1. Introduction

The state-of-the-art InGaN-based light-emitting diodes (LEDs) are rapidly penetrating into a variety of application fields due to their tremendous feature of being able to emit light from ultraviolet to green spectrum. Influenced by the great prospect of next-generation solid-state lighting, their external quantum efficiency (EQE) still requires further enhancement. The EQE of InGaN-based LEDs is determined by two factors: one is internal quantum efficiency (IQE), and the other is light-extraction efficiency (LEE). Owing to the large mismatches in lattice constant and in thermal expansion coefficient between the epitaxial GaN layer and the sapphire substrate, high threading dislocation densities (TDs) occurs. The appearance of TDs will degrade the IQE of InGaN-based LEDs. Moreover, even if IQE is close to unity, the LEE of InGaN-based LEDs is still poor because of the total internal reflection at the interface between the semiconductor and the outer medium. Considering the refractive indices of GaN (n = 2.5) and air (n = 1), the critical angle of total internal reflection for GaN-air interface is merely 23°, and it severely limits the LEE of InGaN-based LEDs [1,2].

On the other hand, InGaN-based LEDs are typically grown along c-plane sapphire substrates. The significant biaxial strain originated from the huge lattice mismatch between the InGaN active layer and the underlying GaN layer possesses piezoelectric electrical polarization; the intrinsic wurtzite crystal structure induces large spontaneous electric polarization as well. The total polarization fields within the multiple quantum wells (MQWs) result in the spatial separation of electron and hole wave functions and thus in restricting the radiative recombination efficiency, given that the low IQE is present. The phenomenon is well known as quantum-confined Stark effect (QCSE) [3]. Many significant methods have been pursued in the literatures on the approaches to suppress QCSE in the InGaN/GaN MQWs active region by using semi/non-polar QWs [4–7], polar QW with large overlap design [8,9], ternary substrate method [10], polarization-matched epitaxial structures [11], nanorod arrays [12], top surface rough process [13], vertical-structure devices [14], and so on.

Currently, the single growth method by patterned c-plane sapphire substrates (PCSSs) [15–17] has attracted much attention by more and more researches thanks to the free contamination and improving the light output power. The InGaN-based LEDs grown on nano-sized PCSSs show more improvement in EQE than those grown on micro-sized PCSSs. The pursuit of nano-sized PCSSs has been widely reported for achieving low TDs in GaN thin film. The growths of GaN materials on nano-sized PCSSs have resulted in 2-order of magnitude reduction in TDs in GaN thin film, which has been applied to achieve improved IQE in LEDs [18–20]. Nevertheless, all prior PCSSs-related studies have been pursued for enabling improved LEE (micron-sized) and reduced TDs (nano-sized). Until now, the effect of QCSE influenced by nano-sized PCSSs with reducing the space on the performance of InGaN-based LEDs has been less reported.

In this paper, the relationship between the nano-sized PCSSs with various spaces and the QCSE within the InGaN/GaN MQWs is investigated. We clarify experimentally that the QCSE within the InGaN/GaN MQWs can be suppressed when the space of the nano-sized PCSSs is shortened. Since the feature size used in photolithography is limited by the wavelength and is unsuitable for nanoscale patterning, the E-beam lithography system was utilized to carry out the study for acquiring the accurate dimensions. However, due to the limited throughput and high cost through the use of E-beam lithography, the experiments is organized as follows. First, four kinds of nano-sized periodic arrays with the same field size of 200$\times$ 200µm² were fabricated on the center of the sapphire substrate. After the epitaxial growth, four types of InGaN-based LEDs having various nano-sized PCSSs were appeared on the same wafer. The samples were then characterized by the constant-excitation power and excitation power dependence of micro-photoluminescence (µ-PL) measurement to indentify the reduction in the internal field in the material. In addition, the constant-excitation power of micro-Raman (µ-Raman) system was used to provide comparison of the strain in the layer. The LEE of the nano-sized PCSSs was also simulated by the ray-tracing method using a Trace-Pro software. Second, the outstanding pattern was chosen among these four InGaN-based LEDs with the field size of 200$\times$ 200µm² and then re-fabricated with the field size of 1$\times$1mm² for achieving the high-power LED die process in the industry. As a result, the electroluminescence (EL) characterizations of the outstanding LED chip and of the conventional one were performed for extracting the light output power and efficiency droop comparison of the LEDs. Moreover, the correlated efficiency droop of the devices was observed with the pulsed-mode measurement to prevent self-heating effect.

2. Experiments

The slightly truncated pyramidal shape nano-sized PCSSs were fabricated with ELS-7000 E-Beam lithography system of ELIONIX company and wet-etching technology. The 100-nm silicon dioxide hard mask layer was deposited on the 2 inch c-plane sapphire substrate. After that, the substrate having 100-nm silicon dioxide hard mask layer was coated with e-beam resist ZEP-520A and exposed with 100-kV electrons at a beam current of 100pA, followed by development in ZEP-N50. Next, a Cr thin-film layer as the etching hard mask was coated on the exposure substrate. After removal of the resistance, the patterns were transferred to the 100-nm silicon dioxide hard mask layer by reactive ion etching. Then, the sapphire substrate having the patterned silicon dioxide hard mask was etched in a mixture of H₂SO₄:H₃PO₄ (3:1) solution at 280°C. Consequently, the four periodic square arrays, having the same field size of 200$\times$ 200µm², comprised the 400nm-diameter hexagonal posts with different spaces, i.e. 200nm, 400nm, 600nm, and 800nm, were formed on the same substrate. The height of the hexagonal posts is about 400nm. The surface morphology, periodicity, depth, space, and diameter of the accomplished nano-sized PCSSs were re-examined by the instrument of FEI Dual-Beam NOVA 600i Focused Ion Beam as shown in Figs. 1(a)-1(d).

 

Fig. 1 The SEM images of nano-sized PCSSs with the space of (a) 200nm, (b) 400nm, (c) 600nm, and (d) 800nm, respectively.

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Next, prior to the growth, the substrate was thermally baked at 1100°C in hydrogen gas to remove surface contamination. The InGaN-based LED structures, which consist of a 25-nm-thick low-temperature GaN nucleation layer, a 2-µm-thick undoped GaN buffer layer, and a 3-µm-thick n-GaN layer, using SiH₄ as the n-type dopant, were firstly grown on the nano-sized PCSSs with Taiyo Nippon Sanso SR2000 atmospheric pressure metal organic chemical vapor deposition (AP-MOCVD) under three-flow gas injection. Then, five pairs of InGaN/GaN MQWs having a 3-nm-thick InGaN well and a 12-nm-thick GaN barrier (grown at 800°C and 850°C, respectively) were deposited, followed by a 20-nm-thick p-AlGaN electron blocking layer, and a 120-nm-thick p-GaN layer, using Cp₂Mg as p-type dopant. The InGaN-based LEDs with a conventional sapphire substrate (CSS) and the nano-sized PCSSs were grown under the same growth conditions without employing an intermediate etch-back and recovery technique, which leads to adding a significant cost to the growths of InGaN-based LEDs [18,19].

For the optical measurements, the 405-nm and 532-nm wavelength laser were used as the excitation source for the µ-PL and the µ-Raman analysis, respectively. In order to accomplish the accuracy of the measured data, the µ-PL and the µ-Raman system were equipped with the C-Focus system, which corrects microscope focus drift. For EL measurement, the encapsulated InGaN-based LEDs were measured based on top-emitting devices. For the pulsed-mode measurement, a pulse width of 1ms and a duty cycle of 0.1% were used with a maximum injection current of up to 1A, and the integrating sphere was employed to collect light output power.

3. QCSE influenced by nano-sized PCSSs

Figure 2(a) reveals the room-temperature PL spectra, and Fig. 2(b) shows the related PL relative peak intensity and line width, of the InGaN-based LEDs having the CSS and nano-sized PCSSs with different spaces varied from 200nm to 800nm. With the decrease of the space, the PL relative peak intensity and line width of the InGaN-based LEDs grown on the nano-sized PCSSs are gradually enhanced and reduced, respectively; what’s more, the PL peak wavelength always appears a blueshift, which may imply the smaller QCSE within the MQWs. These phenomena could be attributed that the growths of the InGaN-based LEDs on the nano-sized PCSSs with the smaller space may help weaken the QCSE within the InGaN/GaN MQWs. Compared with the InGaN-based LED grown on the CSS, the maximum of the enhanced PL relative peak intensity reaches by up to 96% through the sample having the 200nm-space nano-sized PCSS, which also has the largest blueshift and the smallest PL line width.

 

Fig. 2 (a) The room-temperature PL spectra, and (b) the related room-temperature PL relative peak intensity and PL line width, of the InGaN-based LEDs grown on the CSS and the nano-sized PCSSs with the various spaces.

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To further elucidate the effect of the nano-sized PCSSs with reducing the space on the QCSE within the InGaN/GaN MQWs, excitation power dependent PL measurement [21] is carried out as shown in the inset of Fig. 3(a).The inserted figure presents that the differences in the PL peak energy are more pronounced at lower excitation power density where the coulomb screening is reduced. Figure 3(a) shows the difference in the PL peak energy between the lowest and highest excitation power density with respect to the space, calculated from the inserted figure. The difference of the PL peak energy becomes smaller for the InGaN-based LEDs grown on the nano-sized PCSSs with the decrease of the space, and the 200nm-space sample exhibits a difference of only 12.87meV, which can be reasoned by observing the weaker action of the QCSE from the lower polarization fields within the InGaN/GaN MQWs. Also, Fig. 3(b) shows the PL peak intensity versus excitation power density of the InGaN-based LEDs having the CSS and the nano-sized PCSSs with different spaces. With shortening the space, the more linear enhancement of the PL relative peak intensity of the InGaN-based LEDs having the nano-sized PCSSs occurs in comparison with the sample grown on the CSS as the optical excitation power density increases. Saturation in the PL relative peak intensity of the InGaN-based LED grown on the CSS under high excitation power density is attributed to the QCSE significantly corresponding to the larger polarization fields within the InGaN/GaN MQWs.

 

Fig. 3 (a) The difference of PL peak energy versus various spaces, based on the inserted figure. The inset of (a) shows the correlated PL peak energy, and (b) reveals the correlated PL peak intensity, as a function of the excitation power density for the InGaN-based LEDs grown on the CSS and the nano-sized PCSSs with different spaces.

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For more insight into the weaker QCSE obtained from the lower polarization fields within the epitaxial layers, a direct measurement on the strain in the layer will be required. The well known methods of micro-Raman [22] and phonon-assisted anti-Stokes PL [23] measurements can be used to quantify the strain in the layer. In the present work, the relaxation of the compressive strain in the GaN layer is discovered by using micro-Raman measurement. Figure 4(a) shows the room-temperature Raman spectra, and Fig. 4(b) indicates the associated Raman shift and line width of GaN E₂(high) mode, of the InGaN-based LEDs having the nano-sized PCSSs and the CSS [24,25]. With the shrinkage of the space, the Raman shift and line width of GaN E₂(high) mode of the InGaN-based LEDs having the nano-sized PCSSs seem to be continuously reduced in contrast with the sample grown on the CSS. The associated residual compressive strain is calculated to be 1.633$\times$ 10⁻³ for the InGaN-based LED grown on the CSS. The other values are 1.074$\times$ 10⁻³, 1.360$\times$ 10⁻³, 1.392$\times$ 10⁻³, and 1.419$\times$ 10⁻³ for the InGaN-based LEDs having the nano-sized PCSSs with the space of 200nm, 400nm, 600nm and 800nm, respectively. The detail of the present calculation can refer to the reference [16]. This clearly shows that the compressive strain is relaxed and the bulk GaN crystalline quality is improved due to the surface geometry of nano-sized PCSSs with reducing the space [26,27]. Moreover, to provide precise quantification of the dislocation density, future works on cross-sectional transmission electron microscopy are in progress.

 

Fig. 4 (a) The room-temperature Raman spectra, and (b) the related room-temperature Raman shift and Raman line width, of the InGaN-based LEDs grown on the CSS and the nano-sized PCSSs with the various spaces.

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4. Discussion

According to the investigation of PL and Raman measured under the constant excitation power, and excitation power dependent PL measurement, there are three functions of the growths of InGaN-based LEDs on the nano-sized PCSSs with the decrease of the space. One is to enhance the PL peak intensity with the higher PL peak energy. Another is to reduce the difference of the PL peak energy and reinforce the linearity of the PL relative peak intensity while the increase of excitation power occurs. The other is to improve the crystalline quality with the relieved compressive strain. Those behaviors could be reasoned by considering the function of the nano-sized PCSSs with decreasing the space. With reducing the space of the naon-sized PCSSs, the more relaxation of the compressive strain occurs, followed by the increase of crystalline quality and the reduction of the polarization fields within the MQWs, which leads to the suppression in the function of QCSE. Therefore, the improvement of crystalline quality reduces the nonradiative recombination rate, and the abatement of QCSE within the MQWs elevates the overlap between electron and hole wave functions. These behaviors result in the improved IQE of InGaN-based LEDs. As a result, the higher PL relative peak intensity of InGaN-based LEDs having the nano-sized PCSSs with reducing the space can be obtained.

Nevertheless, it is worth noting here that the LEE of the nano-sized PCSSs can also contribute to the enhanced PL relative peak intensity. Figure 5 shows the cross-sectional ray-tracing images and the correlated LEE of InGaN-based LEDs having the nano-sized PCSSs and the CSS, evaluated from the bare LED simulation results. Note that the ray-tracing method used here provides only a simple picture on the light extraction comparison among the LEDs, however a more accurate method based on FDTD analysis [28] is required for LEDs once structural dimensions approach or below the wavelength in material. The ray-tracing images and the associated LEE figure indicate that the InGaN-based LEDs grown on the nano-sized PCSSs always have the larger LEE than that grown on the CSS owing to re-directing the trapped light to the normal light trace. As also shown in the Fig. 5(f), the LEE of InGaN-based LEDs with the CSS is about 29%, and of the samples having various nano-sized PCSSs are always within 38% to 42%. The simulation results point out that the LEE of the InGaN-based LEDs having the nano-sized PCSSs increases slightly as the space is decreased. As a consequence, with shortening the space, the enhancement of PL peak intensity of the InGaN-based LEDs having the nano-sized PCSSs can be attributed to the suppression of the QCSE within the MQWs and of the non-radiative recombination rate. The experimental and simulation results perform the evidence that the growths of InGaN-based LEDs on the nano-sized PCSSs with the smaller space can lead to higher light output power.

 

Fig. 5 Trace-Pro ray-tracing results for the InGaN-based LEDs having the nano-sized PCSSs with the space of (a) 200nm, (b) 400nm, (c) 600nm, (d) 800nm, and (e) grown on the CSS, respectively. (f) The associated LEE with respect to space, evaluated from the bare LED simulation results.

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Based on the above observations, Fig. 6(a) only shows the EL spectra of the InGaN-based LEDs grown on the CSS and the outstanding pattern, i.e. 200nm-space nano-sized PCSS, at a current of 350mA, fabricated in industry with the standard 1$\times$1 mm² high-power LED die process. As demonstrated in the figure, in contrast with the InGaN-based LED grown on the CSS, the sample with the 200nm-space nano-sized PCSS has the shorter EL peak wavelength and the lower operating forward voltage as revealed in the inlet of Fig. 6(a). Figure 6(b) shows the light output power versus forward current. Compared with the InGaN-based LED grown on the CSS at a current of 350mA/1A, the enhanced light output power is by up to 61%/81% through the sample having the 200nm-space nano-sized PCSS, respectively. The EQE versus forward current is as shown in the Fig. 6(c), which presents a maximum EQE of 54% at 0.025A for the InGaN-based LED with the 200nm-space nano-sized PCSS and of 35% at 0.049A for the sample with the CSS. The maximum EQE experiments amount to a 1.54-fold advantage for the InGaN-based LED with the 200nm-space nano-sized PCSS. According to the previous simulation results, the LEE enhancement factor of 1.45 can be derived. The LEE simulation results and the maximum EQE experiments reveal that the IQE is enhanced slightly for the growth of the InGaN-based LED on the 200nm-space nano-sized PCSS at low current regime. Schubert et al. [29] have reported that the crystalline quality do not strongly impact high current performance. Therefore, we believe that the enhanced IQE is mainly attributed to the suppressed QCSE within MQWs. Since the previous literatures [30,31] point out that the weaker QCSE from the lower polarization fields can mitigate the efficiency droop, Fig. 6(d) shows the associated normalized EQE versus forward current of the InGaN-based LEDs having the CSS and the 200nm-space nano-sized PCSS. As shown in the figure, the efficiency droop of the InGaN-based LED grown on the CSS is 17% of its peak value at 350mA and increases to 36% while the forward current reaches 1A. In contrast, it is expected that the efficiency droop of the InGaN-based LED having the 200nm-space nano-sized PCSS decreases to 11%/24% at a current of 350mA/1A, respectively. The shorter EL wavelength, lower operating voltage, minor consideration in crystalline quality, and lessened efficiency droop can conclude that the lower QCSE within the MQWs comes from the use of nano-sized PCSSs with reducing the space.

 

Fig. 6 (a) The EL spectra at an injection current of 350mA, and (b) the light output power, (c) EQE and (d) normalized EQE, as a function of forward current, for the InGaN-based LEDs having the 200nm-space nano-sized PCSS and the CSS, respectively. The inset of (a) shows forward current versus forward voltage of the InGaN-based LEDs.

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5. Conclusion

This paper reports that the growths of InGaN-based LEDs on the nano-sized PCSSs with reducing the space can suppress QCSE within the InGaN/GaN MQWs. Therefore, the mitigation of efficiency droop is observed due to the lower QCSE within the MQWs. As verified by the experimentally measured data and the ray-tracing simulation results, the suppressed efficiency droop for the InGaN-based LED having the nano-sized PCSS with a smaller space of 200nm can be acquired due to the relaxation of the compressive strain within the corresponding epitaxial layers, followed by the lower internal polarization fields. As a result, the reduction of the QCSE within the InGaN/GaN MQWs occurs. Compared with the InGaN-based LED grown on the CSS at a injection current of 350mA/1A, the efficiency droop of the sample having the 200nm-space nano-sized PCSS decreases to 11%/24%, and its light output power is improved by up to 61%/81%, respectively.