1. Introduction
1.1. General background
GaN-based materials have been attracted a great deal of attention due to the large direct band gap and the promising potential for the optoelectronic devices, such as light emitting diodes (LEDs) and laser diodes (LDs). LEDs have the advantages of small size, conserve energy, and have a long lifespan. LEDs of solid-state lighting will be in a position to replace conventional lighting sources within years. At present, the efficiency of LEDs is still lower than that of fluorescence lamps in general lighting applications. Therefore, the ultimate optimization of all aspects of LED efficiency is necessary in solid-state lighting development. Several factors are likely to limit the light extraction efficiency of LEDs. One may think that the main limiting factor is internal light generation as internal quantum efficiency (IQE). Nevertheless, this is not the case in a variety of material where the conversion from carriers to photons reaches 50% to 90% if the material’s quality is high enough. In this case, the strongest limiting factor is that of external extraction efficiency, i.e. the ability for photons generated inside the semiconductor material to escape into air. Unfortunately, most of the light emitted inside the LED is trapped by total internal reflection (TIR) at the material’s interface with air. Although many efficient light extraction strategies have already been applied, they are mostly based on the principle of randomizing the paths followed by the light, such as surface roughening [1-2], flip-chip [3-4], and photonic crystals (PhCs) [5-6].
1.2. Research niche
Light-emitting diodes (LEDs) have become ubiquitous in illumination and signal applications as their efficiency and power level improve. While the improvement of the basic characteristics will benefit the replacement of the conventional light sources, further improvement in other characteristics can bring about unique applications. One notable example is the polarized light emission which is highly desirable for many applications [7], e.g. back-lighting for liquid crystal displays and projectors. For the application of next-generation LEDs, such in projector displays, backlight displays, and automobile headlights, further improvements the light extraction efficiency, the polarized emission, and the directional far-field patterns of light sources are required. Recently, PhC has attracted much attention for the possibility to improve the extraction efficiency [8-9], polarization [10], and directional far-field patterns [11-12] from GaN-based LEDs and GaN-based film-transferred LEDs, respectively. In order to optimize the PhC LED performance for a specific system, detailed knowledge of the light extraction and polarization, especially the angular distribution, is required. The light wave propagating in the PhC LED waveguide, with its propagation partially confined by the TIR, can interact with the reciprocal lattice vectors of the two-dimensional (2D) PhC lattice to exhibit a variety of novel behaviors from the light localization. On the other hand, through the Bragg diffraction with the PhC which fabricated on LEDs can scatter the guided light into the escaping cone to circumvent the deleterious effects due to TIR, which traps the majority of the emitted light in LED chips. In this study, the GaN-based LEDs with PhCs were demonstrated and investigated in the light extraction, and polarization.
In this chapter, we first introduce the theory analysis and design method of GaN-based PhC LED structures in section 2. Then, in section 3, we exhibit the direct imaging of the azimuthal angular distribution of the 2D PhC light extraction using a specially designed waveguide structure. The optical images of the light extraction patterns from the guided electroluminescence (EL) light are obtained with a current injected into the center of the annular structure made on the GaN multilayer. With increasing lattice constant, symmetric patterns with varying number of petals according to the symmetry of the PhC are observed. The observed anisotropy is charted using the Ewald construction according to the lattice constant and the numerical aperture of the observation system. The appearance and disappearance of the petals can be explained using the Ewald construction in the reciprocal space. In addition, several novel features of light propagations associated with the PhC can also be directly observed including the focusing and collimating behavior. These results can be used for the optimization of LED devices with PhC extraction. Next, in section 4, polarization characteristics of the GaN-based PhC LEDs using an annular structure with square PhC lattice have been studied experimentally and theoretically. The observed a strong polarization dependence of the lattice constant and orientation of the PhC. It is found that the PhC can be as a polarizer to improve the
2. Fundamental and modelling of photonic crystal LEDs
2.1. Waveguide properties of LED structures
Although the IQE of GaN-based LEDs have reached up to 90%, the light emission from a multi-quantum well (MQW) into the air is fundamentally limited by TIR. LEDs have such low external extraction efficiency that most of the light generated in a high-index material is trapped by TIR. Due to the GaN-based LED layer behaving as a waveguide, trapped light is distributed in a series of so-called guided modes. The propagation properties, including electromagnetic field distributions and wave vectors of guided modes, affect PhC light extraction behavior. In general, the high order guided modes interact strongly with PhC to have high extraction efficiency. By contrast, the low order guided modes have weak light extraction efficiency due to the poor overlap with the PhC regions. But the light of energy distribution coupling to the low order guided modes is larger. Therefore, our discussion begins with the guided mode properties in a waveguide structure of LED semiconductor layers, which is helpful to optimize the design of PhC structure on LEDs with high light extraction efficiency.
A large number of waveguide modes exist in a typical GaN-based LED structure as asymmetric slab waveguide in geometry. For example, GaN-based blue LED structure is grown by metal-organic chemical vapor deposition (MOCVD) on
2.2. Ewald construction of Bragg’s diffraction theoretical analysis methods for photonic crystals
Photonic crystals (PhCs) are artificial structures containing periodic arrangements of dielectric materials which exhibit unique dispersion properties (e.g. such as photonic bandgap (PBG) [15]) and that manipulate light emission behaviors. In this chapter, we will concentrate on the extraction of waveguide light from GaN-based LED structures. There are several schemes to obtain light extraction through PhC nanostructures [16], as shown in Fig. 4, such as (a) inhibition of guided modes emission by PBG, (b) spontaneous emission enhanced in a small cavity by Purcell effect, and (c) emission extraction on the whole surface by leaky mode coupling. Accordingly, the emission region can be deeply etched with a pattern to forbid propagation of guided modes, as shown in Fig. 4(a), and thus force the emitted light to be redirected towards the outside. Defects in PhCs behave as microcavities, as shown in Fig. 4(b), such that the Purcell effect can be excited for spontaneous emission enhancement. Then, light can only escape through leaky modes coupling, as shown in Fig. 4(c). In addition, PhCs can also act as 2D diffraction gratings in slabs or waveguides to extract guided modes to the air and to redirect the emission directions.
The optimal design of PhC structures for high extraction efficiency is promising, which is strongly dependent on various parameters such as lattice constant (
Figure 4(c) is a schematic of the surface grating devices that can be discussed in relation to the light extraction of the lattice constant of PhCs by using the Ewald construction of Bragg’s diffraction theorem. The light extraction of guided waves through diffraction by PhC is discussed. According to Bragg’s diffraction law,
Further, an actual 2D square lattice of PhC as grating has the anisotropy of the diffraction vector [23]. Figure 6 shows the diffraction vector for various lattices constant
3. Anisotropy light extraction properties of GaN-based photonic crystal LEDs
3.1. Sample prepared and measurement results
In order to optimize the PhC LED performance for high light extraction efficiency, detailed knowledge of light extraction is required especially the angular distribution [9, 26]. Therefore, we present the direct imaging of the azimuthal angular distribution of the extracted light using a specially designed annual PhC structure, as shown in Fig. 7(a). The GaN-based LED samples used in this study were grown by metal-organic chemical vapor deposition (MOCVD) on a
Figure 8 depicts the CCD images for the square PhC structures with lattice constant
3.2. Bragg diffraction theoretical discussion
The appearance and disappearance of the petals observed in Fig. 8 can be qualitatively analyzed using the Ewald construction in the reciprocal space. The above observation established that the use of 2D Ewald construction explains the observed images. It can be invoked to determine the boundaries between regions with varying numbers of petals. As shown in Fig. 9, as
For larger lattice constants, the escape cone and the guided mode circle become larger relative to the reciprocal lattice. For
The above discussion considers the simple case of single mode propagation in the waveguide plane. Since the thickness of the epitaxial layer used for the present study is 3 um, the waveguide is multimode. Every mode can couple with different reciprocal vectors to form their own boundaries for a given number of pedals. When plotted on the map, these boundaries will appear as a band of lines. To present these multimode extractions clearly, only the first and the last mode with modes number ‘
In addition, we also observed that the intensity of the light propagating inside the PhC is found to decrease with a decay length of 70-90 μm, depending on the orientation and the size of the holes. The decay length is determined using the data in the middle dynamic range of the CCD camera where the intensity decay appears as a linear line on the log linear plot. This value is in the same range of that reported in David et al.[17]. Such a parameter is needed for the design of the PhC light extractors.
4. Polarized light emission properties of GaN-based photonic crystal LEDs
Due to valence band intermixing, the side emission of light from quantum well structure is predominantly polarized in the TE direction (along the wafer plane). The observed polarization ratio has been reported to be as high as 7:1 for GaN/InGaN QWs [18]. For common GaN LED structures grown along the
4.1. Measurement results
The GaN-based PhC LED samples used in the present work are the same as described before section 3. The polarization properties of the GaN blue PhC LEDs were measured at room temperature using a scanning optical microscopic system, which included continuous wave (CW) current source (Keithley 238), a 20× microscope objective with numerical aperture (NA) = 0.45, a 40× microscope objective with NA = 0.6, and charge-coupled device (CCD) spectrometer with spectral resolution of 0.1 nm. A 20× objective is used to collect the on-axis emission signal from the sample and formed a high-resolution image with a digital camera CCD. Figure 11(a) shows EL CCD image for the sample with square lattice constant
40× objective lens of the confocal microscope and was transferred to a monochromator for μ-PL measurement through an optical fiber with core diameter of 600 μm. Figure 11(c) shows the EL intensity as a function of the orientation of the polarizing filter placed between the GaN blue PhC LED and the spectrometer, at a drive current of 20 mA. The intensity at various angles was determined from image taken under the same bias condition. Thus the polarization for different propagation direction can be determined as shown in Fig. 11(c). It can be seen that there is a periodic variation of the EL intensity with angular orientation of the polarizer. This indicates that the light collected from the PhC LED is partially polarized, and the P/S ratio [defined as
4.2. Coupled mode theoretical discussion
The experimental results described above can be explained by examining the electromagnetic field distributions of PhC Bloch modes. Field distributions of Bloch modes were calculated by plane wave expansion (PWE) method using the structure with PhC sandwiched in between air and GaN materials. Figure 12(a) schematically shows the device structure where light is generated and extracted through PhCs. Due to the valence band mixing effects in MQW, guided light propagating in the GaN slab is nearly linear polarized in transverse direction as shown in Fig. 12(b). For PhC
At
polarization properties (P/S ratio) of the leaky modes in the ΓX directions as a function of normalized frequency. In the calculation, the polarization of the generated light is assumed to be TE polarized. The calculation was carried for each band alone the ΓX direction up to the light line where the light becomes guided and its polarization is then the same as they were generated. As can be seen in Fig. 13, the trend of P/S ratio is decreasing with normalized frequency although the trend within each band is not uniform depending on the filed distribution. Details of this discussion will appear in later publication. It can also be seen from Fig. 13 that by varying the fill factor the lattice constant, the PhC can be designed to have higher extraction efficiency for TE polarization while discriminating the TM polarization. In such case, very high P/S ratio (>102) can be achieved. The maximum efficiency for the polarized emission that can be obtained in such case is equal to the TE portion of the total emission which be as high as 88% for a 7:1 P/S ratio.
5. Conclusion
In conclusion, we have experimentally and theoretically demonstrated that surface emitted anisotropic light extraction and polarized light from GaN-based LEDs. The EL images of the anisotropy light extraction distribution in the azimuthal direction were obtained with specially designed annual GaN PhC LED structures, which is dependent on the orientations of the PhC lattice and lattice constants and shows a four-fold symmetric light extraction patterns with varying numbers of petals in the plane of the waveguide. The regions corresponding to the various numbers of petals are determined for increasing lattice constant. More petals appear in the observed image with increasing lattice constant, and some of the petals may disappear. The regions for the appearance and disappearance of the petals are determined by the Bragg diffraction analysis using Ewald construction. In addition the angular dependence of the light extraction for waveguided light incidents to plane with various lattice orientations is also determined. The results show that the light extraction for the square lattices can only occur for certain crystal directions according to the lattice symmetry. Further, a P/S ratio of 5.5 (~85% polarization light) has been observed. The polarization characteristics are theoretically discussed by couple mode theory. At lower normalized frequency, PhC LED has better polarization property, and lattice orientation not only affects the extraction efficiency but also P/S ratio of radiative light. This polarization behavior suggests an efficient means to design and control the GaN blue PhC LEDs for polarized light emission.
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