Regular Tandem QLED Outcoupling

This case reproduces the 632 nm optical analysis in Figure 2i-k of Yang et al. The bottom-unit ZnMgO thickness is swept from 22 to 200 nm for the bottom emitter, top emitter, and equal-weight tandem model. The calculation reproduces the larger top-unit contribution and the broad cavity optima, while underestimating the paper's summed outcoupling at its 120 nm design point.

At 120 nm, the paper marks Air fractions of 22.4% for the bottom unit, 32.2% for the top unit, and 54.6% for their summed tandem contribution. The broad maxima and the larger top-unit contribution are the main comparison features.

Background

A tandem QLED places two emissive units in one optical stack. Under ideal charge balance, one injected electron can generate at most one exciton in each unit. Optically, the two QD layers occupy different positions relative to the output interface and metal cathode, so their outcoupling efficiencies are not equal and respond differently to the same transport-layer thickness.

The paper uses an ultrathin ITO charge-generation layer and reports an experimental EQE above 51%. This reproduction addresses the optical power fractions only. Charge generation, carrier balance, and lifetime are outside the model.

Mapping the Paper to the TMM Model

Complete stack (Glass output side → Al cathode)

Reproduction Target and Acceptance Criteria

1. Around 120 nm bottom ZnMgO, the top-unit outcoupling must exceed the bottom-unit outcoupling.
2. All three thickness responses must be smooth and exhibit a cavity optimum rather than a monotonic trend.
3. The bottom- and top-unit curves must peak at different thicknesses, confirming that the two emitters occupy different optical positions.
4. The paper's summed 54.6% value must be compared with the sum of the two isolated-unit simulations. The dual-emitter Mode trace displays the average of two equal-weight inputs and is retained only as a thickness-trend check, not as device EQE.

This is a trend-level acceptance test. Exact agreement at 120 nm is not required because two optical layers use scalar effective-index approximations.

Modeling Path in Dreapex TMM

Structure

The three models share the stack above and differ only in which QD layers have Emission enabled.

Optical settings

Enable Mode and use Top Outcoupling as the comparison channel. The table below records the wavelength, emitter, and sweep settings.

Example Setup

Complete stack

The two QD layers sit on opposite sides of the interconnect and share the Glass output channel.

Emitters

The bottom-unit model enables only this emitter.

The top-unit model enables only this emitter; the tandem model enables both.

Mode and sweep

Only the Top Outcoupling channel is used for the numerical comparison.

All three models use the same 90 thickness values, so their curves are directly comparable.

In this case, Unit White means that the single-wavelength calculation uses no additional PL weighting; it does not indicate white device emission.

Simulation Results and Comparison with Figure 2

The paper separates the bottom, top, and summed tandem power fractions, so the simulation results follow the same i-j-k order.

Figure 2i: bottom unit

The bottom unit gives 17.35% at 120 nm and reaches 19.07% near 152 nm; the paper reports about 22.4% at 120 nm. The broad cavity optimum is reproduced, with visible offsets in both position and magnitude.

Figure 2j: top unit

The top unit gives 29.49% at 120 nm and peaks at 29.98% near 98 nm. Its optimum differs from the bottom unit's 152 nm, showing that the two QD layers occupy different optical positions. The contribution ordering at the design point agrees with the paper's 32.2% > 22.4%.

Figure 2k: tandem device

The dual-emitter trace is the equal-weight average of the two Top Outcoupling results, not the sum of the isolated contributions in Figure 2k or the device EQE. It reaches 23.68% near 136 nm, gives 23.42% at the paper's 120 nm design, and remains between the two isolated traces.

The quantitative Figure 2k comparison uses the isolated-unit sum: 17.35% + 29.49% = 46.84%, which is 7.76 percentage points below the paper's 54.6%. At 120 nm, the dual-emitter 23.42% agrees with the arithmetic mean of the isolated results; it verifies equal-weight combination and the broad optimum, but is excluded from the 54.6% error calculation.

Deviation Analysis

1. The 2 nm Al–Al₂O₃ interconnect uses the paper's single effective value 1.37 + 7.52i. Treating a mixed ultrathin layer as one strongly absorbing homogeneous film can change both the bottom-unit loss and optimum position.
2. The 2PACz:6PA layer uses the scalar 1.72 surrogate reported for the optical calculation; dispersion and absorption are not available.
3. Each QD layer uses a central isotropic delta emitter. Different recombination-zone positions or horizontal-dipole fractions would affect the two units differently.
4. The model excludes electrical charge balance. The experimental 51.2% EQE is therefore not a direct optical acceptance target.

Further Extensions

1. Replace the interconnect effective index with measured complex dispersion and repeat all three sweeps.
2. Sweep bottom ZnMgO and the emitter position together to separate cavity-phase and recombination-zone effects.
3. Assign measured spectra to the two QD units and run spectrum-weighted Mode calculations.
4. Compare equal and unequal emitter weights to represent current imbalance between the two units.

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