基于第一性原理GGA+U方法研究Si掺杂β-Ga2O3电子结构和光电性质

张英楠; 张敏; 张派; 胡文博

doi:10.7498/aps.73.20231147

摘要

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.

关键词:

Abstract

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:

作者及机构信息

辽宁师范大学物理与电子技术学院, 大连　116029

通信作者: 张敏, m.zhang@live.com

基金项目: 兴辽英才计划(批准号: XLYC1807170)和教育部产学合作协同育人项目(批准号: 220900575223357)资助的课题.

Authors and contacts

School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China

Corresponding author: Zhang Min, m.zhang@live.com

Funds: Project supported by the Liaoning Revitalization Talents Program, China (Grant No. XLYC1807170) and the University-Industry Collaborative Education Program of Ministry of Education, China (Grant No. 220900575223357).

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参考文献

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[15]	Guo Q X, Nishihagi K, Chen Z W, Saito K, Tanaka T 2017 Thin Solid Films 639 123 Google Scholar
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施引文献

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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.

下载: 全尺寸图片幻灯片

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).

下载: 全尺寸图片幻灯片

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.

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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).

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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.

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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).

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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	E_f/eV
Models		a/Å	b/Å	c/Å	β	V/Å³	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 物理学报 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 物理学报 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 物理学报 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 物理学报 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
[20]	Gogova D, Wagner G, Baldini M, Schmidbauer M, Irmscher K, Schewski R, Galazka Z, Albrecht M, Fornari R 2014 J. Cryst. Growth 401 665 Google Scholar
[21]	张易军, 闫金良, 赵刚, 谢万峰 2011 物理学报 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 物理学报 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 Google Scholar
[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 Google Scholar
[31]	Kang B K, Mang S R, Go D H, Yoon D H 2013 Mater. Lett. 111 67 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 Google Scholar
[35]	Guo D Y, Wu Z P, Li P G, An Y H, Liu H, Guo X C, Yan H, Wang G F, Sun C L, Li L H, Tang W H 2014 Opt. Mater. Express 4 1067 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
[38]	落巨鑫, 高红丽, 邓金祥, 任家辉, 张庆, 李瑞东, 孟雪 2023 物理学报 72 028502 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 物理学报 63 057102 Google Scholar Zheng S W, Fan G H, He M, Zhao L Z 2014 Acta Phys. Sin. 63 057102 Google Scholar
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基于第一性原理GGA+U方法研究Si掺杂β-Ga₂O₃电子结构和光电性质

Investigation of electronic structure and optoelectronic properties of Si-doped β-Ga₂O₃using GGA+U method based on first-principle

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辽宁师范大学物理与电子技术学院, 大连　116029

通信作者: 张敏, m.zhang@live.com

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School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China

Corresponding author: Zhang Min, m.zhang@live.com

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