Emission Position and Outcoupling Efficiency in a Broad-Recombination OLED

Li et al. (2021): delta emission-plane position curves and recombination-weighted outcoupling efficiency in a single-layer TADF OLED

AuthorLuke Cole

Optical Outcoupling Efficiency of Organic Light-Emitting Diodes with a Broad Recombination Profile

Authors: Yungui Li, Naresh B. Kotadiya, Bas van der Zee, Paul W. M. Blom, Gert-Jan A. H. Wetzelaer

Journal: Advanced Optical Materials 9, 2001812 (2021) · Comparison target: Figure 2 and Figure 3c

Move the emission plane from the cathode side toward the anode side and the outcoupling efficiency first rises and then falls, with the maximum occupying only a short stretch of the emissive layer. A real single-layer device has no such plane — its recombination zone spreads over tens of nanometres and sits on a whole segment of that curve at once.

This case first scans the delta emission-plane position to reproduce the twelve curves of paper Figure 2, then weights them with the paper's recombination profile to get the optimum emissive-layer thickness of Figure 3c.

The published figures are not reproduced here: Figure 2 and Figure 3c are licensed CC BY-NC 4.0 and commercial reuse permission has not been granted. The paper is open access, so the full text and all its figures can be read free of charge at DOI 10.1002/adom.202001812. Every value labelled "paper" below is a data point read off the originals independently; the figures themselves are neither copied nor redrawn.

The maxima of the six curves move toward the anode side as the emissive layer thickens, and become very flat at 125 and 150 nm. The four digitized peaks each land within 0.05 percentage points of the 19.4 %, 28.0 %, 35.1 %, and 55.2 % stated in the paper text.

Background

In a bottom-emitting device, the power that escapes to air through the glass surface is $\eta_{\mathrm{A}}$ ; adding the share trapped by total internal reflection in the glass substrate, which can only leave through the substrate edge, gives $\eta_{\mathrm{SA}}$ . The paper seals the substrate edges with the sample holder so substrate modes are not collected, which matches this split.

The outcoupling efficiency of a single delta emission plane depends only on its position $z$ inside the emissive layer — the distance to the CzDBA/TPBi interface, with $z=0$ on the cathode side. Scanning $z$ point by point produces the curves of paper Figure 2. In a real device excitons are generated along a recombination profile, so the outcoupling efficiency is the average of that curve weighted by the profile.

Structure

The stack is built from the glass substrate side. All seven layer thicknesses take their published values, with no registration. The 560 nm optical inputs below are the interpolated values actually used.

Layer	Thickness	Optical input at `560 nm`	Thickness source
Glass substrate	`1 mm`, incoherent	$n=1.5254$ , $k=0$	Not stated in the paper; assumed here
ITO anode	`120 nm`	$n=1.8877$ , $k=0$	Given in the paper
PEDOT:PSS hole-injection layer	`40 nm`	$n=1.5182$ , $k=0.0213$	Given in the paper
MoO₃ hole-injection layer	`6 nm`	$n=2.0200$ , $k=0.0001$	Given in the paper
C60 interlayer	`3 nm`	$n=2.2143$ , $k=0.0569$	Given in the paper
CzDBA emissive layer	`50 / 75 / 85 / 100 / 125 / 150 nm`	$n=1.7359$ , $k=0$	Given in the paper
TPBi electron-transport layer	`4 nm`	$n=1.7508$ , $k=0$	Given in the paper
Al cathode	`100 nm`	$n=1.0037$ , $k=6.8071$	Given in the paper

The paper publishes no numerical refractive-index table for any layer. CzDBA comes from a Cauchy fit to the published curve endpoints, 1.90 at 380 nm and 1.65 at 900 nm; every other layer uses the matching entry in the built-in material database. This is the largest input uncertainty in the case.

The 85 nm variant once entered. The first row shows glass in mm and flagged incoherent, and the emissive marker on the CzDBA row indicates the Delta emitter in that layer:

Structure page of the 85 nm emissive-layer variant

The six models differ only in CzDBA thickness; every other layer and thickness is identical.

Optical and Emitter Settings

Setting	Value	Source
Emitter count and distribution	One Delta emission plane	The modelling approach of paper Figure 2
Anisotropy factor	Vertical dipole fraction `0.148`	Fitted by the paper from neat-film angle-resolved photoluminescence
Emitter position	`Sweep` `0.01` to `0.99`, step `0.01`, `98` points per thickness	The paper's independent variable
Emission spectrum	Peak `560 nm`, FWHM `84 nm`	The paper gives no intrinsic spectrum; the average of three device electroluminescence spectra is used
Spectrum Unit	`Probability`	Matches the photon-count weighting of Mode
Quantum efficiency, conversion efficiency, multiplier	All `1`	Matches the paper's purely optical convention
Detectors	Emission `Mode` + Propagation `R`	A run requires at least one base detector; the `R` result is not used in the comparison
Wavelength mode	`Weighted Average`, `450–780 nm`, step `5 nm`	—

The Top Outcoupling channel of Mode is $\eta_{\mathrm{A}}$ ; adding the Substrate channel gives $\eta_{\mathrm{SA}}$ .

Mode settings on the Emission side

The emitter position is measured from the C60 interface on the anode side, and the paper's horizontal axis follows $z=(1-p)\,d$ , where $p$ is the relative position in the emissive layer and $d$ its thickness. For the 85 nm device, p = 0.30 corresponds to $z=59.5\ \mathrm{nm}$ . Scanning all six thicknesses gives 588 position points.

This case uses Sweep for the emission-plane position, not Optimize. The optimum emissive-layer thickness is fitted from the six weighted results.

Simulation Results and Comparison with Figure 2 and Figure 3c

Emission-plane position curves

Paper Figure 2 is in the original article.

The same six thicknesses and the same two quantities, with the scan results (solid) overlaid on the digitized paper values (markers):

Digitized paper values overlaid with Dreapex TMM position-scan curves for six emissive-layer thicknesses — Position-scan curve comparison. One column per emissive-layer thickness, solid lines are Dreapex TMM results and markers are digitized paper values, air mode on the top row and air-plus-substrate mode on the bottom row.Paper values digitized from Li et al., Advanced Optical Materials 9, 2001812 (2021), Figure 2; Dreapex TMM data from the real scans of this case study; graphic drawn independently CC BY 4.0, applying to this independently drawn graphic

The extremum position $z^{*}$ is located by a parabolic fit over the top 3 % of each curve, so digitization noise on a flat top does not dominate.

Quantity	Emissive-layer thickness	This run $z^{*}$	Paper $z^{*}$	Difference
$\eta_{\mathrm{A}}$	`50 nm`	`33.5 nm`	`37.6 nm`	`−4.0 nm`
$\eta_{\mathrm{A}}$	`75 nm`	`52.6 nm`	`54.0 nm`	`−1.3 nm`
$\eta_{\mathrm{A}}$	`85 nm`	`58.9 nm`	`59.4 nm`	`−0.5 nm`
$\eta_{\mathrm{A}}$	`100 nm`	`65.1 nm`	`63.6 nm`	`+1.5 nm`
$\eta_{\mathrm{A}}$	`125 nm`	`68.0 nm`	`65.5 nm`	`+2.4 nm`
$\eta_{\mathrm{A}}$	`150 nm`	`67.1 nm`	`65.0 nm`	`+2.2 nm`
$\eta_{\mathrm{SA}}$	`50 nm`	`32.6 nm`	`36.7 nm`	`−4.1 nm`
$\eta_{\mathrm{SA}}$	`75 nm`	`52.4 nm`	`54.7 nm`	`−2.3 nm`
$\eta_{\mathrm{SA}}$	`85 nm`	`59.7 nm`	`61.1 nm`	`−1.5 nm`
$\eta_{\mathrm{SA}}$	`100 nm`	`69.6 nm`	`70.0 nm`	`−0.4 nm`
$\eta_{\mathrm{SA}}$	`125 nm`	`81.1 nm`	`80.2 nm`	`+1.0 nm`
$\eta_{\mathrm{SA}}$	`150 nm`	`87.7 nm`	`85.9 nm`	`+1.8 nm`

Across the twelve curves the maximum difference is 4.1 nm, the RMS difference 2.2 nm, and the mean difference −0.4 nm. The maxima themselves are flat: the plateau above 99 % of peak spans 3.5 to 22.5 nm here and 4.3 to 19.3 nm in the paper. Normalizing each curve to its own peak and comparing point by point gives a mean RMS difference of 3.29 % of peak.

Three positions from the same scan, read on the Mode result. At the optimum, $z=59.5\ \mathrm{nm}$ , 33.19 % escapes to air and 26.28 % stays in the substrate, with a Purcell factor of 1.32:

Mode result of the 85 nm device at the optimum emission-plane position

Pressed against the cathode-side interface ( $z=1.70\ \mathrm{nm}$ ), the air mode drops to 0.85 %, 96.35 % goes evanescent, and the Purcell factor rises to 8.71:

Mode result of the 85 nm device near the cathode-side interface

Pressed against the C60 interface ( $z=84.15\ \mathrm{nm}$ ), the air mode collapses to 0.04 % and the Purcell factor reaches 1264.89:

Mode result of the 85 nm device near the anode-side interface

The paper's curve does not collapse at the same position; the digitized value is still 17.5 %. Replacing C60 with a lossless layer of the same refractive index brings this run back to 23.54 %, which places the difference in the C60 extinction coefficient. It affects only the last 10 nm next to the anode interface.

Recombination-weighted optimum thickness

Weighting each thickness's position curve with the paper's recombination profile collapses the twelve curves into two curves versus thickness, which is what paper Figure 3c reports (see the original article).

The same quantities on one set of axes:

Recombination-weighted outcoupling efficiency versus emissive-layer thickness, digitized paper values overlaid with Dreapex TMM results — Recombination-weighted outcoupling efficiency versus CzDBA thickness. Solid lines are Dreapex TMM results and markers are digitized values from Figure 3c of the paper, with one pair of curves for the air mode and one for the air-plus-substrate mode.Paper values digitized from Li et al., Advanced Optical Materials 9, 2001812 (2021), Figure 3b and Figure 3c; Dreapex TMM data from the real scans of this case study; graphic drawn independently CC BY 4.0, applying to this independently drawn graphic

Emissive-layer thickness	Weighted $\eta_{\mathrm{A}}$ here	Paper $\eta_{\mathrm{A}}$	Difference	Weighted $\eta_{\mathrm{SA}}$ here	Paper $\eta_{\mathrm{SA}}$	Difference
`50 nm`	`18.94 %`	`17.15 %`	`+1.79`	`36.93 %`	`31.92 %`	`+5.01`
`75 nm`	`28.89 %`	`25.04 %`	`+3.85`	`51.73 %`	`44.03 %`	`+7.70`
`85 nm`	`30.59 %`	`26.28 %`	`+4.31`	`55.25 %`	`47.14 %`	`+8.11`
`100 nm`	`30.64 %`	`25.73 %`	`+4.91`	`58.63 %`	`50.16 %`	`+8.47`
`125 nm`	`26.40 %`	`21.42 %`	`+4.98`	`61.05 %`	`51.91 %`	`+9.14`
`150 nm`	`20.37 %`	`16.71 %`	`+3.66`	`61.20 %`	`52.12 %`	`+9.08`

Differences are in percentage points. The optimum emissive-layer thickness, located by a parabola vertex, is 87.8 nm here against 87.9 nm in the paper, a difference of 0.1 nm. A single common scale factor of 0.848 brings the whole thickness curve onto the paper's, with an RMS difference of 0.70 percentage points over the six points.

The cost of broadening is the gap between the delta-plane optimum and the weighted value: for the 85 nm device it is 2.60 percentage points here, a relative loss of 7.8 %, against 1.70 points and 6.1 % in the paper. Spreading the recombination zone from a plane across the whole layer costs about two percentage points of outcoupling efficiency.

Deviation Notes

The CzDBA refractive index is the one published input that could not be obtained, and the largest source of uncertainty. Replacing it with a constant $n=1.80$ shifts the maxima by 0 to −3.8 nm and moves the optimum-thickness vertex from 87.8 nm to 83.7 nm, the same order as the 4.1 nm largest residual of the main comparison.

Absolute outcoupling efficiency runs 15 % to 23 % above the paper, which points at two other assumed inputs: the ITO dataset has an extinction coefficient of exactly zero across the visible and so underestimates anode absorption, and a low CzDBA index widens the escape cone into air. Orientation is not a cause — 0.148 is taken directly from the paper.

The reference values come from independent digitization of the published figures, not from numerical source data.

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