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Abstract
In this work, by using three-dimensional finite-difference time-domain (3D FDTD) method, the effect of conventional nano-patterned sapphire substrate (NPSS) on the optical crosstalk and the light extraction efficiency (LEE) for InGaN/GaN-based flip-chip micro light-emitting diodes (µ-LEDs) are systematically studied. We find that the conventional NPSS is not suitable for µ-LEDs. It is because the inclined mesa sidewall for µ-LEDs possesses a good scattering effect for µ-LEDs, but the introduced conventional NPSS causes part of the light be off escape cone between sapphire and air and become the guided light. To suppress the guided light and improve the optical crosstalk, a thick air layer between the n-GaN layer and the sapphire substrate can be used as a light filter to prevent the guided light from propagating into the sapphire. However, in reality, it is challenging to make the aforementioned air layer from point of fabrication view. Therefore, we propose the air-cavity patterned sapphire substrate (AC-PSS) as the light filter. Our results show that the crosstalk ratio can be decreased to the value even lower than 10%. The LEE can also be enhanced simultaneously due to combination effects of the filtering effect of the AC-PSS and the scattering effect of the inclined mesa sidewall.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
At current stage, different display technologies based on liquid-crystal display (LCD), organic light-emitting diode (OLED) and light-emitting diode (LED) have been developed. When compared with LCD and OLED, LED-based displays have the features of high color-saturation, long lifetime, and less energy consumption [1–3]. Recently, high resolution is required to make AR/VR, portable smart display etc. Hence, the LED size has to be reduced to be smaller than 10 × 10 µm2, which is known as micro-LED (µ-LED) [4]. However, when making µ-LED arrays, the optical crosstalk effect among different µ-LED pixels can take place especially when the space for each pixel becomes further reduced. Crosstalk means that the adjacent pixels and regions appear to be illuminated simultaneously when a single pixel is addressed, and this leads to the poor color saturation and the blurred image [5].Generally, for flip-chip GaN-based µ-LEDs grown on sapphire substrate, there are three propagation paths leading to the optical crosstalk [5–7]. First, the light emitted from one pixel propagates into air and then extends into other pixels, which is known as the air propagation path. To remove such propagation path, sidewall metal reflector [8], optimum mesa inclination angle [9], mold with blocking walls made by using photoresist (PR) [10], and micro-lens [7] have been developed. Moreover, mesa inclination angle can also affect the LEE and electrical properties [11,12]. Second, the emitted light propagates into other pixels through the GaN template, which is known as GaN propagation path. Therefore, a deep etch process is applied to interrupt the GaN propagation path [6]. Moreover, with the specially designed n-metal tracks and p-contact lines, deep etch devices are able to sustain a large light output power and good emission uniformity [13]. Lastly, the emitted light propagates into other pixels through the sapphire substrate, which is known as sapphire propagation path. The sapphire propagation can be disabled if the sapphire substrate is removed by using laser lift-off technology [6]. However, the laser lift-off process is complicated and of high cost. Hence, it is important to explore a low-cost way to prevent sapphire propagation path for flip-chip GaN-based µ-LEDs grown on sapphire substrate. We speculate that the sapphire propagation path can be suppressed if corrugated features can be made at the sapphire/GaN interface. Studies also show that, as a very well developed technology, epitaxial growth on nano-patterned sapphire substrate (NPSS) helps to improve both LEE and crystal quality for conventional LED [14]. Therefore, growing GaN-based µ-LEDs on NPSS can be a possible option for improving the LEE and the optical crosstalk. To our knowledge, there are few reports about NPSS for µ-LEDs.
Hence, in this work, we investigate the impact of the NPSS on the optical crosstalk and the LEE for flip-chip GaN-based µ-LEDs by using 3D finite-different time-domain (FDTD). First, the effects of µ-LED with conventional NPSS on the optical crosstalk and the LEE are investigated. It is found that for the µ-LED with inclined mesa sidewall, the NPSS decreases the LEE and deteriorates the optical crosstalk due to the good scattering effect of inclined mesa sidewall. To prevent all guided light from propagating into the sapphire and decrease the optical crosstalk, an air layer is inserted between sapphire and GaN. Then a crosstalk ratio of 0 can be attained. However, from the point of experimental view, it is of great technical challenge to make an air layer between the sapphire and the GaN layer. Then, the AC-PSS is proposed, such that the AC-PSS contains air gaps and air/sapphire corrugated patterns, which help to reduce the crosstalk and enhance the LEE for GaN-based µ-LEDs.
2. Model and simulation method
Figure 1(a) shows the 3D FDTD simulation model for a flip-chip µ-LED. A 5 µm thick n-GaN layer, a 100 nm thick multiple quantum wells (MQWs) layer and a 200 nm thick p-GaN layer are set on a 1 µm thick sapphire substrate. A layer of 100 nm thick SiO2 covers the device sidewalls except the top of the p-GaN layer. Furthermore, we set a 150 nm thick Al layer on the top of p-GaN layer and SiO2 layer as a reflector. The simulated size in the XY dimension is set to be 12 × 12 µm2. A single dipole source with a peak emission wavelength of 450 nm is placed in the center of the MQWs. The dipole source is polarized in a direction parallel to the XY-plane corresponding to TE mode excitation [15]. Absorption coefficients for MQWs and GaN layer are set as 5000 cm−1 and 10 cm−1 [16], respectively. Then, all the boundary conditions are set as prefect-matched-layer (PML). The power monitor is placed in the sapphire and collects the light from the GaN into the sapphire. The near-field electric field radiation can be attained from the power monitor. By carrying out the Fourier Transformation, the near-field electric field can be converted to the far-field electric field. We define the ratio of total collected light power by the monitor to the total power emitted from dipole source as the LEE in sapphire (LEEsapphire). The refractive indices of GaN and sapphire layers are set to 2.47 and 1.74 for 450 nm wavelength, respectively [17]. Incident light between GaN and sapphire has various angles as shown in Fig. 1(b). As light path ① shows in Fig. 1(b), when the incident angle is smaller than the critical angle (23.8°) of GaN/air interface, the light can escape from the sapphire into the air because the propagation angle of light in sapphire is smaller than the critical angle (35°) of sapphire/air interface. Therefore, the LEE for light escaping into air (LEEair) can be defined as the ratio of the optical power integrating the far-field electric field within 35° to the total light power emitted from dipole source. In addition, it is reasonable to speculate that when the incident angle is smaller than the critical angle (44.7°) of GaN/sapphire interface and larger than that (23.8°) of GaN/air interface, the light can propagate into sapphire but cannot be extracted into air as light path ② shows in Fig. 1(b). Then, the light will become the guided light in sapphire and propagates into the adjacent µ-LEDs through interconnected sapphire propagation path, which leads to the optical crosstalk effect. Hence, the crosstalk ratio can be defined as the ratio of the optical power for the light with propagation angle beyond 35° in sapphire to the total light power emitted from dipole source, which can also be calculated by LEEsapphire-LEEair.
Fig. 1. (a) Schematic diagram of the 3D FDTD simulation model for µ-LED. (b) Different propagation paths of light from GaN into sapphire.
3. Results and discussion
It is well known that for both blue and DUV µ-LED, the mesa inclination angle makes an important effect on the LEE [11,18]. First, we study the effect of mesa inclination angle on the LEE and optical crosstalk ratio for µ-LED. The simulated results show that LEEair reaches its highest value when α is 60°, which is consistent with the research result of Bulashevich et al. [12]. Therefore, for the following simulation about NPSS, the mesa inclination angle of µ-LED is fixed to be 60°.
Next, we investigate the impact of the fill factor for conventional NPSS on the LEE and crosstalk ratio of µ-LED. The µ-LED on flat sapphire substrate is also calculated. We design conical patterns (NPSS A) [19] and cylindrical patterns (NPSS B) [20] for µ-LED models. The schematic structures of NPSS A and NPSS B are shown in Figs. 2(a). The period and the diameter for the NPSS are set to be P and a. The diameter (a) is set to be 500 nm for both of NPSS A and NPSS B. Then, the fill factor can be tuned by changing the period (P). Figures 2(b)-(d) illustrate the LEEsapphire, crosstalk ratio and LEEair as a function of P/a. For comparison, LEEsapphire, crosstalk ratio and LEEair for conventional flip-chip µ-LED on flat sapphire substrate (Reference) are also plotted as the dotted line. It is well known that the NPSS can enhance the LEE of conventional blue LED due to the strong scattering property [21]. However, it is found from Fig. 2(b) that the LEEsapphire of the µ-LED on NPSS A and NPSS B are both similar to the Reference µ-LED. Furthermore, the LEEair and the crosstalk ratio become worse due to the introduced NPSS as shown in Figs. 2(c) and 2(d). To explain it, Figs. 3(a)-(c) show the far-field radiation patterns of µ-LED on NPSS A and NPSS B at P/a = 1.9 and Reference. It can be found that both conical and cylindrical NPSS can enhance the scattering effect leading to the more uniform light distribution in Figs. 3(a) and 3(b) than that in Fig. 3(c). Nevertheless, the scattering effect of NPSS makes propagation angle of much light be larger than critical angle of sapphire/air (indicated by the red dotted line). It is because the optimum mesa inclination angle can scatter much light into escape cone as shown in Fig. 3(c), but the scattering effect of NPSS causes part of the light be off escape cone. As a result, the conventional NPSS decreases the LEEair and increase the crosstalk ratio for the µ-LED with inclined mesa sidewall. Therefore, the conventional NPSS is not suitable to be applied in the µ-LED.
Fig. 2. (a1) Schematic top view and (a2), (a3) cross-sectional view for the nano-pattern distribution of 3D FDTD computational models for µ-LEDs. (b) LEEsapphire, (c) crosstalk ratio and (d) LEEair for Reference µ-LED and µ-LED on NPSS structure as a function of P/a for NPSS.
Fig. 3. Far-field radiation patterns of µ-LED for (a) NPSS A and (b) NPSS B at P/a = 1.9. (c) Far-field radiation patterns of µ-LED for reference.
Note, the crosstalk ratio is still over 30% for the µ-LED with the optimum mesa inclination angle as shown in Fig. 2(c). This indicates that a lot of light is still outside the escape cone and travels into the neighboring µ-LEDs through the sapphire propagation path. To further reduce the crosstalk ratio, it is necessary to make all incident light from GaN into sapphire propagate into escape cone of sapphire/air. The aim can be achieved if a layer of air can be inserted between sapphire and GaN as the schematic diagram shows in the inset of Fig. 4(a). As the light path ① is shown in the inset of Fig. 4(a), the light can propagate from GaN into sapphire and then escapes into external space when the incident angle at the interface of GaN/air is smaller than critical angle. However, the light path ② illustrates when the incident angle of the light is larger than the critical angle, the light will be reflected by the interface between GaN and air layer and cannot propagate into sapphire. As a result, all light that can propagate into sapphire will be extracted into external space. Namely, no light can reach adjacent µ-LEDs through sapphire propagation path resulting in an extremely low crosstalk ratio. Therefore, the inserted air layer serves as a light filter to prevent light with large incident angle into sapphire. Moreover, these light reflected by the interface between GaN and air layer will be scattered again by inclined mesa sidewall until it propagates into the escape cone of GaN/air as the light path ③. To confirm it, we firstly simulate the µ-LED with an ideal air layer between sapphire and GaN. Figure 4(a) shows curves of LEEair, LEEsapphire and crosstalk ratio in terms of the thickness of the inserted air layer. It can be found that when the thickness is over 300 nm, LEEair and LEEsapphire are almost same causing that the crosstalk ratio is close to zero. This is because the total internal reflection from the interface of the inserted air layer and the GaN prevents the light outside escape cone of GaN/air from propagating into sapphire. The result is consistent with the analysis of the insert in Fig. 4(a). However, it can be observed that both the LEEsapphire and the crosstalk ratio fast increase when the air layer thickness becomes small. To explain it, the XY cross sections of electric field intensity for µ-LEDs with various air layer thickness are shown in Figs. 4(b)-(d). It can be found that the electric field intensity in sapphire decreases and that in GaN increases as the increased air layer thickness. The weaker electric field intensity in GaN implies that less light is total internal reflected by the interface of GaN/air layer. The stronger electric field intensity in sapphire implies that more light can penetrate the air layer and propagates into the sapphire. Therefore, it can be inferred that the total internal reflection effect from the interface between a too thin air layer and GaN is weakened, and some light with larger incident angle than the critical angle of GaN/air tunnels through the thin air layer and propagates into sapphire.
Fig. 4. (a) LEEair, LEEsapphire and crosstalk ratio for µ-LEDs versus the thickness of the inserted air layer. Inset: Schematic diagram of the light propagation paths for the GaN/air/sapphire structure. XY cross section of electrical field intensity for µ-LEDs with (b) 0 nm, (c) 100 nm and (d) 300 nm thick air layer.
To further confirm the optical tunneling, a plane wave with an incident angle of 30° is applied in our simulations. Note, 30° is larger than the critical angle of GaN/air. The transmissivity in terms of thickness of air layer is shown in Fig. 5(a). It can be found that the transmissivity decreases as increased thickness of air layer, which is consistent with the variation trend of crosstalk ratio in Fig. 4(a). The cross-section electric field distributions for different air layer thickness are shown in Figs. 5(b)-(d). We can observe that there is almost no light in sapphire for model with 300 nm thick air layer while there is a lot of light in sapphire for model with 100 nm and 200 nm thick air layer. Moreover, the electric field intensity in sapphire increases as the decreased air layer thickness. Hence, there is the obvious optical tunneling phenomenon for the model with 100 nm thick air layer [22]. If we observe carefully Fig. 5(d), it can be found that a strong electric field intensity appears in the inserted air layer, which is from the evanescent wave induced by the total internal reflection at the interface between GaN and air [23]. It is well known that amplitude of the evanescent wave experiences an exponential decay as the propagation length. When the air layer is thin, the evanescent wave can reach the air/sapphire interface and thus its energy can transform into the light in sapphire. As a result, the optical tunneling happens for the model with thin air layer [24]. When the medium layer is air and the penetration depth of evanescent wave is of the order of wavelength, the transmissivity from the optical tunneling is given by [25]:
Fig. 5. (a) Transmissivity of GaN/air/sapphire for the light with 30° incident angle as a function of thickness of air layer. Cross-section electrical field distributions for GaN/air/sapphire with (b) 100 nm thick, (c) 200 nm thick and (d) 300 nm thick air layer.
It has been proven that an enough thick air layer can avoid the optical tunneling and effectively suppress the crosstalk ratio by using the internal total reflection. However, it is impossible for µ-LED epi layer to be grown on air layer. Therefore, we then propose that µ-LED can be grown on the air-cavity patterned sapphire substrate (AC-PSS) to suppress the optical crosstalk. LEDs on AC-PSS can be fabricated successfully depending on the advanced fabrication nanotechnology and MOCVD process [26–29]. Air cavity array can be embodied between GaN and sapphire after µ-LED is grown on the AC-PSS. Therefore, we further investigate the effect of AC-PSS on the LEE and crosstalk ratio for µ-LED. As shown in Fig. 6(a), an air-cavity array is embodied between GaN and sapphire. Air-cavity array is designed into air cylinders with a rectangular lattice array [see Fig. 6(a1)]. Effect of the side length (a) and the fill factor on LEE and crosstalk ratio are studied. The fill factor can be tuned by changing the period (P). The calculated LEE and crosstalk ratio are shown in Figs. 6(b)-(d). We can find the LEEairs for µ-LEDs with the smallest side length are larger at a large P/a. It is because under the same P/a, the space decreases as decreased side length. It is difficult for the light with large incident angle to reach to the GaN/sapphire interface among air columns because the strong shadow effect of AC-PSS with small space. Then some of the light with large incident angle is returned to GaN and is re-scattered to escape cone of GaN/air by inclined mesa sidewall. Hence, the LEEair for AC-PSS for µ-LEDs with the smallest side length is the largest under large P/a. Moreover, comparing Fig. 6 and Fig. 2, it can be found that when the P/a is large, the LEEair for µ-LEDs with AC-PSS is smaller and the crosstalk ratio is larger than that of Reference. It can be attributed to the increased scattering effect of AC-PSS and the decreased filtering effect as the increased P/a. Hence, a small P/a for AC-PSS is benefited to the LEEair and crosstalk. Furthermore, Fig. 7 show the far-field radiation patterns of µ-LED on AC-PSS at P/a = 1.1 when a = 0.2 µm, and a = 1.1 µm. It can be found that light with large propagation angle has been filtered by the AC-PSS leading to the collected light in the center. It also can be found from Fig. 6 (c) that for the smallest P/a = 1.1, the crosstalk ratios for µ-LEDs on various AC-PSS are similar. For the real fabrication process, the AC-PSS with the larger pattern is easier to be fabricated. Hence, a smaller P/a and a larger side length should be selected for the AC-PSS in µ-LED.
Fig. 6. (a1) Top view diagram of AC-PSS and (a2) cross-sectional view diagram for the distribution of air-cavity array; (b) LEEsapphire, (c) crosstalk ratio and (d) LEEair in terms of P/a under a = 0.2 µm, 0.5 µm, 0.8 µm and 1.1 µm respectively.
Fig. 7. (a) Far-field radiation patterns of µ-LED on AC-PSS with a = 0.2 µm and (b) a = 1.1 µm at P/a = 1.1.
According to the above analysis, the P/a and the side length (a) of air-cavity array is set to 1.1 and 1.1 µm, so the period (P) and the space are 1.21 µm and 0.11 µm. Some researches have shown that the high quality GaN film can be grown by using epitaxial lateral overgrowth (ELOG) on PSS when the P/a is about 1.1 [30]. In addition, a smaller P/a than 1.1 is not be proposed because ELOG on PSS requires an enough large P/a. Figure 8 shows curves of LEEair, LEEsapphire and crosstalk ratio with respect to the height of the air-cavity array. According to Fig. 8, both LEEair and crosstalk ratio get better as increased air-cavity height due to the decreased optical tunneling probability. Moreover, a 300 nm height for air-cavity is enough, which is consistent with previous analysis in Fig. 5(a). The LEEair is 40% and the crosstalk ratio is 9% when the height of air-cavity array is 300 nm. In addition, we carefully compare Fig. 4(a) and Fig. 8, it can be found that the crosstalk ratio for µ-LED with air-cavity array is higher because the air-cavity array layer cannot completely prevent the light with larger incident angle than 23.8° from propagating into sapphire. More importantly, the LEEair for µ-LED with air-cavity array is also higher than the µ-LED on flat sapphire substrate (Thickness = 0 nm) as shown in Fig. 4(a). This is because the reflected light by the air-cavity array layer is re-scattered into escape cone by the inclined mesa sidewall as light path ③ shown in Fig. 4(a). Therefore, the combination effect of light filtering effect of AC-PSS and the scattering effect of inclined mesa sidewall can suppress effectively crosstalk ratio and enhance the LEEair.
4. Conclusions
In summary, the effect of conventional NPSS and AC-PSS on optical crosstalk and LEE of µ-LEDs are systematically studied. The conventional NPSS make little effect on improving the crosstalk and the LEE for µ-LEDs because the optimum inclined mesa sidewall of µ-LED has good scattering ability. Hence, we further utilize AC-PSS to reduce the optical crosstalk by the internal total reflection from the interface of GaN/air. The AC-PSS can be used as a light filter to prevent light with large incident angle from propagating into sapphire. Therefore, the crosstalk ratio can be suppressed effectively. However, the height of air-cavity array needs to be large enough to avoid the optical tunneling effect. Moreover, AC-PSS also can enhance the LEE for the µ-LEDs with optimum mesa inclination angle due to the scattering effect of the inclined mesa sidewall and the filtering effect of the AC-PSS. Therefore, µ-LEDs with AC-PSS and the inclined mesa sidewall have good optical characteristics and the structure is of great reference value.
Funding
National Natural Science Foundation of China (61975051, 62074050, 62275073); Natural Science Foundation of Hebei Province (F2020202030); Joint Research Project for Tunghsu Group and Hebei University of Technology (HI1909); Suzhou Institute of Nanotechnology, Chinese Academy of Sciences (19ZS02); Program for 100-Talent-Plan of Hebei Province (E2016100010).
Disclosures
The authors declare no conflicts of interest.
Data availability
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.
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