In this paper, the polarization dependent optical properties of GaN surface relief grating are investigated using dark field angle-resolved photoluminescence (ARPL) spectrometer. The light extraction efficiency with the transverse electric (TE) and transverse magnetic (TM) pumping source represents a TE polarized dominated property. It is found that the TE and TM waveguide modes cannot be simultaneously coupled out, therefore light extraction is polarization dependent. The ARPL spectrum also reveals that the extraction efficiency is relatively high as the dispersion line of the waveguide mode is coincident with the folded free-photon dispersion of the 1D GaN grating.
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The group-III nitride material is one of the most promising semiconductors for optoelectronic applications in the visible light spectral region. Light emitting diodes (LEDs) based on the group-III nitride material have certain desirable characteristics, for example, various color presentations, low power consumption, rapid reaction time, compact size and long life time. Due to these characteristics, LEDs become the next generation light source candidate. Currently, the high power blue and green LEDs are applied in display backlight modules, general lighting, mobile lighting and other applications.
Although LEDs have taken the place of conventional light sources, their efficiency still needs further improvement. The improvements of LED chip performance can be divided into two types; first the transformation efficiency between the injection carrier number to the generated photon number in relation to the internal quantum efficiency (IQE), and second, the generated photon extraction efficiency to the outside ambient, quantified by the light-extraction efficiency (LEE). The major limitation to the light extraction efficiency is the trapping of light due to the low critical angle at the GaN/air interface. Generally, 76% of the photons are trapped inside a planar GaN LED . The refractive index of GaN is 2.5 at 460 nm whereas that of air is 1.0 such a large difference in refractive index restricts the LEE in terms of both Fresnel loss and the total internal reflection (TIR). The enhancement of LEE is an important issue to increase the LEDs performance because most of emitted photons were trapped by the waveguide effect. The enhancement also reduces the number of re-absorbed photons. Most re-absorbed photons are transformed back into heat which causes decays of the quantum efficiency, especially in high current operations. Various methods, including chip shaping , patterned sapphire substrates (PSS) [3–5], imprinting technique [6, 7], the fabrication of photonic crystals (PhCs) [8–12], and surface roughness/texture onto the semiconductor and ambient interfaces [13, 14] have been proposed to enhance the light extraction efficiency.
Membrane-supported 2D-PhCs with the photonic bandgap (PBG) that inhibits the propagation of guided modes in the membrane were utilized to force the spontaneous emission into radiative modes [15–17]. However, this phenomenon was successfully observed only in low temperature operation conditions. The periodic modulation of the refractive index in the PhCs serves as an optical grating to couple guided modes from the semiconductor slab to air, thus increasing the LEE of the LEDs and modulating the out-coupled far-field distribution [18, 19]. In these cases, the 2D-PhCs operate mostly outside the PBG spectral range acting as a 2D diffraction grating placed directly adjacent to the multi-quantum-wells (MQWs). To further improve the modulation of the diffraction grating, cap-layer mode (CLM)  and embedded air-gap PhCs [12, 21, 22] methods, which offer better interaction between the diffraction structure and the guided modes, can be applied. In addition, by combining the m-plane GaN with embedded air-gap PhCs , strongly polarized light extraction can be obtained.
In this study, we experimentally investigate the light extraction of GaN 1D grating to simplify the phenomenon of the light extraction led by diffraction. We use a dark field angle-resolved photoluminescence (ARPL) spectrometer to demonstrate that the light extraction of the waveguide mode inside the LED is highly polarization dependent. The extraction efficiency is relatively high as the dispersion line of the waveguide mode is coincident with the dispersion of the folded free photon band. The far-field angle distribution of the LED shows high light extraction enhancement at large angles. This property can be used for display backlight modules and street lights .
2. Description of fabrication processes and measurement setup
Figure 1 shows a schematic representation of the investigated structure, the InGaN/GaN MQWs blue LED with surface relief structures. The LED wafer used in this study was grown using metal organic chemical vapor deposition (MOCVD) technology. The GaN film is grown on the c-face (0001) 2-inch diameter sapphire substrate. The total thickness of the GaN epitaxy layer, including the nucleation layer, buffer layer, n-GaN, MQWs, electron blocking layer and p-GaN and so on, is about 5μm. The peak wavelength of the GaN wafer is designed to be 460nm. A 1D grating was fabricated on the GaN film using e-beam lithography and inductively coupled plasma (ICP) dry etching techniques. The grating periodicity is denoted by Λg. Five samples with periods of 0.3μm, 0.5μm, 0.75μm, 1μm and 2μm are made.
Deep etching of grating ensures that all the trapped waveguide modes tend to have a higher couple out efficiency. However, in order to avoid the non-radiative lose arisen from the sidewall of the etching grating. The etching depth of the grating is shallow. The etching depth, 0.18μm, of the 1D grating is measured using atomic force microscopy (AFM). The thickness of the p-GaN is 0.2μm, Therefore, the grating is adjacent to the topmost of the MQWs. The refractive index profile is shown in Fig. 1(b). The thickness of the GaN thin film layer is about 5μm which can support tens of TE and TM waveguide modes.
A schematic representation of the angle-resolved photoluminescence spectrum (ARPL) setup is shown in Fig. 2 . The pumping source of the ARPL spectrum is a diode laser with a wavelength of 405nm and an output power of 17mW. The pumping light normally impinges on the sample from the sapphire substrate to the grating structure. The polarization of the laser is controlled by a linear polarizer. Two orthogonal polarization states, TE and TM, are used through all of the ARPL measurements. Here, TE is defined as the electric field parallel to the grating grooves and TM is defined as the magnetic field parallel to the grating grooves. The grating grooves are aligned to be normal to the optical table. Therefore, the TE (TM) polarization is vertical (horizontal) polarization. The emission light is collected by a multimode fiber with a core diameter of 600μm. The working distance between the fiber end and the sample is 5cm. Therefore, the minimum precision of the angle is about 0.7°. The polar emission angle, i.e. the collection angle, is denoted as θ.
In the light extraction process, the GaN grating will influence the polarization of the emitted light. To study these effects, the polarization-dependent far-field angular distributions are examined through a linear analyzing polarizer with a polarization transmission axis normal to the polarizer of the pumping source. Similar to the pumping source; the polarization-dependent photoluminescence (PL) signal can be measured by placing a linear analyzing polarizer in front of the multimode fiber. Although the pumping source is polarized, the excited PL signal presents a spontaneous emission nature which is unpolarized. Therefore, the pumping source can be shuttered using the cross polarizer set. Thus, we call this instrument the dark-field ARPL spectrometer. The PL signal can still be detected due to its random polarization. When the pumping source is TE-polarized, the output fiber collects the TM-polarized PL signal. We call this type of PL measurement a TE-TM state. When the pumping source is TM-polarized, the output fiber collects the TE-polarized PL signal. We call this type of PL measurement the TM-TE state. The emissions of the structure are recorded as a function of both emitting wavelength and collecting angle using a computer controlled rotating stage to support the structure being examined.
3. Angle-resolved photoluminescence spectrum of patterned InGaN/GaN MQWs LED
First, in order to be compared the optical properties of the 1D GaN LED, the ARPL spectrum of an InGan/GaN MQWs bare chip, i.e. without any patterned structure, is measured as shown in Fig. 3 and presents a broad emission peak with a center wavelength of 450nm. The negative and positive collecting angles represent the TM-TE state and TE-TM state, respectively. Results for both polarization states were combined in a single figure with the same color scale. The dark regions correspond to a lower PL signal. Figure 3 also shows broadly periodic oscillating PL signals which arise from the interference between the forward (Air/GaN interface) and back (GaN/sapphire) scattered modes, i.e. the Fabry-Perot (FP) resonance. Through integrating the PL signal in all wavelengths and the collection angles, it can be found that the PL signal of the TE-TM state is 1.13 fold higher than that of the TM-TE state. This is because the TE-polarized PL signal suffers from relatively higher Fresnel reflection than TM-polarized ones.
Figure 4 shows the ARPL spectra of InGaN/GaN MQWs with a grating period of 0.3μm, and 0.75μm. The fiber collects the PL signal along the grating k-vector direction. The sharp and dense lines are due to the extraction of the wave guided modes propagating along the GaN slab waveguides formed by the GaN epitaxial layers between the sapphire substrate at the bottom and air on top. The ARPL shows that the waveguide modes are coupled out by the grating. From the TM-TE case, the dispersion lines of the waveguide modes can be clearly recognized at collection angles from −18° to −23° (high order waveguide modes) and −36° to −50° (low order waveguide modes). In contrast, for the TE-TM case, only the dispersion lines located at collection angles of 22° to 35° can be observed. The oscillation at other collecting angle is less intense. This shows that the light extraction is highly polarization dependent. In addition, the white dashed line shown in Fig. 4(a) represents the cutoff of the waveguide mode extraction which can be simply predicted by the reciprocal space of PhCs. It is interesting that the dispersion for the TE and TM planar waveguide modes are very close for such a thick planar waveguide. Since the TE and TM waveguide mode cannot be simultaneously coupled out, it suffers from low light extraction efficiency.
As the dispersion of the planar waveguide mode coincides with the free-photon dispersion, the light extraction is efficient. There is only one folded free-photon dispersion line shown in Fig. 4(a). In addition, the dispersion line is tilted in the inverse direction to the planar waveguide modes. The dispersion of the folded free-photon is not coincident with the waveguide dispersion. The PL signal of the waveguide dispersion line at θ = 39° and λ = 455nm is almost identical to the adjacent waveguide dispersion line. The area of the reduced Brillouin zone is deceased for an increasing grating period. Therefore, more repeated dispersion lines can be observed in the ARPL spectrum. For Λg = 0.75μm, the ARPL presents four folded free photon dispersion lines, as shown in Fig. 4(b). One of the dispersion lines is coincident with the high order planar waveguide modes. The PL signal of the waveguide dispersion line at θ = 39° and λ = 455nm is 1.35-fold higher than the adjacent waveguide dispersion line. Theoretically, the high order waveguide has relatively low power compared to the low order one. However, the experimental results still present high extraction efficiency. Owing to the fact that the thickness of a conventional blue LED is about 4~5μm, the difference between the dispersion of TE and TM planar waveguide modes is small. Therefore, the dispersion lines for TE and TM polarized light are barely distinguishable. Nevertheless, it can be seen that the extraction efficiency is high as indicated by the coincidence of the dispersion of waveguide modes and the folded free-photon band. Consequently, the dispersion line of the free photon band structure can be modified through modifying the periodicity of the GaN grating. As a result, the far-field angular distribution of the LED can be manipulated.
Here, we theoretically investigate the dispersion characteristics of the GaN planar waveguide. The index of the InGaN is assumed to be identical to that of the GaN. The refractive index of the GaN is measured using a spectroscopic ellipsometer. The ellipsometer parameters are fitted with three Lorentz peaks as shown in the following equation.24]. The Fresnel phase delays are determined by the incident angle of the corresponding waveguide mode and the refractive indices between the boundaries. The polarization dependent property is arisen from the phase delay. From the discrete propagation angle, θd. one can calculate the out-coupled waveguide modes as functions of the wavelengths and collection angles by using the grating equation.
The calculated results for Λg = 0.3μm (Fig. 5 ) show a fair agreement with the experimental results in terms of both the cutoff conditions of light extraction as well as the extracted waveguide mode distribution. In addition, because the thickness of conventional blue LED is about 4~5μm, the dispersion line of each waveguide mode is dense. From Eq. (2), the propagation angle θd depends on the total phase deference within one round trip. The phase deference is dominated by waveguide thickness for a thick waveguide thickness. The influence arisen from Fresnel phase delay is relatively small. In addition, the polarization dependent property is arisen from the Fresnel phase delay. Therefore, the theoretical dispersion lines for TE and TM polarized light are barely distinguishable.
From the examination of the ARPL spectra, the outgoing light can be divided into four parts: one of which is the directly transmissive light refracted by the p-GaN/Air interfaces. This part can be easily calculated using Fresnel equation. The directly transmissive part can be optimized by modifying the geometric of the patterned structure. The second part is the FP resonance causing from the multiple beams interference. The third part is the waveguide mode diffracted by the surface relief structure. This part can be evaluated using the Eq. (3). The final part is the band-folded free-photon dispersion. As shown in Fig. 4, the dispersion line of the free photon band structure is only observable in the TM-TE mode indicating a strong TE polarization with few TM components.
4. Polarization-dependent light extraction
For the GaN grating sample, the enhancement factor of the TM-TE mode is higher than that of the TE-TM mode. From the ARPL spectrum (Fig. 4), the dispersion of grating can only be observed in the TM-TE mode. Nevertheless, the light extraction efficiency is dominated by the extracted light from the grating dispersion. Consequently, the overall light extraction efficiency of the TM-TE mode is higher than that of the TE-TM mode. The enhancement factor for the GaN grating samples was measured using the ARPL, as shown in Fig. 6 . Here, the enhancement factor is the ratio between the PL signal of the patterned and unpatterned structures. The PL signal is the sum of the signal of the wavelength from 430nm to 470nm and the collection angle from 5° to 60°. The experimental results show that the enhancement factor is about 4 and 3 for the TM-TE and TE-TM modes, respectively. As the grating period is increased, the enhancement factor decreases. The enhancement factor is down to 2.6 for both the TM-TE mode and TE-TM mode.
Here, we have to emphasize that only the PL signal emitting along the grating reciprocal wavevector is collected. The ARPL spectrum of the GaN grating sample collected along the grating grooves is almost identical to that of the bare unpatterned LED chip because the PL signal does not obtain any additional momentum from the grating reciprocal wavevector along the direction of the grating grooves.
Figure 7 depicts the arbitrary PL intensity versus collection angles and different grating periods. There are two mechanics that explain the PL intensity variation versus the collection angles and grating periods. First the coincidence of free photon and the wave guide modes, and second the waveguide mode coupled outer by the grating period. The wave guided modes are diffracted at specific angles so that the photon flux integration for a specific collection angle presents a wide range distribution in both TE-TM and TM-TE modes for all periods. A grating period of 1μm presents the maximum polarization separation efficiency in PL intensity. The exciting laser leakage peak is located at the collection angle of 40° in the TE-TM state for the period of 0.75μm.
The LED with a 1D grating structure presents a non-radial-symmetric far-field distribution which can be applied for non-radial-symmetric optical systems, for example a liquid crystal display (LCD) backlight module. In addition, the far-field angle distribution shows a large enhancement in large collecting angles. This kind of far-field angle distribution is useful for street lights with a low glare effect .
In this study, we investigate the polarization dependent ARPL spectra of InGaN/GaN QWs LED with 1D gratings using a dark field angle-resolved photoluminescence spectrometer. It is found that the TE and TM waveguide modes cannot be simultaneously coupled out so that light extraction is polarization dependent. The ARPL spectrum also reveals that the extraction efficiency is relatively high as the dispersion line of the waveguide mode is coincident with the folded free-photon dispersion of the 1D GaN grating. Through modification of the periodicity of the GaN grating, the dispersion line of the free photon band structure can be modified. Therefore, the far-field angular distribution of the LED can be manipulated. 3.8-fold light extraction efficiency enhancement along the grating vector direction is observed. The LED with 1D grating structure presents a non-radial-symmetric far-field distribution which can be applied for non-radial-symmetric optical systems, for example an LCD backlight. In addition, a conceptually simple approach to SP dispersion measurement using the dark field ARPL is presented.
The authors are grateful for the financial support of this research received from the National Science Council of Taiwan, R.O.C. under grant number NSC 99-2221-E-259-011 and NSC 100-2120-M-002-008.
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