence or conduction bands with external counterions supports the formation of charge puddles. (b) Counterion-induced electrostatic potential along the SWNT axis and the corresponding electronic ground state n = 1 for a trapped charge at = 8 and d = 0.7 nm. (c) Dependence of the n = 1 and 2 puddle binding energies Ep and the width ∆ of the corresponding wavefunction |Ψn (z)|2 on dielectric constant for two counterion distances, d = 0.7 nm and 1.5 nm.

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ground state of the on-tube charge is then expected to form a charge puddle, ranging from 2.7 to 3.8 nm in size and with a binding energy between 250 and 103 meV (see Fig. 2c). Independently, a simple estimate of the n = 1 ground state population using Boltzmann's equation and a phase space factor on the order of 50 corresponding to the fractional length of a charge puddle with respect to an otherwise intrinsic SWNT suggests that for a puddle to be occupied most, say 90% of the time, the carrier binding energy should exceed about 8.50 cm = 245 pt 150 meV which is well in line with expectations for a dielectric constant of ≈ 6 or less.

a

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w EGS 0 barriers for exciton motion

w

b frequency 0

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0

+1.10 V

l 0

SWNT length

Figure 3: Spectral signatures of exciton connement. (a) Charged regions in the SWNT are assumed to represent local perturbations of the band structure which act as absorbing barriers for excitons. EGS represents the conned exciton's ground state energy in a box of width w as induced by barriers of width ∆. (b) and (c) Poissonian and lognormal barrier distributions leading to connement of excitons. The rst is expected for randomly scattered doping sites with average distance w while the latter more appropriately describes the distribution of nanotube lengths with average l. (d) One-parameter t to background-corrected exciton bands using a Poissonian barrier distribution.

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The charge localization predicted by this model is also expected to have profound implications for the energetics and dynamics of excitons. Locally doped regions of the band structure can potentially act as connement and as barriers to exciton transport as well as conduits for non-radiative decay. 42 A hard segmentation of SWNTs by localized carriers should impose boundary conditions on the axial component of the exciton wavefunction on non-doped regions and thereby increase their ground state energy (see Fig. 3a), evidence for which will be discussed in the following. Our analysis of changes to the S1 exciton in doped SWNTs will thus have to account for key observations, specically the blue shift, broadening and asymmetry of exciton bands as well as the decrease of oscillator strength. The following model will try to do so by a) allowing exciton transition energies to increase due to axial connement, b) by accounting for a random distribution of charge puddles and thus a Poissonian distribution of connement lengths, and c) by accounting for the reduction of intrinsic SWNT regions due to an increase in the number of charge puddles. The increase of the ground state energy of a conned exciton depends on its eective mass M = mv + mc and is estimated using the ground state energy of a particle in a one-dimensional box EGS (w) = π 2 ~2 (2M w2 )−1 where w is the distance between a specic pair of barriers. If such barriers are randomly distributed along the length of SWNTs, we expect the abundance of barrier spacings to follow Poissonian stochastics with probabilities

pw (w) = w−1 e−w/w as shown in Fig. 3b. 43,44 Here w is the mean barrier spacing. The line shapes of individual nanotube segments between barriers are all assumed to be of the Voigt-type, with a shape function fw (E) that can be determined using a Voigt t to the exciton band of the intrinsic SWNT sample. The index w reminds us that the band center has to be shifted by the appropriate zero point energy EGS (w). The exciton line prole in doped samples is then calculated from the weighted average of absorption bands

1 I(E) = w

Z

∞

pw (w0 )w0 fw0 (E) dw0

0

10


(1)

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The factors w and w−1 take care of weighting the spectral contribution of a particular SWNT segment by its length and of normalizing the weighting function such that the total oscillator strength is conserved. Changes of oscillator strength by phase space lling are included in the model by assigning a nite width ∆ to each of the barriers. This is implemented by replacing the distribution function pw (w) with pˆw,∆ (w) = w−1 e−(w+∆)/w . The resulting two-parameter ts to a series of experimental absorption spectra are shown in Fig. 3d for dierent doping levels. Within this model, the shift of the exciton absorption-band maximum by up to nearly 100 meV, its broadening as well as its asymmetry are solely controlled by the mean barrier spacing w. The fact that changes of all three characteristics are very well captured by this single parameter strongly supports the assumptions underlying the charge puddle and hard segmentation model. The width ∆ of charge puddles in turn exclusively controls the reduction of oscillator strength of the exciton band and links the change in line shape to changes of its intensity. On average ∆ is found to be 4 nm, decreasing somewhat as doping levels increase, in very good agreement with the estimate of charge puddle size estimated by the above calculations.

These nding suggest that excitons and trions appear to be localized on dierent sections of the same SWNT. Further evidence for this hypothesis can be obtained from pump-probe experiments in which selective excitation of a lower subband feature (exciton or trion) is used to identify if the resulting ground state depletion leads to a photobleach (PB) of all or a preferential bleach of a subset of higher lying features. If a subset of absorption bands are photobleached preferentialy following selective excitation in the NIR range this implies that trion and exciton are somewhat decoupled and possibly do not even share the same ground state. The results are shown in Fig. 4 for a moderately doped lm where selective excitation of the S1 exciton and the resulting ground state depletion leads to a strong photobleach at higher

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doped +

δ

PB

S1 pump

pump

S0

c

X2

S2

X2

+

X1

+

X0

+

+

ΔT/T PB @ 2.17 eV

PB @ 2.10 eV

Figure 4: Selective transient photobleach of exciton and trion manifolds. (a), (b) Pump-probe scheme for selective excitation of doped and non-doped SWNT sections. (c) Changes in the photobleach (PB) in the VIS spectral range suggest that trion and exciton manifolds are localized on dierent sections of the same SWNT.

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energies near 2.10 eV and a somewhat weaker bleach at 2.17 eV. The two contributions are clearly visible in Fig. 4 c). On the other hand, if the X1+ trion feature is selectively pumped, optical transients in the VIS range show a clear shift of the bleach signal to the lower energy feature 2.10 eV (see Fig. 4c). This feature is thus attributed to an optical transition localized on doped SWNT segments,

i.e.

on charge puddles while the higher lying 2.17 eV feature

is attributed to the intrinsic exciton structure. This distinct response in the VIS regime indicates that trion and exciton manifolds are only weakly coupled and do not share the same ground state. This can be taken as evidence for spatial separation of the corresponding electronic manifolds,

i.e.

exciton localization on intrinsic and trion localization on doped

SWNT regions. Next we explore the ramications of the hard segmentation model for exciton dynamics. The pump-probe scheme used for these experiments is outlined schematically in Fig. 5a. Excitons in the second subband are excited at 2.17 eV and undergo ultrafast interband relaxation, leading to a rapid photobleach (PB) of the rst subband transition. 4547 Subsequently, excitons can diuse to doped nanotube segments where they decay non-radiatively, for example by coupling to the trion manifold. In Fig. 5b we have reproduced transient spectra for a series of applied potentials, normalized to the peak of individual cross-correlation PB signals. When lms are doped, the transient spectra reveal a blue shift and broadening of the main PB feature, similar to the broadening observed in ground state absorption in Fig. 3d. The spectrally and time-resolved maps of an intrinsic and of a weakly doped lm in Fig. 5c reveal both, a change of the amplitude of optical transients due to the reduction of the S1 oscillator strength as well as a change in their dynamics. Non-radiative decay of excitons in intrinsic SWNTs has previously been suggested to occur primarily at their ends. 48 Accordingly, the pronounced length-dependence of SWNT photoluminescence quantum yields (PL-QYs) as well as their small magnitude of no more than a few percent have been attributed to exciton migration and ecient non-radiative

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a

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S0

c

+ 0.20 V

X1

+

X0

+

+ 0.85 V + 0.90 V

+0.20 V PA

+0.70 V PB

ΔT/T

energy / eV

Figure 5: Ultrafast exciton dynamics in intrinsic and doped SWNTs. (a) Schematic of the pump probe scheme. Doped segments here serve as primary conduits for ecient nonradiative decay. (b) Series of transient absorption spectra for dierent oxidation potentials. (c) Two-dimensional representations of spectral and temporal changes for a non-doped (left) and a doped SWNT sample (right).

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decay at chemical functionalities at tube ends. Diusion coecients in aqueous SWNT samples are reported to be on the order of 2 − 10 cm2 · s−1 . 48,49 The non-radiative decay process itself is assumed to be very ecient and may be facilitated by dierent types of chemical functionalities. 15,42,48,5053 For a quantitative analysis of optical transients we thus need to model both, exciton diusion as well as ecient non-radiative decay, either at nanotube ends or at absorbing barriers, as illustrated schematically in Fig. 6a and b. The initial optical excitation is assumed to generate a homogeneous exciton distribution in-between quenching sites (see Fig. 6b). Diusion and ecient quenching at chemical impurities then leads to a steady depletion of the exciton population which decays asymptotically with kinetics typical of diusionlimited reactions. 5456 Integration of the corresponding analytical expression by Balagurov and Vaks 43 yields the exciton population Pl (t) between two quenching sites a distance l apart

∞ X b2n 8 exp − t Pl (t) = P0 2 b 2τ d n n=0

(2)

with bn = (2n + 1)π . The only free parameter in this analysis is thus the diusion time

τd = l2 /2D, which species the time-scale needed by reactants (excitons) to reach one of the quenching sites where they decay instantly. Lastly, to account for dierent quenching site separations we again have to average over an appropriate distribution of quenching site distances. In Fig. 6c we have contrasted the residuals of the best t to the data using a log-normal distribution (red open circles) with the residuals from a t using a Poissonian distribution (blue open circles) of quenching site spacings. Evidently, agreement with the log-normal weighted length distribution, here with a standard deviation of 0.56, 53 is considerably better than for the Poissonian distribution (see Fig. 6c). A simple mono-exponential t is shown for reference purposes in Fig. 6c (green dot-dashed line). This nding is also in excellent agreement with experimentally determined SWNT log-normal length distributions in similar samples. 53,57 The t yields an ensemble-

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t = t0 t1 > t0 t2 > t1

l, w c Poissonian distribution

log-normal distribution

Figure 6: Exciton diusion and non-radiative decay in intrinsic SWNTs. (a) Schematic illustration of exciton diusion to absorbing chemical functionalities. (b) Schematic illustration of the corresponding diusion limited reduction of the initial exciton distribution. (c) Comparison of a t to experimental data using a log-normal (red open circles) or Poissonian (blue open circles) distribution of quenching sites. Best agreement is found for log-normal statistics, characteristic of nanotube length distributions. The inset shows that agreement with experimental data is improved if one allows for a nite 40 fs rise time of the S1 photo-bleach following excitation of the second subband exciton.

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averaged diusion time τ d of 26 ps. If we use the expected average length of SWNTs in our samples of 250 nm this would yield a diusion coecient D of 12 cm2 ·s−1 , slightly larger but well in line with expectations based on previous measurements of D for SWNTs dispersed with ionic surfactants. 48 As shown in the inset of Fig. 6c, best agreement with experimental data at early times is obtained if we also account for a 40 fs rise time of the rst subband exciton population. This has previously been attributed to second subband exciton decay and interband relaxation. 4547 In Fig. 7 we compare t results for the samples, now using Poissonian stochastics 8.50doped cm = 245 pt to account for the fact that nonradiative decay is expected to be dominated by exciton interactions with randomly distributed charge puddles. At an oxidizing potential of +0.65 V + 0.65 V

⌧ d = 4.9 ps + 0.70 V

⌧ d = 3.2 ps

Figure 7: Normalized cross-correlations for doped samples. Both optical transients were t with Poissonian averaged dynamics of diusion-limited quenching at localized quenching sites/barriers. the t with Poissonian quenching site distribution yields a characteristic diusion time of

τ d = 4.9 ps, while at a potential of +0.70 V we obtain τ d = 3.2 ps. Alternatively, diusion times can also be calculated from the spectral analysis using the corresponding average puddle spacings of 43 and 32 nm using τ d = w2 /2D. The spectral analysis would thus yield diusion times of 6.3 and 3.3 ps, respectively, in qualitative agreement with ndings from the time-domain data. This illustrates that the hard segmentation model is consistent with both, our spectral as well as time-domain analysis and that both types of datasets 17


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point to charge puddles being responsible for segmentation and for providing conduits to non-radiative decay.

Conclusion We have studied reversible electrochemically-controlled eld-doping of semiconducting SWNTs by steady state and ultrafast time-resolved spectroscopy. The experimental ndings are consistent with excess charges in s-SWNTs being localized in roughly 4 nm long charge puddles due to interaction with counterions adsorbed at nanotube surfaces. Excitons and their charged trion counterparts are thus believed to originate from dierent segments of nanotubes, intrinsic and charged, respectively. Charge puddles are also found to give rise to a hard segmentation of nanotubes, leading to exciton peak shifts and asymmetric line broadening, all of which can be attributed to exciton connement in-between neighbouring sites of localized charges. Non-radiative interactions of excitons with doped SWNT segments are evidenced by distinct changes in the dynamics of ultrafast exciton decay. In intrinsic SWNTs the dynamics are well described by diusion-limited non-radiative exciton decay at the ends of SWNTs. Best agreement with optical transients in intrinsic samples is thus obtained for typical lognormal SWNT length distributions and characteristic diusion times, here of 26 ps. By contrast, nonradiative decay becomes successively faster in weakly doped SWNTs and has to be described using Poissonian quenching site distributions as expected if coupling to randomly distributed charge puddles represents the dominant route for non-radiative decay. The ndings of this study may require to re-think non-covalent electrochemical- or redoxdoping of s-SWNTs in the context of homogeneous and band lling models. The study also highlights some of the challenges associated with achieving homogeneous doping in s-SWNTs. Specically, homogeneous doping appears to require more consideration of the distribution and location of counterions in the SWNT environment as well as more suitably engineered

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Coulomb interactions by appropriate choice of surrounding media.

Methods Sample Preparation Toluene (6,5)-SWNT dispersions were prepared by 7 h of sonication of 0.5 mg · ml−1 CoMoCAT raw material (SWeNT SG 65, Southwest Nano Technologies Inc.) with 1.0 mg · ml−1 PFO-BPy (American Dye Source). 58 The resulting dispersions were benchtop centrifuged and the supernatant was collected for SWNT lm preparation. Thin SWNT lms were fabricated by vacuum ltration of the dispersion through cellulose acetate lter membranes (MF-Millipore VCWP, Merck Millipore). The lms were subsequently transferred to a platinum mesh electrode before dissolving the lter membrane in an acetone bath.

Electrochemical Setup Electrochemical experiments were performed in a 0.1 molar solution of tetrabutylammonium hexauorophosphate (Sigma-Aldrich) with dry and degassed tetrahydrofurane under argon atmosphere in a home-built spectroscopy chamber. A three electrode setup was used with a platinum mesh contacting the SWNT lm as working electrode and two platinum wires as counter and as reference electrodes. An EG&G model 363 potentiostat was used for controlling the applied potentials.

UV-vis-NIR Absorption Spectroscopy Spectroelectrochemical absorption measurements under potentiostatic control were performed with a Cary-5000 UV-vis-NIR spectrometer using the same electrochemical setup described above. We allowed for 2 min of settling time after potential changes before acquisition of new spectra.

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Transient Absorption Measurements Femtosecond transient absorption measurements under potentiostatic control were performed using the same electrochemical setup. The output of an optical parametric amplier (OPA9450, Coherent Inc.), driven by a regenerative amplier at 250 kHz (RegA9050, Coherent Inc.) was used for generation of pump-impulses. Samples were excited by sub 50 fs impulses at a central wavelength of 574 nm with a bandwidth of ≈ 40 meV. The pump beam was directed through a BOA prism compressor 59 to obtain nearly transform-limited impulses with an FWHM of 48 fs. Probe impulses were generated with 30 % of the RegA output which was focused into a sapphire plate for white light continuum generation. All measurements were carried out using magic angle conguration of pump and probe impulses. The spatial FWHM of pump and probe beams on the sample was ≈ 120 µm and ≈ 40 µm, respectively. The pump impulse uence was 0.6 µJ · cm−2 (1.7 × 1012 cm−2 photon uence). The intensity of the spectrally dispersed probe beam (Shamrock 303i, Andor Technology PLC, 150 lines/mm grating) was recorded by a 1024x256 pixel CCD camera (Newton DU920P BR-DD, Andor Technology PLC). The probe wavelength-dependence of the instrument response function was determined using a coherent artifact in pure solvent.

Conict of Interest The authors declare no competing nancial interests.

Acknowledgement K.E. acknowledges nancial support by the DFG within the GRK 2112. M.A. and T.H. also acknowledge nancial support by the DFG through grant HE 3355/4-1.

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Graphical TOC Entry charge puddle

exciton emission

counterion

28

4 nm

trion emission


Localized Charges Control Exciton Energetics and Energy Dissipation

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