Russian Physics Journal, Vol. 57, No. 5, September, 2014 (Russian Original No. 5, May, 2014)
INTERNAL QUANTUM EFFICIENCY OF InGaN/GaN LED STRUCTURES GROWN ON A PATTERNED SAPPHIRE SUBSTRATE I. A. Prudaev1, I. S. Romanov,1 Vad. A. Novikov, 1 А. А. Marmalyuk,2 V. A. Kureshov,2 D. R. Sabitov,2 А. V. Маzalov2
UDC 621. 382.2
Effect of a patterned sapphire substrate on the increase of external quantum efficiency in “blue” InGaN/GaN LED structures is studied. It is shown that in structures with high internal quantum efficiency (no less than 60%), an increase of the external quantum efficiency is due to an increase of the coefficient of the radiation output from the crystal. Epitaxial growth of GaN on a sapphire substrate with an array of elements of pyramidal shape with a base of 900 nm and a period of 1200 nm allows to increase by 75% the coefficient of the radiation output. Keywords: LED, heterostructure, gallium nitride, quantum wells, external quantum efficiency.
Structures with multiple InGaN/GaN quantum wells (MQW) are applied for fabrication of light-emitting diodes of visible range. External quantum efficiency (EQE) is the main parameter of LED structures characterizing theirs energy efficiency. In general, EQE is determined by the expression [1]
i ext ,
(1)
where γ is the injection coefficient, ηi is the internal quantum efficiency, and ηext is the coefficient of the radiation output. The product γ·ηi is also denoted in the literature as internal quantum efficiency (IQE) [2]. The value of ηi is determined only by the recombination mechanisms and depends on the crystal quality of an active region. The IQE value is also determined by the design of an active region, since it depends on the number of carriers injected into the active region and emitted out of it. In technology of LEDs with InGaN/GaN MQWs, several alternative methods are known to improve the external quantum efficiency of LED crystals. These methods include the flip-chip technology, the technology of separation of the sapphire substrate (lift-off), and technology of epitaxial layer growth on patterned substrates. To date, the most widespread technology is the growth on patterned sapphire substrates (PSS), which allows to achieve high economic efficiency (the highest ratio lm/$). An analysis of published data shows that the use of the PSS technology can result in the two qualitative effects: an increase in ηext due to an increase in the reflectance coefficient at the GaN/Al2O3 interface [3–5] and an increase in ηi due to a decrease in the density of threading dislocations [6–8]. The contribution of each of the effects to the increase of EQE of LEDs is often not established. In the literature, contradictory data are presented. In this regard, in the present paper, an increase of ηi and ηext at a transition from the technology of growth on planar substrates to that on patterned sapphire substrates is studied. Within the framework of theoretical study, numerical calculation of the ray tracing in a “blue” LED crystal was carried out. The used mathematical model is based on the laws of 2D-geometrical optics and on the concept of a complex refractive index: 1
National Research Tomsk State University, Tomsk, Russia; 2“SigmPlyus” Co. Ltd, Moscow, Russia, e-mail:
[email protected]. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 85–88, May, 2014. Original article submitted November 21, 2013. 1064-8887/14/5705-0657 2014 Springer Science+Business Media New York
657
Fig. 1. Monochrome images of ray tracing (the result of calculation for βmin = 60o) in structures based on a planar (a) and a patterned (b) substrates.
N N i ,
(2)
where N is the real part of the refractive index, and κ is the absorption coefficient. The calculation algorithm includes the following basic steps: 1. Tracing of each ray starts in the source (in the InGaN layer of a quantum well) with a power of P0. The powers from vectors with mutually perpendicular polarizations are: PTE = PTM = P0/2. 2. The power of a ray propagating in a medium decreases according to the Lambert–Buger law:
P( x) P0 exp( x) ,
(3)
where x is the ray path, and α = α (κ) is the absorption coefficient. 3. If the ray falls on the boundary between two media with different indices of refraction, the angle of incidence is equal to the angle of reflection, and the angle of refraction can be calculated by the Snell’s law. The powers of the reflected and transmitted rays are calculated using the Fresnel formulas taking into account the ray polarization. 4. The calculation of the ray tracing is interrupted, when the ray falls outside the LED structure, or when the ray power is decreased to a specified minimum value. To simulate isotropic nature of spontaneous radiation, its own ray direction was calculated for each source in the quantum wells by counting the angle β to the plane of quantum wells using a random number generator. For modeling a real structure with non-uniform widths of quantum wells, calculation was performed for five different specified intervals of the angle β: 1) 0–90o (isotropic nature), 2) 20–90o, 3) 40–90o, 4) 60–90o, and 5) 80–90o. Thus, the variable parameter of the calculation was the smallest possible angle β ≡ βmin, which was varied in the interval 20–80°. It is necessary to use this approach to avoid the propagation of rays only in the active region waveguide (in the quantum well). To reduce the computation time, we chose model samples with sizes smaller than those of real samples: the thickness of the sapphire substrate was 2 μm and the transverse size of the sample was 6 μm. The number of InGaN/GaN quantum wells was 10, the quantum well thickness was 2.5 μm, the barrier thickness was 15 μm, the thickness of the p-GaN layer was 150 nm, and the thickness of the n-GaN layer (distance to the horizontal n-GaN/Al2O3 interface) was 4 μm. The sapphire substrate pattern was set by a periodic sequence of triangles with the base of 900 nm and height of 500 nm (the period of 1200 nm). The results of calculations of the coefficient γ for two identical structures differing only by the type of the substrate (the patterned or planar substrates) are shown in Figs. 1 and 2. Figure 1 shows the monochrome images of the ray tracing. These images allow to qualitatively judge that the patterned substrate efficiently reflects light towards the epitaxial layer (in the region of the patterned substrate, the rays are more discharged than in the structure based on the
658
Fig. 2. Calculated values of the coefficient of radiation output from the LED crystal for structures based on a planar (curve 1) and a patterned (curve 2) substrates.
planar substrate). According to calculations, the coefficient of the radiation output increases by 40–72% at the transition from a planar substrate to a patterned one (Fig. 2). It should be noted that the result of calculations to a large extent is determined by the specified absorption coefficients for GaN, InGaN, and Al2O3. In our calculation, we used the following experimental data: α(GaN) = 23 сm–1, α(InGaN) = 250 сm–1, and α(Al2O3) = 0.04 сm–1 [9]. For experimental research, two “blue” LED structures were fabricated. The structures were grown by Metalorganic Chemical Vapor Deposition on different sapphire substrates (on a patterned substrate and on a planar one) on the (0001) planes and had the same sequence of the active region layers consisting of a Si-doped n-GaN layer with the thickness of 2 µm, 10 InGaN/GaN pairs with the thicknesses of 2.5 nm and 15 nm, and a magnesium doped p-GaN layer with the thickness of 150 nm. The patterned sapphire surface was an ordered array of pyramids with the period of 1200 nm. The triangular shaped base of the pyramids had the diameter of 900 nm. The height of the pyramids was 500 nm. For experimental samples, internal quantum efficiency of photoluminescence and an increase in the coefficient of the radiation output at the transition from the structures grown on the planar substrates to those grown on the PSSs were measured. Internal quantum efficiency was determined using the temperature and power dependences of the photoluminescence intensity [10]. Detailed description of the method is presented in [11]. Measurement of the increase of γ was carried out in an integrating sphere in the photoluminescence mode taking into account the experimentally obtained values of ηi. For this purpose, two samples of the same shape and size grown on a planar and a patterned sapphire substrates were alternately placed in an integrating sphere, and then, the photoluminescence was excited and its intensity was determined. In the experiment, a “Labsphere” integrating sphere with the diameter of 10 inches, an Ocean Optics fiber spectrometer, and a pulsed YAG-laser with an average power of 35 mW (1 kHz, pulse duration of 10 ns, 355 nm) were used. Using the measured values of the integrated photoluminescence intensity and taking into account the identity of active regions in the samples, an increase of γ was calculated according to the following formula: I patt plan K 1 100 % , I plan patt
(4)
where Ipatt and Iplan are the measured integrated photoluminescence intensities for samples based on a patterned and a planar sapphire substrates, respectively, ηpatt and ηplan are the corresponding values of internal quantum efficiency. The results of measurements of internal quantum efficiency of photoluminescence are shown in Fig. 3. The obtained dependences do not qualitatively differ from each other and can be explained within the ABC-model of recombination [11]. A relatively small decrease in ηpatt with respect to ηplan is within the maximum relative random error of the technique, which in our case was 8%. However, it should be noted that a slight worsening of crystalline
659
Fig. 3
Fig. 4
Fig. 3. Power dependence of internal quantum efficiency of photoluminescence (normalized) measured at two temperatures for structures grown on a patterned (PSS) and a planar substrates. Fig. 4. Photoluminescence spectra measured in an integrating sphere for structures on a patterned (curve 1) and a planar (curve 2) substrates.
perfection of structures grown on the patterned sapphire was also observed by X-ray diffraction: the FWHM of the (004) reflex is 261, which is somewhat larger than for structures based on a planar sapphire (236). In this case, worsening of structural perfection may be caused by the non-optimized growth technology of the GaN buffer layer on the PSS. Photoluminescence spectra measured in an integrating sphere are shown in Fig. 4. Using these spectra, the value of K ≈ 75% was calculated, which is close to the maximum calculation value (for βmin = 60°, the coefficient K ≈ 72%). It follows from the results obtained that the increase in IQE of structures grown on patterned sapphire substrates is completely due to an increase in γ. An increase in ηi for structures grown on PSS is more pronounced when comparing structures having high dislocation density [6]. In our case, the density of threading dislocations in structures grown on planar substrates measured using etch pits was ≈ 108 сm–2. This value is small for the GaN/Al2O3 system, which explains high value of ηi ≈ 60%. Apparently, to further effective improvement of internal quantum efficiency, other technological methods, such as introduction of short-period superlattices into the buffer layer, should be used [12]. Thus, it is shown that the growth of LED InGaN/GaN structures on the patterned sapphire substrates results in an increase of external quantum efficiency by 75%. In so doing, for structures with high initial value of internal quantum efficiency (at least of 60%), an increase in the external quantum efficiency is completely determined by an increase in the coefficient of the radiation output due to the reflection at the GaN/Al2O3 interface. This work was supported in part by the Ministry of Education and Science (Federal Target Program State Contract No. 14.516.11.0088 and Russian Foundation of Basic Research (Project No. 13-02-98019). REFERENCES
1. 2. 3. 4.
660
V. I. Gaman, Physics of Semiconductor Devices [in Russian], Publ. House of Sci. and Techn. Liter. Ltd., Tomsk (2000). F. Shubert, Light-Emitting Diodes [Russian translation], Fizmalit, Moscow (2008). V. V. Lundin, E. E. Zavarin, M. A. Sinitsyn, et al., Pisma Zh. Tekh. Fiz., 34, 39 (2008). H. W. Huang, C. H. Lin, J. K. Huang, et al., Mat. Sci. Eng. B, 164, 76 (2009).
5. 6. 7. 8. 9. 10. 11. 12.
Park Hyoungwon, Byeon Kyeong-Jae, Jang Jong-Jin, et al., Microelectr. Eng., 88 3207 (2011). D. S. Wuu, W. K. Wang, K. S. Wen, et al., J. Appl. Phys. Lett., 89, 161105 (2006). Li Ya-Ju, Ching Hua-Chiu, Chih Chun Ke, et al., IEEE J. Select. Top. Quant. Electron., 15, 1137 (2009). T. Kohno, Y. Sudo, M. Yamauchi, et al., Jap. J. Appl. Phys., 51, 072102 (2012). Yu. S. Lelikov, N. I. Bochkareva, R. I. Gorbunov, et al., Fiz. Tekh. Poluprovodn., 12, Vyp. 11, 1371 (2008). S. Watanabe, N. Yamada, M. Nagashima, et al., Appl Phys. Lett., 83, No. 24, 4906 (2003). I. A. Prudaev, I. S. Romanov, V. V. Kop’ev, et al., Russ. Phys. J., 56, No. 7, 757 (2013). I. S. Romanov, I. A. Prudaev, A. A. Marmalyuk, et al., Russ. Phys. J., 56, No. 7, 760 (2013).
661
