Controlled single-electron transfer enables time-resolved excited-state spectroscopy of individual molecules

Set-up and sample preparation

Experiments were carried out with a home-built atomic force microscope equipped with a qPlus sensor³³ (resonance frequency, f₀ = 30.0 kHz; spring constant, k ≈ 1.8 kNm⁻¹; quality factor, Q ≈ 1.9 × 10⁴) and a conductive Pt-Ir tip. The microscope was operated under ultrahigh vacuum (base pressure, P < 10⁻¹⁰ mbar) at T ≈ 8 K in frequency-modulation mode, in which the frequency shift \(\Delta f\) of the cantilever resonance is measured. The cantilever amplitude was 1 Å (2 Å peak-to-peak). AC-STM images¹⁰ were taken in constant-height mode, at a reduced tip height as indicated by the negative Δz values (tip-height change with respect to the set point).

As a sample substrate, an Ag(111) single crystal was used that was prepared by sputtering and annealing cycles (annealing temperature, T ≈ 600 °C). A thick NaCl film (>20 ML) was grown on half of the sample at a sample temperature of approximately 80 °C. In addition, a sub-ML coverage of NaCl was deposited on the entire surface at a sample temperature of approximately 35 °C. The tip was prepared by indentation into the remaining bare Ag(111) surface, presumably covering the tip apex with Ag. The measured molecules (pentacene and PTCDA) were deposited in situ onto the sample inside the scan head at a temperature of approximately 8 K.

The a.c. voltage pulses were generated by an arbitrary waveform generator (Pulse Streamer 8/2, Swabian Instruments), combined with the d.c. voltage, fed to the microscope head by a semi-rigid coaxial high-frequency cable (Coax Japan) and applied to the metal substrate as a gate voltage \({V}_{{\rm{G}}}\). The high-frequency components of the pulses of \({V}_{{\rm{G}}}\) lead to spikes in the AFM signal because of the capacitive coupling between the sample and the sensor electrodes. To compensate these spikes, we applied the same pulses with opposite polarity and adjustable magnitude to an electrode that also capacitively couples to the sensor electrodes. Reflections and resonances in the gate-voltage circuitry were avoided by impedance matching, absorptive cabling and limiting the bandwidth of the external circuit to approximately 50 MHz. Experimental tests showed no indication of severe waveform distortions.

Spectroscopy pulse sequence and data acquisition

The spectra shown in Figs. 2–4 and Supplementary Figs. 2–4 and 7–10 were measured using a voltage pulse sequence similar to the one shown in Fig. 2a, as detailed in the captions of the figures.

To initialize in the D₀⁺ state, the set-pulse voltage and duration were chosen such that it reliably brings the molecule in this state. We chose, therefore, a set pulse with a voltage that exceeds the relaxation energy for the S₀ → D₀⁺ transition having a duration that is much longer than the decay constant of this transition. Specifically, a set-pulse voltage was chosen that is 1 V lower than the D₀⁺–S₀ degeneracy point, having a duration of 33.4 µs (one cantilever period). To initialize in the S₀ and T₁ states (for example, in Fig. 4), the set-pulse sequence consists of two parts: a pulse to bring the molecule to D₀⁺ (the same parameters are used as for the pulse used to initialize in D₀⁺) and another pulse to subsequently bring the molecule in the T₁ state. The second pulse is at −0.3 V (Fig. 4a,d, pentacene) (in general, it was set to V_read-out + 2.5 V for pentacene) or −1.8 V (Fig. 5d, PTCDA), respectively. Note that this pulse sequence has the same effect as the set and sweep pulse for the data at −0.3 V in Fig. 3a or −1.8 V in Fig. 5a, respectively. The duration of the second pulse determines the ratio of population of the T₁ and S₀ states, since the T₁ state will decay during this pulse to the S₀ state according to its molecule-specific lifetime. At the end of a 33.4 µs long second pulse of the set-pulse sequence with V_set = −0.3 V, the T₁ and S₀ population is 0.51 ± 0.01 and 0.49 ± 0.01, respectively, in case of pentacene in Fig. 4. By contrast, the same set-pulse length with V_set = −1.8 V gives a T₁ and S₀ population of 0.79 ± 0.01 and 0.21 ± 0.01, respectively, for PTCDA in Fig. 5d. Supplementary Fig. 3 shows data for pentacene with different initial populations of the T₁ and S₀ states. To this end, pulse durations of 33.4 µs and 100.1 µs were chosen.

A cantilever oscillation amplitude of 1 Å (2 Å peak-to-peak) was chosen to optimize the signal-to-noise ratio for charge-state detection³⁴. The oscillation amplitude modulates the tip height and thereby induces variations in the tunnelling rate and slight variations in the lever arm of the gate voltage. To minimize these effects, the voltage pulses were synchronized with the cantilever oscillation period, such that they started 2 µs before the turn-around point at minimal tip–sample distance. Furthermore, the sweep pulses were chosen to be short, such that the entire sweep pulse occurs around the point of minimal tip–sample distance. If this was not possible, full cantilever-period pulses were chosen. The resulting minor influence of the cantilever’s oscillation amplitude on the excited-state spectroscopy data was neglected in the modelling and, hence, in the fitting. For example, neglecting the cantilever’s oscillation likely causes the deviation between the fit and the data shown in Fig. 5a between voltages (1) and (2) for t_sweep = 3.3 µs (yellow curve).

The tip height was chosen by setting the decay of D₀⁺ into S₀ at a voltage of 1 V above the voltage corresponding to the degeneracy of the D₀⁺ and S₀ states to around 1.5 µs. This tip height is sufficiently large to minimize tunnelling events between the two bistable states during the read-out phase of the pulse sequence, which gives a lower limit to the tip–sample height. The upper limit of the tip–sample height is given by the requirement that the tunnelling rates should be much faster than the slowest triplet decay rate. Typically, these two requirements restrict the possible tip–sample heights to a small range (less than 2 Å) around the relatively large tip–sample height used (estimated to be 9 Å; Supplementary Section 7).

The shortest sweep pulse duration was then chosen such that at the largest V_sweep used, the read-out fraction in the D₀⁺ state was around 0.10. This allowed the observation of transitions at positive voltages, such as (6) in Fig. 3a. By contrast, a longer sweep pulse duration is crucial for the observation of transitions (7), (1) and (8). The longest pulse duration was, therefore, typically set such that the fraction in the D₀⁺ state was close to zero at a voltage of 1 V above the voltage corresponding to the degeneracy of the D₀⁺ and S₀ states. Two or three additional sweep pulse durations were chosen in between the determined shortest and longest pulse duration to improve the reliability of the fitting.

To determine the population in the two charge states during the read-out, the voltage pulse sequences were typically repeated 8 times per second for 80 s for every sweep voltage. The error bars were derived as the s.d. of the binominal distribution (see below). The measurements were performed in constant-height mode. To correct for vertical drift, for example, owing to piezo creep, the tip–sample distance was typically reset every 15 min by shortly turning on the Δf-feedback. Lateral drift was corrected every hour by taking an AC-STM image (similarly as described in ref. ¹⁵) and cross-correlating it with an AC-STM image taken at the beginning of the measurement.

Data analysis

For data analysis, trigger pulses synchronized with the pump–probe voltage pulses were used to identify the start of every read-out interval (dotted lines in Fig. 2c). The remaining effect of the capacitive coupling described above as well as a possible excitation of the cantilever owing to the few µs sweep voltage pulses can cause spikes at the beginning of every read-out period (not present for the data in Fig. 2c), which were removed from the data trace. Subsequently, every read-out interval was low-passed and it was determined if the averaged frequency shift during this interval was above or below the value centred between the frequency shifts of the two charge states. Counting the number of read-out intervals for which the frequency shift was above this value and dividing it by the total number of intervals gives the read-out fraction in the charge state. For the metal tips that we have used, the D₀⁺ and D₀⁻ states always had a less negative frequency shift compared with S₀ (at the respective read-out voltage).

Error bars

The uncertainty on the determined read-out fraction in the charge state is dominated by the statistical uncertainty. Because of the two possible outcomes (charged or neutral), the statistics of a binomial distribution apply (ref. ¹⁶). The s.d. on the counts in a charged state N_c is, therefore, given by

with N₀ being the counts in the neutral state. The error bars on the measured fractions in the charged state are then given by

where the second term in the numerator accounts for the discrete nature of N_c.