臺灣博碩士論文加值系統

由我們實驗室開發的三維有限元素帕松與漂移-擴散模型能夠與
各種方程解結合來模擬載子傳輸與元件特性，不過目前很難與薛丁
格方程式做結合，所以我們使用了三維有限元素帕松與漂移-擴散模
型結合藍斯蓋特理論。藍斯蓋特理論能夠考慮有效的量子位勢，並
解Hu(r) = (-Δ+Ec;v)u(r) = 1 類薛丁格方程式，這不只能夠避免直
接解需耗費大量時間的薛丁格方程式，還能夠在三維帕松與漂移-擴
散模型中考慮到有效量子位勢。在計算帕松與漂移-擴散模型前，我
們運用了隨機合金分佈擾動產生器得到原子分布以及解應變方程。
在第三章中，考慮藍斯蓋特理論之後的位勢較高且較為平滑導致較
平整的載子分佈。在平均銦含量為14、17與20百分比的發光二極體
中，考慮藍斯蓋特後所解出的極化位勢能夠導致啟動電壓降低。但
在銦含量為11百分比的發光二極體中，是否考慮藍斯蓋特的啟動電
壓差距並不大，因為壓電場極化較小且能帶較寬。在第四章中，我
們模擬了載子在波動量子井厚度的傳輸。在量子井厚度有波動的情
況下，極化電場下降導致在位勢屏障，在不考慮藍斯蓋特所解出來
的啟動電壓會隨著波動量子井厚度增加而降低。然而，啟動電壓在
考慮藍斯蓋特理論下，並不會隨著波動量子井厚度增加而降低，波
動量子井的厚度增加會導致量子井變小增加限制。

In the classical 3-D Poisson drift-diffusion self-consistent solver developed by our lab is versatile that we can combine it with other solvers and functions to simulate the carrier transport behavior and electric characteristic. However, it is hard to couple well with Schrodinger equation and solve them self-consistently under current injection conditions. Therefore, we apply the Poisson drift-diffusion with landscape theory. The landscape theory model is able to consider the quantum effective potential. It solvesHu(r) = (-Δ+Ec;v)u(r) = 1, which is a Schrodinger-like equation with uniform right-hand side and modifies the electron and hole density according to the obtained effective potential (1/u). Not only localized landscape theory avoids solving Schrodinger equation, which is a eigenvalues and eigenvectors problem and it costs much computation time, but also provides the effective quantum potential in the classical Poisson drift-diffusion model. In this thesis, we apply the random alloy generator and strain solver to construct the atom distribution and calculate the strain distribution before solving the Poisson drift-diffusion equations. Simulation results show that quantum well potential solved with landscape model is smoother and higher, which leads to the extended carrier distribution. It also lowering the quantum barrier''s potential due to the quantum tunnelling effects. The forward voltage is smaller as a result. When the random atom distribution is obtained by random number generator, the composition map is decided by a Gaussian weighting function with broadening factor sigma. When sigma increases, the potential and carrier density becomes smoother and forward the voltage declines because of lower potential. Different average indium compositions from 11%, 14%, 17% to 20% were studied. It appears that lower piezoelectric potential would be obtained with landscape model which leads to the decrease of forward voltage. But in the In0.11Ga0.89N case, the forward voltages solved with and without landscape are closed because peizo-polarization is smaller and the bandgap is higher. In chapter 4, we simulate the carrier transport behavior in the fluctuate quantum well(QW) thickness. With fluctuated thickness in a larger scale compared to local indium fluctuation, the polarization declines and provides a percolation path at the barrier. The forward voltages solved without landscape decline with increasing fluctuate thickness. However, fluctuated thickness may leads to the stronger confinement, larger effective bandgap and reduction of forward voltage.

目錄
口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . i
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Random Alloy Fluctuation . . . . . . . . . . . . . . . . 4
1.3 3D Drift-Diffusion Charge Control Solver (3D-DDCC) . 5
1.4 Schrodinger solver and Localization Landscape [1] . . . 7
1.5 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . 10
2 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Computation Algorithm . . . . . . . . . . . . . . . . . 12
2.2 Generation of the Random Alloy Composition Map . . 14
2.3 3D FEM Elastic Strain Solver . . . . . . . . . . . . . . 18
2.4 3-D Poisson Drift-Diffusion Self-Consistent Solver . . . 22
2.5 3-D Localization Landscape Drift-Diffusion Self-Consistent
Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Percolation Transport in the Poisson Drift-Diffusion with and
without Localized Landscape Theory . . . . . . . . . . . . . 27
3.1 3D Carrier Transport in LED Structures . . . . . . . . 28
3.2 The Different Broadening Factor in The Gaussian
Weighting Function . . . . . . . . . . . . . . . . . . . . 36
3.3 The Different Average Indium Composition . . . . . . 40
4 The Fluctuation of Quantum Well Thickness . . . . . . . . . 44
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Bibliography
[1] M. Filoche and S. Mayboroda, Universal mechanism for Anderson and weak localization," Proceedings of the National Academy of Sciences, vol. 109, no. 37, pp. 14761{14766, 2012.
[2] D. A. Browne, B. Mazumder, Y.-R. Wu, and J. S. Speck, Electron transport in unipolar InGaN/GaN multiple quantum well structures grown by NH3 molecular beam epitaxy," Journal of Applied Physics, vol. 117, no. 18, p. 185703, 2015.
[3] T.-J. Yang, R. Shivaraman, J. S. Speck, and Y.-R. Wu, The inuence of random indium alloy fluctuations in indium gallium nitride quantum wells on the device behavior," Journal of Applied Physics, vol. 116, no. 11, p. 113104, 2014.
[4] Wikipedia, Trilinear interpolation | Wikipedia, The Free Encyclopedia," 2016. [Online; accessed 30-June-2016].
[5] A. Romanov, T. Baker, S. Nakamura, and J. Speck, Strain-induced polarization in wurtzite III-nitride semipolar layers," Journal of Applied Physics, vol. 100, no. 2, 2006.
[6] S. Nakamura, T. Mukai, and M. Senoh, Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes," Applied Physics Letters, vol. 64, no. 13, pp. 1687-1689, 1994.
[7] Amano, Hiroshi and Kito, Masahiro and Hiramatsu, Kazumasa and Akasaki, Isamu, P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI)," Japanese Journal of Applied Physics, vol. 28, no. 12A, p. L2112, 1989.
[8] Amano, Hi and Sawaki, N and Akasaki, I and Toyoda, Y, Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer," Applied Physics Letters, vol. 48, no. 5, pp. 353-355, 1986.
[9] Delaney, Kris T and Rinke, Patrick and Van de Walle, Chris G, Auger recombination rates in nitrides from rst principles," Applied Physics Letters, vol. 94, no. 19, p. 191109, 2009.
[10] Kioupakis, Emmanouil and Rinke, Patrick and Delaney, Kris T and Van de Walle, Chris G, Indirect Auger recombination as acause of efficiency droop in nitride light-emitting diodes," Applied
Physics Letters, vol. 98, no. 16, p. 161107, 2011.
[11] Iveland, Justin and Martinelli, Lucio and Peretti, Jacques and Speck, James S and Weisbuch, Claude, Direct measurement of Auger electrons emitted from a semiconductor light-emitting diode under electrical injection: identi cation of the dominant mechanism for efficiency droop," Physical review letters, vol. 110, no. 17, p. 177406, 2013.
[12] M. Binder, A. Nirschl, R. Zeisel, T. Hager, H.-J. Lugauer, M. Sabathil, D. Bougeard, J. Wagner, and B. Galler, Identification of nnp and npp Auger recombination as signifi cant contributor to the efficiency droop in (GaIn) N quantum wells by visualization of hot carriers in photoluminescence," Applied Physics Letters, vol. 103, no. 7, p. 071108, 2013.
[13] C.-K. Li, M. Rosmeulen, E. Simoen, and Y.-R.Wu, Study on the optimization for current spreading effect of lateral GaN/InGaN LEDs," Electron Devices, IEEE Transactions on, vol. 61, no. 2, pp. 511-517, 2014.
[14] V. Malyutenko, S. Bolgov, and A. Podoltsev, Current crowding effect on the ideality factor and efficiency droop in blue lateral InGaN/GaN light emitting diodes," Applied Physics Letters, vol. 97, no. 25, p. 251110, 2010.
[15] J.-H. Ryou, P. D. Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, Control of quantum-con ned stark effect in InGaN-based quantum wells," Selected Topics in Quantum Electronics, IEEE Journal of, vol. 15, no. 4, pp. 1080-1091, 2009.
[16] J. Piprek, Efficiency droop in nitride-based light-emitting diodes," physica status solidi (a), vol. 207, no. 10, pp. 2217-2225, 2010.
[17] C.-K. Wu, C.-K. Li, and Y.-R. Wu, Percolation transport study in nitride based LED by considering the random alloy fluctuation," Journal of Computational Electronics, vol. 14, no. 2, pp. 416-424, 2015.
[18] M. Filoche and S. Mayboroda, Universal mechanism for Anderson and weak localization," Proceedings of the National Academy of Sciences, vol. 109, no. 37, pp. 14761-14766, 2012.
[19] D. Watson-Parris, M. Godfrey, P. Dawson, R. Oliver, M. Galtrey, M. Kappers, and C. Humphreys, Carrier localization mechanisms in InxGa1-xN/GaN quantum wells," Physical Review B, vol. 83, no. 11, p. 115321, 2011.
[20] S. E. Bennett, D. W. Saxey, M. J. Kappers, J. S. Barnard, C. J. Humphreys, G. D. Smith, and R. A. Oliver, Atom probe tomography assessment of the impact of electron beam exposure on InxGa1-xN/GaN quantum wells," Applied Physics Letters, vol. 99, no. 2, p. 021906, 2011.
[21] R. Shivaraman, Y. Kawaguchi, S. Tanaka, S. DenBaars, S. Nakamura, and J. Speck, Comparative analysis of 2021 and 2021 semipolar gan light emitting diodes using atom probe tomography," Applied Physics Letters, vol. 102, p. 251104, 2013.
[22] B. Mazumder, M. Esposto, T. H. Hung, T. Mates, S. Rajan, and J. S. Speck, Characterization of a dielectric/GaN system
using atom probe tomography," Applied Physics Letters, vol. 103, no. 15, p. 151601, 2013.
[23] J. R. Riley, T. Detchprohm, C. Wetzel, and L. J. Lauhon, On the reliable analysis of indium mole fraction within InxGa1-xN quantum wells using atom probe tomography," Applied Physics Letters, vol. 104, no. 15, p. 152102, 2014.
[24] S. E. Bennett, T. M. Smeeton, D. W. Saxey, G. D. Smith, S. E. Hooper, J. Heffernan, C. J. Humphreys, and R. A. Oliver, Atom probe tomography characterisation of a laser diode structure grown by molecular beam epitaxy," Journal of Applied Physics, vol. 111, no. 5, p. 053508, 2012.
[25] C.-K. Li, C.-K. Wu, C.-C. Hsu, L.-S. Lu, H. Li, T.-C. Lu, and Y.-R. Wu, 3D numerical modeling of the carrier transport and radiative efficiency for InGaN/GaN light emitting diodes with V-shaped pits," AIP Advances, vol. 6, no. 5, p. 055208, 2016.
[26] H.-H. Hsiao, H.-C. Chang, and Y.-R. Wu, Design of anti-ringback reflectors for thin-film solar cells based on three-dimensional optical and electrical modeling," Applied Physics Letters, vol. 105, no. 6, p. 061108, 2014.
[27] C.-Y. Lee, C.-M. Yeh, Y.-T. Liu, C.-M. Fan, C.-F. Huang, and Y.-R. Wu, The optimization study of textured a-Si:H solar cells," Journal of Renewable and Sustainable Energy, vol. 6, no. 2, p. 023111, 2014.
[28] K.-Y. Ho, C.-Y. Hong, P. Yu, and Y.-R. Wu, Optimization of All-Back-Contact GaAs Solar Cells," in Numerical Simulation of Optoelectronic Devices (NUSOD), 2015 International Conference on, pp. 143-144, IEEE, 2015.
[29] K.-Y. Ho, I.-H. Lu, and Y.-R. Wu, Development of numerical modeling program for organic/inorganic hybrid solar cells by including tail/interfacial states models," in SPIE OPTO, pp. 974308{974308, International Society for Optics and Photonics, 2016.
[30] D. Graham, A. Soltani-Vala, P. Dawson, M. Godfrey, T. Smeeton, J. Barnard, M. Kappers, C. Humphreys, and E. Thrush, Optical and microstructural studies of ingan/ gan single-quantum-well structures," Journal of applied physics, vol. 97, no. 10, p. 103508, 2005.
[31] S. Chichibu, K. Wada, and S. Nakamura, Spatially resolved cathodoluminescence spectra of ingan quantum wells," Applied physics letters, vol. 71, no. 16, pp. 2346{2348, 1997.
[32] S. Chichibu, T. Sota, K. Wada, and S. Nakamura, Exciton localization in ingan quantum well devices," Journal of Vacuum Science & Technology B, vol. 16, no. 4, pp. 2204-2214, 1998.
[33] C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D nite element mesh generator with built-in pre-and post-processing facilities," International Journal for Numerical Methods in Engineering, vol. 79, no. 11, pp. 1309-1331, 2009.
[34] Y. Sun, S. E. Thompson, and T. Nishida, Strain effect in semiconductors: theory and device applications. Springer Science & Business Media, 2009.
[35] A. David and M. J. Grundmann, Droop in InGaN light-emitting diodes: A differential carrier lifetime analysis," Applied Physics Letters, vol. 96, no. 10, p. 103504, 2010.
[36] Q. Dai, Q. Shan, J. Wang, S. Chhajed, J. Cho, E. F. Schubert, M. H. Crawford, D. D. Koleske, M.-H. Kim, and Y. Park, Carrier recombination mechanisms and efficiency droop in GaInN/GaN light-emitting diodes," Appl. Phys. Lett, vol. 97, no. 13, p. 133507, 2010.