A figure of merit for efficiency roll-off in TADF-based organic LEDs

Organic light-emitting diodes (OLEDs) are a revolutionary light-emitting display technology that has been successfully commercialized in mobile phones and televisions1,2. The injected charges form both singlet and triplet excitons, and for high efficiency it is important to enable triplets as well as singlets to emit light. At present, materials that harvest triplets by thermally activated delayed fluorescence (TADF) are a very active field of research as an alternative to phosphorescent emitters that usually use heavy metal atoms3,4. Although excellent progress has been made, in most TADF OLEDs there is a severe decrease of efficiency as the drive current is increased, known as efficiency roll-off. So far, much of the literature suggests that efficiency roll-off should be reduced by minimizing the energy difference between singlet and triplet excited states (ΔEST) to maximize the rate of conversion of triplets to singlets by means of reverse intersystem crossing (kRISC)5–20. We analyse the efficiency roll-off in a wide range of TADF OLEDs and find that neither of these parameters fully accounts for the reported efficiency roll-off. By considering the dynamic equilibrium between singlets and triplets in TADF materials, we propose a figure of merit for materials design to reduce efficiency roll-off and discuss its correlation with reported data of TADF OLEDs. Our new figure of merit will guide the design and development of TADF materials that can reduce efficiency roll-off. It will help improve the efficiency of TADF OLEDs at realistic display operating conditions and expand the use of TADF materials to applications that require high brightness, such as lighting, augmented reality and lasing.

Organic light-emitting diodes (OLEDs) are a revolutionary light-emitting display technology that has been successfully commercialized in mobile phones and televisions 1,2 .The injected charges form both singlet and triplet excitons, and for high efficiency it is important to enable triplets as well as singlets to emit light.At present, materials that harvest triplets by thermally activated delayed fluorescence (TADF) are a very active field of research as an alternative to phosphorescent emitters that usually use heavy metal atoms 3,4 .Although excellent progress has been made, in most TADF OLEDs there is a severe decrease of efficiency as the drive current is increased, known as efficiency roll-off.So far, much of the literature suggests that efficiency roll-off should be reduced by minimizing the energy difference between singlet and triplet excited states (ΔE ST ) to maximize the rate of conversion of triplets to singlets by means of reverse intersystem crossing (k RISC ) [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] .We analyse the efficiency roll-off in a wide range of TADF OLEDs and find that neither of these parameters fully accounts for the reported efficiency roll-off.By considering the dynamic equilibrium between singlets and triplets in TADF materials, we propose a figure of merit for materials design to reduce efficiency roll-off and discuss its correlation with reported data of TADF OLEDs.Our new figure of merit will guide the design and development of TADF materials that can reduce efficiency roll-off.It will help improve the efficiency of TADF OLEDs at realistic display operating conditions and expand the use of TADF materials to applications that require high brightness, such as lighting, augmented reality and lasing.
Organic light-emitting diodes (OLEDs) are now widely used in displays and are being developed for applications in lighting, sensing and communications 1,2 .They consist of layers of charge transporting and light-emitting organic semiconductors in between two electrodes, at least one of which is transparent.When the injected charges recombine, they form both singlet and triplet excitons.Spin statistics suggest three triplets form for each singlet, a ratio that has been verified for evaporated OLEDs using low molecular weight emitters 21 .In OLEDs using fluorescent materials, only the singlets emit light.Phosphorescent OLED materials were therefore developed to obtain light emission from the triplets as well 22 .These work very well for red and green emission, but there is not yet a blue phosphorescent emitter meeting all commercial requirements 23 .Consequently, there is currently great interest in thermally activated delayed fluorescence (TADF) as an alternative approach to obtaining light from triplets 3,4 .Following the pioneering work of Adachi and coworkers in 2011, there have been more than 4,000 papers with the keyword thermally activated delayed fluorescence 24,25 (based on results from 16 February 2024 that mention thermally activated delayed fluorescence or TADF since 2011).
A problem in both organic and inorganic LEDs is that as the drive current is increased for more light output, the efficiency decreases 26 .This is known as efficiency roll-off and is illustrated in Fig. 1a, which shows the efficiency as a function of current density for prototypical examples of fluorescent, phosphorescent and TADF OLEDs 3,27,28 .
Figure 1a shows that the phosphorescent and TADF OLEDs have more than four times the efficiency of the fluorescent OLEDs, but that their efficiency decreases and particularly severely for the TADF OLEDs as the current density is increased.To compare the behaviour of a wide range of OLEDs of each type, we define J 90 as the current density at which the external quantum efficiency (EQE) falls to 90% of its peak value, as illustrated in Fig. 1b.
We have extracted J 90 from published data on a wide range of OLEDs together with their EQE at a practical luminance of 1,000 cd m −2 .These are plotted for each class of OLEDs and each colour in Fig. 1c.The ideal behaviour would be high J 90 (for low efficiency roll-off) and high EQE: that is, the top right quadrant of the graph.Most fluorescent OLEDs fall in the green rectangle (A), which is a region of high J 90 but low EQE.Most phosphorescent OLEDs (and a few others) fall in the blue rectangle (B).The upper half of this rectangle represents OLEDs with high efficiency and fairly high J 90 .TADF OLEDs fall mainly in region C. Notably, there is a much wider spread of both EQE and J 90 than for the other classes of OLEDs, possibly because TADF OLEDs is a much younger field.The upper right part of region C shows that there are some reports of TADF OLEDs with high EQE and moderately high J 90 , although lower than for good phosphorescent devices.However, region C also extends to extremely low values of J 90 that is, there are many TADF devices experiencing significant efficiency roll-off at current densities below 0.1 mA cm −2 .Even for a green device, this would correspond Analysis to a brightness of at most 100 cd m −2 , whereas typical displays run at 400 cd m −2 and their individual pixels often run at much higher brightness to achieve an average 400 cd m −2 on the display 29 .Hence, many reported TADF OLEDs have severe efficiency roll-off and even the best have significant efficiency roll-off ( J 90 of a few mA cm −2 ).

Efficiency roll-off in TADF devices
This brings us to the central question of this analysis, which is, what can be done in terms of emitter design to reduce efficiency roll-off (that is, increase J 90 )?In other words, which photophysical processes need to be tuned by molecular design to minimize inherent limitations of the emitter that contribute to efficiency roll-off?Efficiency roll-off arises both from the emitter design and the device design, but for an optimized device design (for example, balanced charge carriers and wide recombination zone) it will ultimately be limited by the properties of the emitter.
To identify the crucial parameters for emitter design, we first need to consider what causes efficiency roll-off.Studies in phosphorescent OLEDs have shown that triplet-triplet annihilation (TTA) and tripletpolaron annihilation (TPA) are the main loss mechanisms as the current density is increased [29][30][31] .A similar understanding is developing in TADF OLEDs in which TTA, TPA and singlet-triplet annihilation (STA) may all contribute [32][33][34] .These are all bimolecular processes and thus much more severe at higher excitation densities.Furthermore, as all these processes involve triplets, they can be mitigated by reducing the triplet lifetime and hence reducing the triplet population.This has been achieved successfully in phosphorescent OLEDs by engineering the light-emitting material (for example, by using an iridium complex) to show a large radiative rate constant from the triplet state and thus achieving a relatively short triplet lifetime of around 1 µs.
For comparison, delayed fluorescence lifetimes in organic TADF materials range from 1 µs to beyond 500 µs.We briefly note that as well as reducing efficiency, bimolecular processes involving triplets are also a main mechanism of device degradation, providing a further reason to reduce the triplet population in operating devices 35 .
Hence to reduce efficiency roll-off, we need to reduce triplet lifetime or, more precisely, the triplet population during device operation.This, however, is not as simply achieved as in the case of phosphorescence.The key photophysical processes in a TADF emitter are shown in Fig. 2. Singlets are converted to triplets via intersystem crossing (ISC) with rate constant k ISC , and triplets to singlets via reverse intersystem crossing (RISC) at rate constant k RISC .There is potentially radiative and non-radiative decay of both triplets and singlets, although in a good TADF material k r S will be much larger than any of k nr S , k r T and k nr T (refs. 36,37).The main approach advocated in the literature for reducing efficiency roll-off is to increase k RISC , commonly by reducing the energy difference between singlet and triplet excited states (∆E ST ) through molecular design by reducing the exchange integral between the highest occupied and lowest unoccupied molecular orbitals.In addition, there have been other attempts to increase k RISC , for example by the use of heavy atoms, to increase spin-orbit coupling (SOC) 5,38 .The emphasis on k RISC is so strong that since 2016 there have been 16 publications in the Nature family alone exploring k RISC (refs.5-20).However, the expected improvement in J 90 has not always materialized.
To understand how J 90 depends on k RISC , we have plotted the graph shown in Fig. 3.There is some correlation (Spearman correlation ρ = 0.638) in so far as there is a tendency towards higher J 90 for higher k RISC , but there is an enormous spread of the data (considering this is a log-log plot).For example, the blue dashed rectangle shows that J 90 of roughly 2 mA cm −2 can be achieved with k RISC from 2 to 20 × 10 5 s −1 .The insufficiency of k RISC as a guide for molecular design is vividly demonstrated by the red dashed rectangle that shows J 90 for molecules designed with a high k RISC of 8-15 × 10 5 s −1 .The values of J 90 range from 0.03 to 40 mA cm −2 , that is, by more than three orders of magnitude, showing k RISC alone is inadequate as a predictor of efficiency roll-off.

Derivation of FOM
To develop guidelines for TADF materials design to reduce efficiency roll-off in OLEDs, we should first look more closely at Fig. 2 and the mechanism of TADF.  5,38,39, , fl][116][117][118][119][120][121][122][123][124][125][126][127][128][129] and phosphorescent (Phos.) [86][87][88] evices emitting in the red (R), green (G) and blue (B) regions of the spectrum (for the references, see Methods).The physics of TADF is often studied using transient photoluminescence (PL) measurements in which the emitter is excited using a laser pulse.Excitons are generated in the excited singlet state (S 1 ), and the decay of the excited state is slowed by cycling to and from the triplet state (T 1 ) by ISC and RISC, respectively.In an OLED, charge injection leads to a buildup of both S 1 (25%) and T 1 (75%) excitons as well as polarons.There is a dynamic equilibrium between S 1 and T 1 facilitated by the ISC/RISC cycling.To ascertain on which side the dynamic equilibrium lies, an equilibrium constant K eq is defined as eq 1 1 For a three-level TADF OLED under low constant current electrical excitation, the equilibrium constant is given as follows (see Methods for the derivation) As explained earlier, to minimize the EQE roll-off a low T 1 population is necessary to suppress TTA and to a lesser extent STA and TPA.For an OLED operated at high brightness this translates to the requirement of maximizing the S 1 population relative to the T 1 population, which can be achieved by maximizing K eq .Furthermore, according to Le Chatelier's principle, an equilibrium can be moved to a desired product by removing the product from the equilibrium.Here, the radiative decay of S 1 excitons is the desired product.Therefore, to minimize the fraction of triplet excitons in the steady-state OLED emitters should be developed (or selected) to maximize the product of radiative rate constant and equilibrium constant.In a good OLED, nearly all electrically excited excitons decay radiatively, that is k k = =0 nr S nr T .Thus, for a TADF emitter with photoluminescence quantum yield near unity and no phosphorescence contribution k ( =0) r T , which is reasonable for good organic emitters, a figure of merit (FOM) for efficiency roll-off can be formulated as Figure 4 shows J 90 plotted as a function of this FOM.There is a stronger correlation with J 90 (ρ = 0.700) than k RISC with J 90 (ρ = 0.638).Higher k K r S eq leads to higher J 90 .Accordingly, maximizing k K r S eq and thus minimizing the T 1 population under electrical excitation is a better strategy for improving efficiency roll-off than considering k RISC alone.Figure 4 compares efficiency roll-off as a function of our FOM (black circles) with efficiency roll-off as a function of k RISC (small grey circles).The FOM has a narrower spread of values as would be expected for the improved correlation.
It is interesting to apply this FOM to recent attempts to increase k RISC by incorporating heavy atoms into the molecule to increase SOC 5,38 .These studies are shown by red crosses in Figs. 3 and 4.This strategy is broadly successful at leading to fast k RISC but does not necessarily lead to the highest J 90 as k ISC also increases, or k r S decreases.This interplay between these parameters is captured by the FOM as can be seen from the red crosses in Fig. 4 being in the same region as other materials.At the same time, incorporation of these larger atoms that result in weaker bonds also leads to faster non-radiative pathways and potentially poor device stability.Here, we can see that k RISC and the proposed FOM give distinct assessments of the heavy atom approach, and that the latter is a better predictor of J 90 for future molecular design.Another possible guide for design is (as for phosphorescent devices) short delayed fluorescence lifetime (τ DF ) 39 .The correlation of J 90 with τ DF is shown in Extended Data Fig. 1a.There is a good correlation (ρ = −0.685),although still some scatter.Actually, τ DF has a much stronger correlation with the proposed FOM (ρ = −0.801)than with k RISC (ρ = −0.709).In other words, the proposed FOM not only predicts the efficiency roll-off, but also clarifies the key physical processes that need to be optimized to achieve low efficiency roll-off.Although measuring τ DF would be an effective way of screening materials for low potential efficiency roll-off after they have been synthesized, our FOM gives more insight into how to design a material for low efficiency roll-off by showing the exact combination of rate constants that should be optimized.For many TADF materials k ISC is substantially faster than k r S , in which case the FOM can be simplified to with a Spearman correlation coefficient of ρ = 0.700.Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in k RISC .In grey circles, the correlation of J 90 and k RISC from Fig. 3 is shown for comparison.

Analysis
This simplified FOM highlights the competition between k ISC , k RISC and k r S very clearly.It is equivalent to k K r S eq in the regime where k r S is smaller than k ISC (Extended Data Fig. 2).

Other factors affecting efficiency roll-off
Although there is a good correlation between J 90 and the proposed FOM, there is a significant spread of data points in Fig. 4.This can be understood to arise because efficiency roll-off involves a combination of the intrinsic properties of the emitting molecule with the extrinsic properties of the device.An analogous situation exists when using photoluminescence quantum yield as a predictor of device efficiency: whether a material realizes its full potential also depends on the device.Similarly, our FOM describes the best that could be achieved with a particular light-emitting material in a device limited by the triplet population.In real devices, many factors, especially imperfect charge balance, could lead to worse performance than this ideal case, and hence can explain the spread of the data in Fig. 4. In addition, at low current density some devices show efficiency increasing with current density, as can be seen for the devices in Fig. 1a.As J 90 is taken as a reduction from peak efficiency, this will lead to higher values of J 90 than in devices with peak efficiency at very low current.There is another example of this effect in Extended Data Fig. 3 that compares two 2CzPN devices 3,40 .It should also be noted that practice for determining rate constants varies 37,41 , which could also contribute to the spread.Another important factor that could contribute to the spread of data is that the effect of a given triplet population depends on the material.In particular, reported TTA rate constants γ TT are widely spread over eight orders of magnitude (10 −18 -10 −10 cm 3 s −1 ) 32,33,42,43 .So, increasing the FOM will reduce triplet population, and is beneficial (increases J 90 ) but the improvement arising from the reduced triplet population depends on the value of γ TT .Similar considerations apply to STA, in which again there is a range of γ ST , and the relative importance of STA and TTA depends on the relative values of γ TT and γ ST .As these rate constants are not yet widely measured, we have not at this stage attempted to incorporate them into a FOM.However, we show their potential effect in Extended Data Fig. 4, which shows calculations of how J 90 would depend on FOM for systems with k r S between 10 5 and 10 10 s −1 , k k / ISC r S between 10 −1 and 10 3 , and k K r S eq between 10 2 and 10 8 s −1 for a range of values of γ ST , γ TT and k r S .Extended Data Fig. 3a shows how for a given FOM, each order of magnitude change in γ TT leads to an order of magnitude change in J 90 .Extended Data Fig. 4b shows the potential interplay between TTA and STA.The J 90 value behaves nearly linearly with k K r S eq when only TTA is considered (red dots, the slope is 2).If only STA is considered, there is still a correlation; however, at the same FOM, higher J 90 is achieved when k r S is large.If both TTA and STA are significant, then the efficiency is limited by TTA at low FOM and by k r S at high FOM.
We also note that the kinetics of thin films can result in a multiexponential transient PL, which is caused by conformational disorder 44 .Such a decay can be analysed using a Laplace transformation of the three-level kinetics of each conformer 45 .Our analysis does not include conformational disorder but could be applied in a similar manner to the analysis of multi-exponential transient PL caused by conformational disorder.

Conclusion
Our analysis has important implications for the rapidly growing field of TADF OLED development.At present, many such devices suffer such severe efficiency roll-off that they are unsuitable for practical application and, as we have shown, current emitter design focusing on maximizing k RISC alone is not an effective strategy.On the basis of the insight from considering the quasi-equilibrium in TADF, we instead propose that the focus of materials design and development should shift to maximizing a FOM that combines the physical processes that determine efficiency roll-off.Target values of the FOM will depend on the requirements of particular applications, as well as device design and severity of bimolecular effects.We estimate values of FOM required for materials with chromaticity close to the BT2020 standard 46 , and with Gaussian emission spectra of width 15 nm in the blue, 30 nm in the green and 45 nm in the red.We use the calculation for Extended Data Fig. 4a with γ TT = 10 −13 cm 3 s −1 and find the FOM required to achieve 90% of a peak EQE of 25% at a brightness of 1,000 cd m −2 .We find that for a deep blue emitter (λ max = 467 nm, CIE 1931 colour space (0.131, 0.049)) a FOM of at least 1.5 × 10 5 s −1 is required.For a green emitter (λ max = 529 nm, CIE (0.169, 0.772)) a FOM of 5.1 × 10 4 s −1 would be required, and for red (λ max = 650 nm, CIE (0.708, 0.292)) an FOM of at least 1.3 × 10 5 s −1 is needed.
In terms of material design for low efficiency roll-off, it is not necessary to maximize k RISC , but it is very desirable to maximize k RISC relative to k ISC (without sacrificing k r S ).It is also a useful strategy to seek materials with high k r S (providing k RISC /k ISC is not reduced), which is also the underlying physics for hyperfluorescent OLEDs 47 , where the rate constant of Förster resonance energy transfer takes the place of k r S in the FOM and lowers the triplet population on the TADF sensitizer.At the same time, there is a need to understand which process dominates the efficiency roll-off.Whereas all main annihilation processes scale with the triplet population and thus inversely with our proposed FOM, the relative importance of these processes in each OLED is not sufficiently known.Therefore, there is a need to measure both γ ST and γ TT in a wider set of devices to fully understand how the excited-state kinetics of the emitter need to be engineered to reduce efficiency roll-off.We hope that our FOM and these insights will enable the field of TADF OLEDs to overcome the challenge of efficiency roll-off and advance more rapidly to applications in displays, lighting and beyond.

Online content
Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-024-07149-x.

Data collection
We considered the reported efficiency roll-off behaviour of TADF OLEDs published in peer-reviewed journals between 2016 and 2022.The data of the OLED and emitter were included in the analysis if the following criteria were met: 1.The reported OLED was vacuum-processed, in a bottom-emitting device structure with a TADF emitter in a host material.2. Photophysical characterization of the thin film used as the emission layer was reported.3. The photoluminescence quantum of the emitter film was reported to exceed 60%. 4. The calculation of all TADF rate constants was clearly detailed.5. Device data clearly showed J 90 data or the presented device data allowed for a reasonable estimation of J 90 .

Steady-state population of the excited states
The kinetics of a TADF emitter as shown in Fig. 2 under electrical excitation can be described by the rate equations for the excited singlet state (S 1 ) and the triplet state (T 1 ) when neglecting annihilation processes as follows.
where J(t) is the current density at time t, d is the thickness of the emission zone and e is the elementary charge.
In normal device operation, the OLED is driven at constant current density ( J(t) = J const ) so the excited-state populations reach a steady state given by equation (8).
const The steady-state population of S 1 and T 1 ([S 1 ] and [T 1 ], respectively) can be obtained by substituting the differential equation for S 1 in steady state into the differential equation of T 1 steady state By inserting equation ( 8) in equations ( 13) and ( 14) the steady-state populations are given as a function of the current density as  5) and ( 6) was generated, using the permutation of the input variables in Extended Data Table 1, with as well as all other rate constants set to 0.
For the calculation of Extended Data Fig. 3a,b, the bimolecular rate constants were set to the values shown in the figure.J 90 was obtained by minimizing equation ( 18) using the python package scipy 162 .where η IQE ( J) is the internal quantum efficiency (IQE) at current density J considering annihilation processes and η IQE 0 is the IQE without considering annihilation processes.Both are given by For η IQE 0 , the singlet population [S 1 ] and triplet population [T 1 ] were obtained from equations ( 15) and ( 16), respectively.For η IQE ( J), [S 1 ] and [T 1 ] were obtained by minimizing the set of differential equations ( 20) and ( 21) with [n] given by equation ( 7), using the python package scipy 161,162 .where I(λ) is the relative intensity of the OLED at wavelength λ, η EQE is the ratio of photons leaving the OLED to the number of electrons flowing around the electrical circuit (EQE).The total luminous flux Φ V can be calculated from the optical power flux using the photonic sensitivity curve V(λ) as V m e m EQE where K m = 683 lm W −1 is a fudge factor called the peak response.
Under the assumption of Lambertian emission, the luminance L V of the OLED is then given as follows.
V V m EQE Therefore, the current density required to generate a given luminance by an OLED with a given normalized spectrum and given EQE is given as follows.

∫
For the calculation of the target value, we have taken three assumed spectra for red, green and blue with a Gaussian shape and a full-width at half-maximum of 45, 30 and 15 nm, respectively.The centre wavelength was selected so that the colours of the three spectra are as close as possible to the primary colours of the BT.2020 standard in the CIE 1931 colour space, which are given by the coordinates (0.708, 0.292), (0.170,0.797) and (0.131,0.046), respectively 46 .
The calculation was performed at an EQE of 22.5% for L v = 1,000 cd m −2 , indicating a maximum EQE of 25%.The correlation for J 90 to the FOM is taken from the simulated relationship shown in Extended Data Fig. 4a for γ TT = 10 −13 cm 3 s −1 and γ ST = γ TP = 0 as follows.

Fig. 2 |
Fig. 2 | Simplified Jablonski diagram of a TADF emitter.The excited singlet and triplet states S 1 and T 1 , respectively, are shown in equilibrium due to the occurrence of both intersystem crossing (k ISC ) and reverse intersystem crossing (k RISC ) enabled by the small energy gap (ΔE ST ) between S 1 and T 1 .A TADF OLED emits light by radiative decay from k S ( ) 1 r S , whereas non-radiative decay from k S is the sum of the rate constants for ISC (k ISC ), radiative k ( ) r S and non-radiative k ( ) nr S decay from S 1 , and k T is the sum of the rate constants for RISC (k RISC ), radiative k ( ) r T and non-radiative k ( ) nr T decay from T 1 .

Fig. 3 |Fig. 4 |
Fig. 3 | Data analysis.J 90 of the reported TADF OLEDs with respect to k RISC (Spearman correlation ρ = 0.638).Red crosses present TADF molecules containing heavy atoms that benefit from enhanced SOC to increase k RISC .Data inside the dashed boxes are for comparison.
is the sum of the rate constants for ISC (k ISC ), radiative k S 1 , where k T is the sum of the rate constants for RISC (k RISC ), radiative k and γ is the Langevin recombination rate.The derivative of the polaron population [n] t can be sufficiently approximated by not distinguishing between the charge of the polaron as 90 for OLED examplesA set of 1,287 kinetic parameters for the equations ( of the emission zone of d = 10 nm, a Langevin recombination rate161 of γ = 6.8 × 10 −17 m s 3

T
Calculation of target valueThe optical power flux Φ leaving an OLED relates to the current density J

Extended Data Fig. 1 |Extended Data Fig. 2 | 90 Extended Data Fig. 3 |
Correlation with delayed fluorescence lifetime τ DF .(a) Dependence of J 90 on τ DF with a Spearman correlation, ρ, of −0.685.(b) Dependence of τ DF on k RISC (ρ = −0.709).(c) Dependence of τ DF on k K eq r S (ρ = −0.801).Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in k RISC .Simplified Figure of Merit.(a) Correlation between J 90 and the simplified FOM of k r S k RISC /k ISC with a Spearman correlation of ρ = 0.680, showing a better correlation than k RISC but a less precise predictor than the FOM of k K eq r S .Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in k RISC .In grey circles, the correlation of J 90 and k RISC from Fig. 3 is displayed for comparison.(b) Deviation between the FOM of k K eq r S and its simplification of k k k / RISC ISC r S for k RISC = 10 7 s -1 showing a deviation between the FOMs for systems with competitive k r S and k ISC .Device influence on Roll-off.Comparison of efficiency roll-off of two literature 2CzPN OLEDs showing different J 90 because of different efficiency rise at low current densities 3,40 .Extended Data Fig.4| Impact of STA and TTA on roll-off.The impact of STA and TTA on the correlation between J 90 and k K eq r S calculated for a simplified three-level system with k r S between 10 5 s -1 and 10 10 s -1 , k k / ISC r S between 10 -1 and 10 3 and k K eq r S between 10 2 s -1 and 10 8 s -1 (a) for three different TTA rate constants and (b) for a particular STA rate, a particular TTA rate and a particular combination of STA and TTA rate.