Identifying the origin of delayed electroluminescence in a polariton organic light-emitting diode

2.1 Steady-state measurements

TDAF is a well-established polaritonic organic semiconductor that has been used in studies of polariton lasing and superfluidity and exhibits a Rabi-splitting of ∼1 eV [19–21]. The latter is rather important as it enables us here to reach large Δ E S 1 − LP without compromising strong coupling (Figure 2). Density functional theory (DFT) calculations performed at the screened range-separated hybrid LC-whPBE level and refined by measured S₁ and T₁ levels [22] reveal a large energy gap between S₁ and T₁ ( Δ E S 1 − T 1 ) of ∼0.8 eV, which is essential in this study as it hinders RISC from T₁ to S₁ within the molecule. In fact, we can also neglect the opposite ISC process, as the photoluminescence quantum yield of TDAF reported in the literature (90 % [22]) – together with the large energy gap – implies that only a negligible portion of singlets decays directly into triplets. The landscape and character of the TDAF energy levels are further discussed in Supplementary Figure S1. Moreover, TDAF’s ambipolar electrical character makes it a favorable material in POLED studies [23, 24], and here it allows us to directly populate the triplet states under electrical injection due to the spin-statistic rule (25 % singlets and 75 % triplets).

Figure 2:

Polariton characteristics. Angle-resolved reflectivity of (a) POLED 1, (b) POLED 2, and (c) POLED 3. The dashed white line is the molecular exciton energy, the dashed blue line is the cavity energy dispersion, the dashed black lines are fitted polariton dispersions, and the cross points are the experimental reflectivity minima. (d) Exciton (red berry) and photon (grey) content of the LP extracted from the coupled harmonic oscillator model at 15°. (e) Normalized EL spectra of the different POLEDs and the reference device collected at a normal angle.

Figure 1(c) shows a typical time-resolved EL measurement from our POLEDs along with a picture of a blue-emitting POLED in the inset. The POLED having an LP at 2.95 eV yields blue emission with a full-width at half-maximum of 0.13 eV and Commission Internationale de l’Eclairage (CIE) coordinates of (0.167, 0.015). In organic emitters, delayed EL from the S₁ level can be generally associated with either TTA [25], TADF [26], or slowly recombining charges in trapped states (trap emission – TE [27]). This is shown in Figure 1(c) together with the fittings from a rate-equation model that we present in Section 2.3. To investigate whether polaritons influence the dynamics of delayed EL in our POLEDs, we performed detuning- and injection current-dependent experiments. Our results demonstrate that the delayed EL mechanism remained the same regardless of the Δ E LP − T 1 or the existence of strong coupling. To identify the origin of the delayed EL, we carefully compared the experimental data with fittings from our model considering TTA, TADF, and TE parameters. Figure 1(c) demonstrates that TE fitting is in perfect agreement with the experimental data.

We fabricated POLEDs with LP at 2.95 eV, 2.83 eV, and 2.67 eV. The corresponding reflectivity contour plots are shown in Figure 2(a)–(c), respectively. Fittings of the coupled harmonic oscillator model to the reflectivity dip result in the Rabi-splittings of 0.92 eV, 0.88 eV, and 0.96 eV for POLED 1, POLED 2, and POLED 3, respectively, which agree with previous reports on TDAF in strong coupling [19]. Using the same fitting, we also estimated the exciton and photon content in each POLED shown in Figure 2(d). Interestingly, even in a very negatively detuned microcavity with LP at 2.67 eV, we find that the LP band bottom exhibits a large exciton content of 28 % and shows clear anticrossing (see Supplementary Figure S2 for the individual reflectivity spectra). Note that the POLEDs used in reflectivity measurements were top-emitting to avoid absorption through the UV-absorbing MoO₃ layer, and the two POLED configurations showed identical delayed EL profiles albeit with some detuning shifts shown in Supplementary Figure S3. Furthermore, the semitransparent aluminum mirror was thinned to 25 nm (instead of 30 nm) to have better visibility of the UP. We also fabricated TDAF organic light-emitting diodes (OLEDs) in which the bottom electrode was replaced by an indium tin oxide (ITO) transparent layer to eliminate the cavity mode, and we clarified that these reference devices did not exhibit strong coupling. We refer to this OLED device as the reference device throughout this work. The angle-resolved reflectivity shown in Supplementary Figure S4(b) has a Lambertian absorption response and the normal-angle EL [Supplementary Figure S4(c)] is typical for uncoupled TDAF molecule emission, confirming that no polariton modes are supported in these devices. More information on the reference device is shown in Supplementary Figure S4.

Figure 2(e) shows the EL spectra of the studied bottom-emitting POLEDs at the normal collection angle. The POLED with emission at 2.95 eV shows a uniform Lorentzian distribution with a full-width at half-maximum of 0.13 eV, while the POLEDs with LP tuned at 2.83 eV and 2.67 eV have a full-width at half-maximum of 0.14 eV and 0.15 eV, respectively, and exhibit asymmetric emission. Comparing the POLEDs with the reference device’s EL spectrum, shown as a greyed-out area in Figure 2(e) and in Supplementary Figure S4, we attribute this asymmetricity to emission from the uncoupled excitons escaping through the 30 nm-thick aluminum mirror. It is worth noting that shifting the LP resonant closer to T₁ resulted in a substantial reduction of the EL intensity (see Supplementary Figure S5). To our advantage, the thickness variation for the selected detuning is ∼10 nm, while TDAF is ambipolar and thus insensitive to small shifts of the carrier recombination zone [28]. Previously, in TDAF polariton OLEDs, a hole-blocking layer (BPhen) was used between TDAF and LiF [23], which was not used in our study because we found BPhen devices to degrade rapidly during our measurements.

2.2 Time-resolved electroluminescence

We excite our samples using square electrical pulses with rise and fall times of sub-9 ns and collect the time-resolved EL using a custom-built k-space and time-correlated single photon counting (TCSPC) spectroscopy setup. See the Supplementary Figure S6 for details of the experimental setup. To ensure the consistency of the time-resolved EL measurements, we control the excitation pulse duration and repetition rate to allow the system to reach a steady state before we turn off the electrical pulse and collect the emission statistics. The injected current density was controlled by increasing the excitation pulse voltage and measuring the current with an oscilloscope. The EL from the POLEDs was spatially and spectrally filtered before it was collected by the TCSPC sensor. To ensure the consistency and validity of our findings, all the measurements were performed using freshly made POLEDs that were kept in a vacuum of ∼ 1 0 − 3 bar. In addition, throughout the duration of the time-resolved EL measurement we were tracking that the total collected photon counts remained stable. In some cases, samples degraded due to exposure to ambient conditions or due to overuse, showing a decrease of total collected photon counts over the measurement period resulting in an inflation of their delayed EL. We discarded such results from our final evaluation. An example of this inflation due to sample damage is shown in Supplementary Figure S7.

To explore the effect of strong coupling in the delayed EL of TDAF OLEDs, we compared the POLED 1 and the reference device. As it is clearly shown in Supplementary Figure S4(d) the delayed EL of the reference device is dominated by TE statistics, further proving that the EL mechanism in the TDAF remained unmodified by the presence of strong coupling.

Figure 3(a) shows the time-resolved EL from POLEDs 1–3 at an injection current of 90 mA/cm². Despite how closely we approached T₁ with the LP, we observed identical trends. Moreover, all POLEDs display identical matching trends for injection current densities varying from ∼30 mA/cm² to ∼150 mA/cm² (shown in Supplementary Figure S8). This further confirms that the polariton-alignment effect in the delayed emission of TDAF, if any, is negligible and difficult to resolve in raw data. By increasing the current density, interestingly, we observed a small quenching in the delayed EL trends. Nevertheless, to identify its origin and current-induced quenching, we developed a rate equation model that was used to fit the experimental results.

Figure 3:

Time-resolved EL results and fittings. (a) Normalized EL counts of POLEDs 1–3 (E _LP = 2.95 eV, 2.83 eV, 2.67 eV, respectively) at nearly the same current density. (b) Normalized EL counts of POLED 3 (E _LP = 2.67 eV) and fitted TE functions (dashed curves) with four different current densities.

Spin–orbit coupling calculations (SOC) (see Supplementary Figure S1) reveal that S₁–T₂ SOC is an order of magnitude larger than S₁–T₁ SOC. This indicates that under the right conditions, TDAF could demonstrate “hot RISC” [29]. In our case, the LP mode of POLED 2 is aligned with T₂ and also possesses substantial excitonic content of 30 %, thus acting potentially as a “hot RISC” channel directly populating LP from T₂ with a rate k hRISC T 2 → LP > 0 . As indicated by Figures 3 and 4, we did not observe this. We speculate that such a scenario will have interesting implications for the device’s performance, and it is perhaps interesting to investigate further in the future.

Figure 4:

Parameters extracted from the fittings, as functions of current density. (a) The TE amplitude. (b) The characteristic recombination time. (c) The effective decay rate. (d) The DEL-%. The error bars are standard deviations obtained from 100 independent fittings.

2.3 Rate-equation model and fitting

The population dynamics in our system, following the pulse turn-off, can be approximated by the following system of coupled rate equations. Here, we account for the presence of TTA, TADF, and TE [cf. Figure 1(b)] and consider both the strong and weak coupling (i.e., reference device).

Here, S₁, LP, and T₁ are the time-dependent populations of S₁, LP, and T₁. L is the Langevin recombination rate describing trapped charges. We assume that the excitons formed by trapped charges obey the spin-statistic rule: 25 % populating S₁ (or exciton reservoir) and 75 % T₁. k ( n ) r S 1 is the (non)radiative rate of S₁, k r LP is the radiative rate of LP, k nr T 1 is the nonradiative rate of T₁, k S 1 → LP is the rate of internal conversion from S₁ to LP, k ISC LP → T 1 is the rate of intersystem crossing from LP to T₁, k RISC T 1 → LP is the rate of reverse intersystem crossing from T₁ to LP, k _TTA is the rate at which two first-order triplets annihilate, and k TTA T 1 → S 1 is the rate at which TTA populates S₁. Note that, in general, k TTA ≠ k TTA T 1 → S 1 . In the strong-coupling regime, S₁ becomes the exciton reservoir and we have k r S 1 = 0 , whereas all rates involving LP vanish under weak coupling. Note also that we have not considered uncoupled singlet emission in the strong-coupling regime. This is because we only collect photons from the lower polariton, and the uncoupled singlets in TDAF can be treated independently. For example, population transfer from the uncoupled singlets first to the triplets and then to the lower polariton is negligible.

Substituting Eqs. (1) and (2) to the EL intensity I EL ∝ R ≔ k r S 1 S 1 + k r LP LP , we get.

Note that I _EL consists of both the prompt and delayed part. Next, we solve the intensity of delayed EL (I _DEL) in different scenarios. For reasons that we will discuss later, we normalize the solutions so that I _EL(0) = 1.

TTA scenario: If TTA dominates, we have d T 1 d t ≈ − k TTA T 1 2 . Solving for T₁, substituting to Eq. (4) under a similar approximation, and normalizing, we arrive at (cf. Ref. [25])

Here, s is some reference point of time belonging to the TTA-dominant regime.

TADF scenario: If TADF and the ISC-RISC cycle given by k ISC LP → T 1 LP and k RISC T 1 → LP T 1 dominate, we have

Again, we solve for T₁, substitute to Eq. (4), and normalize, this time obtaining (cf. Ref. [26])

TE scenario: Finally, should TE dominate, we can see from Eq. (4) that I DEL ∝ 1 4 L . Here, the Langevin recombination rate L is defined as [27]

where γ is the bimolecular rate constant and ρ _e(h)(x, t) is the density of trapped electrons (holes). Assuming that the charges are normally distributed over the recombination zone of thickness d [27], i.e.,

with N and D denoting the initial concentrations and diffusion coefficients, L becomes

Here, τ ≔ d ²(D _e + D _h )/(4D _e D _h ) is the characteristic recombination time of electrons and holes. Now, we can write the normalized delayed EL intensity as

Fitting Eqs. (5), (8), and (12) to the time-resolved EL data, we find that the TE model fits the best [see Figures 1(c), 3(b), S4(d), and S9]. The mean absolute errors calculated from all the fittings and the time span of 1 ms are given in Table 1. From the errors, we see that also TTA could contribute to delayed EL. Indeed, there surely are intermediate time intervals with competing mechanisms. However, as the TTA model clearly begins to deviate from the data after the characteristic recombination time, while TE persists to fit well, we can explain the dynamics with the latter. With TADF, this is more apparent; Typically, TADF starts much earlier and its contribution dominates the overall EL intensity [26]. That is, we did not change the already negligible RISC rate of TDAF with strong coupling.

In Figure 3(a), we have plotted the time-resolved EL data of POLEDs 1–3 (E _LP = 2.95 eV, 2.83 eV, 2.67 eV) with nearly the same current density. We can clearly see that the delayed EL is independent of detuning.

Figure 3(b) shows the time-resolved EL data of POLED 3 (E _LP = 2.67 eV) and fit functions (12) with different current densities. The TE model describes our data extremely well – and although the model would seem to fit well with the prompt EL too, one should notice that lim _t→0 I _DEL(t) = ∞. That is, prompt I _EL near t ≈ 0 should be solved separately from I _DEL. In addition to the delayed EL models, we fitted monomials to the data and obtained approximately 1/t-tails – a signature of trapped charges [27].

It is of interest to evaluate the delayed emission contribution to the entire EL. We now define DEL-% as the intersection of I _DEL(t) and an exponential function exp(−kt) fitted on the prompt I _EL(t) (cf. [25]) – this is why we normalized the EL intensities. Here, k is the effective decay rate of prompt EL. All the fitting results of POLEDs 1–3 are shown in Figure 4. Figures 4(a)–(d) show the TE amplitude A ≔ γ N e N h / 8 R ( 0 ) π ( D e + D h ) , the characteristic recombination time τ, the decay rate k, and the DEL-%. Note that the resolution of prompt time-resolved EL may cause some error in our estimation procedure. Furthermore, the fitting of τ is quite sensitive to noise, which can explain the more fluctuating values in Figure 4(b) when compared to other quantities. The error bars in Figure 4 were calculated using 100 perturbed data sets per current density and detuning. In each case, we simulated repeated measurements by adding white noise to the data, staying close to the original envelopes.

In Figure 4(a), the TE amplitudes decrease smoothly – perhaps exponentially – while the other quantities behave more interestingly around J ₀ ≈ 30 mA/cm². Until this point, increasing current density means trapping more charges. Due to this aggregation, electrons and holes can recombine faster (τ becomes smaller), increasing the contribution of delayed EL. When we go beyond J ₀, we start to promote different non-radiative processes such as singlet–singlet, singlet–triplet, and singlet–polaron annihilation [30], which dominate over the emission of trapped charges. That is, τ starts increasing and DEL-% decreasing. Furthermore, as the singlets are involved in these processes, the effective decay rates in Figure 4(c) increase at a slower rate.

4.1 Fabrication

The POLED devices were fabricated on pre-cleaned glass substrates using thermal evaporation at a base pressure below 10⁻⁷ Torr (Angstrom Engineering physical vapour deposition system). We used 15 × 15 mm² glass substrates that were cleaned by sonication for 10 minutes in soapy water (3 % Decon 90), acetone, and isopropanol, respectively. The cleaned glass substrates were dried with nitrogen before device fabrication. A 30 nm-thick aluminium was deposited on top of the glass substrate as a bottom electrode, followed by deposition of 5 nm MoO₃ as the hole injection layer, TDAF as emitting layer, 1 nm LiF as the electron injection layer, and a 100-nm-thick aluminium as a top contact. The detuning of the POLEDs was controlled by varying the thickness of the emitting layer.

4.2 Characterization

The angle-resolved reflectivity was measured with a J.A. Woollam VASE ellipsometer in reflectivity configuration. The EL was collected using a custom-made k-space setup (0.2 NA Microscope objective, 250 µm slit width) consisting of a spectrometer coupled to a two-dimensional (2D) CCD camera (Princeton Instruments, 1340 × 400 pixels). Time-resolved EL was acquired using the same spectrometer and a pulse generator (HM8150) as an electrical excitation source. The POLEDs were excited electrically by 250 µs pulse with different current densities. Further details can be found in Supplementary Figure S6.

4.3 Computational methodology

The electronic structure calculations were performed by using the DFT at the screened range-separated hybrid (SRSH) method with optimally-tuned LC-ωhPBE functional and 6-31G (d, p) basis set. The range separation parameter, ω, was optimized using a minimization procedure based on the expression: J(ω) = [ϵ _HOMO(ω) + IP(ω)]² + [ϵ _LUMO(ω) + EA(ω)]². A dielectric constant of ϵ = 3.5 was considered for the SRSH calculations. The excited-state energies were estimated using the Tamm–Dancoff approximation (TDA) within the Time-dependent density functional theory (TDA-TDDFT) approach. The nature of the excited states was characterized using the Natural Transition Orbitals (NTO) analyses. The SOC values between the ground and excited states were estimated using the PySOC code interfaced with TDA-TDDFT calculations. These calculations are performed at two different dielectric constants, ϵ = 3.08 and 3.5, commonly used for such materials and following experimental conditions [35, 36]. Calculations by using two different dielectric constants reproduced similar trends. All DFT and TDA-TDDFT calculations were performed with the Gaussian16 program package [37].