臺灣博碩士論文加值系統

本論文中，使用COMSOL模擬軟體，研究耳語迴廊模態（WGM）的碟型及環形共振腔結構和光學特性並依據光學品質因子（FQ）、光學侷限因子（FC）、模態體積（Vm）和Purcell因子（Fp），作為特性改善的指標。首先，模擬結構的尺寸主要為4um的五邊形和六邊形。五角形碟型結構的FQ、FC、Vm和Fp分別為1613、0.96、16.21 和1.268。對於六邊形微碟型結構，它們分別為1221、0.96、19.02 和0.81。由於五邊形結構具有較低的對稱性而展現出比六邊形微碟型結構更好的特性。接著在使用FIB在結構中心位置蝕刻一個圓形孔洞來改善五角形和六邊形結構的特性，以降低高階模態和quasi-WGM。對於五邊形微碟型結構，當中心孔洞的半徑為1.25μm時，FQ、FC、Vm和Fp分別為4331、0.98、12.1 和4.5。對於六邊形微碟型結構，當中心孔洞的半徑為1.75um時，FQ、FC、Vm和Fp分別為1972、0.97、17.1 和1.46。與微碟型結構相比，五邊形環型結構中的FQ、FC和Fp分別增加1.68倍，0.02倍和2.54倍，Vm降低0.25倍。對於六邊形環型結構，與微碟型結構的FQ、FC和Fp分別增加了0.61倍，0.01倍和0.8倍，Vm降低了0.1倍。五邊形微碟型結構相對於六邊形微碟型結構有較好的特性，接著透過FIB挖洞製程形成環型結構，可以顯著的改善光學特性，有效的消除非WGM的模態。

In this thesis, the structure of ring resonator for whisper gallery mode (WGM) and improvement of its optical characteristics were studied by using simulation software, Comsol, according to the optical quality factor (FQ), optical confinement factor (FC), mode volume (Vm) and Purcell factor (Fp) as the basic criteria. First, the WGM in pentagonal and hexagonal structures with side length of 4 um was computed. The FQ, FC, Vm and Fp of pentagonal structure are 1613, 0.96, 16.21 and 1.268, respectively. For the hexagonal structure they are 1221, 0.96, 19.02 and 0.81, respectively. The pentagonal structure shows the better characteristics than hexagonal one because of its lower symmetry. Second, the characteristics of pentagonal and hexagonal structures were improved by caving a hole in the central to reduce the high order mode and quasi WGM. For the central with radius of 1.25 um in pentagonal structure, the better FQ, FC, Vm and Fp are 4331, 0.98, 12.1 and 4.5, respectively. For the one with radius of 1.75 um in hexagonal structure, the better FQ, FC, Vm and Fp are 1972, 0.97, 17.1 and 1.46, respectively. Compared with the one without central hole, the FQ, FC, and Fp in pentagonal structure increases 1.68 times, 0.02 times and 2.54 times, respectively, and the Vm decrease 0.25 times. For the hexagonal structure the FQ, FC, and Fp increases 0.61 times, 0.01 times and 0.8 times, respectively, and the Vm decrease 0.1 times, comparing to the one without central hole. This method shows a significant improvement when using pentagonal structure for WGM lasing. The central hole structure can further improve the performance as well.

Abstract (Chinese)..................................I
Abstract............................................II
Acknowledgement.....................................IV
Contents............................................V
Figure Captions.....................................VII
Table Captions......................................XI
Chapter 1 Introduction..............................1
1.1 The Properties of Gallium Nitride Material.....1
1.2 The basic carrier transition mechanism.........2
1.3 The Evolution of Semiconductor Laser...........2
1.4 Whisper Gallery Mode Laser (WGML)..............4
1.5 Motivation.....................................5
1.6 Organization of This Thesis....................6
References..........................................12
Chapter 2 Background and Principle..................15
2.1 Theory of Cylindrical Waveguide [1]............15
2.2 Whisper Gallery Modes in Cylindrical Cavities..21
2.3 Resonant Mode Analysis.........................22
References..........................................29
Chapter 3 Simulation of WGML by COMSOL..............30
3.1 Simulation condition...........................30
3.2 Four characteristic factors....................33
3.2.1 Simulation Results of Pentagonal and Hexagonal Micro-disk Structure................................35
3.2.2 Simulation Results of Pentagonal and Hexagonal Micro-ring Structure................................36
3.3 Summary........................................38
References..........................................51
Chapter 4 The Experiment of WGML by Focus Ion Beam..53
4.1. The Micro-disk and Micro-ring Structure on The Sample..............................................53
4.2. The Suspended Structure of Micro-disk and Micro-ring................................................53
4.3. Applicability improvement.....................55
References..........................................69
Chapter 5 Conclusion and Future Prospects...........70
5.1. Conclusion....................................70
5.2. Future Prospects..............................71

[1]C. C. Lin and C. T. Lee, GaN-Based Resonant-Cavity Light-Emitting Diodes With Top and Bottom Dielectric Distributed Bragg Reflectors, Ieee Photonics Technology Letters, vol. 22, pp. 1291-1293, Sep 1 2010.
[2]W. W. Chow, E. D. Jones, N. A. Modine, A. A. Allerman, and S. R. Kurtz, Laser gain and threshold properties in compressive-strained and lattice-matched GaInNAs/GaAs quantum wells, Applied Physics Letters, vol. 75, pp. 2891-2893, 1999.
[3]D. C. Look, D. C. Reynolds, C. W. Litton, R. L. Jones, D. B. Eason, and G. Cantwell, Characterization of homoepitaxial p-type ZnO grown by molecular beam epitaxy, Applied Physics Letters, vol. 81, pp. 1830-1832, 2002.
[4]E. Yablonovitch, Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Physical Review Letters, vol. 58, pp. 2059-2062, 05/18/ 1987.
[5]V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, et al., Optical Gain and Stimulated Emission in Nanocrystal Quantum Dots, Science, vol. 290, pp. 314-317, 2000.
[6]J. H. Quilter, A. J. Brash, F. Liu, M. Glässl, A. M. Barth, V. M. Axt, et al., Phonon-Assisted Population Inversion of a Single InGaAs/GaAs Quantum Dot by Pulsed Laser Excitation, Physical Review Letters, vol. 114, p. 137401, 03/30/ 2015.
[7]B. P. Yonkee, E. C. Young, C. Lee, J. T. Leonard, S. P. DenBaars, J. S. Speck, et al., Demonstration of a III-nitride edge-emitting laser diode utilizing a GaN tunnel junction contact, Optics Express, vol. 24, pp. 7816-7822, 2016/04/04 2016.
[8]D. Kasahara, D. Morita, T. Kosugi, K. Nakagawa, J. Kawamata, Y. Higuchi, et al., Demonstration of Blue and Green GaN-Based Vertical-Cavity Surface-Emitting Lasers by Current Injection at Room Temperature, Applied Physics Express, vol. 4, p. 072103, Jul 2011.
[9]T.-C. Lu, C.-C. Kao, H.-C. Kuo, G.-S. Huang, and S.-C. Wang, CW lasing of current injection blue GaN-based vertical cavity surface emitting laser, Applied Physics Letters, vol. 92, p. 141102, 2008.
[10]R. Chen, B. Ling, X. W. Sun, and H. D. Sun, Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO micro-disks, Adv Mater, vol. 23, pp. 2199-204, May 17 2011.
[11]C. Zou, C. Dong, J. Cui, F. Sun, Y. Yang, X. Wu, et al., Whispering gallery mode optical microresonators: fundamentals and applications, Scientia Sinica Physica, Mechanica ＆ Astronomica, vol. 42, p. 1155, 2012.
[12]J. Wiersig, Hexagonal dielectric resonators and microcrystal lasers, Physical Review A, vol. 67, p. 023807, Feb 2003.
[13]S. L. Mccall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Whispering-Gallery Mode Micro-disk Lasers, Applied Physics Letters, vol. 60, pp. 289-291, Jan 20 1992.
[14]F. Albert, T. Braun, T. Heindel, C. Schneider, S. Reitzenstein, S. Hofling, et al., Whispering gallery mode lasing in electrically driven quantum dot micropillars, Applied Physics Letters, vol. 97, p. 101108, Sep 6 2010.
[15]J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, et al., Single Transverse Whispering-Gallery Mode AlGaInAs/InP Hexagonal Resonator Microlasers, Ieee Photonics Journal, vol. 3, pp. 756-764, Aug 2011.
[16]M. T. Hill and M. C. Gather, Advances in small lasers, Nature Photonics, vol. 8, pp. 908-918, Dec 2014.
[17]A.T.Hajjiah, Design and Analysis of Whispering Gallery Mode Semiconductor Lasers Philosophy In Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, 2009.
[18]R. Chen, B. Ling, X. W. Sun, and H. D. Sun, Room temperature excitonic whispering gallery mode lasing from high-quality hexagonal ZnO micro-disks, Adv Mater, vol. 23, pp. 2199-204, May 17 2011.
[19]H. Baek, C. H. Lee, K. Chung, and G. C. Yi, Epitaxial GaN micro-disk lasers grown on graphene microdots, Nano Lett, vol. 13, pp. 2782-5, Jun 12 2013.
[20]G. Schunk, J. U. Fürst, M. Förtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, et al., Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern, Optics Express, vol. 22, pp. 30795-30806, 2014/12/15 2014.
[21]T. C. Chang, K. B. Hong, Y. Y. Lai, Y. H. Chou, S. C. Wang, and T. C. Lu, ZnO-Based Microcavities Sculpted by Focus Ion Beam Milling, Nanoscale Res Lett, vol. 11, p. 319, Dec 2016.
[22]T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, Whispering Gallery Modes in Nanosized Dielectric Resonators with Hexagonal Cross Section, Physical Review Letters, vol. 93, p. 103903, 09/03/ 2004.
[23]D. J. Gargas, M. C. Moore, A. Ni, S. W. Chang, Z. Zhang, S. L. Chuang, et al., Whispering gallery mode lasing from zinc oxide hexagonal nanodisks, ACS Nano, vol. 4, pp. 3270-6, Jun 22 2010.
[24]comsol, RF Module :Software for Microwave and RF Design, COMSOL Webpage, 2017.
[25]O. C. Zienkiewicz, D. W. Kelly, and P. Bettess, The sommerfeld (radiation) condition on infinite domains and its modelling in numerical procedures, vol. 704, pp. 169-203, 1979.
[26]W. Frei, Using Perfectly Matched Layers and Scattering Boundary Conditions for Wave Electromagnetics Problems, COMSOL BLOG, 2015.
[27]I. J. Cutress, E. J. F. Dickinson, and R. G. Compton, Analysis of commercial general engineering finite element software in electrochemical simulations, Journal of Electroanalytical Chemistry, vol. 638, pp. 76-83, 1/5/ 2010.
[28]H.-Y. Ryu, M. Notomi, and Y.-H. Lee, High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities, Applied Physics Letters, vol. 83, pp. 4294-4296, 2003.
[29]T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, Purcell-Factor-Enhanced Scattering from Si Nanocrystals in an Optical Microcavity, Physical Review Letters, vol. 103, p. 027406, 07/10/ 2009.
[30]G. Björk, H. Heitmann, and Y. Yamamoto, Spontaneous-emission coupling factor and mode characteristics of planar dielectric microcavity lasers, Physical Review A, vol. 47, pp. 4451-4463, 05/01/ 1993.
[31]T. C. Chang, K. B. Hong, Y. Y. Lai, Y. H. Chou, S. C. Wang, and T. C. Lu, ZnO-Based Microcavities Sculpted by Focus Ion Beam Milling, Nanoscale Res Lett, vol. 11, p. 319, Dec 2016.
[32]E. D. Haberer, C. Meier, R. Sharma, A. R. Stonas, S. P. DenBaars, S. Nakamura, et al., Observation of high Q resonant modes in optically pumped GaN/InGaN micro-disks fabricated using photoelectrochemical etching, physica status solidi (c), vol. 2, pp. 2845-2848, 2005.
[33]B. N. Rock, T. Hoshizaki, and J. R. Miller, Comparison of in situ and airborne spectral measurements of the blue shift associated with forest decline, Remote Sensing of Environment, vol. 24, pp. 109-127, 1988/02/01/ 1988.
[34]S. Nakamura and K. Tajima, Ultrafast all-optical gate switch based on frequency shift accompanied by semiconductor band-filling effect, Applied Physics Letters, vol. 70, pp. 3498-3500, 1997.
[35]J. Dai, C. X. Xu, K. Zheng, C. G. Lv, and Y. P. Cui, Whispering gallery-mode lasing in ZnO microrods at room temperature, Applied Physics Letters, vol. 95, p. 241110, Dec 14 2009.
[36]J. Wiersig and M. Hentschel, Unidirectional light emission from high-$Q$ modes in optical microcavities, Physical Review A, vol. 73, p. 031802, 03/08/ 2006.
[37]Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, et al., Whispering-gallery mode resonators for highly unidirectional laser action, Proceedings of the National Academy of Sciences, vol. 107, pp. 22407-22412, December 28, 2010 2010.
[38]M. O. Scully, Collimated unidirectional laser beams from notched elliptical resonators, Proceedings of the National Academy of Sciences, vol. 107, pp. 22367-22368, December 28, 2010 2010.