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研究生:張誌原
研究生(外文):Jih-Yuan Chang
論文名稱:GaN/InGaN p-i-n太陽能電池極化效應之數值分析
論文名稱(外文):Numerical investigation of polarization effect on GaN/InGaN p-i-n solar cells
指導教授:郭艷光Yen-Kuang Kuo
學位類別:博士
校院名稱:國立彰化師範大學
系所名稱:物理學系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:117
中文關鍵詞:III-V族氮化物太陽能電池極化效應數值模擬
外文關鍵詞:III-nitridesolar cellpolarization effectnumerical simulation
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在wurtzite結構的III-V族氮化物材料系統中,由於缺乏反轉對稱性以及壓電張量不為零之故,其晶格在沿著c軸方向具有強烈的自發極化以及壓電極化。於發光元件中,例如發光二極體與雷射二極體,此一極化效應會對載子的傳輸與分佈造成相當嚴重的影響,因而降低元件性能。而在光伏元件的應用上,目前只有少數文獻在探討相關效應,以至於極化效應如何影響元件性能之物理機制目前仍尚缺乏。有鑑於此,本論文以數值模擬的方式探討內部極化效應對氮化鎵/氮化銦鎵p-i-n太陽能電池性能之影響。除此之外,對於傳統沿著(0001)方位成長的p-on-n太陽能電池,亦針對其有害的極化效應提出相對應之有效與實用的解決方法。
在本論文的第一章中,首先對III-V族氮化物材料系統在高效率多接面串接式太陽能電池中所扮演的角色與其重要性做一介紹。其優異的光伏特性以及目前發展上的阻礙與限制亦加以探討。
在第二章中介紹了本研究所使用APSYS模擬軟體的重要物理機制以及模擬相關的材料參數。
第三章分別探討自發極化與壓電極化對Ga-face以及N-face氮化鎵/氮化銦鎵p-i-n太陽能電池光伏特性之影響。關於內部極化效應如何影響元件性能之物理機制將被詳細的分析與探討。另外,更進一步系統性的模擬與比較此一結構太陽能電池在各種銦濃度以及各種極化程度條件下,極化效應之影響。
由於III-V族氮化物元件最常見的結構配置是p-on-n以及Ga-face結構,因此在第四章中將探討如何在各異質層之間使用步階漸變式中間層來降低極化效應之影響。除此之外,亦針對步階漸變式中間層之厚度與p型摻雜濃度進行系統性的探討與分析,以找出具有較佳轉換效率的太陽能電池結構。
最後,在第五章為第三、四章的研究結果做一個完整的結論。

The III–nitride materials in their wurtzite structure possess large spontaneous and piezoelectric polarizations owing to inversion asymmetry and nonvanishing piezoelectric tensors in conventional c-directions. In lighting devices, such as the light-emitting diodes and laser diodes, the polarization effect exerts a substantial influence on the carrier transport and distribution, and thus degrades the device performance. As for the photovoltaic devices, there are few papers which probe into this field and thus the effectiveness of polarization is still debatable. In this dissertation, the effects of internal polarization on the performance of GaN/InGaN p-i-n solar cells are numerically investigated. In addition, efficient and practical solutions to the detrimental polarization effect in the conventional p-on-n solar cells along the (0001) orientation are proposed.
In chapter 1, the role and importance of III-nitride materials in the application of high-efficiency multi-junction tandem solar cells are introduced. The superior photovoltaic characteristics, and the limitations and obstructions of III-nitride materials for the development of photovoltaic devices are also reviewed.
In chapter 2, the physical models relevant to the solar cell structures and the material parameters employed in the simulation are introduced.
In chapter 3, the influences of spontaneous and piezoelectric polarizations on the photovoltaic characteristics of Ga-face and N-face GaN/InGaN p-i-n solar cells are investigated numerically. Detailed physical mechanisms about how the internal polarization affects the solar cell performance is proposed. Specifically, the polarization effect in the solar cell structures with various indium compositions and various degrees of relaxation are analyzed and compared systematically.
Since the most commonly fabricated III-nitride devices are with the p-on-n and Ga-face configuration, in chapter 4, the polarization compensation step-graded interlayers are proposed between the hetero-layers to efficiently mitigate the detrimental polarization effect. Furthermore, optimization of the solar cell to maximize the energy conversion efficiency is attempted by fine-tuning the thicknesses of step-graded interlayers and the p-doping concentrations.
Finally, the research results obtained from chapters 3 and 4 are concluded in chapter 5.

目錄
Outline I
Abstract IV
Figure and table captions VIII
Chapter 1 Introduction to III-nitride solar cells 1
1.1 Efficiency limitation in single-junction solar cell 2
1.1.1 Trade-off between “transparency loss” and “excess-
excitation loss” 2
1.1.2 Trade-off between “short-circuit current”and
“open-circuit voltage” 5
1.1.3 Solution to the limited efficiency: multiple
bandgaps 8
1.2 The possibility of III-nitrides 11
1.2.1 Fill the material vacancy in the short wavelength
region of solar spectrum 11
1.2.2 Superior photovoltaic characteristics 15
1.3 The challenges in III-nitride solar cells 16
1.3.1 Thick and high-quality InGaN layers 16
1.3.2 P-type doping 18
1.3.3 Polarization effect 22
1.3.4 Tunnel junction 25
1.4 Conclusion 30
References 32
Chapter 2 Numerical models and parameters 42
2.1 Numerical models 42
2.1.1 Drift and Diffusion 42
2.1.2 Band structure 44
2.1.3 SRH recombination 46
2.2 Material parameters 49
References 51
Chapter 3 Polarization effect of p-on-n GaN/InGaN p-i-n
solar cells in Ga- and N-face configurations 54
3.1 GaN/InGaN p-i-n solar cell structure 55
3.2 Photovoltaic characteristics without polarization
effect 57
3.3 Calculation of polarizations in III-nitrides 58
3.4 Polarization effect in Ga-face configuration 61
3.4.1 Preliminary aspects 61
3.4.2 Polarization-induced surface charge densities 64
3.4.3 Simulation results and discussions 65
3.5 Polarization effect in N-face configuration 71
3.6 Conclusion 81
References 83
Chapter 4 Effects of step-graded interlayers in p-on-n and
Ga-face GaN/InGaN p-i-n solar cells 87
4.1 Effect of hetero-interfaces 88
4.2 Effect of p-type doping concentration 92
4.3 Effect of polarization charges 93
4.4 Influences of step-graded interlayers 98
4.5 Thickness of step-graded interlayers 102
4.6 P-type doping concentration of step-graded
interlayers 104
4.7 Conclusion 111
References 112
Chapter 5 Conclusion 115
Appendix 1 Publication list i
Appendix 2-Simulation input files vi

圖目錄
Fig.1.1 Schematic diagram of the optical generation process
in various conditions of photon energy 3
Fig.1.2 Graphical indication of the transparency loss and
excess- excitation loss in AM0 solar spectrum 4
Fig.1.3 Schematic diagram of the optical generation process
and the acceleration of excited electron via normal
built-in field in the depletion region of a p-n
junction solar cell 5
Fig.1.4 (a) Schematic diagram of the conversion efficiency,
open-circuit voltage and short-circuit current as a
function of the bandgap of single-junction solar
cell. (b) Calculated efficiency in the literature 6
Fig.1.5 Usable power of the solar spectrum for a 3-junction
tandem solar cell. The bandgaps of the top, middle
and bottom cell are Eg1, Eg2 and Eg3, respectively
(Eg1>Eg2>Eg3) 9
Fig.1.6 Expected output performance of multi-junction
tandem solar cells with a different number of sub-
cells 10
Fig.1.7 The relationships between bandgap energy and
lattice constant for III-V compounds and elemental
semiconductors 12
Fig.1.8 Perfect matching of bandgap of In1–xGaxN to solar
spectrum 14
Fig.1.9 Schematic band diagram of a 10-junction tandem
solar cell designed using InGaN-based materials 14
Fig.1.10 Calculated critical thickness against composition
curves for the single-layer InxGa1–xN/GaN system
from (a) theoretical study and (b) experimental
measurements 17
Fig.1.11 (a) Calculated valance-band diagram and (b) Hall-
effect measurements for the Mg-doped
Al0.2Ga0.8N/GaN superlattice with polarization
fields considered 20
Fig.1.12 Schematic illustration of (A) sheets of charge
dipoles in every unit cell of the graded polar
hetero-structures. The net unbalanced polarization
charge is shown in (B), which leads to the
electric field in (C), and the energy band bending
in the valance band in (D) if holes are not
ionized. Field ionization of holes results in a .
steady-state band diagram shown in (E). (F) is the
temperature- dependent hole concentration 21
Fig.1.13 Schematic diagram of the crystal structure of
wurtzite Ga-face and N-face GaN 23
Fig.1.14 Schematic diagrams of surface charges, and
direction of electric field and polarization
dipole for spontaneous and piezoelectric
polarizations in III-nitrides for Ga- and N-face
orientation 24
Fig.1.15 Appropriate ternary alloy for the material of
intermediate layer between n- and p-GaN layers in
various configurations of polarization-assisted
tunnel structure 26
Fig.1.16 Electrical characteristics of Ga-face p-GaN/p-
InGaN/n-GaN tunnel diode in the reversed bias
regime under various conditions of polarization,
doping concentration and indium composition 27
Fig.1.17 Energy band diagrams of Ga-face p-GaN/p-InGaN/n-
GaN tunnel diode at equilibrium under various
conditions of polarization, doping concentration
and indium composition 28
Fig.3.1 Schematic diagram of GaN/InGaN p-i-n solar cell
under study 56
Fig.3.2 Energy band diagrams under (a) zero and (b) 2 V
biases, and (c) J-V-P performance curves of
GaN/In0.10Ga0.90N p-i-n solar cell under AM1.5G
illumination without polarization 57
Fig.3.3 Spontaneous, piezoelectric and total polarizations
in ternary AlGaN and InGaN alloys based on full-
relaxed GaN basal layer 60
Fig.3.4 Schematic diagram of polarizations in different
epitaxial layers of conventional p-on-n GaN/InGaN p-
i-n structure with Ga-face configuration 62
Fig.3.5 Schematic band diagram of Ga-faced p-on-n GaN/InGaN
p-i-n structure under various conditions of
polarization-induced electric field 62
Fig.3.6 Energy band diagrams under zero and 2 V biases, and
J-V-P performance curves of GaN/In0.10Ga0.90N p-i-n
solar cell with different degrees of relaxation 66
Fig.3.7 Electric field of GaN/In0.10Ga0.90N p-i-n solar
cell (a) at zero bias with different situations of
polarization and (b) under R=0.8 condition with
different values of forward bias 67
Fig.3.8 Energy band diagrams under zero and 2 V biases, and
J-V-P performance curves of GaN/In0.20Ga0.80N p-i-n
solar cell with different degrees of relaxation 69
Fig.3.9 Conversion efficiencies of GaN/InGaN p-i-n solar
cells with different values of R. The inset shows
the enlarged drawing when the value of R is within
the range of 0.5 to 1 70
Fig.3.10 Schematic diagrams of the polarizations in
different epitaxial layers of the p-on-n GaN/InGaN
p-i-n structure with (a) Ga-face and (b) N-face
configurations 71
Fig.3.11 Electric field of GaN/In0.20Ga0.80N p-i-n solar
cell at zero bias with different situations of
polarization under AM1.5G illumination 72
Fig.3.12 Energy band diagram under zero bias and J-V-P
curves of GaN/In0.20Ga0.80N p-i-n solar cell with
different situations of polarization under AM1.5G
illumination 74
Fig.3.13 Enlarged energy band diagrams in the
heterojunction interfaces of GaN/In0.20Ga0.80N
p-i-n solar cell with different situations of
polarization under zero bias and AM1.5G
illumination 75
Fig.3.14 SRH recombination rate of GaN/In0.20Ga0.80N p-i-n
solar cell with different situations of
polarization under zero bias and AM1.5G
illumination. Fig. 3.14(b) is the enlarged plot of
Fig. 3.14(a) by 100 times in magnitude 77
Fig.3.15 Conversion efficiencies of GaN/InxGa1-xN p-i-n
solar cells with different degrees of relaxation
and different situations of polarization under
AM1.5G illumination 78
Fig.3.16 J-V curves of GaN/In0.25Ga0.75N p-i-n solar cell
with different SRH lifetimes and different degrees
of relaxation under AM1.5G illumination in N-face
configuration 80
Fig.4.1 (a) Conversion efficiencies of GaN/InGaN p-i-n
solar cells as a function of indium composition
with various p-type doping concentrations under
the situation of no polarization. (b) J-V curves
of GaN/InGaN p-i-n solar cells with 10%, 20% and
30% indium composition and 5×1018 cm–3 hole
concentration under the situation of no
polarization 89
Fig.4.2 Energy band diagrams of GaN/InGaN p-i-n solar cells
with 10%, 20% and 30% indium composition and 5×1018
cm–3 hole concentration at (a) (b) (c) equilibrium
state and (d) (e) (f) AM1.5G illumination under the
situation of no polarization. The dashed lines
represent the Fermi/quasi-Fermi levels 90
Fig.4.3 (a) Optical generation rates and (b) SRH
recombination rates of GaN/InGaN p-i-n solar cells
with 10%, 20% and 30% indium composition and 5×1018
cm–3 hole concentration at zero bias under the
situation of no polarization. (c) is the enlarged
plot of (b) 91
Fig.4.4 (a) Conversion efficiencies of GaN/InGaN p-i-n
solar cells as a function of indium composition and
(b) J-V curves of GaN/In0.2Ga0.8N p-i-n solar cells
under the situations of no polarization, R=1.0, and
R=0.5 (Ga-face, hole concentration = 5×1018 cm–3)94
Fig.4.5 Energy band diagrams of the GaN/In0.2Ga0.8N p-i-n
solar cells under the situations of no
polarization, R=1.0, and R=0.5 at (a) (b) (c)
equilibrium state and (d) (e) (f) AM1.5G
illumination (Ga-face, hole concentration = 5×1018
cm–3) 96
Fig.4.6 (a) Electric fields of the GaN/In0.2Ga0.8N p-i-n
solar cells at equilibrium under the situations of
no polarization, R=1.0, and R=0.5 (Ga-face, hole
concentration = 5×1018 cm–3). (b) Enlarged plot of
(a) 97
Fig.4.7 Schematic diagram of the structure with step-graded
interlayers 99
Fig.4.8 (a) and (b) Energy band diagrams at equilibrium and
(c) J-V curves of the GaN/In0.3Ga0.7N p-i-n solar
cells with and without 45-nm-thick grading layer
under the situation of no polarization 99
Fig.4.9 (a) and (b) Energy band diagrams and (c) electric
fields at zero bias of the GaN/In0.3Ga0.7N p-i-n
solar cells with and without 45-nm-thick grading
layer under the situation of R=0.5 101
Fig.4.10 Conversion efficiencies of GaN/In0.3Ga0.7N p-i-n
solar cells as a function of R with different
thicknesses of grading layer 103
Fig.4.11 Energy band diagrams and electric fields at
equilibrium of the GaN/In0.3Ga0.7N p-i-n solar
cells with (a) (c) 72-nm grading layer and (b) (d)
27-nm grading layer under the situation of R=0.4
104
Fig.4.12 Conversion efficiencies of the GaN/In0.3Ga0.7N
p-i-n solar cells with 81-nm-thick grading layer
as a function of R with various p-type doping
concentrations for both p-GaN and p-grading
layers 105
Fig.4.13 Energy band diagrams at equilibrium of the
GaN/In0.3Ga0.7N p-i-n solar cells with various
conditions of (a) without grading layer, p-doping:
51018 cm−3; (b) with grading layer (81 nm), p- doping: 51018 cm−3; (c) without grading layer, p-
doping: 51017 cm−3; (b) with grading layer (81
nm), p-doping: 51017 cm−3 107
Fig.4.14 Electric fields at equilibrium of the
GaN/In0.3Ga0.7N p-i-n solar cells with various
conditions of (a) without grading layer, p-doping:
51018 cm−3; (b) with grading layer (81 nm), p-
doping: 51018 cm−3; (c) without grading layer, p-
doping: 51017 cm−3; (b) with grading layer (81
nm), p-doping: 51017 cm−3 108
Fig.4.15 Conversion efficiencies of GaN/In0.3Ga0.7N p-i-n
solar cells with 81-nm-thick grading layer as a
function of R with various hole concentrations of
p-grading layer. The hole concentration of p-GaN
layer is 5×1017 cm–3 110

表目錄
Tab.2.1 Material parameters of the binary semiconductors
GaN, AlN, and InN at room temperature. (Δcr = Δ1,
Δso = 3Δ2 = 3Δ3.) 47
Tab.2.2 Fitting parameters used to calculate the absorption
coefficient of InxGa1–xN alloys 50
Tab.3.1 Polarization-induced surface charge densities in
InxGa1–xN/GaN hetero-interfaces with various
values of R 64
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58. M. J. Grundmann and U. K. Mishra, “Multi-color light emitting diode using polarization-induced tunnel junctions,” Phys. Status Solidi C 4, 2830 (2007).
59. S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett. 73, 2006 (1998).
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61. H. Zhang, E. J. Miller, E. T. Yu, C. Poblenz, and J. S. Speck, “Measurement of polarization charge and conduction-band offset at InxGa1–xN/GaN heterojunction interfaces,” Appl. Phys. Lett. 84, 4644 (2004).


第二章
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16. M. Moret, B. Gil, S. Ruffenach, O. Briot, Ch. Giesen, M. Heuken, S. Rushworth, T. Leese, and M. Succi, “Optical, structural investigations and band-gap bowing parameter of GaInN alloys,” J. Cryst. Growth 311, 2795 (2009).
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20. K. Kumakura, T. Makimoto, and N. Kobayashi, “Mg-acceptor activation mechanism and transport characteristics in p-type InGaN grown by metalorganic vapor phase epitaxy,” J. Appl. Phys. 93, 3370 (2003).
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22. G. F. Brown, J. W. Ager III, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells 94, 478 (2010).


第三章
1. D. A. B. Miller, D. S. Chemla, and T. C. Damen, “Band-edge electroabsorption in quantum well structure: The quantum-confined Stark effect,” Phys. Rev. Lett. 53, 2173 (1984).
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3. Y.-K. Kuo, J.-Y. Chang, M.-C. Tsai, and S.-H. Yen, “Advantages of blue InGaN multiple-quantum well light-emitting diodes with InGaN barriers,” Appl. Phys. Lett. 95, 011116 (2009).
4. M. H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (2007).
5. M. F. Schubert, J. Xu, J. K. Kim, E. F. Schubert, M. H. Kim, S. Yoon, S. M. Lee, C. Sone, T. Sakong, and Y. Park, “Polarization-matched GaInN/AlGaInN multi-quantum-well light-emitting diodes with reduced efficiency droop,” Appl. Phys. Lett. 93, 041102 (2008).
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8. D. Zhu, J. Xu, A. N. Noemaun, J. K. Kim, E. F. Schubert, M. H. Crawford, and D. D. Koleske, “The origin of the high diode-ideality factors in GaInN/GaN multiple quantum well light-emitting diodes,” Appl. Phys. Lett. 94, 081113 (2009).
9. J. R. Chen, T. C. Lu, H. C. Kuo, K. L. Fang, K. F. Huang, C. W. Kuo, C. J. Chang, C. T. Kuo, and S. C. Wang, “Study of InGaN–GaN light-emitting diodes with different last barrier thicknesses,” IEEE Photon. Technol. Lett. 22, 860 (2010).
10. V. Fiorentini, F. Bernardini, and O. Ambacher, “Evidence for nonlinear macroscopic polarization in III–V nitride alloy heterostructures,” Appl. Phys. Lett. 80, 1204 (2002).
11. O. Ambacher, B. Foutz, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, A. J. Sierakowski, W. J. Schaff, L. F. Eastman, R. Dimitrov, A. Mitchell, and M. Stutzmann, “Two dimensional electron gases induced by spontaneous and piezoelectric polarization in undoped and doped AlGaN/GaN heterostructures,” J. Appl. Phys. 87, 334 (2000).
12. S. F. Chichibu, A. C. Abare, M. S. Minsky, S. Keller, S. B. Fleischer, J. E. Bowers, E. Hu, U. K. Mishra, L. A. Coldren, S. P. DenBaars, and T. Sota, “Effective band gap inhomogeneity and piezoelectric field in InGaN/GaN multiquantum well structures,” Appl. Phys. Lett. 73, 2006 (1998).
13. F. Renner, P. Kiesel, G. H. Döhler, M. Kneissl, C. G. Van de Walle, and N. M. Johnson, “Quantitative analysis of the polarization fields and absorption changes in InGaN/GaN quantum wells with electroabsorption spectroscopy,” Appl. Phys. Lett. 81, 490 (2002).
14. H. Zhang, E. J. Miller, E. T. Yu, C. Poblenz, and J. S. Speck, “Measurement of polarization charge and conduction-band offset at InxGa1–xN/GaN heterojunction interfaces,” Appl. Phys. Lett. 84, 4644 (2004).
15. D. Holec, P. M. F. J. Costa, M. J. Kappers, and C. J. Humphreys, “Critical thickness calculations for InGaN/GaN,” J. Cryst. Growth 303, 314 (2007).
16. Y. G. Xiao, Z. Q. Li, M. Lestrade, and Z. M. Simon Li, “Modeling of InGaN PIN solar cells with defect traps and polarization interface charges,” Proc. 35th IEEE Photovoltaic Spec. Conf., 003378 (2010).
17. S. O. Kasap, Optoelectronics and photonics: Principles and Practices, Taiwan: Pearson Education Taiwan LTD., 2012, pp. 130–131.
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19. Z. Q. Li, M. Lestradet, Y. G. Xiao, and S. Li, “Effects of polarization charge on the photovoltaic properties of InGaN solar cells,” Phys. Status Solidi A 208, 928 (2010).
20. M. Lestrade, Z. Q. Li, Y. G. Xiao, and Z. M. Simon Li, “Modeling of polarization effects in InGaN PIN solar cells,” Opt. Quantum Electron. 42, 699 (2011).
21. J.-Y. Chang and Y.-K. Kuo, “Comment on “The impact of piezoelectric polarization and nonradiative recombination on the performance of (0001) face GaN-InGaN photovoltaic devices” [Appl. Phys. Lett. 96, 051107 (2010)],” Appl. Phys. Lett. 98, 036101 (2011).
22. J.-Y. Chang and Y.-K. Kuo, “Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (0001)-face GaN/InGaN p-i-n solar cells,” IEEE Electron Device Lett. 32, 937 (2011).
23. Y.-K. Kuo, J.-Y. Chang, and Y.-H. Shih, “Numerical study of the effects of hetero-interfaces, polarization charges, and step-graded interlayers on the photovoltaic properties of (0001) face GaN/InGaN p-i-n solar cell,” IEEE J. Quantum Electron. 48, 367 (2012).
24. J.-Y. Chang and Y.-K. Kuo, “Simulation of N-face InGaN-based p-i-n Solar Cells,” J. Appl. Phys., accepted 12 July 2012.


第四章
1. P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, and K. H. Ploog, “Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes,” Nature 406, 865 (2000).
2. M. D. Craven, S. H. Lim, F. Wu, J. S. Speck, and S. P. DenBaars, “Structural characterization of nonpolar (11 0) a-plane GaN thin films grown on (1 02) r-plane sapphire,” Appl. Phys. Lett. 81, 469 (2002).
3. Y. S. Park, H. S. Lee, J. H. Na, H. J. Kim, S. M. Si, H.-M. Kim, T. W. Kang, and J. E. Oh, “Polarity determination for GaN/AlGaN/GaN heterostructures grown on (0001) sapphire by molecular beam epitaxy,” J. Appl. Phys. 94, 800 (2003).
4. M.-H. Kim, M. F. Schubert, Q. Dai, J. K. Kim, E. F. Schubert, J. Piprek, and Y. Park, “Origin of efficiency droop in GaN-based light-emitting diodes,” Appl. Phys. Lett. 91, 183507 (2007).
5. Y.-K. Kuo, J.-Y. Chang, M.-C. Tsai, and S.-H. Yen, “Enhancement in hole-injection efficiency of blue InGaN light-emitting diodes from reduced polarization by some specific designs for the electron blocking layer,” Opt. Lett. 35, 3285 (2010).
6. C. H. Wang, C. C. Ke, C. Y. Lee, S. P. Chang, W. T. Chang, J. C. Li, Z. Y. Li, H. C. Yang, H. C. Kuo, T. C. Lu, and S. C. Wang, “Hole injection and efficiency droop improvement in InGaN/GaN lightemitting diodes by band-engineered electron blocking layer,” Appl. Phys. Lett. 97, 261103 (2010).
7. G. F. Brown, J. W. Ager III, W. Walukiewicz, and J. Wu, “Finite element simulations of compositionally graded InGaN solar cells,” Sol. Energy Mater. Sol. Cells 94, 478 (2010).
8. S. D. Burnham, G. Namkoong, D. C. Look, B. Clafin, W. A. Doolitte, “Reproducible increased Mg incorporation and large hole concentration in GaN using metal modulated epitaxy,” J. Appl. Phys. 104, 024902 (2008).
9. A. Bhattacharyya, W. Li, J. Cabalu, T. D. Moustakas, D. J. Smith, and R. L. Hervig, “Efficient p-type doping of GaN films by plasma-assisted molecular beam epitaxy,” Appl. Phys. Lett. 85, 4956 (2004).
10. Y.-K. Kuo, J.-Y. Chang, M.-C. Tsai, and S.-H. Yen, “Enhancement in hole-injection efficiency of blue InGaN light-emitting diodes from reduced polarization by some specific designs for the electron blocking layer,” Opt. Lett. 35, 3285 (2010).
11. C. H. Wang, C. C. Ke, C. Y. Lee, S. P. Chang, W. T. Chang, J. C. Li, Z. Y. Li, H. C. Yang, H. C. Kuo, T. C. Lu, and S. C. Wang, “Hole injection and efficiency droop improvement in InGaN/GaN light-emitting diodes by band-engineered electron blocking layer,” Appl. Phys. Lett. 97, 261103 (2010).
12. J.-Y. Chang, B.-T. Liou, H.-W. Lin, Y.-H. Shih, S.-H. Chang, and Y.-K. Kuo, “Numerical investigation on the enhanced carrier collection efficiency of Ga-face GaN/InGaN p-i-n solar cells with polarization compensation interlayers,” Opt. Lett. 36, 3500 (2011).
13. M. R. Islam, Y. Ohmura, A. Hashimoto, A. Yamamoto, K. Kinoshita, and Y. Koji, “Step-graded interlayers for the improvement of MOVPE InxGa1–xN (x~0.4) epi-layer quality,” Phys. Status Solidi C 7, 2097 (2010).
14. K. Kumakura, T. Makimoto, and N. Kobayashi, “High hole concentrations in Mg-doped InGaN grown by MOVPE,” J. Cryst. Growth 221, 267 (2000).


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