First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

Abstract

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multipulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length (1.3-4.7 μm), in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm 2 /s), and absorption cross sections (2.1-3.6 × 10 −17 cm 2 /atom) among the highest previously reported.Semiconductor nanoscience has rapidly expanded since material engineering enabled control of the dimensionality, with two-dimensional (quantum well), one-dimensional (quantum wire), and zero-dimensional (quantum dot) systems now readily producible. These nanosystems have been particularly useful for optical applications due to their customizable electronic properties and, in contrast to bulk semiconductors, the electronic density of states (DOS) at the band gap is nonzero. In the case of quantum wires, the one-dimensional quantum confinement leads to Van Hove singularities, which are divergences in the DOS at the band gap. An example of a nearly ideal quantum wire is the single-walled carbon nanotube (SWCNT), which is a rolled graphene sheet with radial quantum confinement and translation invariance along the SWCNT axis. The one dimensionality of carriers in SWCNTs results in a strong Coulomb interaction which binds the electron-hole pair into an exciton with a binding energy approximately one third of the single particle band gap. 1,2 For many SWCNT samples, the exciton lifetime is dominated by end quenching, defects/adsorbates, and, when highly excited, interactions between excitons. These decay mechanisms are all strongly dependent on exciton transport, which is often modeled as diffusive, with an effective diffusion length determined by the sample quality. 3,4 The high likelihood of spatial overlap between diffusing excitons results in efficient Auger-like exciton-exciton annihilation (EEA) which limits the maximum exciton density well below the predictions of phase-space filling. 5 In addition to EEA, diffusion also allows quenching of excitons at the ends and defect sites, severely limiting the quantum efficiency for many samples. Interestingly, both diffusion driven end/defect quenching and EEA enable many realized and potential photonic applications. 6 At low exciton densities, the stochastic fluctuations of the optical emission intensity due to the adsorption and desorption of fluorescence quenchers has led to single molecule counting arrays and biological sensors. 7-9 At high exciton densities, the rapid relaxation of excitons due to EEA may give rise ...

Independence of optical absorption on Auger ionization in single-walled carbon nanotubes revealed by ultrafast e–h photodoping

“…In these SWCNTs disorder diffusion, not intrinsic diffusion, is expected resulting in significantly shorter diffusion lengths than those observed in air-suspended SWCNTs [5]. A consequence of the shorter diffusion length is evidenced in figure 4, which has a PL saturation point ∼10 13 photons pulse −1 cm −2 .…”

“…Time-resolved PL measurements are performed using two beam paths: one that is fixed and a second which is delayed in time. Femtosecond excitation correlation spectroscopy (FEC) [5,8,31,32] is used to measure the relaxation of the exciton population while the cumulative optical absorption is measured. Since the total power of the optical excitation is constant, the background remains constant and 1D scans are unnecessary.…”

“…, where t ¢ is the delay time (see [5]). The measured relaxation lifetime was 10 ps, significantly shorter than typical exciton population relaxation times observed in longer pristine SWCNT samples [5,35,36], as expected due to environmental perturbations and end quenching.…”

“…The reduced screening of optical excitations in the single rolled layer of graphene leads to an exciton binding energy which is approximately one third of the single particle bandgap [1,2]. Consequently, excitons are stable even at room temperature where thermal energy enables exceedingly long diffusion lengths [3][4][5]. The diffusion-reaction of excitons in SWCNTs results in many body interactions which leads to strong nonlinear optical properties [6,7], even at very low excitation fluences [8].…”

“…Despite the fact that SWCNTs have long been used as saturable absorbers [12,13] due to their large nonlinear absorption [14,15], the strong nonlinear photoluminescence (PL) has been modeled only considering a reduction in quantum efficiency due to exciton-exciton interactions and not nonlinear optical absorption due to BGR. The presence of BGR would call into question the basic understanding high fluence SWCNT PL saturation experiments [6,8,16] and the consequently extracted SWCNT properties [5,17]. BGR has been previously observed in several one-dimensional systems.…”