Improved Light Extraction in Organic Light‐Emitting Diodes via Semiconductor Dilution

Increasing the internal light extraction efficiency of organic light‐emitting diodes (OLEDs) is key to improving their performance for solid‐state lighting applications; however, it is challenging to do this in a way that is compatible with high volume manufacturing. Here, it is shown that the outcoupling efficiency of OLEDs can be improved by diluting their hole transport layer (HTL) with the low refractive index material trifluoropropyl oligomeric silsesquioxane (F‐POSS). Specifically, co‐evaporating 40 vol.% F‐POSS in the HTL of single and multi‐stack phosphorescent OLEDs decreases its refractive index by Δn ≈ 0.2, which in turn yields a ≈12% increase in their outcoupling efficiency with no impact on electrical performance or operational lifetime. This result is significant because F‐POSS is a small molecule that sublimes cleanly, does not aggregate, and is compatible with state‐of‐the‐art HTL materials, making it a realistic path to increase light extraction in commercial OLEDs manufactured on existing production lines.


Introduction
Organic light-emitting diodes (OLEDs) have matured to the point that state-of-the-art devices operate with 100% internal quantum efficiency (i.e., every injected electron produces a photon) at drive voltages close to the emitted photon energy. [1,2]In most cases, however, a large fraction of the emitted photons remain trapped DOI: 10.1002/adom.202302588within the device. [3,4]Improving light extraction is thus widely seen as the last major opportunity to increase OLED external quantum efficiency (EQE).
The light extraction problem is typically broken down into external light extraction of substrate-confined modes (for bottomemitting devices), and internal light extraction of waveguided/surface plasmon modes from the organic/ITO/metal layers. [3,4]7] The latter has proven more difficult to overcome.Internal light extraction has been addressed extensively in both modeling and experiment using various approaches to scatter out waveguided light via corrugation, [8,9] grids, [10,11] or wrinkles [12] introduced within the ITO anode and/or device stack.Many of these strategies are successful; however, to our knowledge, none have been implemented in industry owing to issues of cost, scalability, and/or reliability.Improving internal light extraction in a way that is practically viable for industry thus continues to be a challenge.
A natural path to increase internal light extraction is to reduce the refractive index of the OLED layer stack. [13]This Figure 1.a) Molecular structure of F-POSS, together with the generic device architecture used to explore the improvement in internal light extraction efficiency ( ILE ) that can be achieved by decreasing the HTL refractive index (n HTL ).ETL: electron transport layer; EML: emissive layer.b) Refractive index dispersion of neat NPB and F-POSS films, together with that of varying F-POSS:NPB blends.c) Color map showing  ILE simulated for the device structure in (a) at a free space emission wavelength of  = 635 nm when n HTL = 1.8.The recombination zone is located next to the HTL/EML interface as indicated in (a), and the refractive index of all other organic layers is fixed at n = 1.7.d) The same simulation, except with n HTL reduced to 1.6, which demonstrates how the first and second antinode optima evolve with decreasing HTL refractive index.e) Summary of the optimal ETL and HTL thicknesses (right-hand axis) that maintain the 1st antinode optimum in  ILE (left-hand axis) as n HTL decreases.f) Dipole power dissipation as a function of normalized in-plane wavevector (u = k ∥ /k 0 , where k 0 is the free space wavevector) for the first antinode optimum at different HTL refractive indices.As n HTL decreases, the guided modes and surface plasmon shift to lower wavevector and the amount of power coupled into them decreases, redistributing emission into the glass at high angle.The evolution of the guided mode power dissipation is expanded for clarity in the inset.
effectively reduces the number of modes confined within the OLED stack and thereby increases the fraction of light radiated into the substrate. [14]This strategy has been pursued using organic semiconductors that have naturally low refractive index (n ≈ 1.6 compared with n > 1.7 for most OLED materials across the visible spectrum), [15][16][17][18][19] nanoporous organic semiconductors, [15,16] and low index electrical contacts made of materials such as poly (3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS; n ≈ 1.5). [20]Alternatively, the refractive index of traditional organic semiconductors can be de-creased by co-evaporating them with low index materials such as LiF, [21] perfluorinated oligomers, [22] and polymers. [23]Although the addition of such insulators would normally be expected to degrade electrical transport, the notion of semiconductor dilution [24,25] and critical percolation threshold [25,26] for small molecule-insulator blends motivates the possibility of lowering index without sacrificing transport. [23,24]If this counterintuitive combination can be achieved in state-of-theart OLEDs while maintaining their operational reliability, it would provide a straightforward path to improve internal light  [23] with the general structure: ITO/MoO 3 (5 nm)/CBP (5 nm)/HTL blend (100 nm)/CBP (5 nm)/MoO 3 (5 nm)/Al (50 nm).The dashed lines indicate fits to the Mott-Gurney law using the field-and temperature-dependent mobility model described in the text.The inset shows the F-POSS:NPB blend energetics based on the HOMO levels measured with ultraviolet photoelectron spectroscopy.b) Zero-field mobility values extracted from the fit results in (a), together with those for similar devices with 20 and 60 vol.%F-POSS:NPB blend layers.Error bars reflect the variation observed for multiple measurements on different devices.
extraction in commercial products made on existing production lines.
Here, we show that diluting the common OLED hole transport material N,N′-Di(1-naphthyl)-N,N′-diphenyl-(1,1′biphenyl)−4,4′-diamine (NPB) with up to 40 vol.%trifluoropropyl oligomeric silsesquioxane (F-POSS) reduces the refractive index by Δn ≈ 0.2 while preserving both hole mobility and morphological stability.Incorporating this blend in the hole transport layer (HTL) of both single and multi-stack red phosphorescent OLEDs increases their EQE and power efficiency by a factor of ≈1.12× without altering their electrical performance or operational lifetime.We confirm that the efficiency increases results from improved internal light extraction and show that a larger outcoupling enhancement is possible in multi-stack devices with optimized low-n HTL thicknesses.Crucially, we show that the benefit of F-POSS HTL dilution extends to commercial OLEDs made with state-of-the-art proprietary materials, underscoring the potential value of this strategy for the OLED industry.

Results
Figure 1a presents the chemical structure of F-POSS along with a prototypical OLED architecture that is used to explore the impact of changing the HTL refractive index on internal light extraction efficiency.Figure 1b shows the range of HTL refractive indices that can be achieved by co-evaporating F-POSS with NPB.Neat films of F-POSS are transparent deep into the ultraviolet (optical absorption edge <200 nm; see Figure S1, Supporting Information) and possess a low, nearly dispersionless refractive index of n ≈ 1.39 owing to the large molecular free volume and low polarizability of F-POSS.The refractive index of F-POSS:NPB blends is well described by the Bruggeman effective medium model [27] (this is also true for the other HTLs explored in this work) and decreases linearly with increasing F-POSS volume fraction, from n ≈ 1.82 at 0 vol.%F-POSS to n ≈ 1.55 at 60 vol.%F-POSS ( = 635 nm).In contrast to perfluorinated polymers such as Teflon AF, [23,28] F-POSS is a small molecule that evaporates cleanly and can be purified via gradient sublimation like any other OLED material.The blend films are also homogeneous and show no signs of phase segregation at the nanoscale, [22] both as-deposited and after annealing at 110 °C for 10 min according to atomic force microscopy data provided in Figure S2 (Supporting Information).
Figure 1c,d shows the internal light extraction efficiency,  ILE (i.e., the quantum yield of light emission into the glass substrate), simulated via the transfer matrix method using the commercial software package SETFOS and assuming monochromatic emission at  = 635 nm for simplicity.These plots predict that decreasing n HTL from 1.8 to 1.6 increases  ILE at the 1st and 2nd antinode optima by more than 10% absolute.Figure 1e summarizes the functional dependence of  ILE on n HTL at the first antinode optimum, as well as the ETL and HTL thicknesses that are required to maintain operation at this point.In contrast to previous work, where decreasing the index of the entire organic stack improves light extraction by cutting off guided modes, [14] the improvement in  ILE observed here mainly results from reduced coupling to existing waveguide and plasmon modes as they shift to lower in-plane wavevector (Figure 1f).Based on the approximate analytical treatment of this mechanism provided in Section S3 (Supporting Information), the optimal HTL thickness for the reduced-index device (d HTL ) is related to that of the original optimized device (d HTL0 ) via: where Δn is the magnitude of the HTL index decrease from the original value, n HTL0 , and u pk is the normalized in-plane wavevector (u = k ∥ /k 0 ; k 0 is the free space wavevector) where emission into the substrate peaks as indicated in Figure 1f.The increase in d HTL with decreasing HTL index in Figure 1e can be understood from the standpoint of maintaining optimal multibeam interference within the device (i.e., preserving the Airy factor for outcoupled light), whereas the roughly constant value of d ETL preserves wide angle intereference associated with reflection from the cathode mirror (i.e., the antinode factor). [29,30]he impact of F-POSS on electrical transport in NPB is investigated through temperature-dependent space charge-limited (SCL) current measurements on a series of hole-only devices (Figure 2).Ultraviolet photoelectron spectroscopy measurements provided in Figure S6 (Supporting Information) confirm that the highest occupied molecular orbital (HOMO) of F-POSS lies well below that of NPB (Figure 2a, inset) and therefore should not trap holes.In support of this point, the current density-voltage (J-V) characteristics in Figure 2a are hysteresis-free and display a quadratic voltage dependence (J∝V 2 ) that is consistent with space charge-limited current at room temperature.Ohmic contacts are facilitated by using MoO 3 (5 nm)/ 4,4′-Bis(N-carbazolyl)−1,1′biphenyl (CBP, 5 nm) buffer layers [31] that also serve to prevent changes in interface energy level alignment that can occur when fluorinated dilution materials directly contact the electrodes. [22,23]he J-V data are fit using the Mott-Gurney relation using a field-and temperature-dependent mobility given by the Murgatroid-Gill model [32,33] as described in Ref. [23] The results, which are summarized in Figure 2b, show that the zero-field mobility changes little with increasing F-POSS concentration up to 40 vol.%, but declines rapidly beyond that, with a tenfold de-crease at 60 vol.%.This type of behavior is often observed in organic semiconductor blends and is associated with a percolation threshold for charge transport.[25,26] The fact that the 1/T 2 Arrhenius slope of each data set in Figure 2b stays roughly the same ( ≈ 90 meV) indicates that blending with F-POSS does not significantly alter the energetic disorder parameter for hole transport.[32] Figure 3 explores the impact of varying F-POSS concentration from 0 to 60 vol.% in the HTL of a typical red phosphorescent OLED (Figure 3a). [34]While F-POSS dilution has no apparent effect on the J-V characteristics of the devices in Figure 3b, it does systematically increase their EQE in Figure 3c.The EQE enhancement in each case (relative to the undiluted control) is independent of current density and reaches a factor of ≈1.12 for the 40 vol.%F-POSS device.Since the emission spectra and J-V characteristics of the devices are the same, the power efficiency in Figure 3d is enhanced by the same factor as the EQE.Crucially, these benefits are realized with no adverse impact on the luminance fade device lifetime as shown in Figure S9 (Supporting Information).
To understand whether the EQE enhancement in Figure 3c results from improved outcoupling, Figure 4a plots the ratio of EQE measured in the glass substrate (using index matching fluid to couple the OLED to the Si photodiode as shown in the inset) to that measured in air (i.e., with an air gap between the OLED and Si photodiode).This ratio is independent of the internal quantum efficiency (IQE), but has a characteristic dependence on HTL index that can be accurately calculated with the transfer matrix method.The fact that the model reproduces the observed ratio up to 40 vol.%F-POSS is a strong indication that the enhanced EQE for these devices is solely due to improved outcoupling.The outlier point at 60 vol.%, along with its lower-than-expected EQE enhancement in Figure 3c, can be explained by a shift in the recombination zone (from the HTL/EML to EML/ETL interface) caused by the large decrease in hole mobility at this concentration (Figure 2b).
Further support for the role of improved outcoupling is provided in Figure 4b, which shows the interference-related variation in EQE that occurs when the HTL thickness of the diluted and control devices from Figure 3a is varied.Apart from the two outlier control device data points, which are attributed to fabrication error, the outcoupling model accurately captures the thickness-dependent EQE difference between the two sets of devices.Figure 4b is also important because it explicitly shows that the optimal thickness diluted device outperforms the optimal thickness control.Finally, Figure 4c,d presents the ratio of transverse electric (TE) to transverse magnetic (TM)-polarized electroluminescence spectra collected at an angle of 60°from several of the devices in Figure 4b.Based on the consistent agreement between model and experiment in Figure 4a-c as well as the current-independent EQE enhancement in Figure 3c, we conclude that the efficiency improvement of F-POSS-diluted devices results from increased optical outcoupling.
Figure 5 shows that the benefit of F-POSS dilution extends to two-stack tandem devices, where each sub-unit is the same as in Figure 3 except for a thicker HTL ( d HTL = 78 nm).As in the single stack case, the J-V characteristics of neat NPB and 40 vol.%F-POSS:NPB tandem devices are the same (Figure 5a), and the EQE of the latter is increased by a factor of ≈1.1 (Figure 5b).The EQE enhancement in this case is smaller than for the single stack in Figure 3 because the upper and lower HTL thicknesses of each tandem device are not optimized for peak outcoupling efficiency per Figure 5(c,d).According to these plots, if optimal HTL thicknesses were used in each case (mainly d HTL2 since it controls the position of EML1 relative to the antinode set by the cathode mirror), the outcoupling enhancement enabled by dilution would reach ≈1.18x.The internal light extraction enhancement is predicted to be even larger (≈1.28x), though the HTL thickness optima in this case are different than for outcoupling to air in Figure 5c,d Motivated by the fact that solid-state lighting and automotive applications typically employ tandem devices with even more stacks (up to six), [35,36] Figure 6a investigates the impact of dilution on  ILE for a range of multi-stack devices with different HTL refractive indices.In each case, the sub-unit is assumed to be the same as in Figure 3a except for the HTL thickness, which is globally optimized (e.g., six d HTL parameters for a 6-stack device) for maximum internal light extraction.The jump in  ILE going from a 1-stack to 2-stack device in all of the curves is because surface plasmon loss is substantially lower for the second EML (i.e., the one farthest from the cathode) since near-field coupling to the plasmon mode quickly diminishes with distance to the metal cathode.By the third EML, coupling to the plasmon is insignificant and waveguide modes become the dominant loss channel (Figure 6b,c). [37]Since thick, multi-stack devices support more waveguide modes than a single-stack device, and coupling to these modes is the primary source of loss for most of the EMLs in the stack, the light extraction benefit of dilution tends to be greater for multi-stack than single-stack OLEDs as evident in Figure 6a. Figure 6b provides an example for a 3-stack device.For EML3 closest to the cathode, coupling to the surface plasmon mode is the primary loss.Since the plasmon mode has relatively little overlap with any of the HTLs in the device, the benefit of dilution for EML3 is modest (a ≈10% improvement in  ILE for EML3).However, in the case of EML1 closest to the anode, waveguide modes account for most of its loss (also evident in Figure 6c).Because these modes have significant overlap with all of the HTLs, dilution produces a sizeable decrease in their effective index, which in turn reduces the power coupled into them and even cuts off one of them, thereby realizing a bigger light extraction benefit for EML1 (a ≈20% increase in  ILE ).Finally, Figure 6d shows the optimized layer structure of the two 3-stack devices, from which it is clear that the usual practice of adjusting HTL thickness to position the recombination zone (red dashed lines) of each associated EML at a field antinode also holds for HTL-diluted multistack devices. [37]

Discussion
Though F-POSS is not the first low index dilution material to be used in OLEDs, [21][22][23]28] it is significant because it is a small molecule that sublimes cleanly, can be purified by gradient sublimation, and does not phase segregate in blends. In hort, F-POSS can be purified, processed, and used just like any other small molecule in vacuum deposited OLEDs, which is critical for adoption in industry.To this point, we have reproduced the performance improvement and stable lifetime of the devices in Figure 3 using a state-of-the-art hole transport material in a commerciallyrelevant proprietary device stack as described in Figure S10 (Supporting Information).
Despite investigating a variety of different HTL-dilution molecule combinations, our lab has yet to identify a system in which the hole mobility of the diluted HTL surpasses that of the neat film as reported in Ref. [24].This also appears to be true for molecularly-doped polymers that were extensively explored in the 1990s. [38]In most cases, however, small changes in HTL mobility -whether an increase or decrease-are irrelevant as far as OLED performance is concerned because the hole mobility of state-of-the-art HTLs is much larger than all of the other The sub-unit structure is the same as the two-stack structure in Figure 5a and the HTL thicknesses are globally optimized to maximize  ILE in each case.Note that the value of  ILE for the single stack here is lower than in Figure 1  In both cases, the optimal choice of HTL thicknesses places the recombination zone (assumed to be at the HTL/EML interface) of each sub-unit at a field antinode within the device.mobilities in the device (i.e., of electrons and holes in every other layer) to begin with.So long as dilution does not drastically decrease the HTL hole mobility (e.g., dilute beyond the percolation threshold), the impact on operating voltage and power conversion efficiency is negligible as shown by drift-diffusion modeling in Section S6 and Figure S8 (Supporting Information).Thus, sacrificing HTL hole mobility in favor of lower refractive index to boost light extraction is generally a good tradeoff.This is not the case for diluted electron transport materials.Adding F-POSS into ETL materials such as 4,7-Diphenyl-1,10phenanthroline (BPhen) leads to strong electron trapping and is detrimental to OLED efficiency and lifetime; see Figure S8 (Supporting Information) for details.As in Refs.[22,23], the electron trapping behavior of F-POSS is presumably associated with fluorination which, unfortunately, is also the key to its low refractive index.Non-fluorinated POSS derivatives exist with slightly higher refractive indices ≈1.5 that may offer a path for ETL dilution.However, given that many ETL materials have a naturally low refractive index ≈1.6 that has already been exploited for improved outcoupling, [16,18] it is unclear how much value there is in diluting the ETL to begin with.In any case, focusing on the HTL holds the greatest potential for outcoupling improvement in multi-stack OLEDs because the hole transport material, owing to its high mobility, is generally used as the spacer to adjust EML positions to antinode optima without incurring an excessive volt-age penalty.The net HTL thickness in a multi-stack device therefore usually exceeds that of any other material, giving changes in n HTL a proportionally larger impact on guided mode effective index.
As discussed previously, lowering the refractive index of OLED layers increases the outcoupling efficiency of both horizontal and vertically-aligned emitters.The relative enhancement in  ILE as a function of n HTL is actually largest for vertically-aligned emitters, but this is mostly just because they start with a lower light extraction efficiency to begin with; the absolute increase in  ILE is similar for horizontal, vertical, and randomly-oriented dipoles as detailed in Figure S12 (Supporting Information).

Conclusion
In summary, we have introduced a new dilution molecule to lower HTL refractive index and improve the outcoupling efficiency of single and multi-stack OLEDs without affecting their electrical performance or lifetime.This development is significant because F-POSS sublimes cleanly, can be purified via gradient sublimation, does not phase segregate in the host matrix, and is compatible with state-of-the-art hole transport materials, which should enable it to be implemented in commercial OLED products made on existing production lines.In this context, F-POSS is one of the first examples to deliver on the promise of dilution (i.e., that properties of existing OLED materials, such as refractive index, glass transition temperature, spontaneous orientational polarization, and so forth can be tuned in blends without sacrificing performance) in a way is meaningful to industry.If more such examples can be realized, dilution molecules may become another standard OLED ingredient, just as hole transport, electron transport, host, and dopant molecules are today.
The single stack OLED device structure consists of ITO/HAT-CN (10 nm)/X wt.% F-POSS:NPB (Y nm)/EML (40 nm)/SBFK (10 nm)/PADN (25 nm)/Li:BPhen (10 nm)/ Ag (140 nm), where X is the weight fraction of F-POSS in NPB and Y is the thickness of the HTL.The tandem device consists of two single-stack sub-units separated by a proprietary charge generation layer (CGL).All of the OLEDs have an active device area of 0.1 cm 2 and were encapsulated in a N 2 glove box using a glass cover with desiccant and an edge bead of epoxy.
Characterization: Spectroscopic ellipsometry was used to determine the refractive index dispersion of each material.Current-voltageluminance characteristics were measured using a Keysight B2912A sourcemeasure unit and a large area Si photodiode.Electroluminescence spectra were collected at different angles using a fiber-coupled CCD spectrograph.A wire grid polarizer was placed in front of the fiber to isolate the transverse electric (TE) and transverse magnetic (TM) polarization components of the spectrum.Temperature-dependent current-voltage measurements were collected using a continuous flow liquid N 2 cryostat with a temperature diode adhered to the surface of each sample.Fade testing to characterize OLED lifetime was carried out at constant current at an ambient temperature of 25 °C.Neat F-POSS films as well as 20% F-POSS:NPB and 40% F-POSS:NPB (≈10 nm thick) were deposited on ITO-coated glass substrates for UPS measurements of valence states and ionization energy.All samples were transferred into the ultrahigh vacuum analysis chamber (base pressure ≈ 10 −9 mbar) without air exposure.A non-monochromated helium-gas-discharge lamp (21.22 eV) was used with a pass energy of 5 eV.The secondary electron cutoff spectra were measured with a bias of −5 V applied to the sample to clear the analyzer work function.
44][45] The HTL thickness optimization for the multi-stack devices in Figure 6a is based on the dividing rectangles method included in SETFOS.A freeware program developed by Felekidis et al. [32] was used to fit the temperaturedependent J-V characteristics of hole-only devices to determine the mobility of F-POSS:NPB blends.

Figure 2 .
Figure 2. a) Temperature-dependent current density-voltage characteristics for neat NPB and 40 vol.%F-POSS:NPB hole-only devices.All of the devices employ MoO 3 and a thin layer of CBP to facilitate Ohmic hole injection[23] with the general structure: ITO/MoO 3 (5 nm)/CBP (5 nm)/HTL blend (100 nm)/CBP (5 nm)/MoO 3 (5 nm)/Al (50 nm).The dashed lines indicate fits to the Mott-Gurney law using the field-and temperature-dependent mobility model described in the text.The inset shows the F-POSS:NPB blend energetics based on the HOMO levels measured with ultraviolet photoelectron spectroscopy.b) Zero-field mobility values extracted from the fit results in (a), together with those for similar devices with 20 and 60 vol.%F-POSS:NPB blend layers.Error bars reflect the variation observed for multiple measurements on different devices.

Figure 3 .
Figure 3. a) OLED architecture used to investigate the effect of F-POSS dilution in the HTL.The device consists of a HATCN hole injection layer, a F-POSS:NPB HTL, a NPB:SBFK:RD40 red phosphorescent emissive layer, a SBFK hole blocking layer, a PADN electron transport layer, and a BPhen:Li electron injection layer.The full name of each abbreviated compound is provided in the Methods section.b) Current density-voltage-luminance characteristics for devices with neat NPB (black), 20 (red), 40 (blue), and 60 vol.%POSS:NPB (green) HTLs.c) External quantum efficiency (EQE) of the devices from panel (b); the ratio of their EQEs to that of the neat NPB control is shown on the right-hand axis.d) Normalized electroluminescence spectra of the devices.Their power efficiency is shown as a function of current density on the top and right-hand axes.

Figure 4 .
Figure 4. a) Ratio of EQE measured at J = 3 mA cm −2 with and without index-matching fluid to couple each device to the photodiode as depicted in the inset.The solid black line shows the transfer matrix-simulated ratio of internal light extraction efficiency in the substrate to outcoupling efficiency in air.Changing the position of the recombination zone from the HTL/EML to EML/ETL interface (dashed line) accounts for the outlier point at 60 vol.%F-POSS.b) Measured EQE of neat NPB control and 40 vol.%F-POSS:NPB devices (at J = 3 mA cm −2 ) with the same architecture as in Figure 3a, but with varying HTL thickness.The right-hand axis shows the simulated EQE for each case, which is calculated from the transfer matrix model outcoupling efficiency ( OC ) assuming a constant internal quantum efficiency of  IQE = 80%.c) Ratio of transverse electric (TE)-to-transverse magnetic (TM) polarized electroluminescence spectra collected at an angle of 60°(inset) for several of the neat NPB devices from (b). d) Similar data for the 40 vol.%F-POSS:NPB devices.The dashed lines in both plots denote the TE:TM ratio predicted by the transfer matrix model.

Figure 5 .
Figure 5. a) Current density-voltage-luminance characteristics for tandem OLEDs with neat NPB (solid curves) and 40 vol.%F-POSS:NPB HTLs (dashdot curves).The sub-unit of each device is the same as in Figure 3a, except for an HTL thickness of 78 nm as illustrated in the inset.b) EQE measured for each device, along with their ratio shown on the right-hand axis.c) Contour plot showing the simulated outcoupling efficiency for the neat NPB tandem device as a function of the lower and upper HTL thicknesses (d HTL1 and d HTL2 , respectively) indicated in the inset of (a).d) The same calculation for a diluted tandem device with 40 vol.%F-POSS:NPB HTLs.The experimental device structures from (a,b) are indicated by white markers in (c,d).

Figure 6 .
Figure 6.a) Internal light extraction efficiency for tandem OLEDs with an increasing number of stacks that incorporate different HTL refractive indices.The sub-unit structure is the same as the two-stack structure in Figure 5a and the HTL thicknesses are globally optimized to maximize  ILE in each case.Note that the value of  ILE for the single stack here is lower than in Figure 1 since this calculation assumes the experimental ETL thickness from Figure 3a instead of the optimum in Figure 1.b) Breakdown of power emitted into the substrate and different loss channels (surface plasmon, guided mode, and parasitic absorption) by each EML in the n HTL = 1.8 and n HTL = 1.5 optimized 3-stack devices from (a).The position of each EML is shown in panel (d).c) Corresponding dipole power dissipation spectrum as a function of normalized in-plane wavevector for each EML in the two devices from (b). d) Local internal light extraction efficiency for an emitting dipole as a function of position throughout the diluted and undiluted 3-stack OLEDs from (b,c).In both cases, the optimal choice of HTL thicknesses places the recombination zone (assumed to be at the HTL/EML interface) of each sub-unit at a field antinode within the device.
Figure 6.a) Internal light extraction efficiency for tandem OLEDs with an increasing number of stacks that incorporate different HTL refractive indices.The sub-unit structure is the same as the two-stack structure in Figure 5a and the HTL thicknesses are globally optimized to maximize  ILE in each case.Note that the value of  ILE for the single stack here is lower than in Figure 1 since this calculation assumes the experimental ETL thickness from Figure 3a instead of the optimum in Figure 1.b) Breakdown of power emitted into the substrate and different loss channels (surface plasmon, guided mode, and parasitic absorption) by each EML in the n HTL = 1.8 and n HTL = 1.5 optimized 3-stack devices from (a).The position of each EML is shown in panel (d).c) Corresponding dipole power dissipation spectrum as a function of normalized in-plane wavevector for each EML in the two devices from (b). d) Local internal light extraction efficiency for an emitting dipole as a function of position throughout the diluted and undiluted 3-stack OLEDs from (b,c).In both cases, the optimal choice of HTL thicknesses places the recombination zone (assumed to be at the HTL/EML interface) of each sub-unit at a field antinode within the device.