Rational Distributed Bragg Reflector Design for Improving Performance of Flip-Chip Micro-LEDs

: The distributed Bragg reflector (DBR) has been widely used in flip-chip micro light-emitting diodes (micro-LEDs) because of its high reflectivity. However, the conventional double-stack DBR has a strong angular dependence and a narrow reflective bandwidth. Here, we propose a wide reflected angle Ti 3 O 5 /SiO 2 DBR (WRA-DBR) for AlGaInP-based red and GaN-based green/blue flip-chip micro-LEDs (RGB flip-chip micro-LEDs) to overcome the drawbacks of the double-stack DBR. The WRA-DBR consisting of six sub-DBRs has high reflectivity within the visible light wavelength region at an incident angle of light ranging from 0° to 60°. Furthermore, the influence of the WRA-DBR and double-stack DBR on performances of RGB flip-chip micro-LEDs is numerically investigated based on the finite-difference time-domain method. Owing to higher reflectivity and less angular dependence of the WRA-DBR, the RGB flip-chip micro-LEDs with the WRA-DBR have a stronger electric field intensity in the top side in comparison with RGB flip-chip micro-LEDs with the double-stack DBR, which indicates that more photons can be extracted from micro-LEDs with the WRA-DBR.

It is well known that the light generated in the multiple quantum wells (MQWs) active region emits in all directions.In flip-chip micro-LEDs, we expect that light emits to air mainly from the top substrates.However, a myriad of light generated in MQWs travels downward, which does not make any contributions to the LEE.A bottom reflector plays an essential role in improving the LEE by reflecting the light back into the top substrates.The distributed Bragg reflector (DBR) has been extensively used as the bottom reflector owing to its high reflectivity in a specific wavelength region [30][31][32].A typical DBR is made by stacking low refractive index dielectric layers (e.g., SiO2) and high refractive index dielectric layers (e.g., TiO2 and Ti3O5), exhibiting a low absorption in the visible light region.Five pairs of TiO2/SiO2 single-stack DBR designed for GaN-based green LEDs exhibited that the reflective bandwidth with a high reflectivity (>80%) was larger than 100 nm [31].A double-stack DBR optimized for two different central wavelengths was designed to provide a higher reflectivity and a larger reflective bandwidth in comparison with a single-stack DBR [33].Nevertheless, the double-stack DBR still shows severe angular dependence, which hinders further improvement of LEE in flip-chip micro-LEDs.A full-angle DBR composed of 14 sub-DBRs optimized for central wavelength in blue, green, and red wavelength regions exhibited a wide reflective bandwidth and alleviated the angular dependence [34].However, the reflective bandwidth of the full-angle DBR is limited in the blue and green light wavelength region, which is not suitable for red micro-LEDs.Therefore, to improve the performance of the RGB flip-chip micro-LEDs, a DBR with wider reflective bandwidth covering the whole visible light wavelength region and less angular dependence is required.
To overcome the above-mentioned drawbacks of the DBRs, we propose a wide reflected angle Ti3O5/SiO2 DBR (WRA-DBR).The WRA-DBR is composed of six sub-DBRs optimized for different central wavelengths ranging from the blue light wavelength region to the red light wavelength region.The WRA-DBR has a superior reflectivity within the whole visible light region and exhibits less angular dependence.The average reflectivity of the WRA-DBR at a normal incident angle of light within the wavelength region from 400 nm to 700 nm can reach up to 99.73%.Furthermore, the average reflectivity of the WRA-DBR is up to 97.93% when the incident angle of light is 60°.Compared to conventional double-stack DBR, the WRA-DBR exhibits a wider reflective bandwidth and alleviates the angular dependence.To further evaluate the effect of the WRA-DBR on the optical performance of RGB micro-LEDs, a simulation was carried out by using finite difference time domain (FDTD) method.The result demonstrates that the WRA-DBR can act as a potential candidate for realizing high-efficiency RGB flip-chip micro-LEDs.

Model and Methods
The DBR, based on the thin-film interference effect, is an array of multilayer stacks composed of two kinds of dielectric layers with high and low refractive indices.The dielectric layer thickness can be calculated by the following formula [35]: where the n1 and n2 are refractive indices of the high refractive layer and the low refractive layer, respectively, the t1 and t2 are thicknesses of the high refractive layer and the low refractive layer, respectively, and λ is the central wavelength.
Figure 1a shows the schematic illustration of the single-stack DBR.The single-stack DBR consists of N periods of layer 1 and layer 2. The refractive indices of layer 1 and layer 2 are n1 and n2, respectively.The thicknesses of layer 1 and layer 2 are t1 and t2, respectively.We consider the refractive indices of the incident medium and the substrate are n0 and n3, respectively.The reflection coefficient and reflectivity of the single-stack DBR can be calculated based on the transfer matrix method (TMM).From the TMM, the total transfer matrix M can be calculated according to the following equation [36,37]: the reflection coefficient can be expressed as the dynamical matrix for the medium α can be expressed as [36,37]

D
for TE wave and for TM wave (4) the propagation matrix is given by and where λ is the wavelength of incident light, and θα is the incident angle of light in the dielectric layer calculated by Snell's law of refraction: Then, the reflectivity of the single-stack DBR can be calculated by the following equation: Figure 1b shows the schematic illustration of the DBR consisting of several singlestack DBRs (sub-DBRs).Ni (i = 1, 2, 3…) is the periods of the sub-DBRs.The total transfer matrix of the DBR is Then, the reflectivity of the DBR can be calculated from the above-mentioned equations.

Results and Discussion
Based on TMM, we investigate the angular dependence and reflective bandwidth of the double-stack Ti3O5/SiO2 DBR.The double-stack Ti3O5/SiO2 DBR is designed and modeled by TFCalc software.The double-stack DBR consists of two sub-DBRs, which are composed of 12 periods of Ti3O5/SiO2.The refractive indices of Ti3O5 and SiO2 in the simulation are fixed at 2.37 and 1.46, respectively.The central wavelengths of the two sub-DBRs are optimized for 465 nm and 630 nm, respectively.Therefore, the thicknesses of Ti3O5/SiO2 dielectric layers are 48.97 nm/79.68nm and 66.34 nm/108.00nm, respectively.Figure 2a shows the schematic illustration of the double-stack DBR structure.Figure 2b shows the reflectance spectra of the double-stack DBR.The electroluminescent (EL) spectra of red, green, and blue micro-LEDs are also shown in Figure 2b.The peak wavelengths of red, green, and blue micro-LEDs are 630 nm, 520 nm, and 465 nm, respectively.It is clearly seen in Figure 2b that the reflectivity of the double-stack DBR is high within the whole visible light region when the incident angle of light is 0°.However, as the incident angle increases, the reflective bands exhibit a blueshift and the reflectivity decreases sharply in blue and green light wavelength regions.This result indicates that the double-stack DBR has a strong angular dependence.To suppress the sharp decrease in the reflectivity in blue and green light wavelength regions, DBR III is designed by inserting a sub-DBR stack into the double-stack DBR.The inserted sub-DBR is optimized for a central wavelength at 520 nm, and the thickness of Ti3O5/SiO2 of the inserted sub-DBR is 55.81 nm/90.82nm.The total periods of DBR III are the same as that of double-stack DBR, which means that DBR III is composed of 24 periods of Ti3O5/SiO2.Therefore, each sub-DBR of DBR III is made of eight periods of Ti3O5/SiO2. Figure 3b shows the reflectance spectra of DBR III as a function of incident angle of light.After adding a sub-DBR, the sharp decrease of reflectivity of the double-stack DBR in the blue and green light wavelength region is alleviated, revealing that the added sub-DBR can broaden the reflective bandwidth.However, the reflectivity of DBR III in the red light wavelength region at a large incident angle of light remains relatively low.To further improve the reflectivity of the DBR in the red light wavelength region, DBR IV with a combination of DBR III and another sub-DBR optimized for the central wavelength at 650 nm is designed, and the thickness of Ti3O5/SiO2 of the inserted sub-DBR is 68.45 nm/111.38 nm.Each sub-DBR of DBR IV is composed of six periods of Ti3O5/SiO2. Figure 4a shows the schematic illustration of the DBR IV structure.Figure 4b shows the reflectance of DBR IV.As shown in Figure 4b, the reflectivity is high when the incident angle of light is below 40°.However, the reflectivity of DBR IV at a large incident angle of light is not greatly improved in comparison with DBR III.To further enhance the performance of DBR IV, we investigate the influence of the sub-DBR optimized for different central wavelengths on the reflectivity.Figure 4c shows the reflectance spectra of DBR IV with the added sub-DBR optimized for different central wavelengths when the incident angle of light is 60°.The average reflectivity increases as the central wavelength of the sub-DBR increases from 650 nm to 730 nm.When the central wavelength of the inserted sub-DBR is 730 nm, the average reflectivity of DBR IV is larger than 90%.Therefore, we adopted the inserted sub-DBR optimized for the central wavelength at 730 nm.To overcome the drawbacks outlined above, the WRA-DBR structure with a combination of DBR IV and another two sub-DBRs is designed.The thicknesses of Ti3O5/SiO2 of the two sub-DBRs are 46.34 nm/75.39nm and 78.98 nm/128.51nm, respectively.Meanwhile, the central wavelengths of sub-DBRs and number of periods of Ti3O5/SiO2 in the WRA-DBR are 440 nm/4 periods, 465 nm/4 periods, 520 nm/4 periods, 630 nm/5 periods, 730 nm/3 periods, and 750 nm/4 periods, respectively.Figure 5a shows the schematic of the WRA-DBR structure.Figure 5b shows the reflectance spectra of the WRA-DBR at different incident angles of light.Among all the mentioned DBRs, the WRA-DBR possesses the widest reflective bandwidth.It should be mentioned that the average reflectivity of the WRA-DBR at a normal incident angle of light is 99.73% within the wavelength region from 400 nm to 700 nm.The reflectivity of the WRA-DBR can reach up to 97.93% within the wavelength region from 400 nm to 700 nm when the incident angle of light is 60°, indicating that the WRA-DBR has alleviated the angular dependence.We investigate the influence of the double-stack DBR and the WRA-DBR on the performance of RGB flip-chip micro-LEDs using the finite-difference time-domain (FDTD) method.Figure 6 shows the simulation models of the RGB flip-chip micro-LEDs with the double-stack DBR and the WRA-DBR.The optical parameters and the thicknesses of each layer of the RGB flip-chip micro-LEDs are shown in Table 1.The AlGaInP-based red micro-LED consists of ITO, p-GaP, p-AlInP, MQWs, n-AlGaInP, and n-GaAs.The GaNbased green and blue micro-LEDs are composed of ITO, p-GaN, MQWs, and n-GaN.The sidewalls of the RGB micro-LEDs are inclined and the inclination angle is 70° [38].For simplicity, the metal electrode layer of the micro-LEDs is neglected.Considering the memory of the computer and computing time, the size of micro-LEDs is set to be 8 μm × 8 μm.The perfect matched layer (PML) is used to avoid the reflected electromagnetic wave at the boundary of the micro-LEDs.A 9 × 9 dipole source array is placed in the MQWs as a light source, and the space between dipoles is set to 0.8 μm.The emission wavelengths of the dipole sources in the RGB micro-LEDs are 630 nm, 520 nm, and 465 nm, respectively.A cross-sectional discrete Fourier transform (DFT) monitor is used to obtain the electric field distribution and a transmission box monitor is used to calculate the LEEs. Figure 7a-f show the electric field distributions of RGB flip-chip micro-LEDs with the double-stack DBR and WRA-DBR.In Figure 7a-f, region I is the bottom external space of micro-LEDs and region II is the top external space of the micro-LEDs.According to the electric field distributions shown in Figure 7a-f, it can be observed that there exists a weaker electric field intensity in the WRA-DBR in comparison with the electric field intensity in the double-stack DBR, indicating that the WRA-DBR has a higher reflectivity than the double-stack DBR.Therefore, more photons will be reflected upward to region II.Furthermore, compared to RGB flip-chip micro-LEDs with a double-stack DBR, stronger electric field intensity exists in the air of region II outside the RGB flip-chip micro-LEDs with the WRA-DBR, implying that the photons are more likely to be extracted from RGB flip-chip micro-LEDs with the WRA-DBR.Moreover, the LEEs of each face of the RGB micro-LEDs with the double-stack DBR and WRA-DBR are shown in Figure 7g-i.In Figure 7g, the LEEs of blue micro-LEDs with the double-stack DBR and blue micro-LEDs with the WRA-DBR are almost same.The reason for the similar LEEs in the blue micro-LEDs with the double-stack DBR and WRA-DBR is that the double-stack DBR and WRA-DBR both perform well in the blue light region.From the results of Figure 7h and Figure 7i, it can be observed that green and red micro-LEDs with the WRA-DBR exhibit higher LEEs than green and red micro-LEDs with the double-stack DBR.

Conclusions
In summary, we have designed a WRA-DBR consisting of six sub-DBRs with high reflectivity and less angular dependence within the visible light wavelength region.The average reflectivity of the WRA-DBR at a normal incident angle of light can reach up to 99.73% in the wavelength range of 400 nm to 700 nm.Moreover, the average reflectivity of the WRA-DBR is up to 97.93% when the incident angle of light is 60°, revealing that the WRA-DBR has less angular dependence.Furthermore, we investigate the influence of the double-stack DBR and WRA-DBR on the performance of RGB flip-chip micro-LEDs using the FDTD method.Compared to RGB flip-chip micro-LEDs with the double-stack DBR, stronger electric field intensity is found in the air outside the substrates of RGB flip-chip micro-LEDs with the WRA-DBR, indicating that the WRA-DBR can significantly improve the performance of RGB flip-chip micro-LEDs.Our work demonstrates the promising potential of the WRA-DBR for realization of high-efficiency RGB flip-chip micro-LEDs.

Figure 1 .
Figure 1.(a) Schematic illustration of a single-stack DBR consisting of N periods of layer 1 and layer 2. (b) Schematic illustration of DBR consisting of several sub-DBRs.Ni (i = 1, 2, 3…) is the periods of the sub-DBRs.

Figure 2 .
Figure 2. (a) Schematic illustration of double-stack DBR structure.(b) Reflectance spectra of the double-stack DBR as a function of incident angle.

Figure 3 .
Figure 3. (a) Schematic illustration of DBR III structure.(b) Reflectance spectra of the DBR III as a function of incident angle.

Figure 4 .
Figure 4. (a) Schematic illustration of DBR IV structure; (b) reflectance spectra of the DBR IV as a function of incident angle; (c) reflectance spectra of DBR IV with an added sub-DBR optimized for different central wavelengths at an incident angle of 60°.

Figure 5 .
Figure 5. (a) Schematic illustration of the WRA-DBR structure.(b) Reflectance spectra of the WRA-DBR as a function of incident angle.

Table 1 .
Optical parameters for each layer of AlGaInP-based red micro-LED and GaN-based blue and green micro-LEDs used in the FDTD simulations.