國立彰化師範大學物理研究所 博士論文 指導教授 : 郭艷光教授. Numerical investigation of polarization effect on. GaN/InGaN p-i-n solar cells 研究生 : 張誌原撰 中華民國一百零一年七月

Transcription

1 國立彰化師範大學物理研究所 博士論文 指導教授 : 郭艷光教授 GaN/InGaN p-i-n 太陽能電池極化效應之數值分析 Numerical investigation of polarization effect on GaN/InGaN p-i-n solar cells 研究生 : 張誌原撰 中華民國一百零一年七月

2 誌謝 誠摯的感謝指導教授郭艷光老師 老師從我大學 碩士班至現今完成博士修業, 始終如一的循循善誘與教誨, 使我從當初懵懂無知的小毛頭成長蛻變為現今的我 在老師的身上, 我不只學習到專業知識與學術能力, 您那正直無私的性格 親切和藹的待人處事以及對事物的熱忱 責任與自信, 在在都不知不覺間對我們產生潛移默化的作用, 使我們在待人接物以及生活態度上更加的積極與成熟 在此致上我最深切誠懇的感謝與祝福, 希望老師能常保身體健康, 替學術界締造更大的福祉並培養更多莘莘學子 感謝黃滿芳老師 您豐富的學術涵養以及認真負責的處事態度是我永遠景仰 學習的對象 修習您開授的相關課程, 對於我充實光電半導體理論與實務知識有莫大的助益 ; 每當學生有任何學習上的問題時, 您總是不厭其煩 用心且詳細的指導我們, 我衷心認為能上到您的課是我回到彰師進修最大的收穫之一 感謝劉柏挺老師 您總是能對我們的研究成果提供全方位角度的看法與建議, 讓我們可以更加完善的完成研究工作 您那自信灑脫的生活態度不僅帶給我們嚴肅的學習生活適度的放鬆與歡笑, 也是我極欲學習與嚮往的人生觀 感謝藍光雷射實驗室的伙伴們 : 由於勝宏與妙嬋的指導與協助, 使我在剛回到實驗室時能很快的進入狀況 ; 我們彼此之間互相的砥礪

3 與學習是我能快速成長與進步的重要動力 謝謝尊信學長在修課與研究上的陪伴與協助 也要謝謝實驗室最可愛的學弟妹們 : 鈺涵 漢威 毅廷 士勛 育瑞以及芳名, 因為他們讓我的生活更加的多采多姿且充滿歡笑 特別要感謝我的家人 : 爸爸 媽媽 欣玲以及楷楷與豪豪, 由於有你們的陪伴 支持與鼓勵, 我才能在辛苦的求學過程中勇敢向前邁進 尤其是欣玲, 如果沒有妳的體諒與承擔, 我將無法在工作與學業之間找到平衡點, 辛苦妳了 謝謝楷楷與豪豪這兩個小搗蛋, 雖然這四年中你們熱情贊助了我不少的黑眼圈與白頭髮, 但你們的存在讓我有勇氣與力量去面對挑戰, 讓我在迷惘無助時能找到方向並堅持不退縮, 謝謝你們, 我愛你們 在此謹以此論文獻給我最摯愛的家人

4 Outline Outline I Abstract..... VI Figure and table captions VIII Chapter 1 Introduction to III-nitride solar cells Efficiency limitation in single-junction solar cell Trade-off between transparency loss and excessexcitation loss Trade-off between short-circuit current and opencircuit voltage Solution to the limited efficiency: multiple bandgaps The possibility of III-nitrides Fill the material vacancy in the short wavelength region of solar spectrum Superior photovoltaic characteristics The challenges in III-nitride solar cells Thick and high-quality InGaN layers P-type doping Polarization effect Tunnel junction Conclusion. 3 Page I

5 References. 3 Chapter Numerical models and parameters 4.1 Numerical models Drift and Diffusion Band structure SRH recombination Material parameters References. 51 Chapter 3 Polarization effect of p-on-n GaN/InGaN p-i-n solar cells in Gaand N-face configurations GaN/InGaN p-i-n solar cell structure Photovoltaic characteristics without polarization effect Calculation of polarizations in III-nitrides Polarization effect in Ga-face configuration Preliminary aspects Polarization-induced surface charge densities Simulation results and discussions Polarization effect in N-face configuration Conclusion. 81 References. 83 Chapter 4 Effects of step-graded interlayers in p-on-n and Ga-face Page II

6 GaN/InGaN p-i-n solar cells Effect of hetero-interfaces Effect of p-type doping concentration Effect of polarization charges Influences of step-graded interlayers Thickness of step-graded interlayers P-type doping concentration of step-graded interlayers Conclusion 111 References 11 Chapter 5 Conclusion Appendix 1 Publication list.. i Appendix Simulation input files. vi Page III

7 中文摘要 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 (1) 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 Page IV

8 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 Page V

9 Abstract 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 (1) 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, the physical models relevant to the solar cell structures and the material parameters employed in the simulation are introduced. Page VI

10 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. Page VII

11 Figure and table captions Fig. 1.1 Schematic diagram of the optical generation process in various conditions of photon energy. 3 Fig. 1. Graphical indication of the transparency loss and excessexcitation loss in AM 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 E g1, E g and E g3, respectively (E g1 >E g >E g3 ) 9 Fig. 1.6 Expected output performance of multi-junction tandem solar cells with a different number of sub-cells. 1 Fig. 1.7 The relationships between bandgap energy and lattice constant for III-V compounds and elemental semiconductors... 1 Fig. 1.8 Perfect matching of bandgap of In 1 x Ga x N to solar spectrum 14 Fig. 1.9 Schematic band diagram of a 1-junction tandem solar cell designed using InGaN-based materials.. 14 Fig. 1.1 Calculated critical thickness against composition curves for the single-layer In x Ga 1 x N/GaN system from (a) theoretical study and (b) experimental measurements. 17 Fig (a) Calculated valance-band diagram and (b) Hall-effect measurements for the Mg-doped Al. Ga.8 N/GaN superlattice Page VIII

12 with polarization fields considered Fig. 1.1 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 temperaturedependent hole concentration 1 Fig Schematic diagram of the crystal structure of wurtzite Ga-face and N-face GaN. 3 Fig 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... 4 Fig Appropriate ternary alloy for the material of intermediate layer between n- and p-gan layers in various configurations of polarization-assisted tunnel structure. 6 Fig 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.7 Fig 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.. 8 Fig. 3.1 Schematic diagram of GaN/InGaN p-i-n solar cell under study.56 Fig. 3. Energy band diagrams under (a) zero and (b) V biases, and (c) J-V-P performance curves of GaN/In.1 Ga.9 N 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 Page IX

13 layer 6 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.. 6 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 6 Fig. 3.6 Energy band diagrams under zero and V biases, and J-V-P performance curves of GaN/In.1 Ga.9 N p-i-n solar cell with different degrees of relaxation Fig. 3.7 Electric field of GaN/In.1 Ga.9 N p-i-n solar cell (a) at zero bias with different situations of polarization and (b) under R=.8 condition with different values of forward bias. 67 Fig. 3.8 Energy band diagrams under zero and V biases, and J-V-P performance curves of GaN/In. Ga.8 N p-i-n solar cell with different degrees of relaxation 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.5 to 1. 7 Fig. 3.1 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 Electric field of GaN/In. Ga.8 N p-i-n solar cell at zero bias with different situations of polarization under AM1.5G illumination 7 Fig. 3.1 Energy band diagram under zero bias and J-V-P curves of GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under AM1.5G illumination.. 74 Fig Enlarged energy band diagrams in the heterojunction interfaces of Page X

14 GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under zero bias and AM1.5G illumination. 75 Fig SRH recombination rate of GaN/In. Ga.8 N 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 1 times in magnitude.. 77 Fig Conversion efficiencies of GaN/In x Ga 1-x N p-i-n solar cells with different degrees of relaxation and different situations of polarization under AM1.5G illumination.. 78 Fig J-V curves of GaN/In.5 Ga.75 N p-i-n solar cell with different SRH lifetimes and different degrees of relaxation under AM1.5G illumination in N-face configuration. 8 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 1%, % and 3% indium composition and cm 3 hole concentration under the situation of no polarization 89 Fig. 4. Energy band diagrams of GaN/InGaN p-i-n solar cells with 1%, % and 3% indium composition and 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. 9 Fig. 4.3 (a) Optical generation rates and (b) SRH recombination rates of GaN/InGaN p-i-n solar cells with 1%, % and 3% indium composition and cm 3 hole concentration at zero bias under the situation of no polarization. (c) is the enlarged plot of (b) 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 Page XI

15 GaN/In. Ga.8 N p-i-n solar cells under the situations of no polarization, R=1., and R=.5 (Ga-face, hole concentration = cm 3 ).. 94 Fig. 4.5 Energy band diagrams of the GaN/In. Ga.8 N p-i-n solar cells under the situations of no polarization, R=1., and R=.5 at (a) (b) (c) equilibrium state and (d) (e) (f) AM1.5G illumination (Ga-face, hole concentration = cm 3 ). 96 Fig. 4.6 (a) Electric fields of the GaN/In. Ga.8 N p-i-n solar cells at equilibrium under the situations of no polarization, R=1., and R=.5 (Ga-face, hole concentration = cm 3 ). (b) Enlarged plot of (a) 97 Fig. 4.7 Schematic diagram of the structure with step-graded interlayers Fig. 4.8 (a) and (b) Energy band diagrams at equilibrium and (c) J-V curves of the GaN/In.3 Ga.7 N 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/In.3 Ga.7 N p-i-n solar cells with and without 45-nm-thick grading layer under the situation of R= Fig. 4.1 Conversion efficiencies of GaN/In.3 Ga.7 N p-i-n solar cells as a function of R with different thicknesses of grading layer 13 Fig Energy band diagrams and electric fields at equilibrium of the GaN/In.3 Ga.7 N p-i-n solar cells with (a) (c) 7-nm grading layer and (b) (d) 7-nm grading layer under the situation of R=.4 14 Fig. 4.1 Conversion efficiencies of the GaN/In.3 Ga.7 N 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 15 Page XII

16 Fig Energy band diagrams at equilibrium of the GaN/In.3 Ga.7 N p-i-n solar cells with various conditions of (a) without grading layer, p-doping: cm 3 ; (b) with grading layer (81 nm), p-doping: cm 3 ; (c) without grading layer, p-doping: cm 3 ; (b) with grading layer (81 nm), p-doping: cm Fig Electric fields at equilibrium of the GaN/In.3 Ga.7 N p-i-n solar cells with various conditions of (a) without grading layer, p-doping: cm 3 ; (b) with grading layer (81 nm), p-doping: cm 3 ; (c) without grading layer, p-doping: cm 3 ; (b) with grading layer (81 nm), p-doping: cm Fig Conversion efficiencies of GaN/In.3 Ga.7 N 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 cm Tab..1 Material parameters of the binary semiconductors GaN, AlN, and InN at room temperature. (Δ cr = Δ 1, Δ so = 3Δ = 3Δ 3.).. 47 Tab.. Fitting parameters used to calculate the absorption coefficient of In x Ga 1 x N alloys. 5 Tab. 3.1 Polarization-induced surface charge densities in In x Ga 1 x N/GaN hetero-interfaces with various values of R. 64 Page XIII

17 Chapter 1 Introduction to III-nitride solar cells The III-nitride semiconductors are extensively employed in the fields of light-emitting diodes (LEDs), laser diodes (LDs), and heterojunction transistors. For the application of photovoltaic devices, due to the tunable energy bandgap (E g ) of InGaN alloys ranging from.7 ev to 3.4 ev with characteristic of direct bandgap and numerous superior PV characteristics, it was predicted that high-efficiency multi-junction and full-spectrum-response tandem solar cells could be achieved based solely on the III-nitride material systems [1 4]. However, despite the superior photovoltaic characteristics, there are still many obstacles that need to be overcome in realizing efficient III-nitride solar cells. The most important challenge might be the difficulty in growing thick and high-quality epitaxial layers of high indium composition. In this chapter, the role and importance, the superior photovoltaic characteristics, and the major limitations and obstructions of III-nitride materials in the development of high-efficiency multi-junction tandem solar cells are introduced. Page 1

18 1.1 Efficiency limitation in single-junction solar cell Trade-off between transparency loss and excess-excitation loss The optical generation process in various conditions of photon energy is schematically plotted in Fig As show in Fig. 1.1(a), if the energy of the incident photon is less than the energy bandgap of solar cell, it will pass through the cell without interaction and thus result in the transparency loss. While when an electron in the valance band is excited to the conduction band by a photon with energy larger than the bandgap of solar cell, the excited electron and hole lose their energies thermally and come down to the bottom of the conduction and valance bands, as show in Fig. 1.1(c). The energy lost under this circumstance (hν E g, so-called excess-excitation loss) remains additional heat and cause detrimental thermal issue to the solar cell. Figure 1. shows the graphical indication of the transparency loss and excess-excitation loss in air-mass zero (AM) solar spectrum [5]. In this figure, λ is the wavelength which corresponds to the bandgap of solar cell, and ΔP is the incident power with a photon energy hν and wavelength λ in a small wavelength width dλ. Note that the normal built-in potential across the depletion region, with which the carriers can be accelerated and thus do work to the outer load, is roughly equal to the bandgap of solar cell and is Page

19 related to the doping concentration and profile of n- and p-layers. We can easily divide ΔP into two parts: ΔP Eg Usable power: Eg = Δ P, (1.1) hν hν ΔP Eg Excess-excitation loss: ( hν Eg ) = (1 ) Δ P, (1.) hν hν where ΔP/hν is the number of photons involved in ΔP. By plotting (E g /hν) ΔP against wavelength, a dashed area in Fig. 1., which corresponds to the usable power in a solar cell with a bandgap energy E g, is obtained, and the ratio of the area to the total spectrum area is the ultimate conversion efficiency. Fig. 1.1 Schematic diagram of the optical generation process in various conditions of photon energy. Page 3

20 Fig. 1. Graphical indication of the transparency loss and excess-excitation loss in AM solar spectrum [5]. If we want the solar cell to cover/absorb greater portion of the solar spectrum, that is, to decrease the transparency loss, an intuitive thought is to reduce the bandgap of solar cell. However, the excess-excitation loss increases correspondingly and thus violates the ultimate goal of largely enhancing the conversion efficiency. Conversely, the excess-excitation loss decreases while the transparency loss increases if a higher bandgap material is employed. As a result, the trade-off between the transparency loss and excess-excitation loss always exists when only one bandgap of single-junction solar cell can be chosen. Page 4

21 1.1. Trade-off between short-circuit current and open-circuit voltage 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. A more practical way to depict the aforementioned trade-off between the transparency loss and excess-excitation loss might be the fact of trade-off between the short-circuit current (I sc ) and open-circuit voltage (V oc ). Figure 1.3 shows the schematic diagram of the optical generation and electron acceleration processes in a single p-n junction solar cell. In this figure, an electron is excited by a photon with energy hν (hν>e g ). The excited electron and hole lose their energies thermally and come down to Page 5

22 the bottom of the conduction and valance bands, as illustrated in Fig. 1.1(c). When the electron moves to the p-n junction edge by diffusion, it is accelerated by the energy difference ΔE (built-in potential). The accelerated electrons can do work to the outer load, which means that we can utilize only ΔE of hν. The energy difference ΔE is positively related to the bandgap of solar cell. 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]. Page 6

23 As a result, if a solar cell is fabricated by a smaller bandgap material, the photovoltaic characteristics of the solar cell should be with a higher short-circuit current due to more solar spectrum covered and thus more electron-hole pairs generated per unit-time, and with a lower open-circuit voltage due to the smaller bandgap of solar cell and thus smaller energy difference ΔE across the depletion region. Since the trends of short-circuit current and open-circuit voltage as a function of the bandgap of solar cell are different, as shown in Fig. 1.4, very small and very large bandgap will lead to too small open-circuit voltage and too small short-circuit current, respectively. Poor photovoltaic characteristics are expected in both cases. Note that the thermal issue resulting from the excess-excitation loss is not included in this discussion. The trade-offs between the transparency loss and excess-excitation loss, and between the short-circuit current and open-circuit voltage are so constitutive and are unavoidable when only single-junction solar cell is considered. Even though an optimal efficiency could be achieved through fine-tuning the bandgap of solar cell (this specific bandgap is known to be around 1.4 ev according to the solar spectrum selected [5 7]), the ultimate efficiency is still limited due to the nature of single-junction solar cell. Page 7

24 1.1.3 Solution to the limited efficiency: multiple bandgaps As illustrated in Fig. 1.1, a single-junction solar cell functions most efficiently with monochromatic light whose photon energy is identical to the bandgap of solar cell. If the solar spectrum could be splitted up and channeled into solar cells with different bandgaps, each electron could be collected with a chemical potential closer to the original photon energy and largely diminish the excess-excitation loss. Under this circumstance, more incident solar energy could be utilized and a higher power could be extracted from the same solar spectrum. Even though various methods are proposed based on this strategy, the more practical one is to fabricate a multi-junction tandem solar cell grown monolithically. The multi-junction tandem solar cell perpendicularly stacks and electrically/optically connects different bandgap sub-cells in series, and allows the wider bandgap sub-cell at the top to absorb most of the high energy photons, while the lower energy photons pass through to smaller bandgap sub-cells below. Figure 1.5 shows the power usable in a 3-junction tandem solar cell [5]. In this case, around 7% of the solar power can be utilized, which is much higher than the usable power in the single-junction solar cell. Page 8

25 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 E g1, E g and E g3, respectively (E g1 >E g >E g3 ) [5]. Since the sub-cells in a tandem solar cell are connected in electrical series, the working voltage of the tandem cell is the summation of that of all the sub-cells. As a result, the pursuits of high short-circuit current and high open-circuit voltage simultaneously can be achieved through the employment of multi-junction tandem solar cell. Figure 1.6 shows the expected output performance of multi-junction tandem solar cells with a different number of sub-cells. It is found that the conversion efficiency increases with the increase of number of sub-cells. Specifically, a conversion efficiency exceeding 5% is achieved under one sun condition for a tandem cell with more than 6 sub-cells. It also reveals that a high Page 9

26 open-circuit voltage of more than 1 V can be obtained for a 1-junction tandem cell. It is noteworthy that the maximum increment of conversion efficiency is obtained when the number of sub-cells is increased from 1 to. If a tandem solar cell is stacked with many sub-cells, the increment of conversion efficiency due to further increasing number of sub-cells is limited. The result is acceptable because that the fabrication of tandem solar cell with many sub-cells is quite difficult. Fig. 1.6 Expected output performance of multi-junction tandem solar cells with a different number of sub-cells [5]. In various literatures, the calculated values of conversion efficiency are different due to the individual assumptions. Nevertheless, the tendency is that more sub-cells will result in higher efficiency. It is necessary for the Page 1

27 tandem cell that the current of sub-cells must be matched to each other to obtain optimal short-circuit current. While the open-circuit voltage enlarges vastly when the number of sub-cells increases, it contributes majorly to the enhanced solar cell performance. 1. The possibility of III-nitrides 1..1 Fill the material vacancy in the short wavelength region of solar spectrum In order to maximize the efficiency of a tandem solar cell, the current generated in each sub-cell should be matched (current matching). This is a basic requirement for a monolithic-cascade tandem solar cell, and severely limits the selection of semiconductor materials. In addition, another demand in real fabrication is that the lattice parameters of the materials used for the sub-cells must be closely matched in order to minimize misfit dislocations in epitaxial layers. Therefore, it is important to consider the relationship between bandgap energy and lattice constant of the conventional III-V compounds and the elemental semiconductors in the photovoltaic applications, which is shown in Fig. 1.7 [8]. Because perfect matching of current and lattice simultaneously between sub-cells is hard to be realized in the materials of Fig. 1.7, recent Page 11

28 Fig. 1.7 The relationships between bandgap energy and lattice constant for III-V compounds and elemental semiconductors [8]. achievements in developing high-efficiency tandem solar cell are based on the ingenious balance between these two requirements. A typical tandem solar cell ever reported is an In.49 Ga.51 P (1.88 ev) / In.1 Ga.99 As (1.4 ev) / Ge (.67 ev) 3-junction cell. This is a lattice-matched system while the Ge bottom cell generates higher current than the other two sub-cells. Conversion efficiencies of 31.% [9] and 4.1% [1] under AM1.5 one and 135 suns, respectively, which are much higher than that for single-junction solar cell, have been obtained. Other efforts have also been made to improve the current-mismatching condition, in spite of the increased lattice mismatch, such as the In.65 Ga.35 P (1.7 ev) / In.17 Ga.83 As (1.16 ev) / Ge Page 1

29 (.67 ev) and In.49 Ga.51 P (1.83 ev) / In.4 Ga.96 As (1.34 ev) / In.37 Ga.63 As (.89 ev) 3-junction cells which have conversion efficiencies of 41.1% and 4.8% under 454 suns and 36 suns conditions, respectively [11,1]. Further efficiency improvement is expected for the two structures by improving the film quality of the lattice-mismatched materials. Due to that the solar radiation covers a wide range of spectrum (from ultraviolet to infrared), the bandgap of semiconductor materials in Fig. 1.7 is insufficient to cover the full solar spectrum, especially in short wavelength region. Therefore, it is necessary to develop a novel material system with which the bandgap energies can fill the vacancy in the short wavelength region of the solar spectrum. The most possible candidate is presumably the III-nitride material. Since, the bandgap of InN was discovered to be around.7 ev as opposed to the previously reported 1.9 ev [13 15]. Under this circumstance, with the combination of InGaN alloy systems, one may design tandem solar cells with optimum bandgaps to absorb photonenergy between.7 ev of infrared and 3.4 ev of ultraviolet regions, as shown in Fig. 1.8 [16]. In this kind of tandem cell, the current matching issue can be easily solved because not only the thickness but also the bandgap of each sub-cell can be tuned. This makes it possible to achieve ultrahigh-efficiency multi-junction and full-spectrum-response tandem Page 13

30 Fig. 1.8 Perfect matching of bandgap of In 1 x Ga x N to solar spectrum [16]. Fig. 1.9 Schematic band diagram of a 1-junction tandem solar cell designed using InGaN-based materials [5]. Page 14

31 solar cells based solely on the III-nitride material system. Figure 1.9 shows the schematic band diagram of a 1-junction cell designed using InGaN-based materials [5]. In this case, the current matching can be achieved and a conversion efficiency of more than 5% is obtained [5]. 1.. Superior photovoltaic characteristics As discussed above, one of the most advantages of III-nitride materials, InGaN alloys especially, in the application of multi-junction tandem solar cells is the feasible engineering of bandgap energy by varying indium composition, which covers almost the entire solar spectrum from ultraviolet to infrared. Most importantly, the bandgap is direct for the entire material system. In contrast, the largest direct bandgap available in the AlGaAs and AlGaP systems is only about. ev [17,18]. The III-nitride materials also exhibit very strong absorption of approximately 1 5 cm 1 at the band edge, allowing a large fraction of the incident light to be absorbed in a few hundred nanometers of material, which is beneficial for reducing the thickness of device [19 1]. This is in contrast to the tens or hundreds micrometers of material as is necessary in traditional Si solar cells. Additionally, it was found that the optical and electronic properties of III-nitride alloys exhibit a much higher resistance to high-energy ( MeV) proton irradiation than the currently used photovoltaic materials such as the GaAs and InGaP, and therefore offer great potential for radiation-hard Page 15

32 high-efficiency solar cells for space applications [16,]. In addition to the abovementioned advantages, the III-nitrides also demonstrate favorable photovoltaic properties such as low effective mass of carriers, high mobility, and high peak and saturation velocities [4,3,4]. 1.3 The challenges in III-nitride solar cells In last section, we comprehend that III-nitride materials have great potential in fabricating multi-junction tandem solar cells. Especially, the current mismatching problem in the conventional III-V compound solar cells will be solved and much higher conversion efficiency will be achieved by solely employing this material system. The study on III-nitride solar cells is just in the early stage, and more efforts are required to overcome the following issues Thick and high-quality InGaN layers The most common substrate for GaN-based epitaxial growth, sapphire, is a very stable substrate in terms of its thermal, chemical, and mechanical properties. However, the lattice constants and thermal conductivities of sapphire and GaN are quite different [5]. In addition, there also exists large lattice and thermal mismatches between InN and GaN. As a result, a quite small critical thickness of InGaN grown on (1) GaN is observed [6 8]. Figure 1 shows the recent calculations of critical thickness in Page 16

33 InGaN/GaN system for both theoretical and experimental demonstrations [6,7]. It is apparent that the critical thicknesses are generally less than 1 nm when the indium composition of InGaN layer is larger than 1% and decrease very rapidly with further increasing indium composition. Consequently, in InGaN-based solar cells, the thickness of InGaN layer is usually thicker than the relevant critical thickness for efficient photovoltaic applications. Under this circumstance, the huge defect densities may act as the non-radiative recombination centers (NRCs) [9] that could lead to the reduction of carrier lifetime and correspondingly the diminished short circuit current density. The situation becomes severer when the InGaN layer is with higher indium composition or with larger thickness. Fig. 1.1 Calculated critical thickness against composition curves for the single-layer In x Ga 1 x N/GaN system from (a) theoretical study [6] and (b) experimental measurements [7]. Page 17

34 Another limiting factor is the low compound miscibility between the InN and GaN binary materials [3,31]. The In-rich clusters and accompanying phase separation can be formed easily in the InGaN layer when the thickness and indium composition are high. In solar cells, this phenomenon results in the reduction of open circuit voltage due to the lowered energy band gap in the In-rich region, diminished fill factor (FF), and enhanced recombination rate, which will degrade the value of short circuit current density [4,3,33]. As a result of the above restrictions, the present reports on InGaN-based solar cells are limited to low indium composition P-type doping The achievement of p-type doping was a critical step in the development of III-nitride semiconductor devices. Although Mg is the most successful p-type dopant for GaN-based materials, high hole concentration and low resistivity of p-doped layer have been limited by many complicated issues. The severest challenges might be the chemical deactivation by hydrogen atoms, high thermal activation energy, and significant compensation at high dopant concentrations of Mg acceptors [34,35]. In addition, the situations of low solubility of Mg into (AlIn)GaN, tendency of Mg accumulation and segregation at surface, formation of Page 18

35 pyramid-shaped defects, memory effect of Mg in a growth chamber, and high vapor pressure of Mg at low temperatures are also factors limiting the achievement of high quality p-doped layers [36]. In the growth techniques that uses NH 3 as a nitrogen source or which furnishes a hydrogen-rich ambient, such as metal organic chemical vapor deposition (MOCVD), it has been demonstrated that H donors form electrically inactive complexes with uncompensated Mg acceptors during cooling after growth [37]. The presence of compensated donors and acceptors and the formation of neutral Mg-H complexes are responsible for the semi-insulting nature of as grown Mg-doped GaN [38]. Various post-growth treatments such as low-energy electron-beam irradiation (LEEBI), thermal annealing, CO laser annealing and so on, and in-situ growth in hydrogen-free ambients (i.e. in N atmosphere) were demonstrated to efficiently dissociate the Mg-H complexes [39 41]. However, the activated hole concentrations are usually two orders of magnitude below the acceptor concentrations because the thermal activation energy for acceptor ionization in Mg-doped GaN layers is quite high [34,36,4,43]. Additionally, it was observed that a serious self-compensation due to the deep donors occurs in Mg-doped InGaN at higher-doping levels [35]. Both phenomena limit the activation efficiency of Mg-doping in III-nitride materials. Page 19

36 Fig (a) Calculated valance-band diagram and (b) Hall-effect measurements for the Mg-doped Al. Ga.8 N/GaN superlattice with polarization fields considered [44]. The employment of AlGaN/GaN superlattices was demonstrated to significantly enhance the Mg-doping efficiency through the assistance of polarization-induced electric field and the corresponding band bending in the superlattice region, as shown in Fig [44,45]. A recent achievement in grading the aluminum composition of thick p-algan layer was found to improve the activated hole concentration via polarization effect as well, as shown in Fig. 1.1 [46,47]. Although some achievements have been obtained, more efforts are surely required to pursue high quality III-nitride epitaxial films with higher p-doping concentration and lower resistivity, especially in the devices grown by MOCVD. In III-nitride solar cells Page

37 grown along the conventional p-on-n and (1) configuration, high quality p-layers with high hole concentration and consequently stronger normal built-in electric field are much more desired comparing with other III-V solar cells due to the unavoidable large band-offset hetero-interfaces and detrimental polarization effect. Detailed exploration about this issue will be discussed in the following chapters. Fig. 1.1 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 [46]. Page 1

38 1.3.3 Polarization effect The most common epitaxial growth direction of III-nitride is the c-plane of the hexagonal wurtzite structure. III-nitride hetero-structures grown on the c-plane have significant interface charges induced by spontaneous and piezoelectric polarizations [48 5]. These charges result in internal electric field, which has significant influences on the optical and electrical properties of devices. The origin of spontaneous polarization comes from the intrinsic asymmetry of the bonding in the crystal structure. In GaN wurtzite structure, the bond directed in the (1) orientation is not equivalent to the other three bonds. Namely, it is longer and of more ionic nature than the others. As a result, the effective electronic charge center of a Ga atom will be slightly off the nucleus position in the direction of the N atom. Thus, there exists an electric dipole moment, which is parallel to the direction connecting the Ga atom with the N atom, along the ( 1) axis. By applying a strain to the GaN crystal, the four bonds with the neighboring atoms can be changed. Under this circumstance, the bond along the direction of strain is shortened or elongated and the native symmetry of crystal is broken. The ensuing polarization is called piezoelectric polarization [49]. Due to the nature of non-centrosymmetry, in binary A B compounds Page

39 with wurtzite structure, the sequence of the atomic layers of the constituents A and B is reversed along the [1] and [ 1] directions. In the case of GaN, where the [1] direction is given by a vector pointing from an N atom to a nearest-neighbor Ga atom, a basal surface should be either Ga- or N-faced, as shown in Fig [5]. By Ga-faced, it means Ga on the top position of the {1} bilayers, corresponding to the [1] polarity. The directions of the spontaneous polarization are opposite between Ga- and N-face crystals. Empirically, the polarity of Ga-face will be found in smooth GaN (1) layers grown by MOCVD on c-plane sapphire [5]. Fig Schematic diagram of the crystal structure of wurtzite Ga-face and N-face GaN [5]. Page 3

40 The strain in the epitaxial layer can be compressive or tensile. In the case of compressive strain, the epitaxial layer is laterally compressed, i.e., InGaN is compressively strained when grown on a thick relaxed GaN buffer layer. In the case of tensile strain, the epitaxial layer is expanded along the lateral direction, i.e., AlGaN is under tensile strain when grown on a thick relaxed GaN buffer layer. The direction of the polarization-induced electric field depends on the strain and the growth orientation (Ga-face or N-face) and is shown for different cases in Fig [49]. Quantitative estimation of the magnitude and direction of polarization in III-nitride epitaxial layers will be introduced, and the significant influences of spontaneous and piezoelectric polarizations on the photovoltaic characteristics in III-nitride solar cells will be discussed in chapter 3. Fig 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 [49]. Page 4

41 1.3.4 Tunnel junction In the application of multi-junction tandem solar cells, possessing efficient tunnel junctions for electrically connecting p-n junction sub-cells of disparate bandgaps is a fundamental requirement. Interband tunneling of electrons in semiconductors is impeded by two factors: tunneling barrier height determined by the bandgap, and tunneling barrier thickness [53]. For wide-bandgap III-nitrides, tunneling is originally believed to be inefficient due to the high barrier heights, and is further hampered by the inability to achieve degenerate p-type impurity doping [53,54]. However, the high polarization-induced electric fields in III-nitrides and other highly polar semiconductor materials provide a new design approach for tunneling structures. In hetero-structures of highly polar materials, the polarization-induced sheet charges can create significantly high electric fields resulting in large band bending over a small distance. The insufficient band-bending for interband tunneling from doping-induced normal built-in electric field can thus be supplemented by the polarization-induced electric field supposing that the two fields are designed to be with the same direction. The tunnel probability is therefore increased. Based on this principle, several approaches have been demonstrated to achieve interband tunneling in III-nitride p-n junction diodes [53 58]. Page 5

42 Fig Appropriate ternary alloy for the material of intermediate layer between n- and p-gan layers in various configurations of polarization-assisted tunnel structure. To achieve the polarization-assisted interband tunneling, materials of III-nitride hetero-structure must be carefully chosen to ensure the consistent directions of normal built-in and polarization-induced electric fields. Conventionally, the III-nitride devices are majorly constructed by GaN layers. Figure 1.15 shows the appropriate ternary alloy for the material of intermediate layer between n- and p-gan layers in various configurations of polarization-assisted tunnel structure. It is noteworthy that the doping in n- and p-gan layers and the indium or aluminum composition in intermediate layer should still follow the trend of the more the better for pursuing low tunneling turn-on voltage and low tunneling resistance. The quaternary AlGaInN alloy can also be utilized as the material of intermediate layer if the correlation of polarization dipoles between Page 6

43 hetero-layers shown in Fig is conformed. (Lower doping) (Higher doping) (Higher doping) Current density (A/cm ) n-gan: 6x1 19 cm 3 p-ingan: 1x1 18 cm 3 Polar. = none Polar. = 3% Polar. = 5% Polar. = 7% Polar. = 1% In=% n-gan: 3x1 cm 3 p-ingan: x1 18 cm Voltage (V) In=% x x1 4 1x1 4 5 n-gan: 3x1 cm 3 p-ingan: x1 18 cm 3 In=3% Fig 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. As mentioned previously, there always exists some degree of relaxation in the epitaxial layers of III-nitride devices due to the nature of mismatched lattice. The actual magnitude of polarization-induced electric field is thus diminished comparing to the theoretically predicted values [59 61]. Since the tunneling in III-nitride tunnel junction structure is majorly contributed by the polarization-induced electric field, the electrical characteristics may be severely degraded by the reduced polarization effect. Figure 1.16 and Fig show the electrical characteristics and energy band diagrams of Page 7

44 4 Lower doping - Polar.: 1% In = % Lower doping - Polar.: 5% In = % Lower doping - Polar.: none In = % - -4 V V V 4 Higher doping - Polar.: 1% In = % Higher doping - Polar.: 5% In = % Higher doping - Polar.:none In = % Energy (ev) - -4 V V V 4 Higher doping - Polar.:1% In = 3% Higher doping - Polar.:5% In = 3% Higher doping - Polar.:none In = 3% - -4 V V V Distance (μm) Fig 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. Page 8

45 Ga-face p-gan/p-ingan/n-gan tunnel diode under various conditions of polarization, doping concentration and indium composition. The results are obtained theoretically and the tunnel diode is constructed based on the structure proposed in [55]. In this figure, the so-called polar. = x% means that the polarization charges utilized in the simulation is reduced to be x% of the theoretically calculated value. In Fig. 1.16, it is obvious that the electrical characteristics vary abruptly in distinct degrees of polarization in all cases. With the decrease of degree of polarization, both the tunneling turn-on voltage and tunneling resistance in the reversed bias regime increase. This can be explained from the relevant energy band diagrams shown in Fig that the valance band of p-gan layer and the conduction band of n-gan layer overlap in energy at equilibrium state when the degree of polarization is high, while the overlapping reduces with the decrease of degree of polarization. In the situation of no polarization effect, these two bands separate in energy no matter what condition is simulated. The probability of electrons tunneling from the valance band of p-gan layer to the conduction band of n-gan layer thus diminishes vastly when the degree of polarization is low. It is also noteworthy that the degradation of electrical characteristics becomes more serious when the doping concentration and indium composition of Ga-face p-gan/p-ingan/n-gan tunnel diode are lower. It is thus better to Page 9

46 promote these quantities as high as possible because it is quite difficult to predict the degree of polarization in real-fabricated nitride solar cells. However, this demand conflicts with the present technology of fabrication. As discussed in sections and 1.3., it is commonly concluded that the crystalline quality will be severely demoted when the doping concentration and indium or aluminum compositions are too high. As a result, it is also desired to seek for the breakthrough of fabricating high-crystalline-quality and highly-doped III-nitride films in the application of efficient tunnel junction. 1.4 Conclusion The III-nitride material system has a great potential in realizing high efficiency tandem solar cell due to the large span in direct bandgaps and numerous superior photovoltaic characteristics. In addition, there are some characteristics existing only in III-nitrides that are not possible in other semiconductor materials. The most important one might be the usable bandgaps that can fill the vacancy in the short wavelength region of solar spectrum. The large electronic polarization is another endowment which we can benefit from, supposing that it is correctly applied via appropriate structure design. However, there still exist many obstructions hindering present applications of III-nitride solar cells, such as the difficulty in Page 3

47 fabricating high quality and/or highly p-doped epitaxial layers, the detrimental influences of polarization effect, and the lack of efficient tunnel junction. As a result, more efforts are still required to overcome these challenges. Page 31

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53 34. J. I. Pankove and T. D. Moustakas, Gallium Nitride (GaN) II: Semiconductors and Semimetals, San Diego: Academic Press, 1999, pp 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, 337 (3). 36. S. D. Burnham, G. Namkoong, D. C. Look, B. Clafin, and W. A. Doolittle Reproducible increased Mg incorporation and large hole concentration in GaN using metal modulated epitaxy, J. Appl. Phys. 14, 49 (8). 37. W. Götz, N. M. Johnson, D. P. Bour, M. D. McCluskey, and E. E. Haller, Local vibrational modes of the Mg H acceptor complex in GaN, Appl. Phys. Lett. 69, 375 (1996). 38. J. Neugebauer and C. G. Van de Walle, Role of hydrogen in doping of GaN, Appl. Phys. Lett. 68, 189 (1996). 39. H. Amano, M. Kito, K. Hiramatsu, and I. Akasaki, P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI), Jpn. J. Appl. Phys. 8, L11 (1989). 4. S. Nakamura, N. Iwasa, M. Senoh, and T. Mukai, Hole compensation mechanism of p-type GaN films, Jpn. J. Appl. Phys. 31, 158 (199). 41. W.-C. Lai, M. Yokoyama, S.-J. Chang, J.-D. Guo, C.-H. Sheu, T.-Y. Chen, W.-C. Tsai, J.-S. Tsang, S.-H. Chan, and S. M. Sze, Optical and Page 37

54 electrical characteristics of CO -laser-treated Mg-doped GaN film, Jpn. J. Appl. Phys. 39, L1138 (). 4. M. Smith, G. D. Chen, J. Y. Lin, H. X. Jiang, A. Salvador, B. N. Sverdlov, A. Botchkarev, H. Morkoc, and B. Goldenberg, Mechanisms of band-edge emission in Mg-doped p-type GaN, Appl. Phys. Lett. 68, 1883 (1996). 43. W. Götz, N. M. Johnson, J. Walker, D. P. Bour, and R. A. Street, Activation of acceptors in Mg-doped GaN grown by metalorganic chemical vapor deposition, Appl. Phys. Lett. 68, 667 (1996). 44. P. Kozodoy, M. Hansen, S. P. DenBaars, and U. K. Mishra, Enhanced Mg doping efficiency in Al. Ga.8 N/GaN superlattices, Appl. Phys. Lett. 74, 3681 (1999). 45. P. Kozodoy, Y. P. Smorchkova, M. Hansen, H. Xing, S. P. DenBaars, U. K. Mi, A. W. Saxler, R. Perrin, and W. C. Mitchel, Polarization-enhanced Mg doping of AlGaN/GaN superlattices, Appl. Phys. Lett. 75, 444 (1999). 46. J. Simon, V. Protasenko, C. Lian, H. Xing, and D. Jena, Polarization-induced hole doping in wide band-gap uniaxial semiconductor heterostructures, Science 37, 6 (1). 47. L. Zhang, K. Ding, J. C. Yan, J. X. Wang, Y. P. Zeng, T. B. Wei, Y. Y. Li, B. J. Sun, R. F. Duan, and J. M. Li, Three-dimensional hole gas induced by polarization in (1)-oriented metal-face III-nitride structure, Appl. Phys. Lett. 97, 613 (1). Page 38

55 48. F. Bernardini, V. Fiorentini, and D. Vanderbilt, Spontaneous polarization and piezoelectric constants of III-V nitrides, Phys. Rev. B 56, 14 (1997). 49. E. F. Schubert, Light-Emitting Diode, nd ed., Cambridge: Cambridge University Press, 6, p O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures, J. Appl. Phys. 85, 3 (1999). 51. 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 (). 5. V. Fiorentini, F. Bernardini, and O. Ambacher, Evidence for nonlinear macroscopic polarization in III V nitride alloy heterostructures, Appl. Phys. Lett. 8, 14 (). 53. J. Simon, Z. Zhang, K. Goodman, H. Xing, T. Kosel, P. Fay, and D. Jena, Polarization-Induced zener tunnel junctions in wide-band-gap heterostructures, Phys. Rev. Lett. 13, 681 (9). Page 39

56 54. S. Krishnamoorthy, D. N. Nath, F. Akyol, P. S. Park, M. Esposto, and S. Rajan, Polarization-engineered GaN/InGaN/GaN tunnel diodes, Appl. Phys. Lett. 97, 35 (1). 55. T. Takeuchi, G. Hasnain, S. Corzine, M. Hueschen, Jr., R. P. Schneider, C. Kocot, M. Blomqvist, Y. Chang, D. Lefforge, M. R. Krames, L. W. Cook, and S. A. Stockman, GaN-based light-emitting diodes with tunnel junctions, Jpn. J. Appl. Phys. 4, L861 (1). 56. I. Ozden, E. Makarona, A. V. Nurmikko, T. Takeuchi, and M. Krames, A dual-wavelength indium gallium nitride quantum well light emitting diode, Appl. Phys. Lett. 79, 53 (1). 57. J. K. Sheu, J. M. Tsai, S. C. Shei, W. C. Lai, T. C. Wen, C. H. Kou, Y. K. Su, S. J. Chang, and G. C. Chi, Low-operation voltage of InGaN/GaN light-emitting diodes with Si-doped In.3 Ga.7 N/GaN short-period superlattice tunneling contact layer, IEEE Electron Device Lett., 46 (1). 58. M. J. Grundmann and U. K. Mishra, Multi-color light emitting diode using polarization-induced tunnel junctions, Phys. Status Solidi C 4, 83 (7). 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, 6 (1998). Page 4

57 6. 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, 49 (). 61. H. Zhang, E. J. Miller, E. T. Yu, C. Poblenz, and J. S. Speck, Measurement of polarization charge and conduction-band offset at In x Ga 1 x N/GaN heterojunction interfaces, Appl. Phys. Lett. 84, 4644 (4). Page 41

58 Chapter Numerical models and parameters In this dissertation, the photovoltaic characteristics of GaN/InGaN p-i-n solar cells grown along c-axis are numerically studied using a self-consistent simulation program APSYS (Advanced Physical Models of Semiconductor Devices) based on two-dimensional (D) models [1]. APSYS employs the 6 6 k p model, which was developed for the strained wurtzite semiconductor by Chuang and Chang [,3], to calculate the energy band structures. The transport model includes drift and diffusion of electrons and holes in the devices. The built-in polarization induced by the spontaneous and piezoelectric polarizations is considered at the hetero-interfaces of III-nitride semiconductor devices. The effect of Shockley-Read-Hall (SRH) recombination is also included in the simulation. Some of the key physical models and material parameters used in this simulation are briefly described in the following sections..1 Numerical models.1.1 Drift and Diffusion The carrier transport in a semiconductor device is majorly governed by the drift and diffusion of electrons and holes. Drift current, which results from an electric field E, is proportional to the conductivity of carriers. Page 4

59 σ = qμ n, (.1) n n σ p = qμ p, (.) p where q is the magnitude of a unit charge, μ n and μ p are mobilities of electron and hole, and n and p are local concentrations of electron and hole. Diffusion current is generated by the concentration gradient of carriers ( n, p) and is proportional to the diffusion coefficient (D n and D p ). The total current density of electrons and holes is thus expressed as [4] J = qμ ne+ qd n, n n n J = qμ pe qd p. p p p (.3) (.4) The continuity equation describes the changes of local carrier concentration over time which involve the spatial change of current flow ( J ), and generation (rate G) and recombination (rate R) of electron-hole pairs. n q = Jn q( R G), (.5) t p q = Jp q( R G). (.6) t By employing the Poisson s equation, the electric field is related to the charge distribution in following expression + ( ε E) = q( p n+ N N ± N ), D A f (.7) where N + D is the ionized donor concentration, N A is the ionized acceptor Page 43

60 concentration, and N f represents other fixed charges such as the sheet charges caused by spontaneous and piezoelectric polarizations in nitride-based devices. The drift-diffusion model consists of carrier transport equations, continuity equations, and Poisson s equation. These equations govern the electrical behavior of a semiconductor device..1. Band structure The 6 6 k p model developed for strained wurtzite semiconductors is utilized to calculate the energy band structures in the simulation [,3]. The conduction band is assumed to be decoupled from valance sub-bands and have isotropic parabolic band due to the large bandgap of nitride semiconductor [5 7]. The band structure for the valance band is more complicated. The three valance sub-bands, including heavy-hole (HH), light-hole (LH), and crystal-field split-hole (CH) bands, are derived by the 6 6 Hamiltonian which has been block-diagonalized into the following upper and lower 3 3 Hamiltonians U H H =, 6 6 L (.8) H where Page 44

61 F K ih t t U H = K G Δ ih, t t ih Δ + ih λ t t (.9) F K ih t t L H = K G Δ + ih. t t ih Δ ih λ t t (.1) The matrix elements are F = Δ + Δ + λ +, (.11) 1 θ G = Δ Δ + λ +, (.1) 1 θ λ = ( A1 kz + Ak t ) + λ ε, m (.13) λ ε = D1ε zz + D( ε xx + ε yy ), (.14) θ = ( A3k z + A4k t ) +θ ε, m (.15) θ ε = D3ε zz + D4( ε xx + ε yy ), (.16) K = A5, (.17) m t k t H t = A6 kzkt, (.18) m Δ = Δ 3, (.19) Page 45

62 and k = k + k. (.) t x y The above Hamiltonian is considered under the assumption that the strained wurtzite crystal is pseudomorphically grown along the c-axis (z-axis) on another thick layer. The basal lattice constant is a and the original (unstrained) lattice constant of the layer under consideration is a. The strain tensor in the plane of the epitaxial growth is ε ε a a a xx = εyy =, (.1) C 13 zz ε, xx C33 = (.) ε xy = εyz = εzx =, (.3) where C 13 and C 33 are the elastic stiffness constants. The band structure parameters for binary nitride wurtzite semiconductors employed in the simulation are listed in Table.1 [8]..1.3 SRH recombination In GaN/InGaN p-i-n solar cells, the major recombination loss is Shockley-Read-Hall (SRH) recombination. The defect-related SRH recombination that is due to deep level traps can be expressed as [9] R = cn(1 f) N cnfn, (.4) n n t t n 1 t t Page 46

63 Table.1 Material parameters of the binary semiconductors GaN, AlN, and InN at room temperature [8]. (Δ cr = Δ 1, Δ so = 3Δ = 3Δ 3.) Parameter Symbol (unit) GaN AlN InN Lattice constant a (Å) Spin-orbit split energy Δ so (ev) Crystal-field split energy Δ cr (ev) Hole effective mass parameter A A A A A A Hydrost. deform. potential (c-axis) a z (ev) Hydrost. deform. potential (transverse) a t (ev) Shear deform. potential D 1 (ev) D (ev) D 3 (ev) D 4 (ev) Elastic stiffness constant c 33 (GPa) c 13 (GPa) Electron effective mass (c-axis) z me m..3.7 Electron effective mass (transverse) t me m..3.7 = (.5) R (1 ), p cppftnt cpp1 ft Nt where c n and c p are the capture coefficients, f t is the trap occupancy, N t is the trap density and n 1 is the electron concentration when the electron Page 47

64 quasi-fermi level coincides with the energy level E t of the trap. A similar definition applies to p 1. Et Ec n1 Nc exp[ ], kt = (.6) Ev Et p1 Nv exp[ ]. kt = (.7) The capture coefficients c n and c p for electrons and holes relate to SRH lifetime τ SRH by 1 τ SRH n 1 τ SRH p = cn, n t = cn. p t (.8) (.9) After matching the steady-state conditions, the net SRH recombination rate can be expressed as cc ( np np). ( ) ( ) n p RSRH = Nt c n n + n 1 + c p p + p 1 (.3) In the simulation, the calculated SRH recombination rate is related to the SRH lifetime and local carrier concentration. It should be noted here that the influence of varied crystalline quality is not considered in this work. Namely, all conditions possess identical SRH lifetime in the simulation. As a result, the higher SRH recombination rate in the simulation is attributed to the difficulty for the photogenerated carriers to escape from the absorption layer. Page 48

65 .1 Material parameters The unstrained bandgap energy of the In x Ga 1 x N ternary alloys is expressed by the following formula E ( In Ga N ) x E ( InN ) (1 x) E ( GaN ) b x (1 x), g x 1 x g g = + (.31) where E g (InN) and E g (GaN) are the bandgap energies of the InN and GaN, which have values of.71 ev and 3.44 ev at 3 K in the simulations of chapter 3 [1,11]. In the cases of chapter 4, the bandgaps are modified to more recent values of.64 ev and 3.4 ev [1,13] based on the curve-fitting procedure in blue InGaN light-emitting diodes [14,15]. The temperature-dependent bandgap energies of the relevant binary semiconductors are calculated using the commonly employed Varshni formula. The bowing parameter (b) and band-offset ratio are set to be 1.4/.8 ev (chapters 3/4) and.7/.3 for the InGaN material system [8,16,17]. The Caughey-Thomas approximation is employed for the mobility as a function of carrier density [18] μ μ μ max min ( N) = μmin ( N / Nref ) α (.3) For the InGaN alloys, the values of μ max, μ min, N ref, and α for electrons are 684 cm /Vs, 386 cm /Vs, cm 3, and 1.37, respectively. The value of hole mobility is assumed to be cm /Vs [19,]. The wavelength-dependent refractive indices of In x Ga 1 x N alloys are expressed Page 49

66 as [1] 1 E E E ne ( ) = Ax ( ) Bx ( ), E g E g E g (.33) Ax ( ) = 9.84(1 x) x, (.34) B( x) =.74(1 x) 9.19 x, (.35) where E is the energy of incident photon and E g is the bandgap of In x Ga 1 x N. As for the absorption coefficients, the values of various indium compositions taken from literatures were fit to the following equation [] α = + (.36) 5 ( E) 1 a( E Eg) b( E Eg), where a and b are dimensionless fitting parameters. The fitting parameters used in the simulation are shown in Table.. A linear interpolation was used to find the fitting parameters over the entire composition range. Table. Fitting parameters used to calculate the absorption coefficient of In x Ga 1 x N alloys []. Indium composition a b Page 5

67 References 1. APSYS Version by Crosslight Software Inc., Burnaby, Canada. ( S. L. Chuang and C. S. Chang, k p method for strained wurtzite semiconductors, Phys. Rev. B 54, 491 (1996). 3. S. L. Chuang and C. S. Chang, A band-structure model of strained quantum-well wurtzite semiconductors, Semicond. Sci. Technol. 1, 5 (1997). 4. J. Piprek, Semiconductor Optoelectronic Device: Introduction to Physics and Simulation, San Diego: Academic Press, 3, pp S. L. Chuang, Optical gain of strained wurtzite GaN quantum-well lasers, IEEE J. Quantum Electron. 3, 1791 (1996). 6. Y. C. Yeo, T. C. Chong, M.-F. Li, and W. J. Fan, Electronic band structures and optical gain spectra of strained wurtzite GaN-Al x Ga 1 x N quantum-well lasers, IEEE J. Quantum Electron. 34, 56 (1998). 7. Y. C. Yeo, T. C. Chong, M. F. Li, and W. J. Fan, Analysis of optical gain and threshold current density of wurtzite InGaN/GaN/AlGaN quantum well lasers, J. Appl. Phys. 84, 1813 (1998). Page 51

68 8. I. Vurgaftman and J. R. Meyer, Band parameters for nitrogen-containing semiconductors, J. Appl. Phys. 94, 3675 (3). 9. J. Piprek, Semiconductor Optoelectronic Device: Introduction to Physics and Simulation, San Diego: Academic Press, 3, pp I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, Band parameters for III V compound semiconductors and their alloys, J. Appl. Phys. 89, 5815 (1). 11. T. Matsuoka, H. Okamoto, M. Nakao, H. Harima, and E. Kurimoto, Optical bandgap energy of wurtzite InN, Appl. Phys. Lett. 81, 146 (). 1. N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin, and H. X. Jiang, Temperature and compositional dependence of the energy band gap of AlGaN alloys, Appl. Phys. Lett. 87, 414 (5). 13. J. Wu, W. Walukiewicz, W. Shan, K. M. Yu, J. W. Ager, S. X. Li, E. E. Haller, H. Lu, and W. J. Schaff, Temperature dependence of the fundamental band gap of InN, J. Appl. Phys. 94, 4457 (3). 14. Y.-K. Kuo, Y.-H. Shih, M.-C. Tsai, and J.-Y. Chang, Improvement in electron overflow of near-ultraviolet ingan leds by specific design on last barrier, IEEE Photonics Technol. Lett. 3, 163 (11). 15. J.-Y. Chang and Y.-K. Kuo, Influence of polarization-matched AlGaInN barriers in blue InGaN light-emitting diodes, Opt. Lett. 37, 1574 (1). Page 5

69 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, 795 (9). 17. J. Piprek and S. Nakamura, Physics of high-power InGaN/GaN lasers, IEE Proc.-Optoelectron. 149, 145 (). 18. J. Piprek, Semiconductor Optoelectronic Device: Introduction to Physics and Simulation, San Diego: Academic Press, 3, pp J. Piprek, R. K. Sink, M. A. Hansen, J. E. Bowers, and S. P. DenBaars, Simulation and optimization of 4 nm InGaN/GaN laser diodes, Proc. SPIE 3944, 8 ().. 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, 337 (3). 1. J. Piprek, Semiconductor Optoelectronic Device: Introduction to Physics and Simulation, San Diego: Academic Press, 3, p 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 (1). Page 53

70 Chapter 3 Polarization effect of p-on-n GaN/InGaN p-i-n solar cells in Ga- and N-face configurations In GaN-based light-emitting devices, the polarization-induced hetero-interface charges and the corresponding electric field are found to significantly influence the light output performance, i.e., the reduction of radiative recombination efficiency due to the electron-hole pairs spatially separation in the quantum wells [1 3] and the enhanced degree of electron leakage resulting from the tilted triangular-shaped band profile of the active region [ 5]. As for the photovoltaic devices, it is believed that the polarization effect shall still play an important role on the device performance; however, a detailed physical mechanism about how the internal polarization affects the photovoltaic characteristics remains rare at present. In this chapter, the influences of spontaneous and piezoelectric polarizations on the photovoltaic characteristics of conventional p-on-n GaN/InGaN p-i-n solar cells are investigated numerically. The simulation results demonstrate that the solar cell performance is seriously affected by the internal polarization. The energy band of InGaN absorption layer is titled into the direction detrimental for carrier collection due to the polarization-induced electric field when the solar cell is constructed in the conventional configuration of p-on-n and (1) orientation. When the Page 54

71 indium composition of InGaN layer increases, this unfavorable effect becomes severer, which in turn further deteriorates the device performance. The effect of polarization becomes a favorite one if the crystal configuration is reversed, i.e., the epitaxial layers are grown along the (1) orientation. 3.1 GaN/InGaN p-i-n solar cell structure The GaN/InGaN p-i-n solar cell structure under study is based on a c-plane sapphire substrate along the (1) orientation. A.-μm-thick undoped GaN layer is first deposited, followed by a p-i-n structure which consists of a 1.5-μm-thick n-gan layer ( cm 3 ), a.-μm-thick undoped InGaN absorption layer, and a.1-μm-thick p-gan top layer ( cm 3 ). The doped carrier densities considered in the simulation represent actual densities of free carriers. The configuration of undoped InGaN and p-gan layers was referring to an experimental structure published by Jani et al. [6], in which the thickness and doping concentration are identical. Similar configuration can be found elsewhere [7]. The schematic diagram of GaN/InGaN p-i-n solar cell under study is depicted in Fig The indium composition of the InGaN layer varies from 5% to 5% in order to explore the situation with different degrees of Page 55

72 polarization. The device geometry is with a square shape of 3 3 μm. The electrode coverage ratio is 1%. In the simulation, the defect-related nonradiative SRH recombination is directly governed by the SRH lifetime. A common value of 1 ns is employed in this study [8,9]. Note that the crystalline quality should be distinct when the InGaN layer suffers from different degrees of relaxation. The influences of various SRH lifetimes on photovoltaic characteristics are also discussed right after the analyses based on standard treatment of 1 ns SRH lifetime. Fig. 3.1 Schematic diagram of GaN/InGaN p-i-n solar cell under study. Page 56

73 3. Photovoltaic characteristics without polarization effect Energy (ev) n-side quasi-fermi level (a) zero bias p-side n-side quasi-fermi level (b) V p-side Distance (μm) Current density (ma/cm ) J sc =.7 ma/cm V oc =.9 V FF=.85 Efficiency=1.5% Voltage (V) Power density (mw/cm ) Fig. 3. Energy band diagrams under (a) zero and (b) V biases, and (c) J-V-P performance curves of GaN/In.1 Ga.9 N p-i-n solar cell under AM1.5G illumination without polarization. The energy band diagrams and current-voltage-power (J-V-P) performance curves of the GaN/In.1 Ga.9 N p-i-n solar cell under illumination with 1 sun air-mass 1.5 global spectra (AM1.5G) without polarization effect are shown in Fig. 3.. In this specific situation, the amount of polarization charges caused by spontaneous and piezoelectric polarizations is assumed to be zero, which serves as a reference situation for subsequent studies in which the polarization effect is applied. In Fig. Page 57

74 3.(a), a typical band-tilting due to the built-in electric field caused by the natural built-in potential is observed and the photogenerated carriers can be collected easily. Even with the forward bias of V, the energy band still tilts in the similar way. As a result, GaN/In.1 Ga.9 N p-i-n solar cell in this condition reveals typical photovoltaic characteristics, as shown in Fig. 3.(c). The conversion efficiency is 1.5% with a fill factor of Calculation of polarizations in III-nitrides In common III-nitride semiconductor devices, the device structure is usually constructed of ternary AlGaN and InGaN alloys. In order to consider the influences of internal polarization in GaN/InGaN p-i-n solar cells, the method developed by Fiorentini et al. is employed to estimate the internal polarization in Ga-face configuration, which is represented by fixed surface charges at hetero-interfaces [1]. Spontaneous polarization of ternary AlGaN and InGaN alloys, in unit of C/m, can be expressed as P ( In Ga N ) =. 413 x. 339 (1 x ) x (1 x), (3.1) sp x 1-x P (A l Ga N) =.898 x.339 (1 x) x (1 x). (3.) sp x 1-x The piezoelectric polarization of ternary nitride alloys can be calculated by Vegard s interpolation and expressed as Ppz ( InxGa1 xn) = x Ppz ( InN) + (1 x) Ppz ( GaN), (3.3) Page 58

75 Ppz ( AlxGa1 xn) = x Ppz ( AlN) + (1 x) Ppz ( GaN), (3.4) where P InN = ε + ε (3.5) pz ( ) , P GaN = ε + ε (3.6) pz ( ) , P ( AlN) 1.88 ε 5.64 ε pz = + for ε <, (3.7) P ( AlN) 1.88 ε ε pz = for ε >, (3.8) while the basal strain for the alloy matched to a GaN layer is defined as ε = (a a) / a, (3.9) bas where a bas and a are the lattice constants of GaN and alloy layers, respectively. The total internal polarization is the sum of the spontaneous and piezoelectric polarizations. The calculated polarizations as a function of alloy compositions in AlGaN and InGaN based on full-relaxed GaN basal/template layer are shown in Fig At an abrupt interface of a top/bottom layer hetero-structure such as InGaN/GaN or AlGaN/GaN, the polarization can decrease/increase within a bilayer, causing a fixed polarization charge density σ defined by [11] σ ( P + P ) = P(bottom) P(top) sp pz = [ P (bottom) + P (bottom)] [ P (top) + P (top)]. (3.1) sp pz sp pz The charge density screened by the injected carriers is determined self- Page 59

76 Polarization (C/m ) The basal strain for the alloy is defined to match to a GaN layer. P pz (InGaN) P sp (InGaN) P total (InGaN) P pz (AlGaN) -.1 P sp (AlGaN) P total (AlGaN) In or Al composition Fig. 3.3 Spontaneous, piezoelectric and total polarizations in ternary AlGaN and InGaN alloys based on full-relaxed GaN basal layer. consistently in the simulation. In conventional III-nitride devices, there always exists some degree of strain-relaxation due to the lattice-mismatched substrate and the huge lattice mismatch between the adjacent GaN and InGaN hetero-layers. As a result, the strain and the corresponding piezoelectric polarization are not as large as the theoretically predicted values [1 14]. In the simulation, the factor degree of relaxation (denoted by R ), which varies from zero (with piezoelectric polarization) to unity (without piezoelectric polarization), is employed to adjust the value of piezoelectric polarization while the spontaneous Page 6

77 polarization is maintained to be equal to the value of theoretical prediction. The total polarization can thus be expressed as P = P + P (1 R). (3.11) total sp pz In addition, it is quite difficult to predict the degree of relaxation of the real-fabricated devices in nitride solar cells. Consequently, in the present study, we explore the issues and their corresponding solutions in a wide range of degree of relaxation, rather than a fixed value. 3.4 Polarization effect in Ga-face configuration The structure grown along the (1) orientation, i.e., Ga-face, is the most conventional configuration in III-nitride semiconductor devices. More comprehensions to the relevant physical mechanisms are significant in the device development. In this section, the specific effect of internal polarization in the Ga-faced GaN/InGaN p-i-n solar cell is investigated Preliminary aspects The schematic diagram of internal polarizations in different epitaxial layers and the corresponding polarization-induced surface charges in hetero-interfaces of conventional p-on-n GaN/InGaN p-i-n structure along the (1) orientation are shown in Fig In typical p-n or p-i-n Page 61

78 Fig. 3.4 Schematic diagram of polarizations in different epitaxial layers of p-on-n GaN/InGaN p-i-n structure with Ga-face configuration. 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. Page 6

79 semiconductor devices, the normal built-in electric field directs from n-type layer to p-type layer and thus can drift the carriers in the way beneficial for carrier collection. As for the polarization-induced electric field of the InGaN layer, which is a combination of the total polarizations in all adjacent layers, it is in the direction from p-type layer to n-type layer, which is against the direction of built-in field and will cause detrimental effect for carrier collection. Therefore, the total electric field of the InGaN layer depends on the joint effect of built-in field, polarization-induced field, and the forward bias. Figure 3.5 shows the schematic energy band diagram of Ga-faced p-on-n GaN/InGaN p-i-n structure under various conditions of polarization-induced electric field. In the situation of short-circuit, which means that there is no external bias applied, the energy band tilting of InGaN absorption layer is determined by the combination of normal built-in and polarization-induced electric fields. If the polarization-induced field is less than the built-in field, the magnitude of the total electric field of InGaN absorption layer reduces while its direction maintains. In this case, the energy band tilting of InGaN absorption layer diminishes and the solar cell performance degrades slightly. If the polarization-induced field is comparable to or larger than the built-in field, the total electric field will be insufficient to drift photognenrated carriers across the potential barrier in Page 63

80 GaN/InGaN hetero-interfaces or even drift carriers in the way detrimental for collection, which reveals in the energy band diagram is a flat or reverse-tilted InGaN absorption layer, as shown in Figs. 3.5(c) and 3.5(d). Under these situations, the carrier collection efficiency is severely degraded and quite bad photovoltaic characteristics are expected Polarization-induced surface charge densities Table 3.1 Polarization-induced surface charge densities (1/m ) in In x Ga 1 x N/GaN hetero-interfaces with various values of R. The polarization-induced surface charge densities in In x Ga 1 x N/GaN hetero-interfaces with various values of R are list in Table 3.1. Since the critical thicknesses (T c ) of In x Ga 1 x N grown on GaN are generally less than 1 nm for x>.1 and decrease very rapidly with increasing x [15], InGaN layers with the thickness exceeding T c are not expected to be full strained. Besides, as will be revealed in the following simulation results, the solar Page 64

81 cell performances are too inferior to separate the photovoltaic characteristics from each other when the values of R are small, especially for the situations with high indium composition. Therefore, we tentatively vary the value of R from.5 to 1 in the following study Simulation results and discussions In this sub-section, various conditions of indium composition and degree of relaxation are simulated systematically to probe into the effect of internal polarization in Ga-face configuration. Figure 3.6 shows the energy band diagrams under zero and V biases, and J-V-P performance curves of GaN/In.1 Ga.9 N p-i-n solar cell with different degrees of relaxation. The tilting of energy band is diminished with the decrease of R because the polarization-induced surface charges and the corresponding electric field increase when the value of R decreases. Consequently, the total electric field which can drift carriers to the n-type and p-type layers reduces and hence the efficiency of carrier collection deteriorates. Note that there is a non-typical solar response at R=.8 shown in Fig. 3.6(i). The current decreases abruptly with the increase of forward bias, and then stays at a relative small value when the forward bias further increases. It can be explained by the energy band diagrams under various conditions of forward voltage. In Fig. 3.6(g), the energy band of InGaN layer is still Page 65

82 Energy (ev) Energy (ev) Energy (ev) Energy (ev) No Polarization AM1.5G zero bias quasi-fermi level (a) R=1. AM1.5G zero bias R=.8 AM1.5G zero bias R=.6 AM1.5G zero bias (d) (g) (j) No Polarization AM1.5G, V R=1. AM1.5G, V R=.8 AM1.5G, V R=.6 AM1.5G, V (b) (e) (h) (k) Current density (ma/cm ) Current density (ma/cm ) Current density (ma/cm ) Current density (ma/cm ) AM1.5G No Polarization AM1.5G, R=1. (c) (f) (i) AM1.5G, R=.8 AM1.5G, R=.6 (l) Power density (mw/cm ) Power density (mw/cm ) Power density (mw/cm ) Power density (mw/cm ) Distance (μm) Distance (μm) Voltage (V) Fig. 3.6 Energy band diagrams under zero and V biases, and J-V-P performance curves of GaN/In.1 Ga.9 N p-i-n solar cell with different degrees of relaxation. Page 66

83 tilted and hence is beneficial for carrier collection under zero bias. However, when the forward bias increases, the energy band of InGaN layer becomes more and more horizontal so that the carriers can hardly be collected by drift motion. Under these circumstances, carriers can only transport by the mechanism of diffusion. However, because the electrons and holes are generated simultaneously in the i-ingan layer, there should be many carriers lost by all forms of recombination. The current density thus drops abruptly under a particular bias when the energy band is changed from tilted to completely flat. As for the case of R=.6, a more serious situation is observed in Fig. 3.6(j) ~ (l). Under this circumstance, the energy band of InGaN layer becomes almost completely flat even at zero bias. Electrostatic field (1 5 V/cm) (a) n- GaN No P R=1. R=.8 R=.6 i-ingan zero bias Distance (μm) Electrostatic field (1 5 V/cm) 1 p- GaN -1 (b) n- GaN zero bias 1 V V i-ingan Distance (μm) R=.8 p- GaN Fig. 3.7 Electric field of GaN/In.1 Ga.9 N p-i-n solar cell (a) at zero bias with different situations of polarization and (b) under R=.8 condition with different values of forward bias. Page 67

84 Figure 3.7 shows the electric field of the GaN/In.1 Ga.9 N p-i-n solar cell under several different situations. As shown in Fig. 3.7(a), the electric field of the intrinsic InGaN layer decreases with the decrease of R due to the increasing effect of polarization. When R=.6, the electric field of the intrinsic InGaN layer almost vanishes, which clarifies the corresponding simulation results in Fig. 3.6(j) ~ (l). In Fig. 3.7(b), the electric fields in the situation of R=.8 with different values of forward bias are presented. The electric field decreases with the increase of forward bias. The electric field of the intrinsic InGaN layer is almost equal to zero at 1 V, which causes the energy band to become flat as shown in Fig. 3.6(h). When the indium composition of InGaN layer increases, the lattice mismatch between the InGaN and GaN layers is enlarged and, hence, the polarization-induced electric field of InGaN layer increases accordingly. Figure 3.8 shows the energy band diagrams and J-V-P performance curves of the GaN/In. Ga.8 N p-i-n solar cells with different degrees of relaxation. Compared to the case of GaN/In.1 Ga.9 N p-i-n solar cells shown in Fig. 3.6, more serious situations are observed for the GaN/In. Ga.8 N p-i-n solar cells as indicated in Fig In this case, when the degree of relaxation is low enough, the magnitude of polarization-induced electric field can even be higher than that of built-in Page 68

85 Energy (ev) Energy (ev) Energy (ev) Energy (ev) No Polarization AM1.5G zero bias (a) quasi-fermi level R=1. AM1.5G zero bias R=.8 AM1.5G zero bias R=.6 AM1.5G, zero bias (d) (g) Distance (μm) (j) No Polarization AM1.5G, V R=1. AM1.5G, V R=.8 AM1.5G, V R=.6 AM1.5G, V (b) (e) (h) Distance (μm) (k) Current density (ma/cm ) Current density (ma/cm ) Current density (ma/cm ) Current density (ma/cm ) AM1.5G, No Polarization (c) (f) AM1.5G, R=1. AM1.5G, R=.8 AM1.5G, R=.6 (i) Voltage (V) (l) Power density (mw/cm ) Power density (mw/cm ) Power density (mw/cm ) Power density (mw/cm ) Fig. 3.8 Energy band diagrams under zero and V biases, and J-V-P performance curves of GaN/In. Ga.8 N p-i-n solar cell with different degrees of relaxation. Page 69

86 field and, thus, the carriers are driven to the detrimental direction. The performance of the GaN/In. Ga.8 N p-i-n solar cell is thus lower than that of its GaN/In.1 Ga.9 N counterpart when the degree of relaxation is low. It is noteworthy that, when the indium composition of InGaN layer increases, the enlarged band offset between the InGaN and GaN layers is also a factor degrading the performance. Detailed exploration about the influence of enlarged band offset in hetero-interfaces will be illustrated in next chapter. Efficiency (%) In=5% In=1% In=15% In=% In=5% Degree of relaxation No polarization 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.5 to 1. Page 7

87 The conversion efficiencies of the GaN/InGaN p-i-n solar cells with different values of R under AM1.5G illumination are plotted in Fig With the increase of indium composition in the InGaN absorption layer, the efficiency deteriorates markedly, especially when the value of R is low. When the indium composition is 5%, the efficiency is the lowest one under all values of R, even though its efficiency is the highest one when the device is without polarization as indicated in Fig Hence, the effect of polarization plays an important role in designing a GaN-based solar cell that contains an InGaN absorption layer of high indium composition, which is desired if we were to extend the absorption spectrum to longer wavelength. 3.5 Polarization effect in N-face configuration Fig. 3.1 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. Page 71

88 As stated in the last section, for the conventional Ga-face configuration, the direction of the polarization-induced electric field in InGaN layer is along the ( 1) orientation, which is opposite to that of the normal built-in field and hence will drift the carriers in the detrimental way. Under this circumstance, the efficiency of carrier collection is reduced and thus the device performance is deteriorated. According to the above analysis, if the direction of the polarization-induced electric field can be reversed to be the same as that of the normal built-in field, such as the situation of N-face along the ( 1) orientation as shown in Fig. 3.1(b), the total electric field will be larger than the original built-in field, which is more beneficial for carrier collection. As a result, the efficiency of carrier collection and, consequently, the device performance can presumably be enhanced. Electrostatic field (1 5 V/cm) (a) n- GaN zero bias No Polarization i-ingan p- GaN (b) n- GaN zero bias G Ga-face (R=.6) i-ingan Distance (μm) p- GaN (c) n- GaN N-face (R=.6) i-ingan zero bias p- GaN Fig Electric field of GaN/In. Ga.8 N p-i-n solar cell at zero bias with different situations of polarization under AM1.5G illumination. Page 7

89 Figure 3.11 shows the electric field of GaN/In. Ga.8 N p-i-n solar cell at zero bias with different situations of polarization under AM1.5G illumination. In Fig. 3.11(a), the situation of no polarization effect, a typical built-in field of p-i-n heterojunction is observed, which serves as a reference to be compared in subsequent analyses. When a normal polarization of Ga-face configuration is present, the built-in field is compensated by the polarization field and the total electric field is reduced, as shown in Fig. 3.11(b). On the other hand, when a reversed polarization of N-face configuration is present, the polarization-induced field is in the direction opposite to the normal polarization and the same as the built-in field. In this case, as shown in Fig. 3.11(c), the total electric field could even be larger than that of the situation without polarization effect. Figure 3.1 shows the energy band diagrams under zero bias and the current-voltage-power (J-V-P) curves of GaN/In. Ga.8 N p-i-n solar cells with different situations of polarization under AM1.5G illumination. In Fig. 3.1(a), the situation of no polarization effect, a typical band-tilting due to the built-in field is observed. In Fig. 3.1(b), when a normal polarization of Ga-face configuration is applied, the tilting of energy band is diminished and then the efficiency of carrier collection and the overall device performance reduce accordingly. When a reversed polarization of N-face configuration is applied, however, the energy band of the InGaN absorption Page 73

90 Energy (ev) Energy (ev) Energy (ev) No polarization zero bias (a) quasi-fermi level Ga-face, R=.6 zero bias N-face R=.6 zero bias (c) (e) Current density (ma/cm ) Current density (ma/cm ) Current density (ma/cm ) No polarization Ga-face R=.6 N-face R= (b) (d) (f) Power density (mw/cm ) Power density (mw/cm ) Power density (mw/cm ) Distance (μm) Voltage (V) Fig. 3.1 Energy band diagram under zero bias and J-V-P curves of GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under AM1.5G illumination. layer is tilted in the favorable direction which can effectively drift the carriers for collection. Under this specific situation, the degree of tilting of Page 74

91 the energy band is higher than that of the situation without polarization due to the enlarged total internal field. Hence, the device performance could be enhanced. It is noteworthy that, contrary to the situation when a normal polarization is present, if an InGaN absorption layer of higher indium composition were utilized, the advantages in device performance for the situation when a reversed polarization is applied would be further enhanced due to the increased internal polarization..5 No polarization (a) 1.5 Ga-face, R=.6.5 N-face, R=.6 Energy (ev) Effective potential height for electrons 13.5 No polarization Effective potential height for holes (b) Ga-face, R= (c) N-face, R= (d) - (e) -.5 (f) Distance (μm) 13.7 Fig Enlarged energy band diagrams in the heterojunction interfaces of GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under zero bias and AM1.5G illumination. Page 75

92 The influence of polarization effect on carrier collection can be demonstrated by the comparison of effective potential height for carriers, which is defined as the potential difference between the band edge and its relevant quasi-fermi level in the heterojunction interfaces, in each case. Figure 3.13 shows the enlarged diagrams of Fig. 3.1 in the heterojunction interfaces. It is apparent that both the effective potential heights for electrons and holes of the structure with reversed polarization are the least among all three situations. Therefore, the carrier transportation crossing these heterojunction interfaces could be much easier, which is beneficial for enhancing the efficiency of carrier collection. On the other hand, the structure with normal polarization has the highest effective potential height for electrons and holes, which will result in inferior efficiency of carrier collection. Figure 3.14 shows the SRH recombination rate, which is one of the major recombination mechanisms in solar cells, of GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under zero bias and AM1.5G illumination. Figure 3.14(b) is the enlarged plot of Fig. 3.14(a) by 1 times in magnitude. It is observed that the SRH recombination rate of the structure with reversed polarization is similar to that of the structure without polarization and is much lower than that of the structure with normal polarization. The structure with normal polarization has a relatively Page 76

93 high SRH recombination rate when compared to the other situations because it is relatively difficult for the carriers to escape from the InGaN absorption layer. SRH recom. rate (1 19 /cm 3 -s) No P Ga-face (R=.6) (a) Distance (μm) N-face (R=.6) (b) Fig SRH recombination rate of GaN/In. Ga.8 N p-i-n solar cell with different situations of polarization under zero bias and AM1.5G illumination. (b) is the enlarged plot of (a) by 1 times in magnitude. Figure 3.15 shows the conversion efficiencies of the GaN/InGaN p-i-n solar cells with different degrees of relaxation and different situations of polarization under AM1.5G illumination. It is apparently found that the photovoltaic characteristics are serious influenced by the normal polarization. The conversion efficiency degrades vastly with the increase of normal polarization, i.e., with decreased degree of relaxation or with increased indium composition in the InGaN absorption layer. Note that the Page 77

94 lower (higher) degree of relaxation normally corresponds to the superior (inferior) crystalline quality. The achievement to reduce detrimental polarization effect and maintain crystalline quality simultaneously in Ga-face configuration is difficult because these two issues provide opposite influences on solar cell performance In=5% N-face Ga-face No P (a) In=1% No P (b) In=15% No P (c) Efficiency (%) In=% (d) (e) 3 No P 3 No P 1 1 In=5% Degree of relaxation Fig Conversion efficiencies of GaN/In x Ga 1-x N p-i-n solar cells with different degrees of relaxation and different situations of polarization under AM1.5G illumination. Page 78

95 As for the solar cell with N-face configuration, the effect of reversed polarization is of great benefit in helping solar cell to maintain or even enhance the conversion efficiency compared to the situation without polarization. In addition, distinct to the situation of normal polarization, the higher polarization effect is responsible for the better performance when the solar cell is under reversed polarization. As a result, fabricating solar cells with N-face configuration may be appropriate when both issues of polarization effect and crystalline quality are concerned. It is worth mentioning here that, the enhancement in conversion efficiency increases with the increase of indium composition in the InGaN absorption layer. The reason is that the band-offset at the GaN/InGaN interfaces enlarges with the increase of indium composition, which is detrimental for carrier transportation across the interfaces, and thus the capability for drifting carriers passing through this potential barrier becomes much more important. As stated previously, the crystalline quality and its corresponding defect density are probable factors influencing the photovoltaic characteristics when the degree of relaxation and the indium composition in InGaN absorption layer vary. In order to probe into its impact, the GaN/In.5 Ga.75 N p-i-n solar cells with N-face configuration are simulated under various SRH recombination lifetimes, as shown in Fig It is Page 79

96 obvious that the photovoltaic characteristics degrade with the decrease of SRH lifetime in all degrees of relaxation while the solar cell performance is still acceptable even though a small SRH lifetime of.1 ns is employed, which is corresponding to a quite inferior crystalline quality. 3.5 (a) (b) (c) Current density (ma/cm ) SRH lifetime.1 ns 1 ns 1 ns 5 ns N-face (R=) SRH lifetime.1 ns 1 ns 1 ns 5 ns N-face (R=.5) SRH lifetime.1 ns 1 ns 1 ns 5 ns N-face (R=1.) Voltage (V) Fig J-V curves of GaN/In.5 Ga.75 N p-i-n solar cell with different SRH lifetimes and different degrees of relaxation under AM1.5G illumination in N-face configuration. In Fig. 3.16, it is obvious that the reduced open-circuit voltage is one of the major factors influencing the solar cell performance when the SRH lifetime is low. The results are identical to those reported in [16]. Under the circumstance of low SRH lifetime, the recombination loss enlarges and thus a higher diode ideality factor η is expected. In addition, the reverse saturation current density J should be enlarged due to the shortened Page 8

97 diffusion length [17]. These two factors influence the open-circuit voltage in the opposite ways (V oc =ηkt/q ln(j sc /J +1)) [18]. Since the simulated open-circuit voltage is reduced, it is judged that the effect of enlarged J to V oc is higher than that of enlarged η when the SRH lifetime is low. Owing to that the structure simulated in this work (double hetero-junctions/p-i-n structure) is more complicated than the conventional hmomjunction solar cell and the effect of internal polarization is unavoidably involved, more detailed mechanisms of this specific issue should be investigated in the future. 3.6 Conclusion The simulation results reveal the fact that the ultimate effect of polarization, which might result in either improvement or deterioration of the overall device performance, depends on the direction and magnitude of the polarization induced electric field. The simulation results suggest that, for the GaN/InGaN p-i-n solar cells grown on the Ga-face template along the (1) orientation, the effect of normal polarization will degrade the device performance, especially when the indium composition of the InGaN absorption layer is high. As for the solar cells grown on the N-face template along the ( 1) orientation, the devices can benefit from the effect of reversed polarization; namely, the conversion efficiency can be Page 81

98 markedly enhanced due to the increased total field in the favorable direction for carrier collection. In the meantime, if an InGaN absorption layer of higher indium composition is used, the advantages in device performance for the situation when a reversed polarization is applied would be further enhanced due to the increased internal polarization. This finding provides the possibility in fabricating high efficiency nitride-based solar cells when both issues of polarization effect and crystalline quality are concerned. It is important to note here that, when we explored the abovementioned effects of internal polarization, parallel works by Li et al. had also been done. The articles are provided as [19] and [] in the References in which their results and conclusions are similar to ours [1 4]. Page 8

99 References 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, 173 (1984).. S.-H. Yen, Y.-K. Kuo, M.-L. Tsai, and T.-C. Hsu, Investigation of violet InGaN laser diodes with normal and reversed polarizations, Appl. Phys. Lett. 91, 1118 (7). 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, (9). 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, (7). 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, 411 (8). 6. O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, Design and characterization of GaN/InGaN solar cells, Appl. Phys. Lett. 91, (7). Page 83

100 7. C. J. Neufeld, N. G. Toledo, S. C. Cruz, M. Iza, S. P. DenBaars, and U. K. Mishra, High quantum efficiency InGaN/GaN solar cells with.95 ev band gap, Appl. Phys. Lett. 93, 1435 (8). 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, (9). 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., 86 (1). 1. V. Fiorentini, F. Bernardini, and O. Ambacher, Evidence for nonlinear macroscopic polarization in III V nitride alloy heterostructures, Appl. Phys. Lett. 8, 14 (). 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 (). 1. 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 Page 84

101 field in InGaN/GaN multiquantum well structures, Appl. Phys. Lett. 73, 6 (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, 49 (). 14. H. Zhang, E. J. Miller, E. T. Yu, C. Poblenz, and J. S. Speck, Measurement of polarization charge and conduction-band offset at In x Ga 1 x N/GaN heterojunction interfaces, Appl. Phys. Lett. 84, 4644 (4). 15. D. Holec, P. M. F. J. Costa, M. J. Kappers, and C. J. Humphreys, Critical thickness calculations for InGaN/GaN, J. Cryst. Growth 33, 314 (7). 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., 3378 (1). 17. S. O. Kasap, Optoelectronics and photonics: Principles and Practices, Taiwan: Pearson Education Taiwan LTD., 1, pp J. Nelson, The Physics of Solar Cells, London: Imperial Collage Press, 3, p 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 8, 98 (1). Page 85

102 . 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. 4, 699 (11). 1. J.-Y. Chang and Y.-K. Kuo, Comment on The impact of piezoelectric polarization and nonradiative recombination on the performance of (1) face GaN-InGaN photovoltaic devices [Appl. Phys. Lett. 96, 5117 (1)], Appl. Phys. Lett. 98, 3611 (11).. J.-Y. Chang and Y.-K. Kuo, Numerical study on the influence of piezoelectric polarization on the performance of p-on-n (1)-face GaN/InGaN p-i-n solar cells, IEEE Electron Device Lett. 3, 937 (11). 3. 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 (1) face GaN/InGaN p-i-n solar cell, IEEE J. Quantum Electron. 48, 367 (1). 4. J.-Y. Chang and Y.-K. Kuo, Simulation of N-face InGaN-based p-i-n Solar Cells, J. Appl. Phys., accepted 1 July 1. Page 86

103 Chapter 4 Effects of step-graded interlayers in p-on-n and Ga-face GaN/InGaN p-i-n solar cells Besides the difficulties in growing high indium-composition layers, there are still many obstructions which need to be overcome in the development of nitride-based solar cells. One of them might be the difficulty of carrier transportation at GaN/InGaN heterojunctions, especially when the indium composition is high. In general design, the GaN layer is usually employed to be the bases and the p-contact layer of the solar cell. It has another benefit that the GaN layers can serve as the natural window layer and back surface field (BSF) layer. However, when the indium composition in the InGaN absorption layer is high, which is desired if we were to extend the absorption spectrum to longer wavelength, the potential barriers due to the large difference of bandgap energy between the InGaN and GaN hetero-layers will seriously impede the carriers from transporting across them. In addition, as discussed in chapter 3, the photovoltaic characteristics are severely degraded by the internal polarization effect in the solar cells with conventional Ga-face configuration along (1) orientation. There are several techniques, such as the usage of non-polar substrates [1,], N-face templates [3], and polarization-matched AlGaInN layers [4], which can be employed to eliminate the detrimental effect caused by Page 87

104 polarization. However, there are some limitations for these methods, such as the difficulty in crystal growth or the degradation of crystalline quality. In nitride-based light-emitting diodes, it has been reported that the usage of compositional-grading interlayers can mitigate the polarization-induced surface charges [5,6]. As for the solar cells, the grading layers were demonstrated by Brown et al. to be beneficial for the mitigation of potential barriers in the hetero-interfaces while the polarization effect was not included in their work [7]. In this study, the impact of polarization compensation step-graded interlayers, which are easy to be fabricated and are beneficial for the mitigation of both above-mentioned impediments, between the hetero-layers of conventional p-on-n and Ga-face GaN/InGaN p-i-n solar cells is investigated. 4.1 Effect of hetero-interfaces First, the GaN/InGaN p-i-n solar cells are simulated under the situation of no polarization, in which the amount of polarization charges caused by the spontaneous and piezoelectric polarizations is assumed to be zero. The purpose of the exclusion of polarization effect in this preliminary simulation is to explore whether there are other significant influence factors or not. Figure 4.1(a) shows the conversion efficiencies of the GaN/InGaN p-i-n solar cells as a function of the indium composition with various Page 88

105 p-type doping concentrations under the situation of no polarization. The J-V curves of GaN/InGaN p-i-n solar cells with 1%, % and 3% indium composition and cm 3 hole concentration with no polarization effect are also depicted in Fig. 4.1(b). It is observed that, with the increase of indium composition, the energy bandgap of the InGaN material reduces which can cover more portions of the solar spectrum and thus the conversion efficiency increases. However, when the indium composition further increases, the conversion efficiency reaches the maximum and then degrades abruptly, which is presumably due to the enlarged potential barrier height in the GaN-InGaN hetero-interfaces, as shown in Fig. 4.. Efficiency (%) No P p-5x1 17 cm 3 p-1x1 18 cm 3 p-5x1 18 cm 3 (a) 1 3 In composition (%) Current density (ma/cm ) 3 1 In=1% In=% In=3% p-5x1 18 cm Voltage (V) (b) 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 1%, % and 3% indium composition and cm 3 hole concentration under the situation of no polarization. Page 89

106 4 3 Light-off, equilibrium (a) In=1% No P Light-off, equilibrium (b) In=% No P Light-off, equilibrium (c) In=3% No P 1-1 Energy (ev) In.1 Ga.9 N AM1.5G, zero bias (d) In=1% No P In. Ga.8 N AM1.5G, zero bias (e) In=% No P In.3 Ga.7 N AM1.5G, zero bias (f) In=3% No P In.1 Ga.9 N In. Ga.8 N In.3 Ga.7 N Distance (μm) Fig. 4. Energy band diagrams of GaN/InGaN p-i-n solar cells with 1%, % and 3% indium composition and 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. The GaN material is usually employed as the base and p-contact layers in InGaN solar cells. The large difference of the energy bandgap between the GaN and InGaN hetero-layers forms a non-negligible potential barrier which retards the photogenerated carriers from transporting across it. When Page 9

107 the potential barrier height is large enough to seriously degrade the carrier collection efficiency, the conversion efficiency will be severely deteriorated. It can be judged from Fig. 4. that the band profile near the InGaN absorption layer in both situations with and without AM1.5G illumination is similar for 1% and % indium composition solar cells. However, as shown in Figs. 4.(c) and 4.(f), the energy band of InGaN becomes flatter when the AM1.5G illumination is turned on in GaN/In.3 Ga.7 N structure. This phenomenon may be due to that many of the photogenerated carriers are confined in the InGaN layer by the relatively high potential barriers in GaN-In.3 Ga.7 N hetero-interfaces, which screen out the normal built-in field. The viewpoint will be further demonstrated in the following analyses. Optical generation rate (1 1 cm 3 s 1 ) 4 In x Ga 1-x N 3 (a) In=3% In=% In=1% Distance (μm) SRH recombination rate (1 1 cm 3 s 1 ) (b) In=1% In=% In=3% x x1 4 1.x1 4.5x1 4 Distance (μm) In=% (c) In=1% Fig. 4.3 (a) Optical generation rates and (b) SRH recombination rates of GaN/InGaN p-i-n solar cells with 1%, % and 3% indium composition and cm 3 hole concentration at zero bias under the situation of no polarization. (c) is the enlarged plot of (b). Page 91

108 Figure 4.3 shows the optical generation rate and SRH recombination rate of the GaN/In.1 Ga.9 N, GaN/In. Ga.8 N and GaN/In.3 Ga.7 N p-i-n solar cells with cm 3 hole concentration at zero bias under the situation of no polarization. It is obvious that the solar cells with higher indium composition in InGaN absorption layer possesses more optical generation rate due to that more solar spectrum is covered/absorbed. Note that the SRH recombination rate of the GaN/In.3 Ga.7 N p-i-n solar cell is much higher than that of its GaN/In.1 Ga.9 N and GaN/In. Ga.8 N counterparts and is comparable to the corresponding optical generation rate. In the simulation, the calculated SRH recombination rate is related to the SRH lifetime and local carrier concentration, and all the simulated structures possess identical SRH lifetime (1 ns, as stated previously). Hence, the higher SRH recombination rate of the In=3% structure is attributed to the difficulty for the photogenerated carriers to escape from the In.3 Ga.7 N absorption layer. 4. Effect of p-type doping concentration Although the p-type doping with high hole concentrations in GaN was considered to be limited by many complications, high conductive p-type GaN layers with resistivities lower than 1.3 Ω cm have been reported recently, which could provide a low-resistance p-contact layer [8,9]. Figure Page 9

109 4.1 shows the performance difference of the GaN/InGaN p-i-n solar cells with various p-type doping concentrations as well. The higher p-type doping concentration will result in higher built-in electric field in the InGaN absorption layer, which is beneficial for the photogenerated carriers to drift across the potential barriers in the hetero-interfaces, and thus higher carrier collection efficiency can be obtained. In the two extremities of the indium composition under study, similar performances are obtained for the structures with various p-type doping concentrations due to the relative low (high) potential barriers in the hetero-interfaces which is negligible (hard to overcome) for carrier transport. The importance of the high p-type doping concentration in InGaN solar cells would be promoted when the polarization effect is considered because of the efficient compensation of the detrimental polarization-induced electric field. As a result, the hole concentration of the p-gan layer is set to a relatively high value ( cm 3 ) in the following study. The influences of p-type doping concentration in the solar cells with step-graded interlayers will also be studied shortly. 4.3 Effect of polarization charges The works explored in this section contain some similar results as those shown in some portions of Chapter 3. However, present study provides more detailed analyses. For examples, the results obtained in Page 93

110 Chapter 3 reveal the joint effect of the polarization effect and potential barriers. In present study, these two issues are discussed separately in the situations of considering only potential barriers (Section 4.1) and considering both polarization effect and potential barriers (Section 4.3). It is believed that, through the comparison of these two specific situations, more clear and convincing mechanism of the polarization effect can be provided. Efficiency (%) No P R=1. R= In composition (%) Current density (ma/cm ) 3 1 No P R=1. R= Voltage (V) In=% 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/In. Ga.8 N p-i-n solar cells under the situations of no polarization, R=1., and R=.5 (Ga-face, hole concentration = cm 3 ). As discussed in Chapter 3, in conventional nitride-based solar cells (p-on-n and Ga face), the polarization-induced electric field whose direction is opposite to that of the normal built-in field will compensate the magnitude of the normal built-in field and thus degrade the carrier collection efficiency. Figure 4.4 shows the conversion efficiencies of Page 94

111 GaN/InGaN p-i-n solar cells as a function of indium composition and J-V curves of GaN/In. Ga.8 N p-i-n solar cells under the situations of no polarization, R=1., and R=.5 (Ga-face, hole concentration = cm 3 ). When the value of R decreases, the polarization-induced surface charge densities in the hetero-interfaces increase and the polarization-induced electric field of the InGaN absorption layer enhances correspondingly. In Fig. 4.4, it is evident that the conversion efficiencies of the InGaN solar cells degrade with the decrease of R. The physical origin of this large performance difference is ascribed to the degradation of carrier collection efficiency with the increase of polarization effect, which can be demonstrated by the observation of the energy band diagrams and electric fields of the InGaN absorption layer in these situations, as shown in Figs. 4.5 and 4.6. In Fig. 4.5, the directions of the energy band tilting, which is responsible for the combination of normal built-in field and polarization-induced field, of the InGaN absorption layer are distinct for the situations of no polarization and various values of R. With the decrease of R, the polarization-induced field increases while the normal built-in field remains unchanged. As a result, the total electric field and the slope of the energy band tilting decrease, which result in the reduced capability of drifting carriers across the potential barriers in hetero-interfaces. In the situation of R=.5, the direction of the energy band tilting is even reversed, which means that the polarization-induced field is higher than the normal built-in field and thus the carrier collection efficiency will be severely Page 95

112 Energy (ev) Light-off, equilibrium (a) (d) In=% No P In. Ga.8 N AM1.5G, zero bias In=% No P In. Ga.8 N Light-off, equilibrium (b) In=% R=1. (e) In. Ga.8 N AM1.5G, zero bias In=% R=1. In. Ga.8 N Distance (μm) Light-off, equilibrium (c) In=% R=.5 (f) In. Ga.8 N AM1.5G, zero bias In=% R=.5 In. Ga.8 N Fig. 4.5 Energy band diagrams of the GaN/In. Ga.8 N p-i-n solar cells under the situations of no polarization, R=1., and R=.5 at (a) (b) (c) equilibrium state and (d) (e) (f) AM1.5G illumination (Ga-face, hole concentration = cm 3 ). degraded. Under this circumstance, similar to the result of Fig. 4.(f), the energy band of InGaN becomes flatter when the AM1.5G illumination is turned on due to the screening of confined carriers. In Fig. 4.6, the total electric field of the InGaN absorption layer decreases with the decrease of R. The negative field in the situation of R=.5 also indicates the larger magnitude of polarization field comparing to that of the built-in field. Page 96

113 Electric field (1 5 V/cm) (a) In=% No P R=1. R= (b) Distance (μm) Fig. 4.6 (a) Electric fields of the GaN/In. Ga.8 N p-i-n solar cells at equilibrium under the situations of no polarization, R=1., and R=.5 (Ga-face, hole concentration = cm 3 ). (b) Enlarged plot of (a). It can be concluded from the above simulation results that both the potential barriers and the polarization-related electric field induced by GaN-InGaN hetero-interfaces are significant and detrimental for the performance of Ga-faced p-on-n GaN/InGaN p-i-n solar cells. Note that the demotion of the crystalline quality with the increase of indium composition of InGaN layer was not included in the simulations. Thus, even perfect crystalline quality of InGaN solar cell can be achieved for the structure with high indium composition, the photovoltaic characteristics will still be too poor to have practical applications due to the aforementioned issues. As a result, some efficient solutions must be employed for the GaN/InGaN Page 97

114 p-i-n solar cells to benefit from better performance. 4.4 Influences of step-graded interlayers In order to overcome the detrimental effects of potential barriers and polarization-induced electric field, one of the solutions might be the employment of step-graded interlayers between the GaN-InGaN hetero-layers. The compositional-grading interlayers are demonstrated to be useful for the release of potential barriers and polarization effect in the InGaN light-emitting diodes and solar cells [7,1 1]. In subsequent studies, more research and analysis about the influences of the thickness and p-type doping concentration of the step-graded interlayers on the performance of Ga-faced p-on-n GaN/InGaN p-i-n solar cells are explored. For the proposed structures, some portions of the p- and n-gan layers adjacent to the In x Ga 1 x N absorption layer are replaced by the InGaN interlayers. The interlayers are divided into nine independent layers with the indium composition varying gradually from to x, where x is the indium composition of the In x Ga 1 x N absorption layer. The doping concentrations of the interlayers are identical to that of the adjacent GaN layer ( cm 3 for n- and p-type layers) in each structure. Schematic diagram of the structure with step-graded interlayers is shown in Fig Page 98

115 Fig. 4.7 Schematic diagram of the structure with step-graded interlayers. 4 Energy (ev) (a) In=3% No P without grading layer (b) In=3% No P with grading layer (45 nm) Current density (ma/cm ) 6 (c) 4 with grading layer (45 nm) without grading layer Distance (μm) Voltage (V) Fig. 4.8 (a) and (b) Energy band diagrams at equilibrium and (c) J-V curves of the GaN/In.3 Ga.7 N p-i-n solar cells with and without 45-nm-thick grading layer under the situation of no polarization. Page 99