Exciton dynamics of C60-based single-photon emitters explored by Hanbury Brown–Twiss scanning tunnelling microscopy

Exciton creation and annihilation by charges are crucial processes for technologies relying on charge-exciton-photon conversion. Improvement of organic light sources or dye-sensitized solar cells requires methods to address exciton dynamics at the molecular scale. Near-field techniques have been instrumental for this purpose; however, characterizing exciton recombination with molecular resolution remained a challenge. Here, we study exciton dynamics by using scanning tunnelling microscopy to inject current with sub-molecular precision and Hanbury Brown–Twiss interferometry to measure photon correlations in the far-field electroluminescence. Controlled injection allows us to generate excitons in solid C60 and let them interact with charges during their lifetime. We demonstrate electrically driven single-photon emission from localized structural defects and determine exciton lifetimes in the picosecond range. Monitoring lifetime shortening and luminescence saturation for increasing carrier injection rates provides access to charge-exciton annihilation dynamics. Our approach introduces a unique way to study single quasi-particle dynamics on the ultimate molecular scale.


Supplementary Note 1: Scanning tunneling spectroscopy
In Supplementary Figure 2 we introduce two scanning tunneling spectra (dI/dU) obtained on the single photon emission center characterized in Fig. 3 of the main text. The spectra presented in Supplementary  Figure 2 b were obtained on top of the positions marked with crosses of their respective colors in Supplementary Figure 2 a. The green spectrum was obtained on one of the three molecules that excite with high yield photon emission in the dislocation. The blue was obtained on a non-emitting molecule.
The green spectrum presents a filled electronic state shifted into the bandgap by 0.2 eV with respect to the blue spectrum. This state inside the bandgap is the cause for the strong emission obtained when electrons are extracted from that molecule and responsible for the single photon emission. The splitting off of the hole trap is typically much more pronounced than the split off of the electron trap. The spectra qualitatively corroborate the energy level diagram presented in the main text. Spatial mapping of the defective charge trap states in ECs will be published elsewhere.
We would like to comment on the difference between the band gap observed in Supplementary Figure 2 b and the luminescence photon energy of 1.7eV. Two corrections have to be applied. The thick dielectric C 60 layer penetrated by the strong electric field in the STM leads to a significant shift of observed electronic states with respect to their true (field free) energies. We found experimentally that under the given tunneling parameters the apparent widening of the band gap with respect to the true gap amounts to an increase of roughly 8% for each additional C 60 layer. Comparison of the value in Supplementary Figure 2 b with our data obtained for a double C 60 layer on Ag(111) (apparent gap 2.8eV) is thus in good agreement with an assumed thickness of 8 C 60 layers in our study. The remaining difference between 2.8eV and the classical literature value of 2.3eV 1 results from the remaining field shift within the last two layers. The second correction comes from the known exciton binding energy (electron-hole attraction) of 0.46eV. 2 Finally, a rather small residual contribution of 0.2eV-0.3eV may be attributed to the exciton trapping in the ECs.

Supplementary Note 2: Obtaining the life time from the correlation measurements:
The antibunching of sub-Poissonian emitters is described by a model containing only ground and excited state by the simple exponential recovery with the recovery time τ 3 : Models containing additional intermediate states may provide deviations from this simple shape. The broadening of function A in (1) by a normalized Gaussian detection function can be calculated analytically: where erf (x) is the error function. Function B with the known Gaussian width of 1.2ns FWHM (σ = 0.5 ns) could be used to fit the experimental g (2) (Δt) curves (Fig.3d) in the main text and to obtain from these fits the recovery times τ. See Supplementary Figure 3a for examples with various σ.
The data in the paper is evaluated and fitted by going even one step further. We employed the photon correlation of the two detectors in response to ps light pulses from a spectrally filtered (690nm) supercontinuum light source. The measured correlation function which is due to the detector characteristics could be described very well by the sum of two Gaussians with different heights and widths. With this approximation it is again possible to obtain the analytical convolution of (1) because the convolution of a sum of two functions is simply the sum of the two convoluted functions. The numerical fit of the analytical function to the measured data is straight forward and directly yields the recovery time τ in the experiment which are the ones we present in the paper.

Supplementary Note 3: Emission intensities and photon correlations in the three-state Model:
Correlation experiments in photo-excitation require a minimum of two states to account for the behavior: ground state and excited (singlet exciton) state. Including an additional long-lived excited state (e.g. triplet exciton) 4 leads to a three-state model (see Supplementary Figure 4).
The electrical excitation requires a minimum of 3 states because the generation of an exciton cannot be achieved in 1 step as in optical excitation but requires the successive creation of a hole and then the capturing of an electron at the monitored site. In the discussed experiments the electron extraction by the tip always precedes the electron capture so that a fourth (trapped electron) state will not be considered. The population of the trap by a hole is assumed to be linear in the tunnel current I tunnel so that the first rate constant (the inverse of the time constant) of the model is given by: In the model we regard, however, only those trapped holes, which are converted into an exciton because a separate detrapping process is not included. α is thus the exciton creation probability for each charge injected by the STM tip.
The capture of an electron requires the pre-existence of a trapped hole since due to the energetic position of electronic states a negatively charged trap lies too high in energy. The existence of a negatively charged trap under typical experimental conditions can be excluded since this electron could tunnel to the STM tip and emit a photon in an inelastic tunneling process thus emitting a broad plasmonic light spectrum, which is, in fact, not observed.
The electron capture by the trapped hole is fast (<< 1ns) as discussed in the main text. Its rate k 2 is assumed to be constant. If a weak dependence on the current exists, we would expect that a higher current would slightly increase the electron capture due to the increased driving force of the electric fields. The experimental observation is, however, opposite why we neglect the dependence of k 2 on current.
The decay of the exciton occurs by its proper time constant τ X 3 = 1 X

(5)
As shown in an earlier publication, this rate constant may contain already non-radiative quenching e.g. by the nearby metal electrodes. 5 This and another publication 6 suggest a life time of the lowest singlet exciton of the order of 1 ns. The rate equation model developed up to here can be solved analytically for the time-dependent occupation numbers of the three states: n g (∆t), n c (∆t), n X (∆t). When a recombination has taken place at time zero (initial condition of the solution), the probability for another exciton recombination at time delay ∆t is obtained as: with the substitutions The curve in Supplementary Figure 3b exhibits the characteristic recovery time of anti-bunching as 0.62 ns which is close although not identical to the inverse rate constant k 3 . The smallest of the rate constants, k 1 , enters into the intensity but does not appear as a time constant. Rate constant k 2 appears through a small parabolic section at the minimum at time-zero (compare to minimum of the red curve in Supplementary Figure 3a). This parabolic section is absent in two-state models and is expected to become measurable only for high enough detector time resolution and excellent correlation statistics.
The detected correlation rate is much lower than obtained by D due to various losses. These comprise a constant fraction of non-radiative recombination, finite coupling to plasmonic light emission and finally the optical transmission and detection efficiencies. We summarize the transmission remaining after all these losses in the constant η so that the experimental correlation rate can be described by: To account for the measured quantum yield of 2.5 * 10 -5 photons/electron we assume an exciton creation efficiency of α = 2.5*10 -3 excitons/charge and a detection loss factor η = 10 -2 . This value of 10 -2 is based on the estimated optical transmission of the optical line (ca 15% for optical transmission and detection 7 ) and the roughly 5% efficiency of plasmonic free space emission. 8 A more precise separation of the measured quantum yield into the two factors cannot be provided here as the two factors cannot be independently determined in the experiment.
From (7) we obtain the time-averaged photon intensity E in one detector as a function of tunnel current: ( tunnel ) = lim Δ →∞ ( ) = = 1 • 2 • 3 1 2 + 2 3 + 3 1 (8) which we plot in Supplementary Figure 5a for similar parameters as used in Supplementary Figure 3b. We find that the function is dominated by a linear dependence on the current and that deviations from linearity would occur only if k 1 becomes comparable to k 3 and k 2 .
Eqns. (7) and (8) do not yet include the current-dependent exciton life time reduction. We introduce parallel to process k 3 the non-radiative charge-induced exciton quenching of the exciton by k 3 '. This process is linear in the current with a charge exciton annihilation efficiency β: This modification turns the list of substitution parameters (6') into and the current dependent light emission (8) into: We conclude with a simplified result by introducing two approximations. We assume (*) that the electron capture process k 2 is by far the fastest of the three processes and that (**) the exciton creation efficiency α is much smaller than 1. Then we obtain wherein we substituted for simplicity tunnel = tunnel , the average time between two tunneling charges. As τ tunnel is given by the tunnel current and τ X is known from the time resolved correlation data, this formula has only two free parameters: The electroluminescence quantum yield α * η which is the slope near zero current and the annihilation quantum efficiency β which accounts for the deviation from linearity. In Supplementary Figure 5b we plot the best fit to the experimental data using eq. (12).
We shall comment that for larger injection rates (i.e. tunneling currents) the photon count rate theoretically completely levels off and even can decline. However, reaching these experimental conditions is a difficult task since high tunneling currents result in more unstable tips, and eventually in crashes destroying the ECs. However exploring these high current ranges can be of interest in future investigations.