Top-Emitting OLED Purcell-Factor Tuning with a Capping Layer

Cho et al. (2019): the 520 nm Purcell-factor response of thin-Ag top-emitting OLEDs with four NPB capping-layer thicknesses

AuthorCodex

Importance of Purcell factor for optimizing structure of organic light-emitting diodes

Authors: Hyunsu Cho, Jin Chung, Jinouk Song, Jaeho Lee, Hyunkoo Lee, Jonghee Lee, Jaehyun Moon, Seunghyup Yoo, and Nam Sung Cho

Journal: Optics Express 27(8), 11057–11068 (2019) · Comparison target: Figure 5

Changing only the layer above a semitransparent OLED electrode can change the emitter's spontaneous-emission rate. This case compares Cho et al.'s thin-Ag top-emitting organic light-emitting diodes (TEOLEDs) with 0, 30, 60, and 90 nm NPB capping layers at 520 nm. The complete published stack is retained, while openly measured same-name materials and two disclosed optical proxies make the comparison reproducible without a proprietary material database.

Independent redraw of the 520 nm TEOLED Purcell-factor anchors in Cho Figure 5.Numerical anchors digitized from Cho et al., Optics Express 27, 11057–11068 (2019), Figure 5; graphic independently redrawn Independent redraw: CC BY 4.0

The published curves place all four top-emitting devices above F = 2 at 520 nm; the 30 nm cap is the lowest of the set, while the uncapped device is the highest. The values shown above were independently digitized with an estimated uncertainty of ±0.05; no publisher figure pixels are reproduced.

Background

The Purcell factor measures how a layered optical environment modifies a dipole's radiative decay rate:

F(\lambda)=\frac{\Gamma_{\mathrm{rad}}^{*}(\lambda)}{\Gamma_{\mathrm{rad}}(\lambda)}.

Here, $F$ is dimensionless, $\lambda$ is the vacuum wavelength, $\Gamma_{\mathrm{rad}}^{*}$ is the radiative decay rate inside the OLED cavity, and $\Gamma_{\mathrm{rad}}$ is the corresponding free-space radiative decay rate. Both decay rates are measured in $\mathrm{s}^{-1}$ , so their ratio is dimensionless. A value greater than one means that the cavity increases the total radiative decay rate at that wavelength; it does not mean that the same fraction escapes to air.

Cho et al. used a 25 nm Ag top electrode and an opaque Al bottom mirror. Both metal interfaces reflect strongly, so the optical phase and reflectance of the top boundary affect $F$ . An NPB cap lies outside the electrically active stack, yet its thickness changes the reflection phase at the semitransparent electrode. Figure 5 provides the four fabricated-device curves used in this comparison.

Mapping the Paper to the TMM Model

Top-emitting stack from the air side

The complex refractive index is written as $n+ik$ : $n$ is the dimensionless refractive index, $k$ is the dimensionless extinction coefficient, and $i$ is the imaginary unit.

Layer	Thickness	Optical input at `520 nm`
NPB capping layer	`0`, `30`, `60`, or `90 nm`	Same-name open quartz-film sample, $n=1.8433$ , $k=0$
Ag semitransparent electrode	`25 nm`	Published thin-film reference, $n=0.1298$ , $k=3.0978$
LiF / Al electron-injection bilayer	`1 / 2 nm`	LiF $n=1.39$ , $k=0$ ; open Al $n=0.6883$ , $k=5.5360$
BmPyPB ETL	`50 nm`	BPhen quartz-film proxy, $n=1.7429$ , $k=0$
26DCzPPy:Ir(ppy)₃ EML	`10 nm`	mCBP quartz-film proxy, $n=1.7591$ , $k=0$
TCTA:Ir(ppy)₃ EML	`10 nm`	Same-name open quartz-film sample, $n=1.8726$ , $k=0$
TAPC HTL	`40 nm`	Same-name open quartz-film sample, $n=1.6815$ , $k=0$
HAT-CN HIL	`10 nm`	HAT-CN6 quartz-film sample, $n=1.8648$ , $k=0$
Al bottom mirror	`100 nm`	Same open Al input as the `2 nm` layer
Glass substrate	Semi-infinite boundary	$n=1.52$ , $k=0$

The NPB, TCTA, TAPC, HAT-CN6, mCBP, and BPhen values are evaluated from the open Aulika et al. OLED optical-constant dataset. Only the single target-wavelength values are required. BPhen substitutes for the unavailable BmPyPB film, while mCBP substitutes for 26DCzPPy; both substitutions are kept identical across all four variants.

The paper confines the recombination zone to the interface between its two 10 nm EML sublayers. Dreapex TMM requires a Delta source to lie strictly inside its host layer, so the model places one isotropic emitter at relative position 0.999 in the 26DCzPPy-proxy layer—0.01 nm from the TCTA interface. Its intrinsic quantum efficiency is 0.8, matching the value used for the paper's top-emitting efficiency analysis.

Emission setting	Value
Calculation wavelength	`520 nm`, single wavelength
Source spectrum	One unit-amplitude sample at `520 nm`
Dipole distribution	Delta `0.01 nm` inside the 26DCzPPy side of the interface
Dipole orientation	Isotropic
Enabled detector	`Mode`
Reported comparison quantity	Purcell factor $F$

A measured photoluminescence spectrum is unnecessary for this monochromatic target. It becomes necessary when extending the case to the complete wavelength-dependent Figure 5 curves or the angle-resolved electroluminescence spectra in Figure 6.

Reproduction Target and Acceptance Criteria

The criteria below were defined before comparing the results:

All four models must complete a Mode calculation.
Every simulated $F(520\ \mathrm{nm})$ should remain above 2, matching the paper's explicit statement for the four top-emitting devices.
The 30 nm variant should have the lowest $F$ , and the 0 nm variant the highest.
The simulated maximum-to-minimum span should be at least 0.20.
Each simulated value should lie within 0.35 of the independently digitized anchor. This wider tolerance covers the two organic proxies, the absence of sample-matched metal data, and curve-reading uncertainty.

A failed criterion remains a reported result; the material choices and thresholds are not retuned after seeing the output.

Modeling Path in Dreapex TMM

Structure

Build the air-to-glass stack in the mapping table. The 0 nm variant omits the NPB cap rather than adding a zero-thickness layer. Keep the 26DCzPPy-proxy layer emissive and place its delta emitter at relative position 0.999, the valid in-layer limit next to TCTA.

Optical settings

Enable only Mode under Emission and select Single at 520 nm. The detector reports both integrated optical channels and the emitter-level Purcell factor; this case compares the latter.

This case does not use an incident-light detector, a wavelength sweep, or Optimize. Those settings do not contribute to the single-wavelength Purcell-factor comparison.

Example Setup

Setting	`0 nm` cap	`30 nm` cap	`60 nm` cap	`90 nm` cap
NPB capping thickness	Omitted	`30 nm`	`60 nm`	`90 nm`
Remaining stack	Published stack	Same	Same	Same
Emitter position	Relative `0.999`, `0.01 nm` from the EML interface	Same	Same	Same
Mode wavelength	`520 nm`	`520 nm`	`520 nm`	`520 nm`

Uncapped TEOLED structure

The uncapped structure begins with the 25 nm Ag electrode on the air side.

TEOLED structure with a 30 nm NPB cap

TEOLED structure with a 60 nm NPB cap

TEOLED structure with a 90 nm NPB cap

The capped variants differ only in the first row; the active OLED stack remains fixed.

Delta emitter at the interface between the two EML sublayers

The emitter is attached to the 26DCzPPy-proxy sublayer at relative position 0.999, placing it 0.01 nm from TCTA while satisfying the strict in-layer validation rule.

Single-wavelength Mode setting at 520 nm

Simulation Results and Comparison with Figure 5

The independently redrawn benchmark keeps the paper's four cap-thickness values adjacent to the simulation results below.

Mode result for the uncapped TEOLED at 520 nm

Mode result for the TEOLED with a 30 nm NPB cap at 520 nm

Mode result for the TEOLED with a 60 nm NPB cap at 520 nm

Mode result for the TEOLED with a 90 nm NPB cap at 520 nm

NPB cap	Paper Figure 5 $F$	Dreapex TMM $F$	Absolute difference	Criterion
`0 nm`	`≈2.42 ± 0.05`	`2.538`	`0.12`	Pass
`30 nm`	`≈2.08 ± 0.05`	`2.272`	`0.19`	Pass
`60 nm`	`≈2.23 ± 0.05`	`2.273`	`0.04`	Pass
`90 nm`	`≈2.32 ± 0.05`	`2.465`	`0.15`	Pass

The simulated span is 0.266, with its minimum at 30 nm and maximum at 0 nm. All five acceptance criteria pass: every value is above 2, every absolute difference is below 0.35, the extrema have the paper's ordering, and the span exceeds 0.20. The 30 and 60 nm values differ by less than 0.002, so their separation is not a robust secondary claim under the disclosed material uncertainty.

Deviation Analysis

Cho et al. publish the complete layer sequence and thicknesses but not sample-matched complex refractive indices. Same-name open measurements are used for NPB, TCTA, TAPC, and HAT-CN6; their deposition conditions and film thicknesses differ from the device.
BmPyPB uses a BPhen optical proxy, and 26DCzPPy uses mCBP. These approximations preserve representative electron-transport and carbazole-host index scales but can shift the cavity phase and absolute $F$ .
The doped EML sublayers reuse the undoped host optical constants. The model does not add an independent extinction term for the Ir(ppy)₃ concentration.
The paper fixes a delta-like recombination zone but does not publish a measured dipole-orientation fraction for this stack. The reproduction uses an isotropic source.
The exact interface coordinate is invalid for a Delta source in Dreapex TMM. Relative position 0.999 is a 0.01 nm inward offset and is treated as the interface limit.
The benchmark values are independently digitized from Figure 5 rather than taken from a numerical source-data table. The paper's explicit F > 2 statement is therefore a stronger absolute check than the last decimal of any bar.
A single-wavelength calculation tests Figure 5 at 520 nm; it does not reproduce the full spectral curves, angle-resolved Figure 6 data, or the measured and calculated EQE values in Table 2.

Further Extensions

Replace BPhen and mCBP with measured BmPyPB and 26DCzPPy films from the actual deposition process, then tighten the absolute tolerance.
Sweep 400–700 nm for all four caps and compare the complete peak positions and line shapes in Figure 5.
Add the measured Ir(ppy)₃ source spectrum and Intensity to reproduce the angle-resolved spectral comparison in Figure 6.
Build the bottom-emitting 30/55 nm n-ETL pair and test the paper's F(520 nm)≈1.48/1.20 anchors alongside the top-emitting set.

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