Microcavity PeLED Angular Emission

This case reproduces the angle-dependent electroluminescence of the 15 nm Au top-emitting PeLED reported by Miao et al. The comparison covers the spectral peak near 800 nm, its shift toward shorter wavelength at oblique viewing angles, and the forward-directed angular distribution. The result is a qualitative reproduction with auditable numerical anchors, not a point-by-point fit.

Figure 2a shows the peak moving toward shorter wavelength and weakening at 60°; Figure 2b shows that the emission remains concentrated around the surface normal. These are the two optical signatures reproduced below.

Background

The device uses a thick Au bottom mirror and a semitransparent Au top electrode as a Fabry–Pérot microcavity. The cavity modifies both the spectrum and the direction in which photons leave the device. An emission calculation is therefore needed: a propagation-only spectrum does not include the position and orientation of the emitting dipoles.

The paper reports a high external quantum efficiency for the optimized device. This reproduction focuses only on the optical behavior shown in Figure 2a-b; it does not model electrical injection or predict the measured device EQE.

Mapping the Paper to the TMM Model

Reproduction Target and Acceptance Criteria

The reproduction is accepted when all of the following are visible:

1. The normal-direction spectrum is concentrated near 800 nm.
2. Increasing the viewing angle moves the spectral maximum toward shorter wavelength, as in Figure 2a.
3. The 60° signal is much weaker than the 0° and 30° signals.
4. The wavelength-resolved angular curves remain forward directed, reproducing the main pattern in Figure 2b.

An exact 14 nm shift between 0° and 60° is not required because the uncavitized source spectrum and emission-zone distribution are unavailable.

Modeling Path in Dreapex TMM

Structure

The stack and thicknesses are listed above. Use the separate optical constants for 15 nm and 100 nm Au, and enable Emission only on the MQW layer.

Optical settings

Enable Intensity, set the wavelength range to 725–875 nm with a 5 nm step, and set the angle range to 0–90° with a 5° step. Use the total-polarization result for the comparison.

Example Setup

The screenshots below come from importing the exported .tmm.json model into the production application. The preceding mapping table records the structure and material data; the remaining reproduction parameters are summarized below.

The Bottom Medium shown in the interface does not represent a usable rear channel; the 100 nm Au mirror blocks the rear optical path, so no glass layer is included.

Relative position 0.5 places the dipole sheet at the center of the MQW; changing this position changes the phase relationship between the dipoles and the two mirrors.

The paper curves are not polarization resolved, so this case uses the Total result rather than a single-polarization result.

Simulation Results and Comparison with Figure 2

Figure 2a compares spectral peak position and amplitude at fixed viewing angles, while Figure 2b compares angular directivity at fixed wavelengths; together they test the shift toward shorter wavelength and the forward-directed emission.

Figure 2a: angular spectral shift

The three representative spectra are each normalized by their own maximum to compare peak position and line shape; amplitude differences use the raw peak intensities in the table below.

The normal-direction peak is reproduced closely, and the raw peak intensity at 60° is strongly attenuated; the calculated shift from 0° to 60° is 5 nm, smaller than the approximately 14 nm shift read from the paper.

Figure 2b: angular emission pattern

The raw heatmap uses viewing angle on the horizontal axis and wavelength on the vertical axis; its dark high-value region is concentrated around 790–810 nm and small viewing angles, then fades rapidly with angle, but the color also contains source-spectrum amplitude and cannot alone compare normalized angular width.

The paper-matched 760, 775, 790, 800, 815, and 830 nm curves are each normalized by their own maximum; they remain high near 0° and decay toward 90°, with no lobe turning toward large angles.

Deviation Analysis

1. The ideal source for this calculation is the uncavitized MQW photoluminescence spectrum. The paper publishes the device EL spectrum instead, so the imported source already contains a microcavity response. Reapplying the cavity can narrow or shift the calculated spectrum.
2. The emission zone is modeled as one delta sheet at the center of the MQW. A distributed recombination zone or a different dipole-orientation ratio would change both intensity and angular width.
3. The 5 nm wavelength grid and 5° angle grid limit peak localization. Finer sampling is appropriate when the target is a quantitative peak-shift fit.
4. Electrical transport, roughness, lateral scattering, and non-planar extraction structures are outside this planar optical model.

These limitations affect the exact shift and line shape. They do not change the reproduced conclusion: the Au microcavity strengthens forward emission and moves the spectrum toward shorter wavelength at larger viewing angles.

Further Extensions

1. Replace the EL source with an independently measured MQW PL spectrum and repeat the comparison.
2. Sweep the emitter position through the 35 nm MQW to quantify the sensitivity of the forward intensity.
3. Compare isotropic and predominantly horizontal dipole populations.
4. Sweep the top Au thickness to reproduce the electrode-thickness optimization discussed elsewhere in the paper.

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