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采用基于密度泛函理论的GGA+U方法, 计算了本征和Si掺杂β-Ga2O3的形成能、能带结构、态密度、差分电荷密度和光电性质. 结果表明, Si取代四面体Ga(1)更容易实验合成, 得到的β-Ga2O3带隙和Ga-3d态峰值与实验结果吻合较好, 且贫氧条件下更倾向于获得有效掺杂. Si掺杂后, 总能带向低能端移动, 费米能级进入导带, 呈现n型导电性; Si-3s轨道电子占据导带底, 电子公有化程度加强, 电导率明显改善. 随着Si掺杂浓度的增加, 介电函数ε2(ω)的结果表明, 激发导电电子的能力先增强后减弱, 与电导率的量化分析结果一致. 光学带隙增大, 吸收带边上升速度减慢; 吸收光谱结果显示Si掺杂β-Ga2O3具有较强的深紫外光电探测能力. 计算结果将为下一步Si掺杂β-Ga2O3实验研究和器件设计的创新及优化提供理论参考.
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关键词:
- GGA+U方法 /
- Si掺杂β-Ga2O3 /
- 电子结构 /
- 光电性质
In this work, the formation energy, band structure, state density, differential charge density and optoelectronic properties of undoped β-Ga2O3 and Si doped β-Ga2O3 are calculated by using GGA+U method based on density functional theory. The results show that the Si-substituted tetrahedron Ga(1) is more easily synthesized experimentally, and the obtained β-Ga2O3 band gap and Ga-3d state peak are in good agreement with the experimental results, and the effective doping is more likely to be obtained under oxygen-poor conditions. After Si doping, the total energy band moves toward the low-energy end, and Fermi level enters the conduction band, showing n-type conductive characteristic. The Si-3s orbital electrons occupy the bottom of the conduction band, the degree of electronic occupancy is strengthened, and the conductivity is improved. The results from dielectric function ε2(ω) show that with the increase of Si doping concentration, the ability to stimulate conductive electrons first increases and then decreases, which is in good agreement with the quantitative analysis results of conductivity. The optical band gap increases and the absorption band edge rises slowly with the increase of Si doping concentration. The results of absorption spectra show that Si-doped β-Ga2O3 has the ability to realize the strong deep ultraviolet photoelectric detection. The calculated results provide a theoretical reference for further implementing the experimental investigation and the optimization innovation of Si-doped β-Ga2O3 and relative device design.-
Keywords:
- GGA+U method /
- Si-doped β-Ga2O3 /
- electronic structure /
- optoelectronic property
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图 1 Si掺杂β-Ga2O3的1×2×2超胞模型, Ga(1)和Ga(2)分别表示四面体和八面体位置
Fig. 1. 1×2×2 supercell model of Si-doped β-Ga2O3, where Ga(1) and Ga(2) represent tetrahedral and octahedral positions, respectively.
图 2 原胞和超胞模型 (a) Ga8O12; (b) Ga31O48Si1 (1×2×2); (c) Ga23O36Si1 (1×3×1); (d) Ga15O24Si1 (1×2×1); (e) Ga7O12Si1
Fig. 2. (a) Primitive cell and supercell models: (a) Ga8O12; (b) Ga31O48Si1 (1×2×2); (c) Ga23O36Si1 (1×3×1); (d) Ga15O24Si1 (1×2×1); (e) Ga7O12Si1.
图 3 β-Ga2O3的能带结构和对应的态密度图谱 (a) GGA; (b) GGA+U
Fig. 3. Band structure and corresponding density of states plots of β-Ga2O3: (a) GGA; (b) GGA+U.
图 4 不同Si掺杂浓度的能带结构图谱 (a) 1.25% (Ga31O48Si1); (b) 1.67% (Ga23O36Si1); (c) 2.50% (Ga15O24Si1); (d) 5.00% (Ga7O12Si1)
Fig. 4. Band structure plots of β-Ga2O3 with different Si doping concentrations: (a) 1.25% (Ga31O48Si1); (b) 1.67% (Ga23O36Si1); (c) 2.50% (Ga15O24Si1); (d) 5.00% (Ga7O12Si1).
图 5 不同Si掺杂浓度的DOS图谱 (a) 0% (Ga8O12); (b) 1.67% (Ga23O36Si1); (c) 5.00% (Ga7O12Si1). (d) 不同Si掺杂浓度的PDOS图谱
Fig. 5. DOS for different Si doping concentrations: (a) 0% (Ga8O12); (b) 1.67% (Ga23O36Si1); (c) 5.00% (Ga7O12Si1). (d) PDOS for different Si doping concentrations.
图 6 未掺杂(a)和Si掺杂浓度为5.00% (b)的β-Ga2O3 010面差分电荷密度分布图
Fig. 6. Differential charge density distribution of undoped (a) and Si-doped β-Ga2O3 (010) surface with a doping atomic concentration of 5.00% (b).
图 7 未掺杂和不同浓度Si掺杂β-Ga2O3的介电函数虚部
Fig. 7. Imaginary part of dielectric function of undoped and Si-doped β-Ga2O3 with different Si concentrations.
图 8 未掺杂和不同浓度Si掺杂β-Ga2O3的吸收光谱, 插图为局部区域(300—790 nm)吸收光谱放大图
Fig. 8. Absorption spectra of undoped and Si-doped β-Ga2O3 with different Si concentrations, illustrated as enlarged absorption spectra of a local region (300–790 nm).
表 1 GGA+U方法优化后未掺杂和Si掺杂β-Ga2O3的晶格参数
Table 1. Lattice parameters of undoped and Si-doped β-Ga2O3 optimized using GGA+U method.
Models a/Å b/Å c/Å β V/Å3 Ef/eV O-Rich O-Poor β-Ga2O3 Exp.[32] 12.220 3.038 5.786 — — — — 0% 12.276 3.065 5.845 104.050 213.329 — — 1.25% 12.359 3.061 5.844 104.025 214.469 5.479 –3.301 1.67% 12.347 3.063 5.847 104.117 214.511 6.121 –2.659 2.50% 12.391 3.061 5.843 104.058 214.961 6.471 –2.309 5.00% 12.719 3.031 5.817 103.047 218.442 6.638 –2.142 
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[1] 刘增, 李磊, 支钰崧, 都灵, 方君鹏, 李山, 余建刚, 张茂林, 杨莉莉, 张少辉, 郭宇锋, 唐为华 2022 71 208501
Google Scholar
Liu Z, Li L, Zhi Y S, Du L, Fang J P, Li S, Yu J G, Zhang M L, Yang L L, Zhang S H, Guo Y F, Tang W H 2022 Acta Phys. Sin. 71 208501
Google Scholar
[2] 郭道友, 李培刚, 陈政委, 吴真平, 唐为华 2019 68 078501
Google Scholar
Guo D Y, Li P G, Chen Z W, Wu Z P, Tang W H 2019 Acta Phys. Sin. 68 078501
Google Scholar
[3] 况丹, 徐爽, 史大为, 郭建, 喻志农 2023 72 038501
Google Scholar
Kuang D, Xu S, Shi D W, Guo J, Yu Z N 2023 Acta Phys. Sin. 72 038501
Google Scholar
[4] 李秀华, 张敏, 杨佳, 邢爽, 高悦, 李亚泽, 李思雨, 王崇杰 2022 71 048501
Google Scholar
Li X H, Zhang M, Yang J, Xing S, Gao Y, Li Y Z, Li S Y, Wang C J 2022 Acta Phys. Sin. 71 048501
Google Scholar
[5] Mi W, Li Z, Luan C N, Xiao H D, Zhao C S, Ma J 2015 Ceram. Int. 41 2572
Google Scholar
[6] Higashiwaki M, Sasaki K, Murakami H, Kumagai Y, Koukitu A, Kuramata A, Masui T, Yamakoshi S 2016 Semicond. Sci. and Technol. 31 034001
Google Scholar
[7] Higashiwaki M, Jessen G H 2018 Appl. Phys. Lett. 112 060401
Google Scholar
[8] Hou Y, Jayatissa A H 2014 Sens. Actuators, B 204 310
Google Scholar
[9] Zhang L Y, Yan J L, Zhang Y J, Li T, Ding X W 2012 Phys. B: Condens. Matter 407 1227
Google Scholar
[10] Leedy K D, Chabak K D, Vasilyev V, Look D C, Boeckl J J, Brown J L, Tetlak S E, Green A J, Moser N A, Crespo A, Thomson D B, Fitch R C, McCandless J P, Jessen G H 2017 Appl. Phys. Lett. 111 012103
Google Scholar
[11] Zhang Y J, Yan J L, Zhao G, Xie W F 2010 Phys. B: Condens. Matter 405 3899
Google Scholar
[12] Ahmadi E, Koksaldi O S, Kaun S W, Oshima Y, Short D B, Mishra U K, Speck J S 2017 Appl. Phys. Express 10 041102
Google Scholar
[13] Yan H Y, Guo Y R, Song Q G, Chen Y F 2014 Phys. B: Condens. Matter 434 181
Google Scholar
[14] Chen Z W, Wang X, Noda S, Saito K, Tanaka T, Nishio M, Arita M, Guo Q X 2016 Superlattices Microstruct. 90 207
Google Scholar
[15] Guo Q X, Nishihagi K, Chen Z W, Saito K, Tanaka T 2017 Thin Solid Films 639 123
Google Scholar
[16] Hu D Q, Wang Y, Zhuang S W, Dong X, Zhang Y T, Yin J Z, Zhang B L, Lv Y J, Feng Z H, Du G T 2018 Ceram. Int. 44 3122
Google Scholar
[17] Xu C X, Liu H, Pan X H, Ye Z Z 2020 Opt. Mater. 108 110145
Google Scholar
[18] Varley J B, Weber J R, Janotti A, Van de Walle C G 2010 Appl. Phys. Lett. 97 142106
Google Scholar
[19] Takakura K, Koga D, Ohyama H, Rafi J M, Kayamoto Y, Shibuya M, Yamamoto H, Vanhellemont J 2009 Phys. B: Condens. Matter 404 4854
Google Scholar
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Google Scholar
[21] 张易军, 闫金良, 赵刚, 谢万峰 2011 60 037103
Google Scholar
Zhang Y J, Yan J L, Zhao G, Xie W F 2011 Acta Phys. Sin. 60 037103
Google Scholar
[22] Orita M, Ohta H, Hirano M, Hosono H 2000 Appl. Phys. Lett. 77 4166
Google Scholar
[23] Li Y, Yang C H, Wu L Y, Zhang R 2017 Mod. Phys. Lett. B 31 1750172
Google Scholar
[24] Dang J N, Zheng S W, Chen L, Zheng T 2019 Chin. Phys. B 28 016301
Google Scholar
[25] 马海林, 苏庆 2014 63 116701
Google Scholar
Ma H L, Su Q 2014 Acta Phys. Sin. 63 116701
Google Scholar
[26] Dong L P, Jia R X, Xin B, Peng B, Zhang Y M 2017 Sci. Rep. 7 40160
Google Scholar
[27] Wei W, Qin Z X, Fan S F, Li Z W, Shi K, Sheng Z Q, Yi Z G 2012 Nanoscale Res. Lett. 7 562
Google Scholar
[28] He H Y, Orlando R, Blanco M A, Pandey R, Amzallag E, Baraille I, Rérat M 2006 Phys. Rev. B 74 195123
Google Scholar
[29] Zheng T, Wang Q, Dang J N, He W, Wang L Y, Zheng S W 2020 Comput. Mater. Sci. 174 109505
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[30] Shu T K, Miao R X, Guo S D, Wang S Q, Zhao C H, Zhang X L 2020 Chin. Phys. B 29 126301
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Google Scholar
[32] Yoshioka S, Hayashi H, Kuwabara A, Oba F, Matsunaga K, Tanaka I 2007 J. Phys. Condens. Matter 19 346211
Google Scholar
[33] Víllora E G, Shimamura K, Yoshikawa Y, Ujiie T, Aoki K 2008 Appl. Phys. Lett. 92 202120
Google Scholar
[34] Janowitz C, Scherer V, Mohamed M, Krapf A, Dwelk H, Manzke R, Galazka Z, Uecker R, Irmscher K, Fornari R, Michling M, Schmeißer D, Weber J R, Varley J B, Van de Walle C G 2011 New J. Phys. 13 085014
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Google Scholar
[36] Yang X Y, Wen S M, Chen D D, Li T, Zhao C W 2022 Phys. Lett. A 433 128025
Google Scholar
[37] Yang K, Dai Y, Huang B 2008 Chem. Phys. Lett. 456 71
Google Scholar
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Google Scholar
Luo J X, Gao H L, Deng J X, Ren J H, Zhang Q, Li R D, Meng X 2023 Acta Phys. Sin. 72 028502
Google Scholar
[39] Oshima T, Matsuyama K, Yoshimatsu K, Ohtomo A 2015 J. Cryst. Growth 421 23
Google Scholar
[40] Lu J G, Fujita S, Kawaharamura T, Nishinaka H, Kamada Y 2008 Phys. Status Solidi C 5 3088
Google Scholar
[41] Guo S Q, Hou Q Y, Zhao C W, Zhang Y 2014 Chem. Phys. Lett. 614 15
Google Scholar
[42] Litimein F, Rached D, Khenata R, Baltache H 2009 J. Alloys Compd. 488 148
Google Scholar
[43] Shimamura K, Víllora E G, Ujiie T, Aoki K 2008 Appl. Phys. Lett. 92 201914
Google Scholar
[44] Mondal A K, Mohamed M A, Ping L K, Mohamad Taib M F, Samat M H, Mohammad Haniff M A S, Bahru R 2021 Materials (Basel). 14 604
Google Scholar
[45] Gajdoš M, Hummer K, Kresse G, Furthmüller J, Bechstedt F 2006 Phys. Rev. B 73 045112
Google Scholar
[46] Sarkar A, Ghosh S, Chaudhuri S, Pal A K 1991 Thin Solid Films 204 255
Google Scholar
[47] Reynolds D C, Look D C, Jogai B 2000 J. Appl. Phys. 88 5760
Google Scholar
[48] Zheng S W, Fan G H, He M, Zhao L Z 2014 Acta Phys. Sin. 63 057102 [郑树文, 范广涵, 何苗, 赵灵智 2014 63 057102
Google Scholar
Zheng S W, Fan G H, He M, Zhao L Z 2014 Acta Phys. Sin.63 057102 Google Scholar
[49] Hou Q Y, Lü Z Y, Zhao C W 2014 Acta Phys. Sin. 63 197102 [侯清玉, 吕致远, 赵春旺 2014 63 197102
Google Scholar
Hou Q Y, Lü Z Y, Zhao C W 2014 Acta Phys. Sin.63 197102 Google Scholar
[50] Liu J F, Gao S S, Li W X, Dai J F, Suo Z Q, Suo Z T 2021 Cryst. Res. Technol. 57 2100126
Google Scholar
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