Quantum dot (QD) displays [1-5] have been in the spotlight as potential leaders in the next-generation display market, due to the following advantages: (1) high brightness under low driving voltages [6]; (2) fabrication based on a solution process [7], which is cost-effective and advantageous for large area; (3) Good color tunability [8] originating from the controllable quantized band gap by tuning dot size and composition; And (4) high photoluminescence (PL) quantum yield [9, 10]. In particular, quantum dots show higher color purity than other light-emitting materials because the full width at half maximum (FWHM) of their emission spectrum is narrower [11, 12]. Thus, QD displays are expected to be able to express more vibrant colors than conventional displays, and theoretically to express all colors [13].

However, toxic heavy metals such as cadmium have issues in being used for commercial devices, and their short lifetime (originating from susceptibility to moisture, oxygen, heat, and other factors) limit the handling of QDs for self-emissive displays. The solution process still has limits, such as the coffee-ring effect [14] and poor orthogonality [15] of multilayered structures. From this point of view, QDs are used as passive devices, such as a color-conversion layer, for the time being. Even the commercial passive QD layers are composed of QD particles with nonuniform size distribution, which causes the fluorescence spectra to widen. Complex synthesis and fabrication methods have been researched to obtain size uniformity, and consequently narrower spectra, for high color purity.

In this paper we suggest, unlike the conventional technical approaches (material technologies to control the intrinsic characteristics of QDs, or development of fabrication processes for high-quality QD films), a novel method to improve the color gamut of QD films by designing an optical structure. The proposed optical device is composed of stacked thin films, without any patterning processes. The Fabry-Perot interferometer (FPI) structure [16-21], which is widely used in existing thin-film optical structures [22-25], has a role in amplifying optical phenomena in the wavelength band corresponding to constructive interference between two reflectors. Resonance characteristics with high Q-factor can be used to form narrow spectra. The FPI is also applied to self-emissive displays for high color purity [26] as well as high efficiency. It is advantageous for application in many fields, because of its structural simplicity. Furthermore, it is widely used in the fields of sensors [27, 28], lasers [29], and spectroscopy [30]. But when the FPI structure is applied to subpixels of different colors [red (R), green (G), and blue (B)], each subpixel has a different thickness; Thus patterning processes are required.

We propose a novel optical structure called the dual Fabry-Perot interferometer (DFPI), which has the same dimension in each R, G, and B subpixel. The suggested structure consists of three reflective materials plus two dielectric materials in between. The resonant peaks corresponding to the R, G, and B emission spectra can be created simultaneously. Also, since the DFPI has control over the intensities of spectral peaks, it helps to obtain the color balance between the R, G, and B backlights. Therefore, the DFPI structure does not require separate patterning, allowing it to be implemented in a thin film and easily manufactured. Additionally, because a full-scale process is employed, it is possible to expand the display area while remaining cost-effective. The designed DFPI structure is demonstrated to reduce the FWHM of the spectra of the light passing through the QD color-conversion layers. Also, the suggested DFPI can tune the light balance between R, G, and B by controlling the relative intensity of each color. The proposed DFPI is expected to provide a wider color gamut than conventional commercial displays do [31, 32].

First, the structure of the dual Fabry-Perot interferometer was designed with a numerical method by MATLAB (MathWorks) and FDTD solutions (finite-domain time-difference method; Lumerical Co., BC, Canada). The refractive indices of silver (Ag) and tungsten oxide (WO₃) were measured with a spectroscopic ellipsometer (M-2000D; J.A.Woollam., NE, USA) [33, 34]. In the visible-light region, Ag has the lowest refractive index of any metal, and was chosen because it has excellent conductive qualities and the lowest absorption rate (<5%) when compared to other metals (like Al and Au). Furthermore, in the case of a dielectric material surface-plasmon coupling with Ag occurs at the interface, and to increase the overall optical transmittance the real part of the dielectric material’s refractive index must be greater than that of Ag. To put it another way, the dielectric permittivity value must be greater than the permittivity of the metal. To ensure high transmittance, WO₃ was chosen [35].

Since our suggested structure must allow light from a distant source to pass through it, a plane-wave source is most suitable for modeling the situation. Thus settings were made for the situation in which light travels by stacking up an infinitely wide film on the xy plane in the direction of the z-axis. The boundary conditions for symmetry and anti-symmetry were set in the x- and y-directions respectively. The light source was a plane wave with wavelengths ranging from 400 to 700 nm, and the calculations were performed for every wavelength in steps of 1 nm. The light propagated along the z-axis, and the perfect-matching layer was set for the boundary condition in this direction [36]. MATLAB was used to compute optical functions and the transfer matrix.

In an ultrasonic bath, a glass substrate was cleaned with isopropyl alcohol. Ag (3–5-mm granules, 4N; Tasco Co., Anyang, Korea) and WO₃ (1-4 mmpcs, 4N; Tasco) were deposited alternately by thermal evaporation with a vacuum pressure of less than 5 × 10⁻⁶ Torr, without vacuum break. Each material was deposited on the glass substrate in the following order: WO₃ (50 nm), Ag (25 nm), WO₃ (638 nm), Ag (10 nm), WO₃ (120 nm), Ag (35 nm), and WO₃ (60 nm). For Ag and WO₃, the evaporation rates were 1 Å/s and 2 Å/s respectively.

The transmittance spectra of DFPI films were measured using a UV-vis spectrometer (LAMBDA 365; PerkinElmer, MA, USA). A field-emission scanning electron microscope (SU-8230; Hitachi, Ibaraki, Japan) was used to capture cross-sectional images of the deposited film. The blue light source was a micro-LED of area 2 cm × 2 cm. The intensity of transmitted light was measured by a Black Comet UV-vis spectrometer and SpectraWiz-shortcut software (Stellarnet Inc., FL, USA). MATLAB with built-in software that converts the RGB component to the HSV component was used to perform an image analysis by counting the number of pixels that matched the hue angle.

We designed a DFPI structure applicable to the quantum dot films. The DFPI structure, as shown in Fig. 1(a), is designed to be attached to a glass substrate. The structure is made up of three reflector layers (Ag) and two dielectric layers (WO₃) that are sandwiched together. Above and below the DFPI structure, WO₃ is also included as a passivation layer. First, the Fabry-Perot interferometer (FPI) is a thin-film optical device used to improve color reproducibility. It also enhances the optical phenomena of the wavelength band corresponding to constructive interference between the two reflectors.

Figure 1. The designed DFPI structure and light source information used as reference. (a) The structure of the DFPI film. (b) The normalized light spectrum of blue LED, green QD, and red QD with resonance spectral peak values at wavelengths of 466, 542, and 643 nm respectively. DFPI, dual Fabry-Perot interferometer; LED, light emitting diode; QD, quantum dot.

Fabry-Perot interferometer 1 (FPI1) in the proposed DFPI structure can generate several resonance spectral peaks based on a specific wavelength, by utilizing a high-order resonance mode between FPIs. Fabry-Perot interferometer 2 (FPI2) adjusts the intensity of multiple peaks in the spectrum generated by the FPIs.

Therefore, the transmittance of light passing through the entire DFPI structure can be modulated by adjusting the optical path, which changes as the thickness of the material constituting each FPI layer changes.

The proposed DFPI structure can express wavelength bands with resonance spectral peaks in the red, green, and blue regions at the same time. Also, it is possible to produce each subpixel of red, green, and blue without the need for a patterning process, allowing for the realization of a thin-film form. To that end, the DFPI structure must be designed with the wavelength bands for each R, G, and B resonance spectral peak in mind.

Figure 1(b) depicts a graph of the normalized wavelength-band information used to design the DFPI structure. The blue light that passes through the blue LED has a peak wavelength of 466 nm. The peak wavelengths of the PL intensities of green and red that passed through the blue LED and green or red QD respectively are 542 nm and 643 nm. The maximum electroluminescence (EL) intensity in the actual R, G, and B wavelength bands is approximately 19,100, 41,700, and 65,300 W/m², with red light having the lowest intensity. Experiments were used to measure the spectrum of each region of R, G, and B.

With the measured values of the R, G, and B peak wavelengths, we design the thickness of each layer of DFPI structure. First, the Ag layer in the middle of the DFPI structure is designed to be 10 nm in size. Figure 2(a) depicts a model of the FPI1 structure, which is made up of a WO₃ layer between the 10-nm Ag layer and the 25-nm Ag layer at the bottom. The two Ag layers are reflectors. Several resonance spectral peaks can be obtained by adjusting the thickness d of WO₃. The Fabry-Perot factor used for this can be calculated by using the equation below:

Figure 2. Analysis of high-order resonance mode in Fabry-Perot Interferometer 1 (FPI1). (a) A graphical image of the FPI1 structure composed, of WO₃ between 10 nm and 25 nm of Ag, which are reflector layers. (b) Fabry-Perot factor of FPI1’s λ_Blue (466 nm)-matched high-order resonance mode. (c) Fabry-Perot factor of FPI1’s λ_Green (542 nm)-matched high-order resonance mode. (d) Fabry-Perot factor of FPI1’s λ_Red (643 nm)-matched high-order resonance mode.

(1)$$f_{FP}\left(\lambda \right)=\frac{t_1^2}{1+R^2-2Rcos\left(-{\varphi }_1-{\varphi }_2+2k_{0}nd\right)}$$

Here r₁ and r₂ are the reflection coefficients of reflectors 1 and 2 respectively, and ϕ₁ and ϕ₂ are the reflection coefficient’s phases at the top and bottom respectively. The transmission coefficient of reflector 1 is represented by t₁. The complex refractive index of the material used between the two reflectors is expressed as n − jκ, where n is the real part and κ is the imaginary part. k₀ is a wave number in free space that has the relationship k₀ = 2π/λ with the resonance spectral peak wavelength λ. R is calculated by r₁ ∙ r₂ ∙ e^−2κk₀d, and under resonance conditions the following formula can be used to generate various resonance spectral peaks.

(2)$$\Delta {\varphi }_{FP}=-{\varphi }_1-{\varphi }_2+2n{k}_{0}d=2m\pi$$

The order of the resonance mode is represented by m, an integer. As m increases, more peak wavelengths are generated in the wavelength band. Also, when Eq. (2) is applied to the resonant wavelength, the result is as follows:

(3)$$\lambda =\frac{4\pi nd}{2m\pi +{\varphi }_1+{\varphi }_2}$$

Using the above equations, the thickness of WO₃ suitable for the red, green, and blue wavelength bands is calculated. Figures 2(b)–2(d) show Fabry-Perot factors in high-order resonance mode, with peak wavelengths corresponding to λ_Blue (466 nm), λ_Green (542 nm), and λ_Red (643 nm) respectively.

When the Fabry-Perot factor is calculated using λ_Blue (466 nm), it is seen that when d = 615 nm (m = 6), three peaks in the visible light region can be created. When d = 739 nm (m = 6), three peaks are formed in the case of λ_Green (542 nm). As previously stated, in the case of λ_Red (643 nm), d = 738 nm (m = 5) is optimal. As a result, the thickness of WO₃ in FPI1 must be between 615 and 739 nm to show the R, G, and B peak wavelengths simultaneously.

In the FPI structure, however, multiple peaks can be formed based on a single central wavelength. There is a limit to simultaneously expressing three resonance spectral peaks (λ_Blue, λ_Green, λ_Red) all in matched position using the resonance modes. As a solution to the above limitations, the structure’s design was expanded by adding an additional FPI2 structure on top of FPI1, allowing three resonance spectral peaks (λ_Blue, λ_Green, λ_Red) to be displayed simultaneously.

A parameter study was performed for each layer of the DFPI structure to confirm its role. Figure 3(a) illustrates the thickness of each parameter to be designed in the DFPI structure. First, as in Eq. (1), the resonance mode can be adjusted by varying the thickness of the dielectric material, and multiple peaks can be obtained. To that end, the positions of the three resonance spectral peaks were determined by varying d₁. The total transmittance of light passing through the DFPI was investigated while increasing the thickness of WO₃ from 608 to 668 nm in 15-nm increments. Figure 3(b) depicts the change in total transmittance of the entire DFPI structure as the thickness d₁ changes (WO₃ on the lower side, in FPI1). As the thickness of WO₃ varies from 608 to 668 nm, the peak wavelengths of the R, G, and B regions shift from 483, 562, and 662 nm respectively to 450, 522, and 623 nm. Furthermore, as d₁ increased, the transmittance peak intensity in the red wavelength band increased, while intensities in the other wavelength bands decreased.

Figure 3. Parameter study for the main layers in dual Fabry-Perot interferometer (DFPI) structure. (a) Expressing each parameter’s thickness in terms of the DFPI structure. (b) A graph demonstrating how the thickness d₁ (lower WO₃) affects the transmittance of the entire DFPI structure. (c) A graph demonstrating how the thickness d₂ (upper WO₃) affects the transmittance of the entire DFPI structure. (d) A graph showing how the change in d₃ affects overall transmittance (lower Ag). (e) A graph showing how the change in d₄ affects overall transmittance (upper Ag).

On the other hand, the intensity at each resonance spectral peak wavelength can then be adjusted as the dielectric thickness changes in the FPI2 structure. The numerical simulations were carried out by increasing the thickness of WO₃ of FPI2 (d₂) in 10-nm steps from 100 to 140 nm, as shown in Fig. 3(c). The peak wavelengths of the R, G, and B regions increase by about 10 nm as the thickness of d₂ increases from 100 to 140 nm, from 460, 531, and 615 nm to 471, 549, and 662 nm. The changed range of the resonant peak wavelength of the red region is very large, in particular. As d₂ increases, the transmittance peak intensity increases and then decreases in the red wavelength band, and decreases overall in the other wavelength bands, in contrast to the change pattern for d₁. Both d₁ and d₂ of the DFPI structure, which correspond to the desired resonance spectral peak wavelengths of 466, 542, and 643 nm, were optimized for thicknesses of 638 and 120 nm respectively.

The reflector then plays a role in adjusting the intensity of the entire Fabry-Perot factor in the FPI structure in Eq. (1), and has a significant effect on the change in FWHM. The thicknesses of the Ag layers at the top and bottom were determined using the same sort of parameter study. Figure 3(d) depicts a graph of the change in total transmittance as a function of d₃ thickness change (the Ag layer at the bottom). The transmittance peak intensity decreased in the red wavelength range while increasing in the other ranges, as the thickness of d₃ increased. The FWHM decreased in all wavelength regions as d₃ increased. The overall structure’s transmittance was investigated by increasing the thickness of Ag in 5-nm increments. As the thickness of the Ag layer increased from 15 to 35 nm, the transmittance in the R, G, and B regions changed from 22.38%, 35.45%, and 64.87% to 36.50%, 56.74%, and 48.30% respectively. In addition, the FWHM decreased from 20.04 to 6.98 nm for blue, from 29.38 to 9.14 nm for green, and from 38.06 to 16.33 nm for red.

Next, the thickness of the Ag layer at the top (d₄) was increased from 25 to 45 nm in 5-nm increments, with the results shown in Fig. 3(e). In this case, the transmittance peak intensity decreased in all regions as the thickness d₄ increased. The FWHM decreased in all regions as thickness d₄ increased. As a result, the amount of transmittance decreased from 51.21%, 73.07%, and 62.27% respectively to 17.66%, 29.86%, and 50.72%. The FWHM for blue decreased from 12.08 to 10.16 nm, for green from 17.88 to 12.96 nm, and for red from 37.21 to 16.61 nm. However, as shown in Fig. 1(b), the absolute value of the amount of light in the R, G, and B resonance peak wavelengths (λ_Blue, λ_Green, λ_Red), which were designed as references for this work, was greatest in blue, followed by green and red. To balance between colors, the transmission of the red region should be superior to those of green and blue. As a result, d₃ and d₄ of the DFPI structure were designed to be 25 and 35 nm respectively, due to the superiority of red’s transmittance over that of the green and blue regions.

Finally, to prevent light from being reflected to the outside of the top and bottom reflector materials of the DFPI structure, the design was optimized by setting the WO₃ passivation layers, which also serve as antireflection coatings, to 60 nm and 50 nm thick respectively. This is also a passivation of the Ag layers to protect them from oxidation.

The structure of the optimally designed DFPI is composed of WO₃ (50 nm) / Ag (25 nm) / WO₃ (638 nm) / Ag (10 nm) / WO₃ (120 nm) / Ag (35 nm) / WO₃ (60 nm) on the glass substrate respectively. A DFPI film was fabricated on the glass substrate using a thermal evaporation method, and the transmittance between the fabricated film and the result of the structure designed by optical simulation were compared.

Figure 4(a) compares the transmission characteristics of the designed DFPI structure to those of the experimentally produced DFPI film. The calculated spectrum (black solid line) has resonance spectral peak wavelengths of 466, 542, and 643 nm. When the characteristics of the fabricated DFPI film (red dotted line) are examined, it has resonance spectral peaks in the R, G, and B regions of 472, 543, and 644 nm respectively. Furthermore, the total transmittance changed from 31.71%, 51.17%, and 65.62% of R, G, and B respectively to 29.52%, 53.74%, and 51.96%. The resonance spectral peak wavelengths differed by about 1 to 6 nm between the designed structure and the experimentally produced film, and the transmittance differed by about 2.14% to 13.66%. It was found that the FWHM in R, G, and B of the fabricated film increased slightly when compared to the designed structure.

Figure 4. Verify the fabricated DFPI film’s color purity performance effect. (a) An illustration showing how the designed DFPI structure and the experimentally made DFPI film compare, in terms of transmittance. (b) Comparison of FWHM modification caused by the application of the blue LED and the DFPI film made thereon (expressed as normalized values). (c) Comparison of FWHM modification caused by the application of the green QD and the DFPI film made thereon (normalized). (d) Comparison of FWHM modification caused by the application of the red QD and the DFPI film made thereon (normalized). DFPI, dual Fabry-Perot interferometer; FWHM, full width at half maximum; LED, light emitting diode; QD, quantum dot.

To check the improvement in color purity, the fabricated DFPI film was attached to a blue LED. When comparing the change in the normalized spectrum, as shown in Fig. 4(b), the FWHM decreased by approximately 37.78%, from 25.92 to 16.13 nm.

The fabricated DFPI film was then attached to the red and green QDs, and the spectral change was measured to check the color-purity improvement. At this point, all spectral data had been normalized. In the case of the green QD, when DFPI film was attached the FWHM decreased by approximately 47.29%, from 38.34 to 20.21 nm, as shown in Fig. 4(c). Similarly the change in FWHM for the red QD is shown in Fig. 4(d); When the DFPI film was attached; The FWHM decreased by approximately 51.07%, from 47.39 to 23.19 nm.

To design the structure more simply, we analyze the DFPI by dividing the structure into two FPI structures that affect the transmission characteristics of the DFPI dominantly. The effects of each FPI are then combined. The higher-order resonance mode’s order can be adjusted by changing the dielectric layer’s thickness in FPI1. Additionally, by changing the thickness of the dielectric layer in FPI2, the resonance spectral peak wavelength can be adjusted. The intensity and FWHM of the transmission spectrum can be adjusted by changing the metal’s thickness.

As a result, the red, green, and blue regions of our suggested DFPI structure can all display three resonance spectral peaks simultaneously. The DFPI structure can have high transmittance at all three resonance wavelengths, if its resonance wavelengths match the resonance peaks of the reference blue LED, green QD, and red QD. Additionally, a greater reduction in FWHM than before can be realized.

As shown in Fig. 4(a), the experimental results matched the design results, but there were minor differences in peak positions and broadness. This is expected to be influenced by manufacturing imperfections, such as fine surface roughness. The cross section was examined with a scanning electron microscope. Figure 5(a) is a photograph of a cross section of the entire DFPI film deposited on glass, magnified 2,200 times. Figure 5(b) shows the cross section magnified 60,000 times. In the case of the Ag, layers 29, 10, and 31 nm thick were deposited from the bottom side respectively, resulting in around a 4-nm error. Similarly, in the case of WO₃ errors of about 5 nm occurred when deposited at 45, 637, 116, and 63 nm thick, compared to the design. Therefore, a minor error occurred in the process results, as well as a minor difference between the experimental details and the design’s contents. Because of this, a difference in transmittance characteristics was discovered between the designed and manufactured DFPI films.

Figure 5. Scanning electron microscope images of dual Fabry-Perot interferometer (DFPI) film: (a) Image enlarged to 2,200×, (b) Images enlarged to 60,000×.

Finally, the color coordinates were determined and compared to the QD-only case and sRGB color coordinates, to verify the effect of the fabricated DFPI film. The color-coordinate values for each sample and the sRGB standard are expressed in CIE 1,931 color coordinates in Fig. 6. The blue LED backlight, green QD, and red QD have color coordinates of (0.1349, 0.0640), (0.3011, 0.6581), and (0.6556, 0.3107) respectively. After attaching the DFPI film, their color coordinates change to (0.1405, 0.0675), (0.2781, 0.6903), and (0.6862, 0.2955). Compared to the references, the red and green coordinates move toward the edge of the color space.

Figure 6. Comparison of the DFPI sample and the sRGB standard color-coordinate values, as expressed in CIE 1931 color coordinates.

When the DFPI film was applied, the color gamut increased by 14.96% compared to when only the existing QD was applied, and the color gamut increased by 37.66% compared to the sRGB coordinate system. As a consequence, when the DFPI structure is used, optical design methods and experiments demonstrate that red and green colors with higher color purity can be implemented.

For quantum dots, an applicable DFPI optical structure was optimized. When the suggested DFPI was applied to the QD color-conversion film, it resulted in a narrower FWHM than for QD-only devices. In a structure containing two Fabry-Perot interferometers, the relationship must be investigated through the derivation of the actual formula, rather than optimization via parameter study. However, organic materials or other diverse materials can be used as dielectrics. In addition, thin film can be easily fabricated by various conformal evaporations or wet processes. Although we have demonstrated a standalone DFPI device, this structure could be integrated onto other optical or imaging devices as only additional film layers. Thus the DFPI structure is expected to be applied to various optical devices, such as cameras and lenses as well as quantum dots, to achieve better color reproduction.

A novel optical structure is proposed to improve color purity. Generally the FPI structure used in displays based on low-order mode resonance requires patterning for subpixel division. Also, there is a limit to the simultaneous display of matched resonance peaks in the desired R, G, and B regions in a higher-order mode’s resonance. The proposed DFPI with two stages of FPIs has multiple resonance spectral peaks that correspond well to the specified R, G, and B values. In addition, the DFPI provides controllability between the intensity peaks. The optimized DFPI film was fabricated by a thermal evaporation method. When the fabricated film was applied to QD color-conversion films, the color gamut in the color coordinates increased by 14.96% when compared to the QD-only case, and by 37.66% when compared to sRGB. This DFPI structure is expected to be used in various display products, among other things, to achieve a wider color gamut.

The authors declare no conflict of interest.

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

Technology Innovation Program (20016350, Development of ultra high quality with life longtime of color converting material, process and module for extremely large-area micro LED display) funded by the Ministry of Trade Industry & energy (MOTIE, Korea); Alchemist Project grant funded by Korea Evaluation Institute of Industrial Technology (KEIT) and the Korea Government (MOTIE) (Project Number: 1415179744, 20019169); Korea Institute of Energy Technology Evaluation and Planning(KETEP) and the Ministry of Trade, Industry & Energy(MOTIE) of the Republic of Korea (No. 20224000000150).