Numerical and Analytical Study of Tunable Color Control in Quantum-Dot Top-Emission Light-Emitting Diodes Using a Liquid-Crystal-Assisted Metal–Insulator–Metal Cavity

Abstract

Ultrahigh-resolution displays for augmented and virtual reality require compact pixel architectures, but conventional red, green, and blue subpixel layouts increase lateral complexity as the pixel size decreases. Active color tuning within a single emissive unit offers an alternative route, although practical device architectures remain challenging. Here, we report a numerical and analytical study of a quantum-dot light-emitting diode architecture combined with a liquid-crystal-assisted metal–insulator–metal cavity for electrically tunable color control. Reorientation of the embedded liquid-crystal layer changes the effective optical path length of the cavity, which shifts the Fabry–Pérot resonance and thereby reweights the spectral content transmitted from a fixed quantum-dot emission spectrum. The structure was optimized using an analytical plane-wave multilayer model and cross-checked against finite-element-method simulations, with the wavelength dependence of all optical constants retained throughout. The optimized design reached a CIE 1931 chromaticity triangle area of 0.124 in the analytical model and 0.113 in the numerical model and retained an area of 0.121 averaged over a 15° viewing cone. Alternative tuning branches and a quasi-white operating state were also identified. These results suggest that liquid-crystal-assisted metal–insulator–metal cavities may serve as compact, electrically tunable spectral-control elements for high-density display architectures and reconfigurable photonic systems.

Introduction

Full-color light-emitting devices usually generate red, green, and blue emissions using spatially separated subpixels. This architecture is well-established, but its lateral complexity becomes increasingly restrictive for ultrahigh-resolution displays, particularly augmented reality and virtual reality systems that require several thousand pixels per inch pixel densities. − Top-emission quantum dot light-emitting diodes (QD-LEDs) have therefore attracted attention because optical microcavity effects can improve light extraction, spectral selectivity, color purity, and directional emission. −

An alternative approach to reducing pixel complexity is to tune the optical response of a cavity structure rather than laterally patterning independent red, green, and blue emitters. Metal–insulator–metal (MIM) cavities are attractive for this purpose because they provide strong wavelength selectivity in a compact geometry. Their transmission response is governed by the optical thickness of the cavity medium and the phase response of the metallic mirrors. − Fabry–Pérot-type resonance engineering has likewise been widely used in wavelength-selective optical systems and tunable photonic structures. ,

Here, we present a color-control architecture in which a liquid-crystal (LC) layer is embedded in a MIM cavity placed above a top-emission QD-LED. The LC layer acts as a voltage-reconfigurable optical medium whose effective refractive index sets the cavity optical path length, so that reorienting the director shifts the resonance wavelength and changes its spectral overlap with fixed QD emission bands. Combining these elementsa MIM cavity, an LC-tuned path length, and a top-emission QD stackinto a single compact unit allows all three primary chromaticity regions to be reached from one emissive pixel, without lateral patterning. We develop a quantitative design framework for this architecture, using an analytical multilayer model to optimize the stack and finite-element-method simulations to validate it, and use it to establish the accessible color gamut, its angular stability, and the alternative operating regimes the cavity supports.

Device Concept and Computational Methods

The proposed structure, shown in Figure a, combines an upper Ag–LC–Ag MIM cavity with a lower top-emission QD-LED stack. From bottom to top, the QD-LED stack consists of a reflective Al electrode, an indium tin oxide (ITO) layer, organic hole-transport layers, a QD emissive layer, a ZnO electron-transport layer, and a semitransparent Ag layer that serves both as the cathode and as the lower mirror of the LC-MIM cavity. Al was selected for the bottom reflective electrode primarily for its good adhesion to the substrate. Ag was used for the middle and upper metallic layers because its lower optical absorption than Al in the visible range reduces transmission losses in the LC-assisted MIM cavity. A linear polarizer is used for polarization selection, with its transmission axis parallel to the initial in-plane LC director. The upper Ag layer completes the MIM filter. The LC bias controls the director orientation within the cavity, while the LED bias drives carrier injection and radiative recombination in the QD layer; the two are therefore independently addressable. The cavity preferentially transmits wavelengths that satisfy the Fabry–Pérot resonance condition, so that reorientation of the LC director changes the effective refractive index of the LC layer, modifies the cavity optical path length, and shifts the resonance wavelength. The director angle θ _LC is defined with respect to the substrate plane (Figure c), so that θ _LC = 0° is the planar state and θ _LC = 90° the vertically aligned state.

1.

Device concept of the liquid-crystal-assisted metal–insulator–metal cavity. (a) Schematic device structure integrated with a top-emission quantum-dot light-emitting diode. (b) Voltage-dependent cavity filtering of the fixed RGB quantum-dot emission components; suppressed colors are weakened but not completely removed, and the intrinsic emission wavelengths are unchanged. (c) Definition of the liquid-crystal director angle θ _LC, measured from the substrate plane.

It is worth stating explicitly what is and is not tuned. The QD emission spectrum itself is fixed; the cavity acts as a reconfigurable spectral filter that reweights this fixed spectrum. The LC-MIM cavity therefore neither eliminates the other colors completely nor shifts the intrinsic QD emission wavelengthsthe voltage-dependent cavity transmission modifies only the relative outcoupled intensities, as indicated in Figure b. At any given director angle, the dominant transmitted band is accompanied by residual transmission of the remaining bands, which are attenuated rather than removed. The accessible chromaticity is thus set by the contrast between the dominant and residual bands, and the chromaticity triangle area used below is the appropriate figure of merit precisely because it accounts for this incomplete suppression.

The polarizer is not an optional refinement but a functional requirement of the architecture. In a uniaxial LC layer, the incident field decomposes into an extraordinary component, whose index varies between n _e and n ₀ as the director rotates, and an ordinary component, which sees n ₀ irrespective of the director orientation. Only the extraordinary component therefore experiences a tunable optical path length; the ordinary component passes through a cavity whose resonance is fixed. Without polarization selection, the normal-incidence output would also contain an untuned ordinary component, which could reduce color selectivity. The polarizer is used to suppress this component with its transmission axis parallel to the initial in-plane LC director. Aligning the polarizer transmission axis with the plane of director rotation removes this background at the cost of discarding the orthogonal half of the emission.

The optical response of the multilayer cavity was calculated by using a plane-wave formalism for stratified media. , The Ag thicknesses were optimized by sweeping the top and middle layers and evaluating the figure of merit,

$$\mathrm{FoM}=\frac{T}{\mathrm{FWHM}}$$ 1

where T is the peak transmittance at the target wavelength and FWHM is the full width at half-maximum of the transmission peak, so that the metric rewards cavities that are both transmissive and spectrally selective. With the Ag thicknesses fixed, the bottom ITO and LC thicknesses were then swept to maximize the CIE 1931 chromaticity triangle area.

The LC was treated as a uniaxial anisotropic medium. For a field polarized parallel to the director, its effective refractive index is

$$\frac{1}{n_{\mathrm{eff}}{({\theta }_{\mathrm{LC}},\lambda )}^2}=\frac{{\cos }^2{\theta }_{\mathrm{LC}}}{n_e{(\lambda )}^2}+\frac{{\sin }^2{\theta }_{\mathrm{LC}}}{n_o{(\lambda )}^2}$$ 2

where n _o (λ) and n _e (λ) are the wavelength-dependent ordinary and extraordinary refractive indices. Increasing θ _LC therefore reduces the effective optical path length and shifts the resonance toward shorter wavelengths. Because the birefringence n _e – n _o itself varies across the visible spectrum, the tuning range available at a given director angle is also wavelength-dependent; this dispersion is retained throughout the optimization. The director angle was varied from 0° to 90°. Because the polarizer transmits only the extraordinary component, a single polarization state was propagated throughout; no polarization averaging was applied. At oblique incidence, this fixed polarization was evaluated in two orthogonal azimuthal planes, as described below.

All refractive indices used in this work, including the ordinary and extraordinary indices n ₀ and n _e of the LC and the indices of the Ag and Al mirrors, ITO, ZnO, the QD layer, and the organic transport layers, were treated as wavelength-dependent and were taken from the literature. ,− The metallic mirrors were described by their full complex permittivity. Because the cavity resonance is evaluated across the full visible range, this dispersion is not a second-order correction: the effective index of the LC layer varies with wavelength at every director angle, and the resonance condition is solved on a per-wavelength basis rather than at a single design wavelength. No layer in the stack was treated as index-matched or was omitted from the optical model.

The transmitted spectra were obtained by evaluating the cavity transmission T _cav(λ,θ _LC) independently at each wavelength and multiplying it by the assumed RGB QD emission spectra,

$$S_{\mathrm{out}}(\lambda ,{\theta }_{\mathrm{LC}})=\sum _{i=R,G,B}{A}_i{S}_i(\lambda )T_{\mathrm{cav}}(\lambda ,{\theta }_{\mathrm{LC}})$$ 3

where S _i (λ) is the normalized emission spectrum of the ith QD band and A _i its relative amplitude. Rather than assuming idealized line shapes, the S _i (λ) were taken from experimentally measured photoluminescence spectra of Cd-based QDs, with emission peaks at 465 nm (blue), 527 nm (green), and 628 nm (red) and corresponding full widths at half-maximum of 21.9, 35.8, and 24.3 nm. The measured spectra are plotted in Figure c. Using measured rather than idealized profiles matters here because the asymmetric tails of real QD emission overlap the neighboring cavity passbands and therefore contribute to the residual transmission discussed above.

3.

Connection between LC-dependent cavity transmission and chromaticity reconstruction. (a,b) Analytical and numerical transmission maps as functions of wavelength and LC director angle; vertical dashed lines indicate the fixed RGB quantum-dot emission peaks. (c) Assumed normalized RGB quantum-dot emission spectra together with the CIE 1931 color-matching functions x̅, y̅, and z̅ used for chromaticity integration. (d) CIE 1931 chromaticity trajectories calculated from the analytical and numerical output spectra.

The resulting spectra were converted to CIE 1931 chromaticity coordinates in the standard way by integrating S _out(λ,θ _LC) against the color-matching functions x̅(λ), y̅(λ), and z̅(λ) to obtain the tristimulus values and normalizing these to the coordinates (x,y). , The color gamut metric used throughout, A _CIE, was calculated by selecting, from the chromaticity states accessible over the director sweep, the state closest in the (x,y) plane to each of the three sRGB/Rec. 709 primaries and then computing the area of the triangle defined by those three selected states.

Finite-element-method simulations were performed in COMSOL Multiphysics using the same wavelength-dependent optical constants as the analytical model. A Gaussian source was used, and the maximum mesh size was set below λ/60; the LC layer was modeled with a full anisotropic relative-permittivity tensor constructed from n _o (λ), n _e (λ), and the director angle. The numerical transmission spectra were calculated at each wavelength and director angle, multiplied by the QD spectra according to eq , and converted to chromaticity coordinates by the same procedure used for the analytical model.

Results and Discussion

To optimize the thicknesses of the two Ag layers in the MIM cavity, the transmission spectra were calculated while varying the middle and top Ag thicknesses, with the ITO and LC thicknesses fixed at 124 and 550 nm, respectively. Over this Ag-thickness sweep, the resonance peak wavelengths ranged from 473 to 482 nm in the blue spectral region. Figure a and b shows the FoM defined in eq and the spectral quality factor Q ≈λ_peak/FWHM, respectively.

2.

Optimization of the LC-assisted MIM cavity. (a) FoM, defined as T _peak/FWHM, and (b) spectral quality factor Q of the blue resonance as functions of the middle and top Ag-layer thicknesses. White circles in (a) and (b) indicate the thickness combination selected by maximizing the FoM. (c) CIE 1931 chromaticity triangle area as a function of the LC and ITO thicknesses, with the selected Ag-layer thicknesses fixed.

Within the investigated thickness range, increasing the Ag-layer thicknesses generally lowers the peak transmittance while narrowing the resonance line width. The FoM was therefore used to balance the transmission and spectral selectivity. It reached its maximum at a top Ag thickness of 58 nm and a middle Ag thickness of 37 nm, where the peak transmittance was 0.306, the FWHM was 8.56 nm, and the Q factor was 55.6. These Ag thicknesses were fixed for subsequent optimization of the LC and ITO thicknesses.

With the Ag thicknesses fixed, the LC and bottom ITO thicknesses were swept to maximize the chromaticity triangle area (Figure c). The largest area, 0.124, was obtained at an ITO thickness of 30 nm and an LC thickness of 380 nm, indicating that a single device structure can access three well-separated chromaticity states through refractive-index modulation alone. The map in Figure c shows a semiperiodic modulation along the LC-thickness axis. This arises because the cavity supports successive Fabry–Pérot resonance orders: once the thickness increases by approximately one additional half-wave of the optical path, the next resonance order enters the visible range and reproduces a comparable chromaticity condition. The recurring bright regions therefore correspond to higher-order resonances rather than to distinct physical mechanisms, although the achievable area decreases gradually at large thickness because higher-order resonances are more closely spaced and admit more residual transmission from neighboring bands.

The optimized structure was then evaluated by finite-element-method simulations. Figure a,b compares the analytical and numerical transmission maps. The vertical dashed lines mark the fixed QD peak wavelengths, which makes clear that color tuning arises from the changing overlap between the fixed QD emission bands and the LC-angle-dependent cavity resonances rather than from any change in the intrinsic QD emission wavelengths. Figure c shows the assumed QD emission spectra together with the CIE 1931 color-matching functions, making the spectral integration explicit.

The analytical calculation in Figure a represents the LC as an isotropic layer with a director-angle-dependent effective refractive index. In contrast, the FEM calculation in Figure b directly incorporates the anisotropic permittivity tensor, retaining the direction-dependent dielectric response. The finite angular content of the Gaussian excitation used in FEM may also contribute to the residual discrepancies relative to the plane-wave analytical calculation; therefore, these differences cannot be attributed solely to the tensorial treatment. Nevertheless, the overall agreement supports the analytical model as an efficient tool for initial design and parameter optimization, while the FEM provides a complementary check of the predicted resonance positions and transmission levels.

Two features of this spectral overlay are important. First, the color-matching functions are broad and overlapping, with x̅ in particular possessing a secondary lobe in the blue, so residual transmission of a non-dominant band contributes to the chromaticity coordinate even when its peak transmittance is low. Second, the cavity resonance does not necessarily coincide exactly with a QD peak at every LC angle. At intermediate angles, the resonance can fall between two emission bands, so the transmitted spectrum may contain two or three bands of comparable weight; the apparent shift in the transmitted peak position therefore reflects reweighting of fixed emission lines by a moving filter rather than any shift of the QD emission wavelengths themselves. The chromaticity coordinates in Figure d follow from integrating each transmitted spectrum against the functions of Figure c, so states whose resonances are offset from the QD peaks move toward the interior of the chromaticity diagram rather than lying near the spectral locus.

The analytical model yielded a chromaticity triangle area of 0.124, compared to 0.113 from the numerical model. Despite this difference, the overall color tuning trajectory and spectral response were reproduced.

The output emission spectrum is obtained by multiplying the cavity transmission spectrum by the fixed QD emission spectrum and is converted to CIE chromaticity coordinates using the color-matching functions. As the LC director angle varies, the shifting cavity resonances selectively enhance or suppress the relative contributions of the RGB bands, determining the shape and extent of the chromaticity trajectories. At certain cavity thicknesses, different resonance orders can overlap with multiple emission bands, producing mixed-color states and motivating a broad thickness scan. The reported trajectories are specific to the QD emission spectra used in this study. Changes in the QD peak wavelengths alter their overlap with the cavity resonances, while variations in line widths and relative intensities affect the degree of color mixing. Different QD spectra should therefore be evaluated using the same calculation framework, with the cavity parameters reoptimized if necessary.

The peak transmission of the optimized structure is approximately 35% or lower, as shown in Figure a. The design prioritizes the suppression of undesired spectral components and the maximization of the accessible chromaticity range, while the polarizer introduces an additional optical loss. Reducing the Ag-layer thicknesses or relaxing the chromaticity-area requirement may improve transmission at the expense of spectral selectivity or color gamut. For example, reducing both the middle and top Ag layer thicknesses to 30 nm increased the peak transmission to over 60%, while the CIE 1931 chromaticity triangle area decreased to 0.0721. The design parameters can therefore be adjusted according to the balance required between the transmission and color performance. The reported peak transmission should not be interpreted as the spectrally integrated throughput or the overall efficiency of a complete display system. A complete system efficiency evaluation would additionally require spectral integration, the electrical-to-optical conversion efficiency of the QD-LED, and other system-level losses.

The angular response was evaluated as a function of the external emission angle θ _ext, defined with respect to the surface normal in air. Since the polarizer fixes the transmitted polarization, the relevant variable at oblique incidence is not the polarization state but the azimuthal plane of observation, and two orthogonal cases were considered: φ = 0°, in which the observation plane contains the plane of director rotation, and φ = 90°, perpendicular to it.

At oblique incidence, the extraordinary phase response was not obtained by substituting the normal-incidence scalar n _eff(θ _LC,λ) of eq . Instead, the extraordinary dispersion relation of the uniaxial layer was solved for the longitudinal wavenumber at every combination of θ _ext, φ, θ _LC, and λ, so that the effective index follows the projection of the wavevector onto the optic axis rather than the director tilt alone. Because the optic axis is tilted with respect to the surface normal, the forward- and backward-propagating solutions are not degenerate; both were kept when constructing the round-trip cavity phase, which accounts for the walk-off of the extraordinary beam.

The remaining approximation lies in the modal decomposition rather than in the index. At φ = 0°, the ordinary and extraordinary waves coincide exactly with the s- and p-polarized components, so the polarizer selects a pure eigenmode and the treatment is rigorous. At φ = 90°, the transmitted field is not a pure eigenmode at intermediate director angles, and the ordinary admixture, which an exact calculation would resolve through a coupled 4 × 4 formalism, is neglected. This approximation is exact for fully planar and fully homeotropic states, and the φ = 90° curve is used here only to gauge the azimuthal spread.

Figure a shows how the chromaticity trajectory contracts with increasing θ _ext. At 15°, the edge of the viewing cone considered here, the three primary states remain well-separated in both azimuthal planes; by 30°, they have migrated toward the interior of the diagram, as the cavity resonances shift away from their design overlap with the QD emission bands. The contraction is consistently faster in the φ = 0° plane (Figure b), because the observation plane there contains the optic-axis tilt, and the effective index of the extraordinary wave therefore varies more rapidly with angle. Within the 15° viewing cone, the two azimuths differ by about 5% in triangle area (0.110 versus 0.116 at θ _ext = 15°). The device maintained an averaged chromaticity triangle area of 0.121 over the 15° viewing cone, falling from 0.124 on the axis to 0.113 at the edge of that cone.

4.

Angular dependence of the optimized LC-MIM QD-LED structure. (a) CIE 1931 chromaticity trajectories at the edge of the 15° viewing cone, θ _ext = 15° (top row), and at θ _ext = 30° (bottom row), for the azimuthal planes φ = 0° (left) and φ = 90° (right). The grayscale indicates the LC director angle θ _LC, running from 0° (white) to 90° (black). (b) Chromaticity triangle area versus θ _ext for the two azimuthal planes and their average.

At larger viewing angles, the cavity transmission peaks shift relative to the fixed RGB QD emission bands, changing their relative contributions to the output spectrum and leading to an observed chromaticity contraction. In near-eye displays, a wide image field of view does not necessarily require an equally wide emission cone from each pixel because different pixel positions are mapped to different image field angles by the imaging optics. Directional emission can improve optical efficiency when matched to the display-side acceptance cone and chief-ray angles. Nevertheless, the angular response of the proposed device remains a practical design constraint, particularly when the optical system collects substantial off-axis emission.

Beyond the primary red–green–blue sequence, further operating regimes were identified by modifying the ITO and LC thicknesses while holding the Ag thicknesses at their optimized values. A secondary branch was obtained at d _ITO = 168 nm and d _LC = 542 nm (Figure a) and a quasi-white operating region at d _ITO = 10 nm and d _LC = 1280 nm (Figure b). The quasi-white state arises when the cavity line width is broad enough to transmit all three emission bands with comparable weight, which is the opposite limit to the narrow-resonance condition optimized in Figure . These results indicate that the same cavity concept can be tailored to different color trajectories and spectral-control modes.

5.

Alternative chromaticity trajectories obtained by changing the cavity thicknesses, with Ag thicknesses fixed at the optimized values of Figure a. (a) Nonprimary tuning branch, d _ITO = 168 nm and d _LC = 542 nm. (b) Quasi-white operating region, d _ITO = 10 nm and d _LC = 1280 nm.

Taken together, these results show that color tuning can be performed at the cavity level rather than through lateral patterning of separate emitters, which may reduce subpixel complexity in high-density display architectures. Several practical considerations remain, however. The present study is confined to optical modeling and numerical validation. The director angle was swept continuously from 0° to 90° as an idealized upper bound; in a real LC cell, the achievable range and the sharpness of the director distribution depend on the alignment layer, cell gap, electrode configuration, drive scheme, and applied bias. ,, A finite director distribution would broaden the effective index at each state and reduce the accessible triangle area relative to the idealized values reported here. Experimental implementation will therefore require careful control of LC alignment, electrode configuration, and cavity fabrication tolerance. The polarizer introduces additional optical loss by rejecting the orthogonal polarization component. The off-principal-plane results are based on a single-branch approximation. A full coupled-mode calculation would be required to quantify the effect of the neglected ordinary component.

A possible fabrication route is to prepare the top-emission QD-LED by sequential spin-coating of its solution-processable layers and assemble the LC-assisted MIM cavity separately on the encapsulation glass in reverse layer order. LC alignment, filling, and sealing would be incorporated into the cavity assembly, followed by integration with the QD-LED through lamination. The polarizer could be attached above the MIM cavity or on the outer surface of the encapsulation glass, with its transmission axis parallel to the initial in-plane LC director. In a pixelated implementation, the nominal pixel area would be defined by the overlap of the crossed electrodes in the LC-assisted MIM cavity. A lateral pixel size of approximately 10 μm could be considered as an initial fabrication target using lithographic patterning, given that QLEDs with emitting pixels as small as 2 μm have been demonstrated. The initial LC director could be uniformly aligned parallel to the polarizer transmission axis across the array using photoalignment, without requiring pixel-specific alignment patterns. Independent pixel operation at this scale remains to be experimentally validated.

Conclusion

We have numerically and analytically evaluated a liquid-crystal-assisted metal–insulator–metal cavity for electrically tunable color control in a top-emission quantum-dot light-emitting diode architecture. Modulating the effective refractive index of the embedded LC layer shifts the cavity resonance and reweights a fixed quantum-dot emission spectrum, enabling control of the output chromaticity from a single emissive unit. The optimized structure achieved a CIE 1931 chromaticity triangle area of 0.124 analytically and 0.113 in finite-element-method simulations, while maintaining an area of 0.121 averaged over a 15° viewing cone. Alternative tuning branches and a quasi-white operating state were identified by changing the cavity thicknesses. These results suggest that LC-assisted compact cavities offer a flexible route to electrically reconfigurable spectral control, of potential use in high-density and near-eye display architectures and in compact tunable photonic systems.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

S.-Y.C. and H.K. conceived the device concept and discussed the manuscript. H.K. performed the analytical and numerical optical simulations and wrote the manuscript draft. All authors reviewed and approved the final manuscript.

The authors declare no competing financial interest.