**1. Introduction**

Quantum dots (QDs) have a unique property that originates almost individually due to the size regime in which they exist. The unique optical properties of quantum dots take place because of the quantum confinement effect [1]. The current study focused on wide bandgap II-VI semiconductors quantum dots because of their fundamental structural, electrical, and distinguished optical properties [2].

Zn (Te, Se) ternary alloy QDs are considered one of the essential types of II–VI semiconductors that possess favorable optical properties, as they displayed tunable and narrowband photoluminescence (PL) emission [3,4].

Zn (Te, Se) is considered a good candidate for Cd-free and green emission materials with a long lifetime. The existence of the green band emission of Zn (Te, Se) partially results from the combination of ZnTe QDs and Te isoelectronic centers in ZnSe. The fact that ZnTe quantum dots as a partial source of green emission was confirmed by the power-dependent PL spectra. In addition, a long lifetime of the PL emission arises from the alignment of the type-II band between ZnSe and ZnTe [5]. The electrons from the conduction band in ZnSe and holes from the valence band in ZnTe were involved in the recombination process, leading to a smaller energy bandgap than that of either of ZnTe or ZnSe.

**Citation:** Shaaban, I.E.; Samra, A.S.; Muhammad, S.; Wageh, S. Design of Distributed Bragg Reflectors for Green Light-Emitting Devices Based on Quantum Dots as Emission Layer. *Energies* **2022**, *15*, 1237. https:// doi.org/10.3390/en15031237

Academic Editors: Dino Musmarra and Francesco Nocera

Received: 6 January 2022 Accepted: 3 February 2022 Published: 8 February 2022

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The energy of the bandgap of an alloyed system such as Zn (Te, Se), which consists of materials with considerably numerous chemical features and lattice constants, exhibited a significant negative deviation from the mean of the bandgap mole fraction weighted. Therefore, the Zn (Te, Se) system is named a highly mismatched semiconductor alloy [6]. The band gaps of this alloy possess much smaller energies than their constituents of unalloyed materials. The band gaps of ZnTe and ZnSe, are, respectively, 2.25 and 2.72 [7], while the minimal energy of the bandgap of the Zn (Te, Se) alloy is considered to be 2.03 eV at Zn (Te0.63Se0.37) [8]. Thus, the green emission of Zn (Te1−xSex) QDs can be realized by controlling their particle size and composition [3].

It is worth mentioning the importance of semiconductor nanocrystals generated from their unique size-dependent optical and electrical properties, which can be utilized in constructing optoelectronic devices [9]. Therefore, semiconductor nanostructures are promising for application as a pure source of monochrome light-emitting diodes [10]. Light-emitting devices based on organic and inorganic structures with electrically excited quantum dots have experienced a large development. This type of configuration becomes competitive to the organic light-emitting devices for the application in displays because of their unique outstanding features of simple solution processability, tunable emission color with high saturation, and high brightness [11,12].

This paper demonstrates the realization of bottom green emission of QD-organic light emitting devices (QD-OLED) by using Distributed Bragg Reflector (DBR) as an optical reflector. The DBR is characterized by having a periodic structure with alternating dielectric layers. Therefore, it can be utilized to afford a high degree of reflection in a certain range of wavelengths by manipulating the thickness and differences in the refractive indexes of the dielectric layers [13]. DBR mirrors have high reflectivity and a small intrinsic absorption coefficient. The high reflectivity of light comes from the constructive interference between the incident light and the reflected light due to Fresnel reflection. The utilization of high-purity dielectric material leads to the production of highly efficient DBR mirrors. It suppresses absorption and controls the thickness of layers during fabrication, leading to obtaining the desired reflection wavelength [14]. According to these features, DBRs can be used in photovoltaic devices [15], vertical-cavity surface-emitting lasers (VCSELs) [16], lightemitting diodes (LEDs) [17], and solar cell actuators [18]. Furthermore, DBR is sensitive toward electric, magnetic, mechanic, and chemical stimuli, giving various characters to be used in different applications [19].

Kitabayashi and co-workers fabricated OLED with ZnS/CaF2 DBR with different pairs and evaluated their reflectance [20]. High-efficiency white OLED with ZrO2/Zr DBR investigated by Yonghua et al. [17]. In addition, Zhang and co-workers fabricated green OLEDs with ZrO2/Zr DBR by atomic layer deposition, and it was found that the ZrO2/Zr DBR structure significantly improves the light purity of green OLEDs without interfering with intrinsic electroluminescence properties [21].

In this work, we have attempted theoretically to compare the performance of green QD-OLED based on different types of DBRs. We have chosen the materials of DBRs with different index contrast to show the effect of this parameter on the performance of the devices. In addition, different pair numbers of DBRs were used to demonstrate the effect of this parameter on the performance of the devices. DBRs have been used as a bottom mirror for light-emitting devices based on organic and inorganic QD structures with green emission to investigate their microcavity effects on device performance. Zn (Te, Se) alloy QD with green emission at a wavelength of 550 nm has been applied as an active layer. The schematic structure of the designed device of QD-OLED with multilayered film at the bottom side are shown in Figure 1a. As shown in the figure, we used indium tin oxide (ITO)/DBR as a reflector anode. *N*,*N* -Di(1-naphthyl)-*N*,*N* -diphenyl-(1,1 -biphenyl)- 4,4 -diamine (NPB) was used as the hole transport layer and ZnTeSe alloy QD as an emissive layer. Bis[2-(2-hydroxyphenyl)-pyridine]-beryllium (Bepp2) was used as the electron transport layer. Finally, Lithium quniolate (Liq) was used as an electron injection layer and Al as a cathode.

**Figure 1.** (**a**) Schematic structure of device, (**b**) energy level diagram.

The investigation of light-emitting devices with green emission is very important for many applications, one of them that can be used as a source of illumination for oxygen saturation measurements in blood. Additionally, the green color has an important application in non-pharmacological therapy. Recent investigations proved that green light acts as a potential therapy in patients with episodic or chronic migraines with no side effects. It amended the number of headache days/months and improved the quality of life in both episodic and chronic migraine. In addition, the green light provides an additional therapy for the prevention of episodic and chronic migraine [22].

The energy-level diagram of the device is shown in Figure 1b. According to the energylevel diagram, the emission zone is confined to the QD layer due to good energy-level alignments at interfaces of adjacent layers.

## **2. Theoretical Analysis**

#### *2.1. Distributed Bragg Reflector*

The most common OLED microcavity architectures incorporate two similar metal mirrors with variant thicknesses; one of them is fractional reflective. Another design includes one mirror with extreme reflection consisting of a dense dielectric distributed Bragg reflector (DBR) and other metal mirrors with low work function [17].

DBRs have tremendous relevance and acceptance in optoelectronic and photonic devices due to their high reflectance and wavelength selectivity compared to metallic mirrors [19]. DBR mirror contained alternating high and low refractive index layers of semiconductor compounds. The thickness of each of the layers is one-quarter wavelength (*λ*/4). The reflectivity of DBR is determined by the refractive index contrast and a number of periods [23].

A DBR mirror optical principle is based on successive Fresnel reflection at normal incidence at interfaces between two alternating layers with high and low refractive indices *nh* and *nl* respectively: *<sup>r</sup>* = *nh*−*nl nh*+*nl* . When each layer's quarter wavelength (*λ*/4) optical thickness is maintained, the path difference between reflections from successive interfaces equals half of the wavelength (*λ*/2), or 180◦ out of phase. Despite the reflections (r) at successive interfaces having alternating signs, the 180◦ compensation phase shift can be obtained through the differences in path length, and all the reflected components interfere constructively. In this case, the cumulative reflection can be enhanced by changing the design. The transmission matrix theory has been used in calculating the reflectance spectrum of a DBR [24].

Reflected light from multiple films is due to the interference from the numerous lights reflected from each of the different surfaces. The interference of light reflected and transmitted by other contact surfaces of multiple film layers is depicted in the scheme shown in Figure 2 [25]. The structure is designed so that all reflected components from the interfaces interfere effectively, leading to a strong reflection. The range of wavelengths that are reflected is termed a photonic stopband. The stopband is controlled mainly by the index contrast of the two materials [19] that can be calculated by [24]:

$$
\Delta\lambda\_{\text{max}} = \frac{4\lambda\_B}{\pi} \sin^{-1}\left(\frac{\Delta n}{n\_h + n\_l}\right) \tag{1}
$$

**Figure 2.** Reflectance of DBR structure.

Δ*λmax* is proportional to the Bragg wavelength *λ<sup>B</sup>* and is sensitively affected by the index contrast (Δ*n* = *nh* − *nl*). Thus, the elevation in Δ*n* is very desirable in DBR fabrication for both a high peak reflectance and a wide stopband width.

#### *2.2. Cavity Emission Characteristics*

Based on the concept of interfaces, the most straightforward formula for the emission of light from the thin-film structure, including an emissive layer, can be developed into a method that explains the transmission of a Fabry–Perot resonator structure [26]. In this study, the microcavity was designed as shown in Figure 3 of a top mirror composed of (Bepp2, Liq, and Al) and a bottom mirror is consisting of (NPB, ITO, and DBR), with using ZnTeSe alloy QD as an active emission layer. The theoretical spectrum for external emission normal to the plane of the layers of the device can be calculated based on classical optics by the following equation [27]:

$$\left| \left| E\_{\rm curv}(\lambda) \right|^2 = \frac{\frac{(1 - R\_b)}{l} \sum\_{i} \left[ 1 + R\_l + 2 \left( R\_l \right)^{0.5} \cos \left( \frac{4 \pi x\_i \cos \theta\_0}{\lambda} + \Phi\_l \right) \right]}{1 + R\_l \left R\_b - \left( R\_l \ R\_b \right)^{0.5} \cos \left( \frac{4 \pi L \cos \theta\_0}{\lambda} + \Phi\_l + \Phi\_b \right) \right]} \times \left| E\_{\rm nc}(\lambda) \right|^2 \tag{2}$$

where *Rt* and *Rb* are the reflectivities of the top and bottom mirrors, respectively, *L* is the optical thickness of the cavity, |*Enc*(*λ*)| <sup>2</sup> is the free space emission intensity at wavelength *λ* and *xi* is the optical thickness between the emitting sublayer and top mirror. *θ*<sup>0</sup> is the internal observation angle from the surface normal to the microcavity; Φ*<sup>t</sup>* and Φ*<sup>b</sup>* are the phase changes upon reflection to the effective reflectivities of *Rt* and *Rb*. According to Equation (3), the resonance condition to maximize luminance from a cavity is given by [26]:

**Figure 3.** Microcavity structure used for an optical analysis.

A measure of the quality of the resonance of the cavity is given by the finesse [28]. Finesse is described as the number of light oscillations between two mirrors at the free space wavelength (λ) before its energy decays by a factor of *e*−2*π*. A higher finesse exists as a result of a higher average number of times a photon is reflected back and forth within the cavity [29]. The finesse can be written in terms of reflectivity as follows [30]:

$$F = \frac{\pi \sqrt{R\_t \ R\_b}}{1 - R\_t \ R\_b} \tag{4}$$

A cavity quality factor *Q*, which is defined as the reciprocal of the energy loss per cycle per energy stored in the cavity and may also be interpreted as the number of oscillations observed before decay below *e*−2*π*, can be expressed as [31]:

$$Q = \frac{4\ R\_t\ R\_b}{\left(1 - R\_t\ R\_b\right)^2} \tag{5}$$

Cavity photon lifetime *τ<sup>p</sup>* is a time constant that represents the rate at which photons are lost from the cavity and is given by [32],

$$\tau\_p = \frac{\frac{2nL}{c}}{1 - R\_t \, R\_b} \tag{6}$$

where *c* is the speed of light.
