Subband Exciton Research Articles

Empirical formulation of broadband complex refractive index spectra of single-chirality carbon nanotube assembly.

Assemblies of single-walled carbon nanotubes with a specific chiral structure are promising future optofunctional materials because of their strong light-matter coupling arising from sharp optical resonances of quasi-one-dimensional excitons. Their strong optical resonances, which lie in the infrared-to-visible wavelength region, can be selected by their chiralities, and this selectivity promises a wide range of applications including photonic and thermo-optic devices. However, the broadband complex optical spectra of single-chirality carbon nanotube assemblies are scarce in the literature, which has prevented researchers and engineers from designing devices using them. Here, we experimentally determine broadband complex refractive index spectra of single-chirality carbon nanotube assemblies. Free-standing carbon nanotube membranes and those placed on sapphire substrates were fabricated via filtration of the nanotube solution prepared by the separation method using gel chromatography. Transmission and reflection spectra were measured in the mid-infrared to visible wavelength region, and the complex refractive indices of nanotube assemblies were determined as a function of photon energy. The realand imaginary parts of the refractive indices of thenanotube membrane with a bulk density of 1gcm-3 at the first subband exciton resonance were determined to be approximately 2.7-3.6 and 1.3i-2.4i, respectively. We propose an empirical formula that phenomenologically describes the complex refractive index spectra of various single-chirality nanotube membranes, which can facilitate the design of photonic devices using carbon nanotubes as the material.

Signatures of subband excitons in few-layer black phosphorus

Recent experimental measurements of light absorption in few-layer black phosphorus (BP) revealed a series of high and sharp peaks, interspersed by pairs of lower and broader features. Here, we propose a theoretical model for these excitonic states in few-layer BP within a continuum approach for the in-plane degrees of freedom and a tight-binding approximation that accounts for interlayer couplings. This yields excitonic transitions between different combinations of the subbands created by the coupled BP layers, which leads to a series of high and low oscillator strength excitonic states, consistent with the experimentally observed bright and dark exciton peaks, respectively. The main characteristics of such subband exciton states, as well as the possibility to control their energies and oscillator strengths via applied electric and magnetic fields, are discussed, towards a full understanding of the excitonic spectrum of few-layer BP and its tunability.

(Invited) Ultrafast Spectroscopy of Free-Carrier like Dynamics in Heavily Doped Semiconducting Carbon Nanotubes

We have investigated the photophysical properties of heavily doped semiconducting single-wall carbon nanotubes (s-SWNTs) in the vis and NIR spectral range. Doping is here achieved either by electrochemical gating or by redox chemistry, using AuCl3 as oxidizing agent. Stationary and time-resolved absorption spectroscopy show that the dynamical behaviour of electrochemically- and redox-doped s-SWNT samples are identical, indicating that doping mechanisms and the character of charged states is the same for both doping processes. Spectroscopically, the heavily doped regime is defined by the disappearance of NIR trion and neutral exciton signatures. The remaining absorption band in heavily hole-doped (6,5) s-SWNTs is broad, flat and practically featureless over a very broad spectral range from about 1150 nm to 620 nm. It carries nearly all the oscillator strength of the first subband exciton of intrinsic s-SWNTs. The transient spectral response of this so-called H-band (for heavily doped) is surprisingly weak, suggesting that signal contributions from ground- and excited state absorption and from stimulated emission cancel out nearly perfectly. We discuss these findings also in the context of UV-IR measurements of the optical conductivity which shows an ambiguous response in the low THz regime.

Diameter Selective Chemical Doping of Semiconducting Single-Wall Carbon Nanotubes

Doping of semiconductors, such as single-wall carbon nanotubes (SWNTs), by the introduction or removal of charges can be used for modification of their electronic and optical structure. This offers unique opportunities for the fabrication of versatile materials with new properties. However, despite a broad body of work,1−3 the control and spectroscopic assessment of the doping of SWNTs is still being developed4,5 in order to be able to reproducibly tailor semiconductor properties. Here, we have studied the photophysical properties of chemically doped SWNTs by absorption and photoluminescence spectroscopy. Polychiral samples of purified HiPCO soot were charged by oxidation with gold chloride. Thanks to very well-resolved and narrow exciton bands in these samples, the trionic signatures induced by charges could be resolved for up to five distinct nanotube species. An investigation of spectral changes in absorption measurements as a function of gold chloride concentration reveals that tubes with smaller bandgaps are doped at lower gold chloride concentrations. The trion binding energy with respect to the dipole-allowed first sub-band exciton transition was also found to increase systematically with decreasing diameter in agreement with previous findings.1,2 In addition, we find that SWNT oxidation potentials decrease nearly linearly with increasing nanotube diameter. Lastly, a surprisingly abrupt change of exciton oscillator strengths at redox potentials near the nanotube band edge provides evidence for band gap renormalization.

13 nm Exciton Size in (6,5) Single-Wall Carbon Nanotubes.

Electron-hole correlation lengths, also termed exciton size, for (6,5) single-wall carbon nanotubes (SWNTs) are determined using femtosecond time-resolved pump-probe spectroscopy. The phase space filling model is used to obtain the sizes of the first subband exciton in samples of isolated and of bundled SWNTs. The experiments indicate that the exciton size of (13 ± 3) nm is a factor of 6 higher than previous experimental estimates and theoretical predictions for vacuum suspended SWNTs. This surprising result may be attributed at least in part to the effect of the dielectric environment on exciton sizes and supports recent theoretical findings predicting that screening in SWNTs may enhance rather than reduce electron-hole interactions for separations larger than the tube diameter. Thereby, the work also points to the unique nature of screening and electronic correlations in one-dimensional semiconductors.

Trion Dynamics in Hole-Doped (6,5) Single-Wall Carbon Nanotube Films

Doping of semiconductor nanostructures is essential for their application in electronic as well as photonic devices. Recent studies have focused on the assessment of electrochemical gate doping (1,2) or chemical doping (3) of semiconducting single-wall carbon nanotubes (SWNTs) by absorption and photoluminescence spectroscopy. Moderate doping levels on the order of 0.5 holes·nm-1 were found to lead to a redistribution of oscillator strength from the first subband exciton (S1) to the trion (2). Here, we report on an investigation of trion dynamics by femtosecond pump-probe transient absorption experiments (VIS pump/NIR probe and NIR pump/NIR probe) in moderately doped (6,5)-SWNT films. SWNTs were charged by gate-doping or by interaction with redox-active gold chloride. We find that optical excitation of energetically lower lying trionic states leads to a delayed rise of the first subband exciton’s S1 photobleach (PB) signature on the ps time-scale. However, the amplitude of the S1 PB signal is surprisingly high considering that the energy separation of trion and exciton exceeds thermal energies by nearly an order of magnitude, making uphill thermal population transfer highly unlikely. Extremely weak photoluminescence from the S1 exciton following trion excitation in hole-doped films indicates that energy transfer from the trion to the first subband exciton is indeed negligible (≲ 10-3). The photobleach is thus essentially due to ground state depletion and reflects the ps-dynamics of the trion decay. Excitation energy and temperature dependent transient absorption experiments reveal that this process is thermally activated. (1) J. Park et al., J. Am. Chem. Soc., 134, 14461 (2012). (2) H. Hartleb, F. Späth and T. Hertel, ACS Nano, 9, 10461 (2015). (3) R. Matsunaga, K. Matsuda and Y. Kanemitsu, Phys. Rev. Lett., 106, 037404 (2011).

(Invited) Evidence for Strong Electronic Correlations and Band-Gap Renormalization in Doped Single-Wall Carbon Nanotubes

We have investigated the photophysical properties of chemically and gate-doped semiconducting single-wall carbon nanotubes (s-SWNTs). The first subband exciton oscillator strengths as obtained from a global analysis of absorption spectra are used for assessment of carrier densities and provide evidence for band-gap renormalisation (BGR) in (6,5) SWNTs. We predict that BGR of one-dimensional gate doped semiconductors is accompanied by a stepwise increase of the carrier density by Δn=32meff b/(πℏ) 2once the electrochemical potential reaches the valence or conduction band offset with b = (0.15 ± 0.05) eV nm (meff - effective carrier mass). Moreover, we show that the width of the spectroelectrochemical window of the first subband exciton of (1.55±0.05) eV corresponds to the fundamental band gap of the undoped (6,5) SWNTs in our samples and not to the renormalized band gap of the doped system. We also compare spectral changes in gate doped with those of chemically doped SWNTs. Femtosecond time-resolved pump-probe spectroscopy of chemically doped SWNTs provides evidence of exciton-trion coupling. These observations as well as a previously unidentified absorption band emerging at high doping levels in the Pauli-blocked region of the single-particle Hartree band structure, provide clear evidence for strong electronic correlations in the optical spectra of SWNTs.

Photoluminescence from Thin Carbon Nanotube Films

Their remarkable light absorption and energy transport characteristics make single-wall carbon nanotubes (SWNTs) intriguing candidates for photovoltaic applications. Here, we study the photophysical properties of polymer wrapped SWNT films with varying thickness, so as to help identify processes which may affect device performance and that may impose limitations on the use of SWNT thin films as active layers in photovoltaic devices. Non-radiative exciton decay is of particular interest in this context and we have studied its dependence on the thickness of monochiral SWNT films. The films were made of PFOBPy wrapped and highly (6,5) enriched SWNT suspensions using a modified version of the filtration wet transfer technique reported earlier.1 Non radiative decay was probed by means of photoluminescence (PL) spectroscopy and by comparison of thin film data with data obtained from bulk suspensions. For thicker films we observe a pronounced decrease of the PL quantum yield (QY) for emission from the first subband S1 exciton state. However, the total PL QY is much less strongly affected by interactions within the thin film network because of a considerable shift of PL intensity to lower lying states. Surprisingly, some of the lower energy emission resembles PL phonon-sidebands of the first subband exciton which was previously attributed to the coupling between K-point phonons and dark excitons by Murakami et. al.2 Wu, Z.. Science 305, Nr. 5688 (2004): 1273–76.Murakami, Y., Benjamin L., Said K., Nobutsugu M., Tatsuya O., Shigeo M. Phys. Rev. B 79, Nr. 19 (2009): 195407.

Evidence for Strong Electronic Correlations in the Spectra of Gate-Doped Single-Wall Carbon Nanotubes.

We have investigated the photophysical properties of electrochemically gate-doped semiconducting single-wall carbon nanotubes (s-SWNTs). A comparison of photoluminescence (PL) and simultaneously recorded absorption spectra reveals that free-carrier densities correlate well with the first sub-band exciton or trion oscillator strengths but not with PL intensities. We thus used a global analysis of the first sub-band exciton absorption for a detailed investigation of gate-doping, here of the (6,5) SWNT valence band. Our data are consistent with a doping-induced valence band shift according to Δϵv = n × b, where n is the free-carrier density, ϵv is the valence band edge, and b = 0.15 ± 0.05 eV·nm. We also predict such band gap renormalization of one-dimensional gate-doped semiconductors to be accompanied by a stepwise increase of the carrier density by Δn = (32meffb)/(πℏ)(2) (meff is effective carrier mass). Moreover, we show that the width of the spectroelectrochemical window of the first sub-band exciton of 1.55 ± 0.05 eV corresponds to the fundamental band gap of the undoped (6,5) SWNTs in our samples and not to the renormalized band gap of the doped system. These observations as well as a previously unidentified absorption band emerging at high doping levels in the Pauli-blocked region of the single-particle Hartree band structure provide clear evidence for strong electronic correlations in the optical spectra of SWNTs.

Invited Presentation: Ensemble and Single Particle Spectroelectrochemistry of Semiconducting Single-Wall Carbon Nanotubes

Spectroelectrochemical studies were used to investigate the photophysics of electrochemically doped (6,5) SWNTs. The optical properties of SWNT ensembles were here studied by quasi simultaneous absorption and photoluminescence spectroscopy over the NIR and VIS spectral ranges. This allowed correlating changes in the oscillator strength of first and second subband excitons with changes in the photoluminescence signals from the bright singlet exciton. The data thus provides a key link between photoluminescence quantum yields affecting PL measurements and the extent of SWNT p or n doping as evidenced by absorption spectra. The data also provides evidence for a shift of oscillator strength from exciton transitions to free carrier type transitions in higher lying subbands.

Fluorescence Spectroscopy of Gel-Immobilized Single-Wall Carbon Nanotubes with Microfluidic Control of the Surfactant Environment

We describe the design and use of a microfluidic fluorescence cell for nanoparticle spectroscopy. The cell allows for microfluidic control of solvent and surfactant environments to study interfacial processes of nanoscale systems. We present a spectroscopic investigation on the effect of surfactant type and concentrations on the first subband exciton transition of (6,5) single-wall carbon nanotubes (SWNTs). SWNT fluorescence here serves as a surface-sensitive probe of changes at the surfactant–nanotube interface. The experiments show that a displacement of H2O or of adsorbed DNA by sodium cholate from solution leads to a pronounced blue-shift of exciton emission features and a roughly 5-fold increase of photoluminescence (PL) intensities. This is due to a combination of physical and chemical interactions. The major contribution to changes in PL quantum yield and exciton peak position can be attributed to changes in dielectric screening and its effect on exciton oscillator strengths.

Ultrafast Charge Photogeneration in Semiconducting Carbon Nanotubes

We show that excitons are not the unique outcome of photoexcitation in single-walled carbon nanotubes (SWNTs). Our experiments of transient photoinduced absorption suggest that charge carriers are formed with quantum yield of a few percent and that such species strongly affect the long-lived transient spectrum. Photogenerated charge carriers induce strong local electric fields that shift by the Stark effect the second subband exciton absorption in SWNTs, resulting in a characteristic derivative shape of the transient absorption spectra.

Free-Carrier Generation in Aggregates of Single-Wall Carbon Nanotubes by Photoexcitation in the Ultraviolet Regime

We present evidence for the generation of free carriers in aggregated single-wall carbon nanotubes by photoexcitation in the energetic range of the π→π(*) transition associated with the M saddle point of the graphene lattice. The underlying broad absorption culminating at 4.3 eV can be fit well with a Fano line shape that describes strong coupling of a saddle-point exciton to an underlying free electron-hole pair continuum. Moreover, it is demonstrated that transitions in this energetic region autoionize into the continuum by detecting features unique to the presence of free charges in the transient transmission spectra of the continuum-embedded second sub-band exciton, S(2).

Carrier multiplication in carbon nanotubes studied by femtosecond pump-probe spectroscopy

Carbon nanotubes are one of the excellent materials for studying the many-body effects of excitons because of their unique band structures and large exciton binding energies. We studied exciton population dynamics in single-walled carbon nanotubes using pump-probe transient absorption measurements. The temporal profiles of the transient absorption signals depend on the excitation intensity and excitation photon energy. We observe carrier multiplication in carbon nanotubes at room temperature, when the excitation photon energy exceeds the third subband exciton energy.

Exciton dynamics probed in carbon nanotube suspensions with narrow diameter distribution

AbstractWe report on a pump–probe study of CoMoCAT nanotube suspensions with narrow chirality distribution. Visible pump pulses and a white light continuum are used for resonant excitation of the strongest dipole allowed E 22 subband exciton in the semiconducting (6, 5) tube and for broadband probe of the resulting spectral transients between 1300 nm and 480 nm, respectively. Transient spectra show signatures of both photobleaching (PB) and photoabsorption (PA) with practically identical decay‐ but slightly different rise‐times. The experiments reveal that apparent variations of decay rates at different wavelengths do not reflect dynamics of different relaxation processes but are a consequence of the superposition of PB and blue‐shifted PA response. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ratio problem in single carbon nanotube fluorescence spectroscopy.

The electronic band gaps measured in fluorescence spectroscopy on individual single wall carbon nanotubes isolated within micelles show significant deviations from the predictions of one electron band theory. We resolve this problem by developing a theory of the electron-hole interaction in the photoexcited states. The one-dimensional character and tubular structure introduce a novel relaxation pathway for carriers photoexcited above the fundamental band edge. Analytic expression for the energies and line shapes of higher subband excitons are derived, and a comparison with experiment is used to extract the value of the screened electron-hole interaction.

Light scattering from self-assembled quantum disks

We present results of calculations and experiments probing the electronic structure of self-assembled Ga 0.8In 0.2As semiconductor quantum dots by inelastic light scattering. The inelastic light scattering signal is strongly enhanced when the energy of the incident light is resonant with the first excited subband. Both the optical phonon and the low frequency scattering spectra exhibit a strong effect of optical alignment, i.e., when the exciting and the scattered light have the same linear polarization. To understand the results of measurements we calculate both the single particle energy levels and excitonic states in the disk. The calculations of the resonant light scattering cross section are interepreted in terms of the one-phonon resonant Raman process involving bulk acoustical phonons interacting with excited subband excitons of the quantum dot.

Oscillator strength of higher-subband excitons in InGaAs/GaAs quantum wells

The oscillator strength of different subband excitons in InGaAs/GaAs quantum wells is studied for the first time using Fourier transform reflectance spectroscopy, and is found to take maxima with the well width variation. However, the maximum oscillator strength occurs at a wider well width for excitons with higher quantum numbers. It is shown that the reduced masses of different subband excitons can be accurately determined from the measured oscillator strength.

Photoluminescence Studies on Very High-Density Two-Dimensonal Electron Gases in Pseudomorphic Modulation-Doped Quantum Wells

We present photoluminescence studies on highly dense two-dimensional electron gases in selectively Si δ-doped GaAs/In0.18Ga0.82As/Al0.25Ga0.75As quantum wells (Ns = 4.24 × 1012 cm-2). Five well-resolved photoluminescence lines centered at 1.4194, 1.4506, 1.4609, 1.4695 and 1.4808 eV were observed, which are attributed to the subband exciton emission. The subband separations clearly exhibit the feature of a typical quantum well with triangle and square potential. These very intensive and sharp luminescence peaks with linewidths of 2.2 to 3.5 meV indicate the high quality of the structures. Their dependence on the excitation intensity and temperatures are also discussed.

Two-dimensional Franz-Keldysh effect in MQW structures with lateral electric fields

In multiple quantum well (MQW) structures strong excitonic absorption peaks can be observed at room temperature due to enhanced electron hole confinement. If an electric field is applied parallel to the layers very weak fields are sufficient to cause field-ionization of the exciton. As a consequence, the excitonic absorption peak is expected to disappear at low in-plane fields. The phenomenology of the electroabsorption is qualitatively similar to the bulk Franz-Keldysh effect (FKE). The excitonic interaction, however, which is known to strongly affect the absorption spectra of bulk semiconductors, is expected to be even more pronounced in the multiple quantum well system ("Two-dimensional Franz-Keldysh effect"). We report on results of room temperature photocurrent, electro-transmission and -reflection measurements on GaAs/Al 0.3Ga 0.7As-MQW and In 0.18Ga 0.82As/GaAs-MQW structures. With increasing electric field the excitonic peak degrades fast and transforms into the first maximum of the Franz-Keldysh oscillations in qualitative agreement with the results known from the bulk material. Maximum absorption changes larger than 10,000 cm -1 at 75 kV/cm in the GaAs/Al 0.3Ga 0.7As-MQW system have been achieved. For each subband exciton the increase of the absorption below and the FK-oscillations above the transition energy can be observed. Similar observations are also obtained in pseudomorphic In 0.18Ga 0.82As/GaAs-MQW structures, where absorption changes of almost 6000 cm -1 have been achieved with similar field changes. In both cases the experimental results are in good agreement with a theory based on a strictly 2-dimensional description of field-dependent excitonic absorption.