**3. Results and Discussion**

This study focuses on the use of a DBR as a bottom mirror; three DBRs labeled DBR1(ZrO2/Zr), DBR2 (SiNx/SiO2), and DBR3 (ZnS/CaF2) have been applied as bottom mirrors. (Zr, SiO2, CaF2) played as low refractive index materials, while (ZrO2, SiNx, ZnS) were used as high refractive index materials. Schematic-layer structures of ZnTeSe *QD*-OLED with three periods of DBR1, DBR2, and DBR3 are shown in Figure 5a–c, respectively. The thicknesses of all layers are also displayed in Figure 5. For designing the thickness of each layer in the DBRs, we have applied *<sup>L</sup>* <sup>=</sup> *<sup>λ</sup>Bragg* <sup>4</sup>*<sup>n</sup>* . According to the Bragg wavelength of 550 nm, and by using the refractive indices shown in Table 1, the thickness of multilayer films can be deduced as follows: the thicknesses of the ZrO2 and Zr of DBR1 are:

$$L(\text{ZrO}\_2) = \frac{550}{4 \times 2.17} = 63.4 \text{ (nm)}\tag{19}$$

$$L(\text{Zr}) = \frac{550}{4 \times 1.62} = 84.8 \text{ (nm)}\tag{20}$$

**Figure 5.** Schematic layer structure of three devices at 550 nm based on (**a**) DBR1 (**b**) DBR2 (**c**) DBR3.


**Table 1.** Refractive indexes of multilayer films at 550 nm.

The thicknesses of the SiNx and SiO2 of DBR2 are:

$$L(\text{SiN}\_{\text{x}}) = \frac{550}{4 \times 2.16} = 63.7 \text{ (nm)}\tag{21}$$

$$L(\text{SiO}\_2) = \frac{550}{4 \times 1.46} = 94.2 \text{ (nm)}\tag{22}$$

The thicknesses of the ZnS and CaF2 of DBR3 are:

$$L(\text{ZnS}) = \frac{550}{4 \times 2.38} = 57.8 \text{ (nm)}\tag{23}$$

$$L(\text{CaF}\_2) = \frac{550}{4 \times 1.43} = 96.2 \text{ (nm)}\tag{24}$$

Three structures were designed with a variation of a number of periods of DBR from one to three. The reflectivities calculated by the transfer matrix model and their reflectance are displayed in Figure 6. The refractive index at 550 nm for ITO is 1.9251 + i0.0021684 [43], Al is 0.6 + i5.2745 [44], and the refractive index of organic materials is assumed to be 1.8. The main parameters that affect the performance of DBR are the number of periods (*N*) and index contrast (Δ*n*). Therefore, the comparison of the performance of devices with emission at 550 nm based on different DBRs by changing (*N*) and (Δ*n*) is estimated and tabulated in Table 2.

**Table 2.** Comparison of the main characteristics for devices based on different designs of DBRs at 550 nm.


The main feature for the effect of variation of DBR periods can be observed in Figure 6. Clearly, the calculated reflectance seems to achieve higher values with the increasing number of DBR periods. In addition, the maximum reflectivity increased for DBR based on ZnS/CaF2, which has the highest (Δ*n*) relative to DBRs consisting of ZrO2/Zr and SiNx/SiO2.

**Figure 6.** Reflectance spectra by the number of pairs for devices based on (**a**) DBR1 (**b**) DBR2 (**c**) DBR3.

It is worth mentioning that the reflectivity of DBR3 with a number of periods equal to 2 is larger than that for the DBR1 with *n* = 3; this is because of the large differences between the values of index contrast. The values of Δ*n* for DBR1 and DBR3 are 0.55 and 0.95, respectively. Consequently, by using DBR3 consisting of ZnS/CaF2, we can obtain high reflectance and a wide stopband by applying a small number of periods. The decreasing number of periods has many scientific and economic benefits, such as avoiding scattering losses and saving time and materials.

The calculated finesses of DBR structures with a varying number of periods are presented in Table 2. Figure 7 shows the finesse as a function of a number of DBR periods for three configurations applied in this work; the finesse increases with an increasing number of periods for the three devices with various DBR structures; additionally, the highest finesse (15.613) was found for DBR3 with three periods due it is the highest reflectivity of (0.914).

**Figure 7.** Calculated finesse versus number of DBR periods for devices based on (DBR1, DBR2, and DBR3).

The graph of stopband against index contrast is shown in Figure 8. Obviously, the increase in index contrast leads to an increase in the stopband width, reaching 178. CaF2 clearly exhibits a smaller refractive index than ZnS, leading to a high index contrast (Δ*n* = 0.95) compared to SiNx/SiO2 (Δ*n* = 0.7) and ZrO2/Zr (Δ*n* = 0.55), as reported in Table 2. The enhancement of the stopband width of DBR3 arises from the highest refractive index contrast between high and low refractive index materials (Δ*n* = 0.95).

The characteristics of the multimode cavity of the device with emissions at 550 nm based on three periods of DBR are discussed. We have investigated different devices based on the three types of DBR with varying cavity modes through changing the cavity length. The cavity lengths of several resonance modes are given by Equation (3); by varying mode index (*m* = 1, *m* = 2 and *m* = 3), the cavity length can be adjusted for resonance mode. Table 3 summarizes the main characteristic parameters of the device with emission at 550 nm for three cavity modes. Clearly, the highest cavity enhancement factor and photon lifetime is obtained for the device with mode index *m* = 3 and attributed to the increase in the cavity length at this mode.

**Figure 8.** Plots of stopband width and bottom mirror peak reflectance versus refractive index contrast.


**Table 3.** Cavity characteristics of the device with three periods of DBR3 at 550 nm.

The external emission intensity spectrum of the devices was simulated using Equation (2) with an increasing number of periods of DBR1, DBR2, and DBR3. The obtained intensities of the emission peaks are presented in Table 2. The emission spectra of all devices with different structures of DBR are shown in Figure 9a–c. Clearly, the number of periods causes a pronounced effect on the emission characteristics. The emission spectrum's full width at half maximum (FWHM) decreases, and the peak intensity increases at the resonance wavelength as the number of periods increases. The improvement in the output light intensity of devices with increasing period number is ascribed to the increase in reflectivity. It is worth mentioning that the performance of the device based on DBR3 consisting of ZnS/CaF2 revealed better performance relative to other devices. Consequently, we selected the device based on DBR3 consisting of ZnS/CaF2 to investigate the effect of resonance mode on the emission spectra. Furthermore, ZnS/CaF2 possesses low absorption and a high index of contrast for emission at 550 nm. In addition, future fabrication of ZnS/CaF2 can be carried out on the substrate at room temperature, which benefits consuming time and avoiding damage to soft materials. The electroluminescence spectra of the device with three cavity modes are shown in Figure 10. Increasing the mode index of the cavity leads to a pronounced improvement in emission intensity. The increase in emission intensity is attributed to the increase in cavity length. Furthermore, the increase in cavity mode leads to the enhancement of the central wavelength at the expense of the other wavelengths and consequently causes a pronounced decrease in the line width.

**Figure 9.** Electroluminance spectra for devices based on (**a**) DBR1 (**b**) DBR2 (**c**) DBR3.

**Figure 10.** Electroluminescence spectra of device based on DBR3 at three-resonance mode.

To verify the validity of the methodology (TMM) that we used in this work, we applied this method to calculate the bottom reflectance of the device fabricated by Kitabayashi et al. [20]. In this calculation, we have considered the same values of layer thickness in the published work. Figure 11 shows the calculated bottom reflectance spectra of the device fabricated by Kitabayashi et al. [20] with 3, 5, and 7 pairs of ZnS/CaF2 DBR. The comparison between the calculated bottom reflectance and the measured values at a wavelength of 550 nm of the device fabricated by Kitabayashi et al. [20] is shown in Table 4. The results indicated that the calculated bottom reflectances are compatible with the measured experimental results.

**Figure 11.** Calculated bottom reflection spectra of the device fabricated by Kitabayashi et al. [20].


**Table 4.** The measured and calculated bottom reflectance at 550 nm of the device fabricated by Kitabayashi et al. [20] with different pairs of ZnS/CaF2 DBR.

#### **4. Conclusions**

The external emissions of microcavity light-emitting devices based on Zn (Te, Se) alloy quantum dots as an active layer and organic structures as electron and hole-transporting layers were investigated. The mirrors of the microcavity consist of one mirror with extreme reflection, consisting of a dense dielectric distributed Bragg reflector (DBR), and other metal mirrors with low work functions. The emission characteristics based on the variation in the number of periods of DBR and cavity length were investigated. The increase in the number of periods of DBR or refractive index contrast causes a pronounced increase in reflectivity, which in turn improves the eternal emission of the light-emitting devices. Additionally, the increase in the mode index of the cavity with adjusting cavity length leads to a pronounced improvement in emission intensity.

**Author Contributions:** Conceptualization, I.E.S., A.S.S. and S.W.; methodology, I.E.S. and S.W.; software, I.E.S. and A.S.S.; formal analysis, I.E.S., A.S.S., S.M. and S.W.; investigation, I.E.S., A.S.S., S.M. and S.W.; data curation, I.E.S., A.S.S., S.M. and S.W.; writing—original draft preparation, I.E.S.; writing—review and editing, I.E.S., A.S.S., S.M. and S.W.; supervision, A.S.S. and S.W.; project administration, S.M.; funding acquisition, S.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors acknowledge the support and funding of Research Center for Advanced Material Science (RCAMS) at King Khalid University through Grant No. RCAMS/KKU/009-21. Authors acknowledge the support provided by King Abdullah City for Atomic and Renewable Energy (K.A.CARE) under K.A.CARE-King Abdulaziz University Collaboration Program.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data generated or analyzed during this study are included in this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

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