臺灣博碩士論文加值系統

在這一篇文章中，一個以嚴格耦合波分析結合泊松擴散飄移電流以及薛丁格的模型被嘗試的去建立了，可以達到去模擬有關面射型雷射的研究，並且進一步的嘗試優化，嚴格耦合波分析在這裡是為了要模擬布拉格面鏡的反射率，整個結構下的電場，從得到的電場能再去得到量子井佔所有電場的比例，之後用這一比例可以去獲得閥值增益，之後使用泊松擴散飄移電流以及薛丁格，去得到波函數以及電子電洞的交疊以及電流，此外帶尾態這一個概念被引進了，之後得到增益，最後利用增益大於閥值增益時，會達成雷射條件，以此去獲得閥值電流，此外二維的嚴格耦合波分析以不同的極化方向得到布拉格面鏡的反射率，以及遠場圖也被建立了。

In this thesis, a RCWA module is combined with our Poisson, drift-diffusion and Schrodinger solver(1D-DDCC) to enable the capability of modeling and optimization of VCSELs. The RCWA method built into the simulation program is used to simulate the reflectivity of DBRs for different periods. When the electric field at resonance, the optical modes are obtained to calculate the gamma factor of the cavity. The confinement factor gamma is then used to calculate the threshold gain of the device. Then the Poisson, drift-diffusion, and Schrodinger solver is used to calculate eigen states, electron-hole overlap, emission spectrum and intrinsic gain. It is note that to accurately model the I-V and emission spectrum, it cannot simply use a smaller polarization value as other software did. Instead, the tail state model is used to account for the possible percolation transport due to the potential fluctuation. Finally, the threshold condition is used to get the threshold current and the lasing emission. Besides the 1D program, 2D RCWA is developed to model the emission of different angles and patterns.

Veri cation letter . . . . . . . . . . . . . . . . . . . i
Acknowledgement . . . . . . . . . . . . . . . . . . . .ii
Chinese Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . iii
English Abstract . . . . . . . . . . . . . . . . . . . iv
Contents . . . . . . . . . . . . . . . . . . . . . . . .v
List of Figures . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . xi
1 Introduction . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction in Vertical Cavity Surface Emitting Laser device . . . . . . . . . . . . . . . . . . . . . .1
1.2 The advantages of RCWA . . . . . . . . . . . . . . .2
1.3 RCWA review . . . . . . . . . . . . . . . . . . . . 3
2 Methodology . . . . . . . . . . . . . . . . . . . . . 4
2.1 Homogeneous Plane Wave . . . . . . . . . . . . . . .4
2.2 2D Homogeneous Multiple Stacks . . . . . . . . . . .7
2.3 2D RCWA theory . . . . . . . . . . . . . . . . . . 13
2.4 Far eld pattern . . . . . . . . . . . . . . . . . .18
2.5 Threshold gain . . . . . . . . . . . . . . . . . . 19
2.6 Poisson and drift-diffusion equation self-consistent solver . . . . . . . . . . . . . . . . 19
2.7 Schrodinger equation and emission rate . . . . . . 21
2.8 Optical gain . . . . . . . . . . . . . . . . . . . 23
2.9 Flow chart . . . . . . . . . . . . . . . . . . . . 25
3 Results . . . . . . . . . . . . . . . . . . . . . . .27
3.1 Blue light GaN based VCSEL . . . . . . . . . . . . 27
3.1.1 1D Simulation . . . . . . . . . . . . . . . . . .30
3.1.2 VCSEL with 2QWs . . . . . . . . . . . . . . . . .41
3.2 GaAs based VCSEL . . . . . . . . . . . . . . . . . 45
3.2.1 2D Simulation . . . . . . . . . . . . . . . . . .45
4 Conclusion . . . . . . . . . . . . . . . . . . . . . 55
Bibliography . . . . . . . . . . . . . . . . . . . . . 57

[1] N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, "Diode-laser random-modulation CW lidar," Appl. Opt., vol. 25, pp. 63-67, Jan 1986.
[2] M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave
analysis of planar-grating diffraction," J. Opt. Soc. Am., vol. 71, pp. 811-818, Jul 1981.
[3] N. Y. Chang and C. J. Kuo, "Algorithm based on rigorous
coupled-wave analysis for diffractive optical element design," J. Opt. Soc. Am. A, vol. 18, pp. 2491-2501, Oct 2001.
[4] M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of metallic surface-relief gratings," J. Opt. Soc. Am. A, vol. 3, pp. 1780-1787, Nov 1986.
[5] M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analy-57sis for surface-relief gratings: enhanced transmittance matrix ap-proach," J. Opt. Soc. Am. A, vol. 12, pp. 1077-1086, May 1995.
[6] P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A, vol. 13, pp. 779-784, Apr 1996.
[7] P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A, vol. 14, pp. 1592-1598, Jul 1997.
[8] L. Li, "Use of fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A, vol. 13, pp. 1870-1876, Sep 1996.
[9] L. Li, "New formulation of the fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A, vol. 14, pp. 2758-2767, Oct 1997.
[10] M. Filoche, M. Piccardo, Y.-R. Wu, C.-K. Li, C. Weisbuch, and S. Mayboroda, "Localization landscape theory of disorder in semiconductors. I. Theory and modeling," Phys. Rev. B, vol. 95, p. 144204, Apr 2017.
[11] 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, no. 14, p. 141102, 2008.
[12] T. Onishi, O. Imafuji, K. Nagamatsu, M. Kawaguchi, K. Ya-manaka, and S. Takigawa, "Continuous wave operation of GaN vertical cavity surface emitting lasers at room temperature," IEEE Journal of Quantum Electronics, vol. 48, pp. 1107-1112, Sep. 2012.
[13] H. M. Ng, T. D. Moustakas, and S. N. G. Chu, High reflectivity and broad bandwidth AlN/GaN distributed bragg reflectors grown by molecular-beam epitaxy," Applied Physics Letters, vol. 76, no. 20, pp. 2818-2820, 2000.
[14] T.-C. Lu, S.-W. Chen, T.-T. Wu, P.-M. Tu, C.-K. Chen, C.-H.Chen, Z.-Y. Li, H.-C. Kuo, and S.-C. Wang, "Continuous wave operation of current injected GaN vertical cavity surface emitting lasers at room temperature," Applied Physics Letters, vol. 97, no. 7, p. 071114, 2010.
[15] "Ta2O5 refractive index and absorption index." https://iopscience.iop.org/article/10.1088/16741056/26/5/057801/metareferences.
[16] "Refractive index and absorption index." https://www. lmetrics.cn/refractive-index-database.
[17] "PGaN refractive index and absorption index." https://www.researchgate.net/fi gure/The-optical- constants-of-GaN-on-sapphire-vs-wavelength-a-Thefig3202846325.
[18] B. Weigl, M. Grabherr, C. Jung, R. Jager, G. Reiner,
R. Michalzik, D. Sowada, and K. J. Ebeling, "High-performance oxide-confined GaAs vcsels," IEEE Journal of Selected Topics in Quantum Electronics, vol. 3, pp. 409-415, April 1997.
[19] L. Goldstein, C. Fortin, C. Starck, A. Plais, J. Jacquet, J. Bou-cart, A. Rocher, and C. Poussou, "GaAlAs/GaAs metamorphic bragg mirror for long wavelength VCSELs," Electronics Letters, vol. 34, pp. 268-270, Feb 1998.
[20] B. Tell, K. F. Brown?Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, "Temperature dependence of GaAs vertical cavity surface emitting lasers," Applied Physics Letters, vol. 60, no. 6, pp. 683-685, 1992.
[21] S. Mogg, N. Chitica, U. Christiansson, R. Schatz, P. Sundgren, C. Asplund, and M. Hammar, "Temperature sensitivity of the threshold current of long-wavelength InGaAs-GaAs VCSELs with large gain-cavity detuning," IEEE Journal of Quantum Electronics, vol. 40, pp. 453-462, May 2004.
[22] P. Klar, G. Rowland, T. Sale, T. Hosea, and R. Grey, "Reflectance and photomodulated reflectance studies of cavity mode and excitonic transitions in an InGaAs/GaAs/AlAs/AlGaAs VCSEL structure," physica status solidi (a), vol. 170, no. 1, pp. 145-158, 1998.
[23] L.-K. Kwac, W.-C. An, H.-G. Kim, G.-H. Park, J.-S. So, I.-K.Jang, and H.-J. Lee, "Effect of GaP barrier on efficiency enhancement of 860-nm vertical-cavity surface-emitting laser," Infrared Physics Technology, vol. 96, pp. 61 - 67, 2019.