• 沒有找到結果。

Mechanisms of the Asymmetric Light Output Enhancements in a-Plane GaN Light-Emitting Diodes With Photonic Crystals

N/A
N/A
Protected

Academic year: 2021

Share "Mechanisms of the Asymmetric Light Output Enhancements in a-Plane GaN Light-Emitting Diodes With Photonic Crystals"

Copied!
6
0
0

加載中.... (立即查看全文)

全文

(1)

Mechanisms of the Asymmetric Light Output

Enhancements in a-Plane GaN Light-Emitting

Diodes With Photonic Crystals

Hsiang-Wei Li, Yu-Feng Yin, Chen-Yu Chang, Chen-Hung Tsai, Yen-Hsiang Hsu, Da-Wei Lin, Yuh-Renn Wu,

Hao-Chung Kuo, Senior Member, IEEE, and Jian Jang Huang, Senior Member, IEEE

Abstract— The unique properties of nonpolar GaN

light-emitting diodes (LEDs) have the advantages of generating polar-ized light emission. The employment of asymmetric 2-D photonic crystals (PhCs) can further enhance the light polarization ratio. In addition, it was generally recognized that the Purcell effect can increase the internal quantum efficiency of the LEDs with PhCs. In this paper, we study the properties of optical modes from different crystal planes. The Purcell effect is analyzed based on the PhCs and material crystal orientations. With different transition probability of the polarized photons in valence bands, the corresponding Purcell effect enhancement on the quantum efficiency varies.

Index Terms— Light-emitting diodes, non-polar GaN, photonic

crystal, purcell effect.

I. INTRODUCTION

L

IGHT-EMITTING DIODES (LEDs) have found their

wide applications in general lighting and backlight for flat panel displays. Despite their penetration to our daily life, the tremendous demand has driven people in the industry and academia to continue improving LED performance. For conventional LEDs, because the material growth direction is along polar c-axis, the energy band structures of the quan-tum wells (QWs) are tilted due to the induced piezoelectric polarizations and spontaneous polarization. The tilted bands separate electron and hole wavefunctions [1] and degrade the internal quantum efficiency. The effect is called quantum-confined Stark effect (QCSE). To reduce the internal polariza-tion, an effective way is to fabricate LEDs with non-polar or semi-polar GaN crystalline orientations [2]. Due to the absence of the polarization-related electric field along the growth direction, non-polar GaN is nearly QCSE free, which ensures

Manuscript received September 11, 2014; revised October 2, 2014; accepted October 7, 2014. Date of publication October 13, 2014; date of current version October 17, 2014. This work was supported by the National Science Council of Taiwan under Grant 103-2218-E-002-002 and Grant 103-2221-E-002-110. H.-W. Li, Y.-F. Yin, C.-Y. Chang, C.-H. Tsai, Y.-H. Hsu, Y.-R. Wu, and J. J. Huang are with the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan (e-mail: nois_41@hotmail.com; radiant1016@gmail.com; r02941065@ntu.edu.tw; andygood6709@gmail.com; hsiangalan@gmail.com; yrwu@ntu.edu.tw; jjhuang@ntu.edu.tw).

D.-W. Lin and H.-C. Kuo are with the Department of Photonics, Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan (e-mail: davidlin1006@hotmail.com; hckuo@faculty.nctu.edu.tw).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JQE.2014.2362552

the enhancement of radiative recombination by the strong overlap of electron and hole wavefunctions [3], [4]. In addi-tion to the performance improvement, non-polar epi-material has the advantage of generating polarized light. Because the biaxial stress in the QWs splits the valence bands into the several states, linearly polarized emission was observed in non-polar GaN LEDs [5]–[7]. Non-polar GaN light sources have the opportunity to be applied to the backlight of flat panel displays [8], which has the advantage of removing one polarization film. The degree of polarization depends on several material factors such as the crystalline orientations, the indium compositions and growth temperatures of the GaN LEDs [9], [10]. Moreover, the polarized light emission can be improved by photonic crystals (PhCs) [11]–[13]. The PhC structure offers both the advantages of better light extraction and higher degree of light polarization.

Furthermore, it was previously demonstrated that Purcell effect in the MQWs is strengthened by the resonance in LEDs with PhCs [14], [15]. The anisotropic biaxial stress in non-polar/semi-polar GaN LEDs raises an interesting question on the corresponding Purcell effect of photons from various valance band states and light polarization. In this work, we designed asymmetric two-dimensional PhCs on a-plane GaN LEDs. We established a model to study Purcell effect on polar and non-polar GaN LEDs. Since the transition prob-ability of the polarized photons in different valence bands is different, Purcell effect depends not only on the PhC structures but also on the material crystalline orientations.

II. EXPERIMENTS

To enhance the polarized emission, PhCs were designed and fabricated on the surface of a-plane GaN LEDs. The detailed process steps were described elsewhere in [16]. For

a-plane GaN crystal structure, as shown in Fig. 1, the a-axis

is the growth direction while the m- and c-axis are in the lateral direction. The PhCs have the period of 260 nm along the m-axis and 470 nm along c-axis. The idea of having asymmetric PhCs is to enhance light polarization of the device. The scanning electron microscopic (SEM) image of the PhCs is shown in Fig. 1(a). The current spreading layer, mesa definition and metal contacts were fabricated subsequently in the process. The device structure of the a-plane GaN PhC LED is illustrated in Fig. 1(b).

0018-9197 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

(2)

Fig. 1. (a) SEM image of the PhCs along the m- and the c-axis. (b) Illustration of the PhCs on the a-plane GaN LED. The PhCs were fabricated on top of the p-type GaN.

Fig. 2. (a) Total light output powers of PLED and PhCLED at different injection currents. (b) Light intensities of PhCLED and PLED at different polar angles in the vertical direction. The measurement was conducted by placing the detector on top of the chip with the insertion of the polarizer. The polar angle is adjusted by rotating the polarizer. The E//m modes are obtained by rotating the polarizer to 90° (parallel to m-axis), while E//c modes are at 0°.

III. RESULTS ANDDISCUSSION A. Characterizations of Light Outputs

Optical properties of the photonic crystal LED (PhCLED) and the planar LED (PLED, the device without any PhC patterns) were first characterized. As shown in Fig. 2(a), at the injection current of 20 mA, light output of PhCLED is 21.4% higher than that of PLED, which is mainly attributed to the diffraction of the PhC structure. The contribution of E//m and E//c modes to light output in the vertical direction (surface normal) was then analyzed. The polarizer was placed in between the detector and device. And the detector for such a measurement was located right on top of the sample. The emission profiles of PhCLED and PLED are shown in Fig. 2(b). The degree in Fig. 2(b) is obtained by rotating the polarizer while the photo detector is still placed on top. For both devices, at 90° (the direction of linearly polarized

Fig. 3. Radiation profiles of E//m modes and E//c modes along (a) a-c plane and (b) a-m plane in PLED and PhCLED.

light along the m-axis), E//m modes can be readily extracted because the direction of light polarization is parallel to the

m-axis. Likewise, E//c modes are measured at 0° or 180°, at

which the direction of light polarization is along the c-axis. The higher E//m mode light output is understood from the band split of non-polar a-plane material. For QWs grown on a-plane GaN orientation, the anisotropic biaxial strain results in the energy band separations. The valence bands split into the sub-bands of the |Y>, |Z>, and |X> states [13]. According to Fermi’s golden rule, the transition in each state can be described by the corresponding electric dipoles which determine the direction of electric fields [11], [17]. Because of the valence band separations, the electric field of most polarized photons oscillates along the m-axis, while only a small portion of photons has the electric fields polarized along the c-axis. The enhanced polarized emission is observed in PhCLED, which further increases the intensity of E//m modes. The enhancement of light output by the PhC structure depends on the diffraction modes. More E//m photons are detected from PhCLED than those from PLED. The total light output of E//m and E//c modes are asymmetric with the presence of PhCs.

The above results indicate that the radiative characteristics of non-polar GaN LEDs are dependent on non-polar crystalline properties as well as the designated periodic arrangement of the PhCs. For PhCs with a small period, photons congregate within the small angular ranges due to the large lattice recip-rocal vector [13]. The lattice reciprecip-rocal vector G (G= 2π/a, where a is the period of the PhCs) can change the out-coupled modes of in-plane k-vector k’||, based on the diffraction condition (k’||= kg,||+ pG, kg,|| is the in-plane k-vector and p is an integer). With the smaller period, the lattice reciprocal vector G becomes large, and the guided modes tend to radiate towards the smaller angular scopes. In our experiment, the radiation profiles were measured on a-c and a-m planes, which E//m and E//c photons are collected, respectively. In Figs. 3(a) and 3(b), as compared with PLED, light output enhancements of PhCLED for both E//m modes and E//c modes are observed. It is worth mentioning that the PhCs in Fig. 1(a) is imperfect. It is mainly due to the interference during e-beam exposure. The effect will cause bandwidth broadening in the PhC energy bands

(3)

Fig. 4. Illustration of the photon (E//m and E//c modes) transmission in a-plane PhCLED. E//m and E//c photons are generated from CB-|Y> and CB-|Z> transitions, respectively. And both photons are diffracted by the PhC structure.

so that side lobes in the radiation patterns of Fig. 3 broaden accordingly. And the light extraction of E//m modes along both a-c and a-m planes is higher than that of E//c modes. In Fig. 3(a), the integrated intensities over all of the angles of E//m and E//c modes in PhCLED are increased by 29.4% and 12% on a-c plane, respectively. In Fig. 3(b), in a-m plane, E//m modes are increased by 29.4% while E//c modes are only enhanced with 12.6%. As to the measurement in the vertical direction, the light intensities of E//m and E//c modes are increased by 47.1% and 20.4% in PhCLED, respectively. The above results agree with our original design to achieve asymmetric light enhancements.

As to the light output polarization of the devices, the degree of polarization is enhanced by the PhC structure. When the angular profile was scanned along a-c plane, the degree of polarization is increased from 36.5% in PLED to 42.6% in PhCLED. Also in a-m scan, the degree of polarization is enhanced from 36.3% in PLED to 42.2% in PhCLED. Moreover, in the vertical direction, the degree of polarization increases from 39.7% in PLED to 47.8% in PhCLED. The above results indicate a strong diffraction for E//m modes by the asymmetric two-dimensional PhCs.

B. Model for Extracting Purcell Effect in the Device

Before we numerically compare the optical properties of the devices to understand Purcell effect, we first study light extraction paths of photons in a-plane PhCLED. As illustrated in Fig. 4, photons are detected after photon generation in the MQWs and followed by the diffraction of PhCs. In the band structure of a-plane GaN QWs, the injected electrons in the conduction band (CB) tend to recombine with holes in the ground |Y> state. A large number of E//m photons are thus generated in QWs. On the other hand, less E//c photons are generated because the probability of transition in the |Z> state is lower. In the corresponding crystal orientations, non-polar

a-plane GaN is grown on the a-axis direction, and the

gener-ated E//m and E//c photons possess electric fields oscillating, respectively, along the m- and c-axis. E//m and E//c photons

then interact with the PhC structure and are radiated to the air. The PhC periodic structure determines the photonic band profiles and light extraction efficiency of E//m and E//c modes.

There are two main mechanisms to improve LED efficiency by photonic crystals [14], [18]. First, the periodic surface patterns allow photons in the semiconductor to escape to the air by Bragg scattering so that the extraction efficiency of LED is improved. In our case, E//m modes have a higher extraction efficiency than E//c modes due to the design of two-dimensional PhCs. Second, the artificial PhC structure changes the spontaneous emission rate and enhances the internal quantum efficiency by Purcell effect (Fp≡ lm/ f r, wherelm andf r are the spontaneous emission rates in the photonic environment and free space, respectively) [15], [19]. In a-plane PhC structure, Purcell effect modifies the emission rates of CB-|Y> and CB-|Z> recombination. Therefore, in addition to the extraction by the PhCs, Purcell effect affects the internal quantum efficiency and has the asymmetric enhance-ment of E//m and E//c modes.

Next, we study Purcell effect in the PhC structure based on the internal and external light extraction of the LEDs. The measured LED intensities are expressed by the following equation:

IaPhC= ηextPhC(a)· η PhC

int(a)· Iinjection (1)

whereηPhCext(a)andηintPhC(a)are the extraction efficiency and inter-nal quantum efficiency of PhCLED, respectively. Iinjection is

the injection carrier intensity at the injection current of 20 mA. The subscript parameter a describes the specific polarized modes. In our case, parameter a indicates E//m modes and E//c modes. Based on Eq. (1), the optical intensities of PhCLED and PLED in both vertical and integrated (over the whole angular domain) cases are compared for both E//m and E//c modes.

To understand how Purcell effect is influenced by the crystal orientation, we first compare the measured inten-sity of PhCLED with that of PLED. Ratios of intensities (ra = IaPhC/I

planar

a ) are shown in Table I, in which ra of E//m modes (rE//m) is higher than that of E//c modes (rE//c)

in both vertical and integrated light measurement. The higher

rE//m suggests the asymmetric enhancement in PhCLED.

Furthermore, rE//m/rE//c is related to the combined effect of

the extraction efficiency and Purcell effect in PhCLED. The equation is expressed as:

rE//m rE//c = ηPhC ext(E//m) ηPhC ext(E//c) · FP,E//m FP,E//c (2) where FP,E//m and FP,E//c are factors of Purcell effect of E//m and E//c modes in the PhCs. As in our case, the value of

r E//mr E//c (shown in Table I) higher than 1 indicates that

the combined effect of the extraction efficiency and Purcell effect contributes to the larger light output enhancement of E//m photons, as compared with that of E//c photons.

The above discussion can’t distinguish extraction effi-ciency from Purcell effect. To understand the role of Purcell effect, we fabricated the same PhC structure on c-plane

(4)

TABLE I

RATIOS OFINTENSITIES AND THECOMBINEDINFLUENCES OF THE EXTRACTIONEFFICIENCY ANDPURCELLEFFECT

GaN LED. Due to the identical transition rate in the heavy- and light-hole states in c-plane GaN QWs, Purcell effect is regarded the same in all crystalline directions. As a result, the extraction efficiency is only correlated to the asymmetric PhC design in c-plane GaN epi-structure. Also, because the same PhC structures are fabricated on both

a-plane and c-plane GaN LEDs, the extraction from c-plane

PhC is the same as the a-plane PhC case. By understanding the extraction ratio between E//m and E//c photons in a-plane PhCLED, Purcell enhancement can be derived.

To verify, we prepare additional samples with conventional

c-plane GaN LED epi-structure. The nomenclature of the PhC

and planar devices on c-plane GaN is c-PhCLED and c-PLED, respectively. In order to correlate the scan direction of c-plane devices with that of a-plane, we define -X and X-M planes for c-PhCLED and c-PLED. For c-plane GaN, -X plane is similar to a-m plane (a-plane), and X-M plane to a-c plane (a-plane) because of the PhC periodic arrangement. In Fig. 5(a), c-PhCLED possesses the PhC periods of

260 nm and 470 nm along -X plane and X-M plane,

respectively. The angular emission profiles of c-PhCLED and c-PLED in the vertical direction are shown in Fig. 5(b). At 90°, the direction of electric fields can only exist along

-X plane, while at 0° or 180°, the electric fields are only

along X-M plane. In c-PLED, it’s not surprising to observe nearly the same intensity at both polarizations, because of weak energy band separations (of heavy- and light-hole states). On the other hand, as for the polarized emission properties of c-PhCLED, the intensities at 90° and 0° (or 180°) are different, which is attributed to the electric field interaction with the PhCs. Fig. 6(a) and (b) show the radiation profiles of c-PLED and c-PhCLED scanned along X-M and

-X planes, respectively. The light output enhancements of

c-PhCLED over c-PLED are compared in Table II for the

electric field parallel to 260 nm period (E//260 modes) and 470 nm period (E//470 modes). The intensity enhancement of E//260 modes is larger than that of E//470 modes, which is

Fig. 5. (a) Measurement of the radiation profile from the c-plane LED. The radiation plane along the long PhC period (470 nm) is X-M plane while

-X plane is along the short period (260 nm). (b) Optical intensities of

c-PhCLED and c-PLED at different polar angles (rotated with c-axis or. . .). The measurement setup is the same as in Fig. 2(b).

Fig. 6. Radiation profiles of c-PLED and c-PhCLED along (a) X-M and (b)-X planes. For both devices, E//-X (E//X-M) indicates that the electric field is along-X (X-M) plane.

TABLE II

ENHANCEMENTS OFE//260ANDE//470 MODES INc-PhCLED

ASCOMPAREDWITHTHAT INc-PLED

associated with the extraction efficiencies of the interaction of lateral propagation modes with the PhC lattice (see Table III), despite the same transition probability from conduction to valence band. For both PhCLED and c-PhCLED, we assume the same extraction efficiency when the electric field interacts with the same PhC periodic arrangement. Thus, light extraction from the GaN/air interface of E//260 for c-plane case will be the same as the E//m modes for the nonpolar case, while E//470 for the c-plane is the same as the E//c modes for the a-plane case. Based on Eq. (2), Purcell effects are derived from the extraction ratio of E//m modes to E//c modes in PhCLED, which is obtained from the optical properties of c-plane LEDs in Fig. 5 and 6.

(5)

TABLE III

RATIOS OF THEEXTRACTIONEFFICIENCY INc-PhCLEDANDPURCELLEFFECT OFE//MMODES TOE//CMODES INPhCLED

As a result, once the extraction ratio was obtained and plugged in Eq. (2), ratios of Purcell effect of E//m modes to E//c modes (FP,E//m/FP,E//c) are calculated to be in the range of 1.11–1.18 (in Table III). Purcell enhancement of E//m modes is higher than that of E//c modes. In general, Purcell effect is proportional to the transition rate in the energy band [14], [20]. Due to the intrinsic properties of a-plane GaN, the transition rate of the lower energy level (E//m modes) is larger than that of the higher band (E//c modes). In PLED, the value of planarE//m/ planarE//c (which

planar E//m and 

planar

E//c are the spontaneous emission rates of

E//m and E//c modes, respectively) is 2.32. On the other hand, in our PhC structure, the value ofPhCE//m/ PhCE//c is 2.74 in PhCLED. The result shows that the spontaneous emission rate of E//m modes is further enhanced by Purcell effect as compared with that of E//c modes.

Purcell effect modifies the spontaneous emission rate and changes the internal quantum efficiency. With a suitable PhC structure, it means that more photons can be generated and the corresponding light output is increased. Also, Purcell effects of polar and non-polar GaN LEDs with the same PhC structures are different. The transition probabilities of E//m modes and E//c modes in non-polar a-plane GaN are different due to the separation of the valence bands. The transition probability of E//m modes is higher than that of E//c modes. Thus, Purcell effect exhibits different ratio of emission rate enhancement which is dependent on the transition probability. In our non-polar LEDs, spontaneous emission of E//m modes is enhanced more than E//c ones by Purcell effect.

IV. CONCLUSION

The optical performance of the a-plane GaN LEDs with two-dimensional PhCs was demonstrated. It was found the E//m modes possesses higher light output than E//c modes, which is mainly due to the higher valence band transition probability of the E//m modes. In order to understand Purcell enhancement on the internal quantum efficiency, we conduct the experiment work to compare light extraction from the PhC GaN/air interface of E//m and E//c modes. Light extraction from a c-plane GaN LED with asymmetric PhC arrangement was measured and the results feedback to the non-polar device with the same PhCs. Due to different transition probabilities,

E//m photons are favored. Purcell effect exhibits asymmetric modification of the emission rates in a-plane GaN PhCs. The ratio of emission rate of E//m to E//c modes increases from 2.32 in the planar device to 2.74 in the device with our PhC arrangement. Therefore, Purcell effect primarily enhances the spontaneous emission rates of E//m photons, dedicating to the larger E//m photon generations as compared with E//c modes.

REFERENCES

[1] D. F. Feezell, M. C. Schmidt, S. P. DenBaars, and S. Nakamura, “Development of nonpolar and semipolar InGaN/GaN visible light-emitting diodes,” MRS Bull., vol. 34, no. 5, pp. 318–323, 2009.

[2] C. Wetzel et al., “Light-emitting diode development on polar and non-polar GaN substrates,” J. Crystal Growth, vol. 310, no. 17, pp. 3987–3991, Aug. 2008.

[3] H. Masui, S. Nakamura, S. P. DenBaars, and U. K. Mishra, “Nonpo-lar and semipo“Nonpo-lar III-nitride light-emitting diodes: Achievements and challenges,” IEEE Trans. Electron Devices, vol. 57, no. 1, pp. 88–100, Jan. 2010.

[4] T. S. Ko et al., “Optical characteristics of a-plane InGaN/GaN multiple quantum wells with different well widths,” Appl. Phys. Lett., vol. 90, no. 18, pp. 181122-1–181122-3, 2007.

[5] S. E. Brinkley et al., “Polarized spontaneous emission from blue-green m-plane GaN-based light emitting diodes,” Appl. Phys. Lett., vol. 98, no. 1, pp. 011110-1–011110-3, 2011.

[6] N. F. Gardner, J. C. Kim, J. J. Wierer, Y. C. Shen, and M. R. Krames, “Polarization anisotropy in the electroluminescence of m-plane InGaN–GaN multiple-quantum-well light-emitting diodes,” Appl. Phys. Lett., vol. 86, no. 11, pp. 111101-1–111101-3, 2005. [7] H. Tsujimura, S. Nakagawa, K. Okamoto, and H. Ohta,

“Characteris-tics of polarized electroluminescence from m-plane InGaN-based light emitting diodes,” Jpn. J. Appl. Phys., vol. 46, nos. 41–44, p. L1010, 2007.

[8] H. Masui, H. Yamada, K. Iso, J. S. Speck, S. Nakamura, and S. P. DenBaars, “Non-polar-oriented InGaN light-emitting diodes for liquid-crystal-display backlighting,” J. Soc. Inf. Display, vol. 16, no. 4, pp. 571–578, Apr. 2008.

[9] C. H. Chiu et al., “Optical properties of a-plane InGaN/GaN multiple quantum wells on r-plane sapphire substrates with different indium compositions,” J. Appl. Phys., vol. 105, no. 6, p. 063105, 2009. [10] S. Nakagawa, H. Tsujimura, K. Okamoto, M. Kubota, and H. Ohta,

“Temperature dependence of polarized electroluminescence from non-polar m-plane InGaN-based light emitting diodes,” Appl. Phys. Lett., vol. 91, no. 17, pp. 171110-1–171110-3, Oct. 2007.

[11] E. Matioli et al., “High-brightness polarized light-emitting diodes,” Light, Sci. Appl., vol. 1, p. e22, Aug. 2012.

[12] T.-T. Wu, S.-Y. Lo, H.-M. Huang, C.-W. Tsao, T.-C. Lu, and S.-C. Wang, “High quality factor nonpolar GaN photonic crystal nanocavities,” Appl. Phys. Lett., vol. 102, no. 19, p. 191116, 2013.

[13] H.-H. Huang and R.-R. Wu, “Study of polarization properties of light emitted from a-plane InGaN/GaN quantum well-based light emitting diodes,” J. Appl. Phys., vol. 106, no. 2, p. 023106, 2009.

(6)

[14] M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhance-ment from thin-film 2-D photonic crystals,” J. Lightw. Technol., vol. 17, no. 11, pp. 2096–2112, Nov. 1999.

[15] Y.-F. Yin, Y.-C. Lin, Y.-C. Liu, Y.-C. Shen, H.-P. Chiang, and J. Huang, “Correlation of angular light profiles of light-emitting diodes to spatial spontaneous emissions from photonic crystals,” J. Appl. Phys., vol. 114, no. 14, p. 143104, 2013.

[16] S.-C. Wang et al., “Interactions of diffraction modes contributed from surface photonic crystals and nanoholes in a GaN-based light-emitting diode,” J. Lightw. Technol., vol. 29, no. 24, pp. 3772–3776, Dec. 15, 2011.

[17] E. Matioli et al., “Polarized light extraction in m-plane GaN light-emitting diodes by embedded photonic-crystals,” Appl. Phys. Lett., vol. 98, no. 25, p. 251112, 2011.

[18] J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nature Photon., vol. 3, pp. 163–169, Feb. 2009.

[19] E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev., vol. 69, nos. 1–2, p. 681, 1946.

[20] J. Canet-Ferrer et al., “Excitation power dependence of the Purcell effect in photonic crystal microcavity lasers with quantum wires,” Appl. Phys. Lett., vol. 102, no. 20, pp. 201105-1–201105-4, May 2013.

Hsiang-Wei Li received the B.S. degree in electrical engineering from

National Tsing Hua University, Hsinchu, Taiwan, in 2012, and the M.S. degree from the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan, in 2014. His current research interest is on the semipolar and nonpolar GaN light-emitting diodes.

Yu-Feng Yin received the B.S. degree in electrical engineering from National

Tsing Hua University, Hsinchu, Taiwan, in 2010. He is currently pursuing the Ph.D. degree with the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan. His current research interests include the far-field characterization of GaN-based light-emitting diodes (LEDs) by photonic crystal embedded LED fabrication.

Chen-Yu Chang received the B.S. degree in engineering science and ocean

engineering from National Taiwan University, Taipei, Taiwan, in 2013, where he is currently pursuing the M.S. degree with the Graduate Institute of Photonics and Optoelectronics. His current research interest is on the bio-material detection GaN-based light-emitting diodes.

Chen-Hung Tsai received the B.S. degree in physics from National Tsing Hua

University, Hsinchu, Taiwan, in 2012, and the M.S. degree from the Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan, in 2014. His research interest is on the AlN light-emitting diode.

Yen-Hsiang Hsu received the B.S. degree in electrical engineering from

National Taiwan University, Taipei, Taiwan, in 2012, where he is currently pursuing the M.S. degree with the Graduate Institute of Photonics and Opto-electronics. His current research interests include the far-field characterization of GaN-based light-emitting diodes (LEDs) by photonic crystal embedded LED fabrication.

Da-Wei Lin received the B.S. and M.S. degrees in photonics from National

Chiao Tung University, Hsinchu, Taiwan, in 2009 and 2010, respectively, where he is currently pursuing the Ph.D. degree in photonics. His current research interests include the epitaxy of III–V compound semiconductor materials by MOCVD and analysis for GaN-based light-emitting diodes.

Yuh-Renn Wu received the bachelor’s degree in physics from National

Taiwan University, Taipei, Taiwan, in 1998, the master’s degree from the Graduate Institute of Communication Engineering, National Taiwan Univer-sity, in 2000, and the Ph.D. degree in electrical engineering and computer science from the University of Michigan, Ann Arbor, MI, USA, in 2006. After being a short period of Research Fellow position in Michigan, he joined the Graduate Institute of Photonics and Optoelectronics at National Taiwan University in 2007, where he is currently an Associate Professor.

Prof. Wu’s research area is focusing on the analysis and characterization of optical and semiconductor devices. During his study at the University of Michigan, he joined the Solid-State Electronic Laboratory at the Depart-ment of Electrical Engineering and Computer Science, and worked on the analysis and modeling of high-power electronic devices. He developed multi-dimensional Poisson, drift-diffusion, and Schrodinger equation solver. He also developed Monte Carlo techniques in analysis of carrier transport and heat dissipation in high-power GaN heterostructure field-effect transistor devices. He also worked on the research of ferroelectric multifunctional devices, and developing the full bands Kaiser Permanente’s simulation programs for analysis of nitride quantum-dot and quantum-well band structures.

Hao-Chung Kuo (S’98–M’99–SM’06) received the B.S. degree in physics

from National Taiwan University, Taipei, Taiwan, the M.S. degree in electrical and computer engineering from Rutgers University–Camden, Camden, NJ, USA, in 1990 and 1995, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Illinois at Urbana-Champaign, Champaign, IL, USA, in 1999. He has an extensive professional career both in research and industrial research institutions. From 1995 to 1997, he was a Research Consultant with Lucent Technologies, Bell Labs, Holmdel, NJ, USA. From 1999 to 2001, he was a Research and Development Engineer with the Division of Fiber-Optics, Agilent Technologies, Santa Clara, CA, USA. From 2001 to 2002, he was the Research and Development Manager with LuxNet Corporation, Taoyuan, Taiwan. Since 2002, he has been a faculty member with the Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan. His current research interests include the epitaxy, design, fabrication, and measurement of high-speed InPand GaAs-based vertical-cavity surface-emitting lasers, GaN-GaAs-based lighting-emitting devices, and nanostructures.

Jian Jang Huang (M’98–SM’08) received the B.S. degree in electrical

engineering and the M.S. degree from the Graduate Institute of Photonics and Optoelectronics (GIPO), National Taiwan University (NTU), Taipei, Taiwan, in 1994 and 1996, respectively, and the Ph.D. degree in electrical engineering from the University of Illinois, Urbana-Champaign, Champaign, IL, USA, in 2002. He is currently a Professor with GIPO, NTU.

Prof. Huang has been involved in applying nanostructures to optoelectronic devices. He developed a spin-coating method for nanosphere lithography, which can be applied to nanomaterials or nanostructures for significant performance improvement of light-emitting diodes, solar cells, and nanorod devices. His recent focus is on GaN-based power electronics, and applying nanostructures and field-effect transistors to biosensing. He is a member of the Phi Tau Phi Scholastic Honor Society. He was a recipient of the Wu Da-Yu Award in 2008, the most prestigious one for young researchers in Taiwan sponsored by the National Science Council. He also received the award for the most excellent young electrical engineer from the Chinese Institute of Electrical Engineering in 2008. He was the Chair of the International Society for Optics and Photonics, San Diego, CA, USA, and the International Conference on Solid State Lighting in 2011 and 2012. He has also served as the Board Director of Global Communication Semiconductor, Inc., Torrance, CA, USA, since 2010.

數據

Fig. 3. Radiation profiles of E//m modes and E//c modes along (a) a-c plane and (b) a-m plane in PLED and PhCLED.
Fig. 4. Illustration of the photon (E//m and E//c modes) transmission in a-plane PhCLED
TABLE II
TABLE III

參考文獻

相關文件

Once you get down to a purely business level, your influence is gone and the true light of your life isdimmed. You must work in the missionary spirit, with a breadth of charity

You are given the wavelength and total energy of a light pulse and asked to find the number of photons it

Reading Task 6: Genre Structure and Language Features. • Now let’s look at how language features (e.g. sentence patterns) are connected to the structure

Wang, Solving pseudomonotone variational inequalities and pseudocon- vex optimization problems using the projection neural network, IEEE Transactions on Neural Networks 17

volume suppressed mass: (TeV) 2 /M P ∼ 10 −4 eV → mm range can be experimentally tested for any number of extra dimensions - Light U(1) gauge bosons: no derivative couplings. =>

Define instead the imaginary.. potential, magnetic field, lattice…) Dirac-BdG Hamiltonian:. with small, and matrix

incapable to extract any quantities from QCD, nor to tackle the most interesting physics, namely, the spontaneously chiral symmetry breaking and the color confinement.. 

• Formation of massive primordial stars as origin of objects in the early universe. • Supernova explosions might be visible to the most