SPP Mode Suppression in an Inverted Single-Layer OLED

When the same 80 nm blue-emitting layer is close to a metal cathode, a large fraction of its power enters non-outcoupled surface-plasmon-polariton (SPP) modes. Moving the cathode to the transparent-electrode side moves the recombination zone away from the top metal. This case uses the published emitter optical constants, dipole orientation, and spatial recombination profile to test whether Dreapex TMM reproduces the strong reduction of the high-wavevector SPP peak in Figure 4b, then uses Mode to integrate the corresponding channels.

The light-blue curve in Figure 4b has a sharp SPP-region peak of about 10.35, whereas the inverted dark-blue curve peaks at about 2.77; Figure 4a also provides outcoupling anchors of 10.15% and 20.47% at 80 nm.

Background

In a planar OLED, emitting dipoles can couple power into air, the glass substrate, organic waveguide modes, and SPP modes at the metal interface. Figure 4b separates these channels by in-plane wavevector. To map the published Source Data directly to the dimensionless Dreapex TMM axis, this case converts the in-plane wavevector to effective index:

Here, $n_{\mathrm{eff}}$ is the effective index, $k_{\parallel}$ is the wavevector parallel to the layers, $k_0$ is the vacuum wavenumber at wavelength $\lambda$, and $\pi$ is the circle constant. This case fixes $\lambda=490\ \mathrm{nm}$. The three published boundaries become 1.00, 1.50, and 1.67, matching the light lines of air, the glass substrate, and the 2tCz2CzBN emissive layer.

The Power Dissipation spectrum retains peak positions and modal density. Mode integrates the spectrum into outcoupling, substrate, waveguide, absorption, and evanescent channels. Together, they show whether inversion genuinely moves power away from the high-wavevector loss region.

Mapping the Paper to the TMM Model

The tables use $n$ for the real part of the refractive index and $k$ for the extinction coefficient.

Conventional device (glass emission side → top metal)

Inverted device (glass emission side → top metal)

Layer order and thicknesses follow SI Table 1. The Methods section gives 45 nm for PEDOT:PSS, while SI Table 1 and the supporting captions used for the figures give 40 nm; the primary model uses the latter. The paper does not report the ITO thickness or publish sample-matched optical constants for the auxiliary layers. Both devices therefore use the same open datasets and proxies fixed before running, leaving layer order and recombination-profile direction as the comparison variables. The n-TFB proxy is the TFB value digitized from the open Miao et al. 2020 paper.

All emitter-specific inputs come from the Springer Nature Figshare Source Data:

The Figure 3b source sheet labels its position axis only as Thickness. From the paper's statement that the recombination zone is close to the cathode and the distribution peak near 12 nm, this case interprets $x$ as distance from the cathode. The cathode is on the top-metal side in the conventional device, so its imported position is $80\ \mathrm{nm}-x$; the cathode is on the glass side in the inverted device, so its imported position is $x$. Mirroring the same electrical recombination profile into the two physical electrode directions is the main structural variable in this case.

Reproduction Target and Acceptance Criteria

The fixed Source Data anchors over 0≤n_eff≤4 are a conventional SPP peak at 1.9768, an inverted SPP peak at 2.0684, an inverted/conventional peak-height ratio of 0.2679, and an SPP-region integral ratio of 0.4115.

The primary reproduction passes when all of the following hold:

1. The conventional SPP-region maximum lies within 1.70–2.25.
2. The inverted SPP-region maximum lies within 1.70–2.40.
3. The inverted/conventional SPP peak-height ratio is no greater than 0.65.
4. The inverted/conventional Power Dissipation integral over 1.67≤n_eff≤4 is no greater than 0.75.
5. The inverted Top Outcoupling is at least 1.5 times the conventional value.

The Figure 4a values of 10.15471% and 20.46790% are thickness-dependent, spectrally integrated paper results. The monochromatic Mode result at 490 nm uses their approximately twofold relationship only as a supporting check; an exact absolute match is not required.

Modeling Path in Dreapex TMM

Structure

Build the two glass-to-top-metal stacks in the mapping tables. Glass is the only incoherent layer and is first in the finite stack; 2tCz2CzBN is the only coherent layer with Emission enabled. Map the 3.0 V File distribution in opposite EML depth directions for the conventional and inverted models.

• Download the conventional model
• Download the inverted model

Optical settings

Enable Power Dissipation and Mode. Both use Single at 490 nm. For Power Dissipation, select nEff, set the range to 0–4, and use a 0.01 step. The comparison curve is $K_{\mathrm{total}}$ for Total polarization and Total direction. Here, $K_{\mathrm{total}}$ is the power coupling coefficient $K$ summed over all polarizations and both propagation directions.

Example Setup

The conventional stack retains the geometrical 5 nm Ba layer and labels its optical input explicitly as an effective Al proxy.

Both emitter screenshots use the same 51 density samples. Reversing the coordinate places the peak next to the top metal cathode in the conventional device and next to the bottom transparent cathode in the inverted device.

Simulation Results and Comparison with Figure 4

Figure 4b tests high-wavevector SPP suppression through the curve shape. The 80 nm points in Figure 4a provide a supporting outcoupling scale.

Figure 4b: Power Dissipation spectra

The simulated inverted/conventional peak-height ratio is 0.4024, and the SPP-region integral ratio is 0.6945. Both are below the limits fixed in advance at 0.65 and 0.75, so all five primary mechanism checks pass. Peak detection starts at 1.70 to exclude the narrow light-line boundary feature near the EML; the conservative integral still starts at 1.67 and includes it.

Figure 4a: supporting mode integral

The monochromatic Mode result and the spectrally integrated Figure 4a result use different averaging conventions, so the first row is not an absolute-error criterion. The simulated conventional and inverted values differ from the paper's 80 nm anchors by +0.69 pp and +4.81 pp. The more robust result is that both show an approximately twofold increase, supporting the interpretation that a lower high-wave-vector PDS integral transfers more power into an outcoupled channel.

Deviation Analysis

1. The paper publishes continuous $n,k$ for 2tCz2CzBN but not sample-matched data for the auxiliary layers. ITO, PEDOT:PSS, MoO₃, TPBi, and Al use open measurements; n-TFB, C₆₀, and Ba use the disclosed proxies above. Residual peak-position and absolute-mode differences are therefore interpreted primarily as input differences.
2. The ITO thickness is not reported and is fixed at 100 nm. Its phase and absorption affect the air and substrate channels, but using the same ITO input in both stacks does not create an artificial inversion advantage.
3. Figure 4b does not state which voltage-dependent recombination profile was used, and the Figure 3b source sheet does not label the coordinate origin or direction. This case freezes the public 3.0 V curve and interprets its coordinate as distance from the cathode from the paper text and peak location; the published 2.5–5.0 V arrays support a later sensitivity envelope.
4. The recombination array comes from the paper's drift-diffusion calculation. Dreapex TMM consumes it as a File emission distribution and does not re-solve electrical transport here.
5. The planar model excludes roughness, lateral scattering, edge emission, and electrode morphology. These effects can redistribute high-wavevector power but do not reverse the causal direction that moving the recombination zone away from metal reduces SPP coupling.

Further Extensions

1. Import every 2.5–5.0 V recombination array and report voltage envelopes for SPP peak height and Top Outcoupling.
2. Sweep ITO thickness and open ITO datasets to quantify the effect of the unreported transparent-electrode input on peak position.
3. Replace the n-TFB, C₆₀, and ultrathin Ba proxies with measured film data and tighten the peak-position and integral tolerances.
4. Add the intrinsic PL spectrum and an EML-thickness sweep to extend the benchmark to the full spectrally integrated Figure 4a result.

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