Localized Charges Control Exciton Energetics and Energy

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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*,†,‡ †

Institute of Physical and Theoretical Chemistry, Julius Maximilian University Würzburg, Würzburg 97074, Germany Röntgen Research Center for Complex Material Systems, Julius Maximilian University Würzburg, Würzburg 97074, Germany

‡

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 pdoped 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 first exciton absorption band also reveals that doping leads to hard segmentation of sSWNTs with intrinsic undoped segments being separated by randomly distributed charge puddles approximately 4 nm in width. Light absorption in 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 diffusive exciton transport to, and nonradiative decay at charge puddles within 3.2 ps in moderately doped s-SWNTs. The results suggest that conventional band-filling in s-SWNTs breaks down due to inhomogeneous electrochemical doping. KEYWORDS: carbon nanotubes, band-filling, electrochemical doping, carrier localization, exciton confinement, exciton transport, energy dissipation charges, forming so-called trion absorption bands.12,13 Seemingly in contradiction to these results, quantum beats in fourwave 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 noncovalently or electrochemically doped sSWNTs are also found to give rise to red-shifted trion absorption.16−21 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 a clear temperature-dependence of trion photoluminescence intensities suggests that such excitations are localized.19 The character of the distribution of excess carriers in noncovalently doped s-SWNTs, homogeneous vs in-homogeneous, is thus still a 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

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ost of today’s 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 fields. 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 efficient, allowing carriers to become delocalized. The importance of Coulomb interactions between charged impurities and free carriers, however, is enhanced in lowdimensional semiconductors due to both weaker screening and constraints on wave functions in reduced dimensionality.4−6 The hydrogenic ground-state binding energy, for example, increases dramatically as dimensionality is decreased.6,7 Accordingly, exciton binding energies in quasi 1D single-wall carbon nanotubes (s-SWNTs) are nearly 2 orders of magnitude higher than in their three-dimensional counterparts.8−11 However, the degree to which weak screening affects 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 © 2017 American Chemical Society

Received: August 4, 2017 Accepted: September 7, 2017 Published: September 7, 2017 10401

DOI: 10.1021/acsnano.7b05543 ACS Nano 2017, 11, 10401−10408

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Cite This: ACS Nano 2017, 11, 10401-10408

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ACS Nano 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 nonradiative exciton decay. These findings 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.5,24−26 Dominant exciton bands are clearly seen in the topmost spectrum of Figure 1a, which shows the absorption spectrum of a thin intrinsic (nondoped) nanotube film made from semiconducting (6,5) SWNTs. The S1 absorption band at 1.24 eV corresponds to the first 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 first exciton.27−29 The electrochemical potential of this film 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 film is fully reversible. Thus, the role of the electrolyte is to deliver the electrical field to the interface between SWNT and WE and thereby to allow a controlled realignment 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 defined by the onset of reduction and oxidation of (6,5) s-SWNTs, seen in Figure 1b, serves as an internal reference, facilitating a comparison of redox potentials for different experimental runs and setups. The spectra in the lower part of Figure 1a were recorded at positive WE potentials of +0.90 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 X+1 at 1.06 eV and by a decrease of the first exciton’s oscillator strength. Trion absorption is associated with the formation of a charged exciton state.16−21,31−35 As seen in Figure 1b the trion band reaches its peak intensity at +0.90 V with a similar behavior 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 first subband oscillator strength of the intrinsic system.21 The transition energies of exciton bands in noncovalently doped SWNTs are typically found to be blue-shifted from a few meV33,36 up to over 80 meV.21,37 This has previously been attributed to changes of exciton binding and band gap renormalization in doped s-SWNTs33,36,38 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.

Figure 1. Spectral changes in doped s-SWNT films. (a) Absorption spectra of an intrinsic, moderately and heavily p-doped (6,5) film at different electrode potentials. Dominant absorption features belong to the first S1 and second S2 subband exciton. The first subband exciton becomes more asymmetric, blue-shifted, and broadened as doping levels increase. (b) Overview of absorption changes at specific energies.

If carrier densities in (6,5) SWNTs at different 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 into question due to evidence indicating that inhomogeneous carrier distributions dominate both electrochemical and redox-chemical doping. To better understand how excess charge carriers in SWNTs may become localized, we begin by looking at the expected magnitude of carrier interactions with counterions at the SWNT−electrolyte interface (see Figure 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 10402


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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 Figure 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 first and second eigenstate binding energies and the full width at half-maximum Δ (fwhm) of the corresponding charge distributions are shown in Figure 2c as a function of the dielectric constant ϵ. Dielectric screening is expected to range from ϵ = 4, typically used for free SWNTs,27,41 to about 8 for tetrahydrofuran as solvent. For a directly adsorbed counterion, the n = 1 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 Figure 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 150 meV, which is well in line with expectations for a dielectric constant of ϵ ≈ 6 or less. 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 confinement and as barriers to exciton transport as well as conduits for nonradiative decay.42 A hard segmentation of SWNTs by localized carriers should impose boundary conditions on the axial component of the exciton wave function on nondoped regions and thereby increase their ground-state energy (see Figure 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, specifically 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 confinement, (b) by accounting for a random distribution of charge puddles and thus a Poissonian distribution of confinement 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 confined exciton depends on its effective mass M = mv + mc and is estimated using the ground-state energy of a particle in a one-dimensional box, EGS(w) = π2ℏ2(2Mw2)−1, where w is the distance between a specific 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 pw̅ (w) = w̅ −1 e−w/w̅ as shown in Figure 3b.43,44 Here w̅ 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 f w(E) that can be determined using a Voigt fit 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 profile in doped samples is then calculated from the weighted average of absorption bands:

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 ϵ = 8 and d = 0.7 nm. (c) Dependence of the n = 1 and 2 puddle binding energies Ep and the width Δ of the corresponding wave function |Ψn(z)|2 on dielectric constant for two counterion distances, d = 0.7 and 1.5 nm.

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 field-induced charge localization can be estimated using the local electrostatic potential surrounding a counterion, V(z) = −e2/(4πϵ0ϵ(d2 + z2)1/2), with a homogeneous dielectric constant ϵ at counterion distance d from the nanotube axis and at an axial displacement z (see Figure 2a and b). This potential can trap and locally confine 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 = −ℏ2∇2/2meff + V(z). The effective hole mass of 0.07 me is taken from a chirality-corrected tight-binding calculation of the (6,5) tube using a nearest neighbor hopping matrix element γ0 = 4.1 eV to reproduce the

I ̅ (E ) = 10403

1 w̅

∫0

∞

pw (w′)w′fw ′ (E) dw′ ̅

(1) DOI: 10.1021/acsnano.7b05543 ACS Nano 2017, 11, 10401−10408

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average Δ 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 finding suggest that excitons and trions appear to be localized on different 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 Figure 4 for a moderately doped film where selective excitation of the S1 exciton and the resulting ground-state depletion leads to a strong photobleach

Figure 3. Spectral signatures of exciton confinement. (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 confined exciton’s ground-state energy in a box of width w as induced by barriers of width Δ. (b and c) Poissonian and log-normal barrier distributions leading to confinement of excitons. The first is expected for randomly scattered doping sites with average distance w̅ , while the latter more appropriately describes the distribution of nanotube lengths with average l ̅. (d) One-parameter fit to background-corrected exciton bands using a Poissonian barrier distribution.

The factors w and w̅ −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 filling are included in the model by assigning a finite width Δ to each of the barriers. This is implemented by replacing the distribution function pw̅ (w) with p̂w̅ ,Δ(w) = w̅ −1 e−(w+Δ)/w̅ . The resulting two-parameter fits to a series of experimental absorption spectra are shown in Figure 3d for different doping levels. Within this model, the shift of the exciton absorption band maximum by up to nearly 100 meV, its broadening, and its asymmetry are solely controlled by the mean barrier spacing w̅ . 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 Δ 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

Figure 4. Selective transient photobleach of exciton and trion manifolds. (a, b) Pump−probe scheme for selective excitation of doped and nondoped SWNT sections. (c) Changes in the photobleach (PB) in the VIS spectral range suggest that trion and exciton manifolds are localized on different sections of the same SWNT. 10404


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In Figure 5b we have reproduced transient spectra for a series of applied potentials, normalized to the peak of individual cross-correlation PB signals. When films are doped, the transient spectra reveal a blue shift and broadening of the main PB feature, similar to the broadening observed in groundstate absorption in Figure 3d. The spectrally and time-resolved maps of an intrinsic and of a weakly doped film in Figure 5c reveal both a change of the amplitude of optical transients due to the reduction of the S1 oscillator strength and a change in their dynamics. Nonradiative 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 efficient nonradiative decay at chemical functionalities at tube ends. Diffusion coefficients in aqueous SWNT samples are reported to be on the order of 2− 10 cm2·s−1.48,49 The nonradiative decay process itself is assumed to be very efficient and may be facilitated by different types of chemical functionalities.15,42,48,50−53 For a quantitative analysis of optical transients we thus need to model both exciton diffusion and efficient nonradiative decay, either at nanotube ends or at absorbing barriers, as illustrated schematically in Figure 6a and b. The initial optical excitation is assumed to generate a homogeneous exciton distribution in-between quenching sites (see Figure 6b). Diffusion and efficient quenching at chemical impurities then leads to a steady depletion of the exciton population, which decays asymptotically with kinetics typical of diffusion-limited reactions.54−56 Integration of the corresponding analytical expression by Balagurov and Vaks43 yields the exciton population Pl(t) between two quenching sites a distance l apart:

at higher energies near 2.10 eV and a somewhat weaker bleach at 2.17 eV. The two contributions are clearly visible in Figure 4c. On the other hand, if the X+1 trion feature is selectively pumped, optical transients in the vis range show a clear shift of the bleach signal to the lower energy feature at 2.10 eV (see Figure 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 ramifications of the hard segmentation model for exciton dynamics. The pump−probe scheme used for these experiments is outlined schematically in Figure 5a. Excitons in the second subband are excited at 2.17 eV and undergo ultrafast interband relaxation, leading to a rapid PB of the first subband transition.45−47 Subsequently, excitons can diffuse to doped nanotube segments, where they decay nonradiatively, for example by coupling to the trion manifold.

∞

Pl(t ) = P0 ∑ n=0

⎡ b2 ⎤ 8 exp⎢ − n t ⎥ 2 bn ⎣ 2τd ⎦

(2)

with bn = (2n + 1)π. The only free parameter in this analysis is thus the diffusion time τd = l2/2D, which specifies the time-scale needed by reactants (excitons) to reach one of the quenching sites where they decay instantly. Lastly, to account for different quenching site separations, we again have to average over an appropriate distribution of quenching site distances. In Figure 6c we have contrasted the residuals of the best fit to the data using a log-normal distribution (red open circles) with the residuals from a fit using a Poissonian distribution (blue open circles) of quenching site spacings. Evidently, agreement with the lognormal weighted length distribution, here with a standard deviation of 0.56,53 is considerably better than for the Poissonian distribution (see Figure 6c). A simple monoexponential fit is shown for reference purposes in Figure 6c (green dot-dashed line). This finding is also in excellent agreement with experimentally determined SWNT log-normal length distributions in similar samples.53,57 The fit yields an ensemble-averaged diffusion time τd̅ of 26 ps. If we use the expected average length of SWNTs in our samples of 250 nm, this would yield a diffusion coefficient 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 Figure 6c, best agreement with experimental data at early times is obtained if we also account for a 40 fs rise time of the first subband exciton

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 efficient nonradiative decay. (b) Series of transient absorption spectra for different oxidation potentials. (c) Two-dimensional representations of spectral and temporal changes for a nondoped (left) and a doped SWNT sample (right). 10405


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Figure 7. Normalized cross-correlations for doped samples. Both optical transients were fit with Poissonian averaged dynamics of diffusion-limited quenching at localized quenching sites/barriers.

CONCLUSION We have studied reversible electrochemically controlled fielddoping of semiconducting SWNTs by steady-state and ultrafast time-resolved spectroscopy. The experimental findings 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 different 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 confinement in-between neighboring sites of localized charges. Nonradiative 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 diffusion-limited nonradiative exciton decay at the ends of SWNTs. Best agreement with optical transients in intrinsic samples is thus obtained for typical log-normal SWNT length distributions and characteristic diffusion 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 nonradiative decay. The findings of this study may require rethinking noncovalent electrochemical or redox doping of s-SWNTs in the context of homogeneous and band filling models. The study also highlights some of the challenges associated with achieving homogeneous doping in s-SWNTs. Specifically, homogeneous doping appears to require more consideration of the distribution and location of counterions in the SWNT environment as well as more suitably engineered Coulomb interactions by appropriate choice of surrounding media.

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

population. This has previously been attributed to second subband exciton decay and interband relaxation.45−47 In Figure 7 we compare fit results for the doped samples, now using Poissonian stochastics 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 the fit with Poissonian quenching site distribution yields a characteristic diffusion time of τd̅ = 4.9 ps, while at a potential of +0.70 V we obtain τd̅ = 3.2 ps. Alternatively, diffusion times can also be calculated from the spectral analysis using the corresponding average puddle spacings of 43 and 32 nm using τd̅ = w̅ 2/2D. The spectral analysis would thus yield diffusion times of 6.3 and 3.3 ps, respectively, in qualitative agreement with findings from the time-domain data. This illustrates that the hard segmentation model is consistent with both our spectral and time-domain analysis and that both types of data sets point to charge puddles being responsible for segmentation and for providing conduits to nonradiative decay.

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 10406


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ACS Nano SWNT film preparation. Thin SWNT films were fabricated by vacuum filtration of the dispersion through cellulose acetate filter membranes (MF-Millipore VCWP, Merck Millipore). The films were transferred to a platinum mesh electrode after dissolving the filter membrane in an acetone bath. Electrochemical Setup. Electrochemical experiments were performed in a 0.1 M solution of tetrabutylammonium hexafluorophosphate (Sigma-Aldrich) with dry and degassed tetrahydrofuran under an argon atmosphere in a home-built spectroscopy chamber. A three-electrode setup was used with a platinum mesh contacting the SWNT film 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. Transient Absorption Measurements. Femtosecond transient absorption measurements under potentiostatic control were performed using the same electrochemical setup. The output of an optical parametric amplifier (OPA9450, Coherent Inc.) driven by a regenerative amplifier 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 compressor59 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 configuration of pump and probe impulses. The spatial fwhm of pump and probe beams on the sample was ∼120 and ∼40 μm, respectively. The pump impulse fluence was 0.6 μJ·cm−2 (1.7 × 1012 cm−2 photon fluence). The intensity of the spectrally dispersed probe beam (Shamrock 303i, Andor Technology PLC, 150 lines/mm grating) was recorded by a 1024 × 256 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.

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AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Phone: +49 931 3186300. ORCID

Tobias Hertel: 0000-0001-7907-4341 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS K.E. acknowledges financial support by the DFG within the GRK 2112. M.A. and T.H. also acknowledge financial support by the DFG through grant HE 3355/4-1. REFERENCES (1) Sze, S. M. Modern Semiconductor Device Physics; Wiley: New York, 1998. (2) Mahan, G. D. Many-Particle Physics; Springer: Boston, 2000. (3) Xiao, C.; Yang, D.; Yu, X.; Xiang, L.; Que, D. Determination of the Boron and Phosphorus Ionization Energies in Compensated Silicon by Temperature-Dependent Luminescence. Silicon 2017, 9, 147−151. (4) Yoffe, A. D. Low-Dimensional Systems: Quantum Size Effects and Electronic Properties of Semiconductor Microcrystallites (ZeroDimensional Systems) and Some Quasi-Two-Dimensional Systems. Adv. Phys. 1993, 42, 173−262. 10407


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Localized Charges Control Exciton Energetics and Energy

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