**4. Improvement of the light-emitting efficiency by the imprint structure**

### **4.1 The Effect of surface structures**

As previously discussed, the light-emitting efficiency can be improved by a roughened surface, which can be achieved by the imprint of a surface structure. A uniform size and the periodicity of the structures benefit the homogeneity of the emitted light. In 2007, Chang et al. [26] applied hot embossing nanoimprint lithography to imprint the PMMA into a transparent conductive layer ITO of an LED. Inductively coupled plasma (ICP) etching was used for cleaning the process residues to expose the ITO, followed by etching in hydrochloric acid to produce periodic ITO holes, which were 90nm in depth, 0.85 μm in diameter, and 0.5μmin spacing. Compared to conventional LEDs, the periodic structure of

Fig. 6. Schematics of the UV-assisted roller imprint equipment

which applies nickel film on the roller [22, 23]. If the substrate is flexible, structures can be reproduced massively via continuous roll-to-roll process. This method is suitable for the thermoplastic polymer films. The diffuser film used for current backlights of TFT-LCD panel can be fabricated via roll-to-roll process transferring of the microstructure to the PET film by roller imprint. The roller imprint, in practice, can adapt a process similar to the aforementioned imprint process. That is, PDMS soft mold is applied over the surface of the quartz roller, thereby enabling the continuous imprinting process, as shown in Figure 6. [24]. Various light sources can be used to harden the imprint material. For example, the hot embossing imprint can be heated up rapidly using an infrared light or an infrared laser [25]. The UV-hardening can be achieved via the UV light or UV laser. Using the laser has the

Continuous imprinting process is demonstrated using the roller imprint method. Instead of imprinting the entire surface at once, the roller and the substrate are imprinted progressively, rendering the roller imprint useful for the fabrication of structures on a large

benefit of using optical lenses to focus the beam to the ideal imprint area.

Fig. 6. Schematics of the UV-assisted roller imprint equipment

**4.1 The Effect of surface structures** 

**4. Improvement of the light-emitting efficiency by the imprint structure** 

As previously discussed, the light-emitting efficiency can be improved by a roughened surface, which can be achieved by the imprint of a surface structure. A uniform size and the periodicity of the structures benefit the homogeneity of the emitted light. In 2007, Chang et al. [26] applied hot embossing nanoimprint lithography to imprint the PMMA into a transparent conductive layer ITO of an LED. Inductively coupled plasma (ICP) etching was used for cleaning the process residues to expose the ITO, followed by etching in hydrochloric acid to produce periodic ITO holes, which were 90nm in depth, 0.85 μm in diameter, and 0.5μmin spacing. Compared to conventional LEDs, the periodic structure of

surface.

an LED with size 350×350μm2showeda 12% improvement in the light-emitting efficiency with an input current of 20 mA. Huang et al. [27] fabricated p-GaN nanostructures on the surface of a 1×1 mm2 high-power green LED chip. An SiO2 thin film was first deposited onto p-GaN, and a silicon mold was used for the hot embossing imprint process. Reactive ion etching (RIE) was used for cleaning the residues of the imprinting material and SiO2, to complete the transferring of the structure using SiO2 as the resist. A p-GaN nanostructure of 75 nm depth was later produced viaICP etching. The residual SiO2 was removed using a buffer oxidation etchant (BOE). Finally, an ITO thin film was deposited onto p-GaN. Due to high scattering effect, the light-emitting efficiency of the nanostructured LED was 48% higher than that of conventional LEDs with an input current of 350 mA. Zhou et al. [28] used the soft UV-nanoimprint lithography to fabricate nanostructures onto a 1×1 mm2 p-GaN high-efficiency LED chip. A porous membrane mold with a nanohole approximately100 nm in size was first fabricated using theanodic aluminum oxide (AAO) method. A two-inch PDMS soft mold was replicated for UV-nanoimprint process. The process followed was similar to that of Huang et al. [27]. The light-emitting efficiency of the unpackaged nanostructured LED chip was 10.9% higher than that of conventional LEDs with an input current of 350 mA. The enhancement of efficiency would be 48% when the LED chip is packaged.

Other than the imprint method that imprints structures onto the LED surface via etching, Lee et al. [29] fabricated the microstructure directly onto the ITO. Figure 7 is the SEM image of the one-dimensional and two-dimensional imprint structures. The imprinting material is not a conventional polymer, but is a spin on glass (SOG), which is similar to SiO2. The chemical and mechanical properties of this material are superior when compared to the polymer.

Fig. 7. SEM images of the one-dimensional and the two-dimensional imprint structures

Figure 8 is the schematic diagram that combines the imprint and the conventional LED fabrication process. The mesa etching (to expose the n-GaN) was first achieved usingICP. The electrode patterns were defined and deposited with p-type and n-type electrodes to fabricate conventional LED chips. After the hot embossing imprint process, the imprinting material on the electrodes was removed. Finally, the electrical and optical properties of the

Improving the Light-Emitting Efficiency of GaN LEDs Using Nanoimprint Lithography 183

Comparing the micro-pyramid-structured LED (3 μm width and 2 μm spacing) with the nano-pyramid-structured LED (750 nm width and 500nm spacing), the light output power of the nano-pyramid-structured LED, which has a more densified structure, is superior to that of the micro-pyramid-structured LED as the input current increases

Fig. 10. A comparison of the light output powers of the microstructured, nanostructured,

The study of the roller imprint in the application of fabricating LEDs is shown in Figure11. The light output power of the micro-cylinders with different heights increases in conjunction with the current. Theoretically, taller cylinder LED has more surface area to emit light compared to the short cylinder. However, as shown in the results, the light output power was higher for the imprint cylinder-structured LED with 3μm diameter, 2μm spacing, and 1.5μm height, compared to the cylinder-structured LED with 2.5μm or 5.0 μm height. This is because of the light absorption from the imprinting material, and thus, an optimal height of the imprint structure exists that maximizes the light emitting efficiency

(Figure 10.) [30].

and conventional LEDs.

[24].

LED were then measured. The results showed the forward bias of the imprinted LED is extremely similar to that of the conventional LED. Compared to the electrical property of the LED fabricated by etching above the p-GaN, the electrical property of the LED produced via this method was not damaged.

Fig. 8. Process flow of the conventional LED chip and imprint process

Regarding optical property, for a size of 300×300μm2, composed of a cylinder array 3μm in diameter and 2μm in spacing of the LED chip, the efficiency enhancement is 26.2% with 20 mA current. Figure 9 is the diagram that illustrates the possible optical paths of a light incident to cylinder and pyramid structures, showing that the surface structures are beneficial to ruin total internal reflection.

Fig. 9. The possible optical routes of an LED light incident to a micro-cylinder and to a pyramid structure

LED were then measured. The results showed the forward bias of the imprinted LED is extremely similar to that of the conventional LED. Compared to the electrical property of the LED fabricated by etching above the p-GaN, the electrical property of the LED produced via

Fig. 8. Process flow of the conventional LED chip and imprint process

beneficial to ruin total internal reflection.

pyramid structure

Regarding optical property, for a size of 300×300μm2, composed of a cylinder array 3μm in diameter and 2μm in spacing of the LED chip, the efficiency enhancement is 26.2% with 20 mA current. Figure 9 is the diagram that illustrates the possible optical paths of a light incident to cylinder and pyramid structures, showing that the surface structures are

Fig. 9. The possible optical routes of an LED light incident to a micro-cylinder and to a

this method was not damaged.

Comparing the micro-pyramid-structured LED (3 μm width and 2 μm spacing) with the nano-pyramid-structured LED (750 nm width and 500nm spacing), the light output power of the nano-pyramid-structured LED, which has a more densified structure, is superior to that of the micro-pyramid-structured LED as the input current increases (Figure 10.) [30].

Fig. 10. A comparison of the light output powers of the microstructured, nanostructured, and conventional LEDs.

The study of the roller imprint in the application of fabricating LEDs is shown in Figure11. The light output power of the micro-cylinders with different heights increases in conjunction with the current. Theoretically, taller cylinder LED has more surface area to emit light compared to the short cylinder. However, as shown in the results, the light output power was higher for the imprint cylinder-structured LED with 3μm diameter, 2μm spacing, and 1.5μm height, compared to the cylinder-structured LED with 2.5μm or 5.0 μm height. This is because of the light absorption from the imprinting material, and thus, an optimal height of the imprint structure exists that maximizes the light emitting efficiency [24].

Improving the Light-Emitting Efficiency of GaN LEDs Using Nanoimprint Lithography 185

In an ideal non-dispersive medium, the permittivity and permeability are independent of the frequency of the electromagnetic wave. Therefore, a linear relation between the wave number and the frequency exists. However, nearly all media are dispersive to a certain extent. That is, the permittivity and permeability are dependent on the frequency and lead to a nonlinear relation between the wave number and the frequency. In such a case, the

When the medium (where the electromagnetic wave travels in) is a periodic structure in space with a periodicity comparable to the wavelength of the wave, the permittivity can also be regarded as a periodic distribution (Bloch's theorem) in space (assuming the permeability is 1). Though solving the Helmholtz equation in these periodic medium results in a harmonic solution that is similar to above equation, this solution carries the information of the periodic structure of the medium. The photonic crystal is a medium with such a periodically distributed permittivity, and the spatial periodicity of a photonic crystal is

The solution to Helmholtz equation can be affected by the following factors: polarization of the electromagnetic wave, the interaction length between the electromagnetic wave and the photonic crystal, and the permittivity difference between the periodic structure and the substrate. Therefore, when the electromagnetic wave enters the photonic crystal, different eigen modes are formed, capable of interfering constructively or destructively to create energy bands. If the eigen modes form destructive interference in a specific direction, such a

Because the existence of the photonic band gap is related to the frequency and the propagation direction of the electromagnetic wave, the photonic band gap can be used as a reflector for the large angle bending of electromagnetic wave propagation in integrated optics. Applying the photonic crystal to the LED chip can manipulate the directions of emitted photons. When the photonic crystal structure suppresses the photons with large emitting angular, the LED can be approximated a collimated light source. Conversely, when the photonic crystal structure suppresses the photons with small angular, the LED behaves akin to an expansion light source. This is the underlying principle of the far-field light pattern effect found in the photonic crystal. In addition to the far-field effect, the photonic crystal can be used to form a photonic bandgap within the active region of the LED. In this manner, photons generated by the active region are forced to escape the active region promptly, hence increasing the light-extraction efficiency [31]. If the photonic crystal is applied to the LED surface, high order diffraction lights are generated by the momentum compensation that occurred during the interaction of the photonic crystal and the guided photons. The otherwise confined photons in the LED can be coupled to the free space by the diffraction, which is another means to improve the light-extraction efficiency of the LED. Researchers at U.C. Santa Barbara conducted a series of discussions regarding the photonic

Analyzing the escape paths of the emitted photons from LEDs provided the observation that the chip surface's escape photons comprise 12 % of photons generated in the active region when a highly reflective coating is applied to the sapphire substrate. Approximately 22 % of the photons are confined within the sapphire substrate, while 66 % of the trapped photons are located in the chip region. Trapped photons, confined in the air/sapphire/GaN interfaces, are known as guided light. A longer interaction length between the photonic crystals and emitted

photons typically results in an increased optical modulation effect on the guided light.

group velocity and the phase velocity of the wave would not be the same.

slightly smaller than the wavelength of the wave.

phenomenon is called the photonic band gap.

crystal effect [32-35].

Fig. 11. A comparison between the light output power of micro-cylinder-structured LEDs of different height and conventional LEDs

#### **4.2 The photonic crystal effect**

The behavior of an electromagnetic wave traveling in a homogeneous medium can be obtained by solving the Helmholtz equation (the Helmholtz equation is derived from Maxwell's equations). The Helmholtz equation is:

$$\nabla^2 \mathbf{E} + k^2 \mathbf{E} = 0$$

where E is the electromagnetic wave and *k* is the wave number. Combined with the boundary conditions, Helmholtz equation can be solved via a harmonic solution. While solving for the equation, the wave number, frequency (ω=2π×ν), permittivity (ε), and permeability (μ) must satisfy below equation:

> 2 2 *k*

Fig. 11. A comparison between the light output power of micro-cylinder-structured LEDs of

The behavior of an electromagnetic wave traveling in a homogeneous medium can be obtained by solving the Helmholtz equation (the Helmholtz equation is derived from

2 2 E E0 *k*

where E is the electromagnetic wave and *k* is the wave number. Combined with the boundary conditions, Helmholtz equation can be solved via a harmonic solution. While solving for the equation, the wave number, frequency (ω=2π×ν), permittivity (ε), and

> 2 2 *k*

different height and conventional LEDs

Maxwell's equations). The Helmholtz equation is:

permeability (μ) must satisfy below equation:

**4.2 The photonic crystal effect** 

In an ideal non-dispersive medium, the permittivity and permeability are independent of the frequency of the electromagnetic wave. Therefore, a linear relation between the wave number and the frequency exists. However, nearly all media are dispersive to a certain extent. That is, the permittivity and permeability are dependent on the frequency and lead to a nonlinear relation between the wave number and the frequency. In such a case, the group velocity and the phase velocity of the wave would not be the same.

When the medium (where the electromagnetic wave travels in) is a periodic structure in space with a periodicity comparable to the wavelength of the wave, the permittivity can also be regarded as a periodic distribution (Bloch's theorem) in space (assuming the permeability is 1). Though solving the Helmholtz equation in these periodic medium results in a harmonic solution that is similar to above equation, this solution carries the information of the periodic structure of the medium. The photonic crystal is a medium with such a periodically distributed permittivity, and the spatial periodicity of a photonic crystal is slightly smaller than the wavelength of the wave.

The solution to Helmholtz equation can be affected by the following factors: polarization of the electromagnetic wave, the interaction length between the electromagnetic wave and the photonic crystal, and the permittivity difference between the periodic structure and the substrate. Therefore, when the electromagnetic wave enters the photonic crystal, different eigen modes are formed, capable of interfering constructively or destructively to create energy bands. If the eigen modes form destructive interference in a specific direction, such a phenomenon is called the photonic band gap.

Because the existence of the photonic band gap is related to the frequency and the propagation direction of the electromagnetic wave, the photonic band gap can be used as a reflector for the large angle bending of electromagnetic wave propagation in integrated optics. Applying the photonic crystal to the LED chip can manipulate the directions of emitted photons. When the photonic crystal structure suppresses the photons with large emitting angular, the LED can be approximated a collimated light source. Conversely, when the photonic crystal structure suppresses the photons with small angular, the LED behaves akin to an expansion light source. This is the underlying principle of the far-field light pattern effect found in the photonic crystal. In addition to the far-field effect, the photonic crystal can be used to form a photonic bandgap within the active region of the LED. In this manner, photons generated by the active region are forced to escape the active region promptly, hence increasing the light-extraction efficiency [31]. If the photonic crystal is applied to the LED surface, high order diffraction lights are generated by the momentum compensation that occurred during the interaction of the photonic crystal and the guided photons. The otherwise confined photons in the LED can be coupled to the free space by the diffraction, which is another means to improve the light-extraction efficiency of the LED. Researchers at U.C. Santa Barbara conducted a series of discussions regarding the photonic crystal effect [32-35].

Analyzing the escape paths of the emitted photons from LEDs provided the observation that the chip surface's escape photons comprise 12 % of photons generated in the active region when a highly reflective coating is applied to the sapphire substrate. Approximately 22 % of the photons are confined within the sapphire substrate, while 66 % of the trapped photons are located in the chip region. Trapped photons, confined in the air/sapphire/GaN interfaces, are known as guided light. A longer interaction length between the photonic crystals and emitted photons typically results in an increased optical modulation effect on the guided light.

Improving the Light-Emitting Efficiency of GaN LEDs Using Nanoimprint Lithography 187

a triangular lattice and a complex basis. The unit cell is formed by 7 holes, and a is the hole interval. The lattice constant of photonics crystalis b a(1 3) . Applying this photonic crystal structure to the surface of GaN LEDs resulted in a high order crystal, thereby diffracting the light into air, instead of onto the substrate. Diffraction occurred in the various Brillouin zone of the reciprocal lattice, demonstrating the omnidirectionality of the A7

Shields et al. [44] used the higher rotational symmetry of the photonic quasicrystals (PQCs) to achieve omnidirectionality. The designed PQCs patterns were based on square-triangular tiling using three different pitches: 450, 550, and 750 nm. Shield's experiments revealed a plateau on the far-field profile that was independent of the measurement angle. The finite-

Increasing light-extraction efficiency and adjusting the emission profile can be achieved simultaneously by optimizing the coupling distance between the emitted photon and the photonic crystal. The momentum of photons parallel to the photonic crystal plate are coupled with the reciprocal lattice constant of the photonic crystal via the diffraction effect, generating photons with momentum perpendicular to the photonic crystal plate. Using an appropriate reciprocal lattice constant can increase the number of photons within the escape cone. An LED emission profile can also be adjusted using the same approach [34]. A triangular lattice photonic crystal is applied to both transparent electrodes of the LED. On the ITO side, the depth and the area of the photonic crystal is 120 nm and 400x400 μm2, respectively. On the Ni/Au side, the depth and the area of the photonic crystal is 250 nm and 500x500 μm2, respectively. The lattice constants of the photonic crystal are 185, 200, 215, and 230 nm. The experiment demonstrated that the vertical emission profile peaks occur at the second order diffraction (periodicity of photonic crystals/wavelength=0.5), and corresponds to 215 nm of lattice period/430 nm in ITO thickness, and 200 nm of lattice period/405 nm in Ni/Au thickness. Changing the lattice constant altered the vertical emission of various modes. In this

Methods to modulate the far-field light patterns and to improve the light-extraction efficiency of LEDs using sub-microstructures lead to that most photons confined within the LED can be coupled outside the LED, using photonic crystals. Therefore, coupling photons to the escaping cone is a major mechanism enabling photonic crystals to improve the light extraction efficiency and to adjust the far-field light pattern. Though the depth, the lattice constant and the filling factors of the photonic crystal adjust the mode of the trapped photons to enter the air lightline, the polarization and propagation directions of the photons interacting with the photonic crystals require consideration. Photons generated by the spontaneous emission process in the LED have poor temporal and spatial coherences, and therefore, the roughening effect caused by the photonic crystal should also be considered. Numerous studies have investigated the application of nanoimprinted photonic crystals in

Cho et al. [45] used the nanoimprint lithography and ICP etching to fabricate photonic crystal structures of various depths onto the ITO/GaN surface of a 375 μm x 330 μm blue LED chip. Upon optical efficiency optimization, the efficiency of the packaged LED can be further enhanced by 25 %, using a 20 mA current injection. Using the 3D-FDTD simulation, light-extraction efficiency increases in correlation with the etching depth of the photonic crystals. However, the light-extraction efficiency decreases when the ratio

difference time-domain (FDTD) simulation also demonstrated similar behavior.

sample, the extraction of cap layer mode photons into air was evident.

LEDs. Examples are listed below:

(wavelength/effective refractive index) is exceeded.

structure.

The significant difference (1.4) between GaN and air refraction indices makes the GaN/air interface an excellent waveguide material, which confines photons of the active region within the GaN. Photonic crystals are used to extract the guided light into the air. Considering diffraction, the guided light-extraction efficiency is dependent on the mode of the confined photons. Photons of lower order modes are confined to the center of GaN, and prevented from interacting with the photonic crystal structures on the chip's surface, which leads to inefficient photon diffraction of the lower-order modes and limits improvements to light-extraction efficiency.

A shallow photonic crystal layer on the GaN surface slightly affects the diffraction efficiency of the guided light, and therefore, the photonic crystal structure is typically 1 μm in thickness to enhance the interaction between the photonic crystal and the guided photons. However, a deep photonic crystal layer has a reduced effective refractive index, resulting in rapid evanescence of the lower-order modes in the photonic crystal. In such circumstances, the light-extraction efficiency cannot be improved. To improve the efficiency of the shallow photonic crystal layer, David et al. [32] inserted a low-refractive index material AlxGa1-xN in the GaN to couple the lower-order photons trapped in the center of the GaN buffer layer to the GaN cap layer (Figure 12.). The diffraction efficiency of the lower-order photons substantially improved upon inserting the AlxGa1-xN.

Fig. 12. Insert a low-index layer to improve mode coupling with photonics crystal

An LED is a light-emitting device comprising point light sources that emit photons in random directions. Therefore, an omnidirectional light-extraction structure reflects photons with various modes and directions from the active layer to outside the GaN, would be an ideal photonic crystal structure. To achieve the isotropic light extraction, the photonic band gap in the various directions must be of equal efficiency. Numerous photonic crystal structures designed to achieve the aforementioned objective have been proposed, including Archimedean tilings [36], Penrose lattices [37-39] and quasicrystals [40-43]. Expanding on previous discussions regarding photonic crystals, David et al. [33] used A7 Archimedean tilings as the photonic crystal layer on GaN LEDs. The A7 photonic crystal was composed of

The significant difference (1.4) between GaN and air refraction indices makes the GaN/air interface an excellent waveguide material, which confines photons of the active region within the GaN. Photonic crystals are used to extract the guided light into the air. Considering diffraction, the guided light-extraction efficiency is dependent on the mode of the confined photons. Photons of lower order modes are confined to the center of GaN, and prevented from interacting with the photonic crystal structures on the chip's surface, which leads to inefficient photon diffraction of the lower-order modes and limits improvements to

A shallow photonic crystal layer on the GaN surface slightly affects the diffraction efficiency of the guided light, and therefore, the photonic crystal structure is typically 1 μm in thickness to enhance the interaction between the photonic crystal and the guided photons. However, a deep photonic crystal layer has a reduced effective refractive index, resulting in rapid evanescence of the lower-order modes in the photonic crystal. In such circumstances, the light-extraction efficiency cannot be improved. To improve the efficiency of the shallow photonic crystal layer, David et al. [32] inserted a low-refractive index material AlxGa1-xN in the GaN to couple the lower-order photons trapped in the center of the GaN buffer layer to the GaN cap layer (Figure 12.). The diffraction efficiency of the lower-order photons

Fig. 12. Insert a low-index layer to improve mode coupling with photonics crystal

An LED is a light-emitting device comprising point light sources that emit photons in random directions. Therefore, an omnidirectional light-extraction structure reflects photons with various modes and directions from the active layer to outside the GaN, would be an ideal photonic crystal structure. To achieve the isotropic light extraction, the photonic band gap in the various directions must be of equal efficiency. Numerous photonic crystal structures designed to achieve the aforementioned objective have been proposed, including Archimedean tilings [36], Penrose lattices [37-39] and quasicrystals [40-43]. Expanding on previous discussions regarding photonic crystals, David et al. [33] used A7 Archimedean tilings as the photonic crystal layer on GaN LEDs. The A7 photonic crystal was composed of

light-extraction efficiency.

substantially improved upon inserting the AlxGa1-xN.

a triangular lattice and a complex basis. The unit cell is formed by 7 holes, and a is the hole interval. The lattice constant of photonics crystalis b a(1 3) . Applying this photonic crystal structure to the surface of GaN LEDs resulted in a high order crystal, thereby diffracting the light into air, instead of onto the substrate. Diffraction occurred in the various Brillouin zone of the reciprocal lattice, demonstrating the omnidirectionality of the A7 structure.

Shields et al. [44] used the higher rotational symmetry of the photonic quasicrystals (PQCs) to achieve omnidirectionality. The designed PQCs patterns were based on square-triangular tiling using three different pitches: 450, 550, and 750 nm. Shield's experiments revealed a plateau on the far-field profile that was independent of the measurement angle. The finitedifference time-domain (FDTD) simulation also demonstrated similar behavior.

Increasing light-extraction efficiency and adjusting the emission profile can be achieved simultaneously by optimizing the coupling distance between the emitted photon and the photonic crystal. The momentum of photons parallel to the photonic crystal plate are coupled with the reciprocal lattice constant of the photonic crystal via the diffraction effect, generating photons with momentum perpendicular to the photonic crystal plate. Using an appropriate reciprocal lattice constant can increase the number of photons within the escape cone. An LED emission profile can also be adjusted using the same approach [34]. A triangular lattice photonic crystal is applied to both transparent electrodes of the LED. On the ITO side, the depth and the area of the photonic crystal is 120 nm and 400x400 μm2, respectively. On the Ni/Au side, the depth and the area of the photonic crystal is 250 nm and 500x500 μm2, respectively. The lattice constants of the photonic crystal are 185, 200, 215, and 230 nm. The experiment demonstrated that the vertical emission profile peaks occur at the second order diffraction (periodicity of photonic crystals/wavelength=0.5), and corresponds to 215 nm of lattice period/430 nm in ITO thickness, and 200 nm of lattice period/405 nm in Ni/Au thickness. Changing the lattice constant altered the vertical emission of various modes. In this sample, the extraction of cap layer mode photons into air was evident.

Methods to modulate the far-field light patterns and to improve the light-extraction efficiency of LEDs using sub-microstructures lead to that most photons confined within the LED can be coupled outside the LED, using photonic crystals. Therefore, coupling photons to the escaping cone is a major mechanism enabling photonic crystals to improve the light extraction efficiency and to adjust the far-field light pattern. Though the depth, the lattice constant and the filling factors of the photonic crystal adjust the mode of the trapped photons to enter the air lightline, the polarization and propagation directions of the photons interacting with the photonic crystals require consideration. Photons generated by the spontaneous emission process in the LED have poor temporal and spatial coherences, and therefore, the roughening effect caused by the photonic crystal should also be considered.

Numerous studies have investigated the application of nanoimprinted photonic crystals in LEDs. Examples are listed below:

Cho et al. [45] used the nanoimprint lithography and ICP etching to fabricate photonic crystal structures of various depths onto the ITO/GaN surface of a 375 μm x 330 μm blue LED chip. Upon optical efficiency optimization, the efficiency of the packaged LED can be further enhanced by 25 %, using a 20 mA current injection. Using the 3D-FDTD simulation, light-extraction efficiency increases in correlation with the etching depth of the photonic crystals. However, the light-extraction efficiency decreases when the ratio (wavelength/effective refractive index) is exceeded.

Improving the Light-Emitting Efficiency of GaN LEDs Using Nanoimprint Lithography 189

them to be applied to nonplanar surfaces. Obducat's solution has already found a significant number of industrial users, including two LED manufacturers from Taiwan, Luxtalek and

The PSS on the micrometer scale has been experimentally demonstrated to improve the light extraction efficiency of LEDs significantly. Furthershrinking the size of PSS can increase the

Changing the condition on the current micron scale PSS process usually requires careful/tedious optimization of the subsequent epitaxial process parameters. By shrinking the patterning size into nanoscales, this optimization step can be neglected, facilitating a

A thick buffer layer is typically necessaryto smooth out the PSSpatterned surface prior to the epitaxy process. If the size of the PSS structures is in nanoscales, the required buffer layer is thin and may be achieved by the side growth of the epitaxial layer, streamlining the LED

Huang et al. [58] created polymer nanostructures on the sapphire substrate using the thermal pressing technique. The imprint material also acted as the resist layer for the ICP etching process. A concave NPSS pattern was obtained with a periodicity of 450 nm, a diameter of 240 nm, and a depth of 165 nm. SEM measurements showed that the GaN did not fulfill the the NPSS holescompletely, causing a hole array at the GaN/NPSS interface. Due to the difference in the refraction indices between these holes and the surrounding matrix, the light originating from the MQW underwent scattering and multiple reflections at the GaN/NPSS interface. The light was bounced back to the GaN/Air interface, increasing the likelihood of light escaping the LED. Under a 20 mA electrical current injection, the NPSS was found to enhance the light extraction efficiency by as much as 1.33 times that ofconventional LEDs. Huang et. al. [59] used a similar thermal pressing technique combined with ICP etching to create a convex NPSS with a periodicity of 750 nm and a diameter of 450 nm. The height of the NPSS structures was 182 nm. Under a 20 mA electrical excitation, the 300×300 μm2 NPSS had 35% more light-extraction efficiency compared toconventional LEDs. If the quasi-photonic crystal effect wereconsidered, the efficiency could be further increased to48%. C.C. Kao et al. [60] used a similar process for creating NPSS to study the dependance of the light extraction on the aspect ratios of the NPSS. Their experiment showed that efficiency was higher for higher aspect ratios. The efficiency was increased from 11% to 27%

Results from the micron scale PSS structures shows that increasing the aspect ratio of the PSS can also increase the light-extraction efficiency. However, the height of the ICP-etched NPSS is directly related to the size of the nanoimprinted polymer structures. Due to the high mechanical strength and the soundchemical stability, the etching selective ratio between the sapphire and the polymer resist is small, resulting in a less than desired etching depth on the sapphire substrate. Figure 13 shows the NPSS structures etched by the sulfuric acid and the phosphoric acid at high temperatures. The periodicity is 1.25 nm and the depth is 340

structural density, and hence,enhancing the light extraction efficiency even more.

Epistar.

**4.3 The Effects of NPSS** 

NPSS has three distinct advantages:

1. **Enhancing the light extraction efficiency** 

3. **Reducing the thickness of the buffer layer** 

growth process and increasing the process yield.

for aspect ratios from 2.00 to 2.50, respectively.

2. **Simplifying the process parameters** 

more rapid LED growth process.

Cheng et al. [46] applied the photonic crystal [1x1 mm2] to the green power chip and combined the omnidirectional reflector at the back of the chip. The overall efficiency increased by 88 %, with a collimated far-field light pattern.

Nao et al. [47] attached a photonic crystal in a triangular lattice (diameter=100~250 nm, height=120 nm) to the flip chip between the sapphire and the GaN, allowing the diffractive coupling of photons to enter the air from the back of the sapphire substrate. The far-field pattern was collimated, and a lobe was observed near the horizontal direction. The lobe was attributed to the intermixing of light emitted from the side and front of the chip.

Huang et al. [48] applied quasi-photonic crystals to both n- and p-GaN layers in a vertical LED. The optical efficiency exceeded that of a single photonic crystal LED.

Byeon et al. [49] created a hexagonal array of holes with a diameter of 250 to 380 nm and 600 to 900 nm of pitch as the photonic crystal layer on the ITO of a green LED, using soft imprint technology (to prevent damages on the GaN LED). The light emitting efficiency improved maximally by 25 % under a 20 mA current injection.

Khokhar et al. [50] compared e-beam lithography and nanoimprinting technology concerning the creation of photonic crystal structures. Though the e-beam lithography created a more precise and accurate pattern, it is not suitable for mass production, and while nanoimprinting technology is suitable for mass production, several issues remain. For example, the residual layer must be removed using etching, which limits the practical thickness of the photonic crystal layer, and the imprint material requires a high-etching selectivity.

The photonic crystal structure can be applied quickly and accurately to the surface and the interior of the LED via the nanoimprint lithography technique [51, 52]. However, because the electrical characteristics of the LED will be degraded using dry etching of the p-GaN, T. A. Truong et al. [53] applied sol gel titania to the substrate (soft imprint plus a 300 C solidification process) to form titanium oxide photonic crystal structures on the LED without damaging the LED surface.

Motivated by the great potential of photonic crystal application on LED, several equipment manufacturers have devised intriguing strategies to develop this field. Molecular imprints Inc. [54] sprays the imprint material to a 6" quartz substrate. Using a step-and-repeat exposure procedure, they progressively transfer the structure of a hard mother mold (5×5 mm2) to the entire area of the quartz substrate, which now acts as a substitute mold. The nanoimprint of the 3" GaN LED occurs from the quartz mold. Due to the hard imprint nature of this technique, the cleanness of the mold and the substrate play crucial roles. Suss MicroTec Lithography GmbH [55] uses a PDMS soft mold adhered to the substrate by the vacuum force before imprinting. To prevent trapping air between the mold and the substrate during imprinting, the PDMS mold is gradually released from the vacuum force until the mold and the imprinting material are held together by the capillary force. After UV exposure, the gradual vacuum force removes the mold once more. EV Group Inc. [56] also adopted PDMS molds. The difference is that the mold comprises two soft PDMS layers with different degrees of hardness. The harder layer is the outer layer that directly touches the imprinting materials, which is believed to solve the rigidity issue of a typical soft mold, and prevent the deformation of the mold. Obducat AB [57] uses non-reusable polymer stamp as the mold. The polymer stamp is fabricated by pressing a hard master stamp against the polymer film. Once the polymer stamp is used, it is disposed. Due to its single usage nature, the stamp has no lifetime issues. In addition, the flexibility of the polymer stamp allows them to be applied to nonplanar surfaces. Obducat's solution has already found a significant number of industrial users, including two LED manufacturers from Taiwan, Luxtalek and Epistar.
