褶皱状单层GeSe各向异性的能带漏斗效应

刘俊杰; 左慧玲; 谭鑫; 董健生

doi:10.7498/aps.73.20241155

摘要

褶皱结构引起的周期性连续变化应变为调控二维材料电子和光电性质提供了重要手段. 然而, 关于褶皱状二维材料的形成机理及其对相关物性的调控研究仍缺乏理解. 本文基于原子键弛豫理论和连续介质力学方法, 系统研究了褶皱状单层GeSe能带结构随波长和位置的变化规律. 结果表明, 由于各向异性的力学性质和褶皱引起的周期性连续变化应变, 褶皱状单层GeSe表现出各向异性的能带漏斗效应, 激子会定向聚集在褶皱的谷区域, 且聚集能力随着波长的减小而增强. 此外, 当波长减小至106 nm, 锯齿型褶皱状单层GeSe的能带漏斗消失, 而扶手椅型褶皱状单层GeSe的能带漏斗依然得以保持. 这些结果为褶皱状单层GeSe在激子输运中的应用提供了理论基础, 并为设计高性能基于二维材料的光电器件提供了新策略.

关键词:

Abstract

Two-dimensional materials with tunable wrinkled structures open up a new way to modulate their electronic and optoelectronic properties. However, the mechanisms of forming wrinkles and their influences on the band structures and associated properties are still unclear. Here, we investigate the strain distribution, bandgap, and anisotropic energy funneling effect of wrinkled monolayer GeSe and their evolution with the wrinkle wavelength based on the atomic-bond-relaxation approach and continuum medium mechanics. We find that the top region and valley region of wrinkled monolayer GeSe exhibit tensile and compressive strains, respectively, and the strain increases with wrinkle wavelength decreasing. Moreover, the periodic undulation strain in the wrinkles can lead to continuously adjustable bandgaps and band edges in wrinkled monolayer GeSe. For zigzag wrinkled monolayer GeSe, when the wrinkle wavelength is long, the conduction band minimum value (valence band maximum value) continuously decreases (increases) from the top to the valley, forming an energy funnel. As a result, the excitons accumulate in the valleys of wrinkles, and their accumulation capability increases with wrinkle wavelength decreasing. However, as the wavelength further decreases, the energy funnel will disappear, causing some excitons to t accumulate at the top of wrinkles, while the remaining excitons will accumulate in the valleys of wrinkles. The critical wavelength for the energy funnel of zigzag wrinkled GeSe to disappear is 106nm. The physical origin is that when the top strain exceeds 4%, the bandgap will decrease. Owing to the monotonic variation of bandgap with strain, the energy funneling effect of armchair wrinkled monolayer GeSe is still retained when the wavelength decreases to 80 nm, and the accumulation of excitons is further enhanced. Our results demonstrate that the energy funneling effect induced by nonuniform can realize excitons’ accumulation in one material without the need of p-n junctions, which is of great benefit to the collection of photogenerated excitons. Therefore, the proposed theory not only clarifies the physical mechanism regarding the anisotropic energy funneling effect of wrinkled monolayer GeSe, but also provides a new avenue for designing the next-generation optoelectronic devices.

Keywords:

作者及机构信息

吉首大学物理与机电工程学院, 吉首　416000

通信作者: 董健生, jsdong@jsu.edu.cn

基金项目: 国家自然科学基金(批准号: 12364007)、湖南省研究生科研创新项目(批准号: CX20240945)、湖南省大学生创新创业训练项目(批准号: S202310531036)和国家级大学生创新创业训练项目(批准号: S202410531045)资助的课题.

Authors and contacts

College of Physics and Electromechanical Engineering, Jishou University, Jishou 416000, China

Corresponding author: Dong Jian-Sheng, jsdong@jsu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12364007), the Innovation Foundation for Postgraduate of Hunan Province, China (Grant No. CX20240945), Hunan Students' Platform for Innovation and Entrepreneurship Training Program, China (Grant No. S202310531036), and the National Students' Platform for Innovation and Entrepreneurship Training Program of China (Grant No. S202410531045).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 褶皱状单层GeSe/衬底结构示意图以及单层GeSe的俯视图和侧视图

Fig. 1. Schematic illustration of wrinkled monolayer GeSe/ substrate as well as the top and side views of monolayer GeSe.

下载: 全尺寸图片幻灯片

图 2 (a) 褶皱状单层GeSe振幅与波长之间的关系; (b) 不同波长下褶皱状单层GeSe应变的分布情况; (c) 单层GeSe带隙随应变的变化规律; (d) 不同波长下褶皱状单层GeSe带隙的分布情况

Fig. 2. (a) The relationship between the amplitude and wavelength of wrinkled monolayer GeSe; (b) distribution of strain of wrinkled monolayer GeSe with different wavelengths; (c) strain dependent bandgap of monolayer GeSe; (d) distribution of bandgaps of wrinkled monolayer GeSe with different wavelengths.

下载: 全尺寸图片幻灯片

图 3 (a) 锯齿型褶皱状单层GeSe和 (b) 扶手椅型褶皱状单层GeSe在不同波长下单个周期内带边的分布情况

Fig. 3. Energy profiles of (a) zigzag wrinkled monolayer GeSe and (b) armchair wrinkled monolayer GeSe with different wavelengths.

下载: 全尺寸图片幻灯片

图 4 褶皱状单层GeSe峰导带底和价带顶的一阶导数随波长的变化规律

Fig. 4. The first derivatives of CBM and VBM of top as a function of wavelength in zigzag wrinkled GeSe and armchair wrinkled GeSe.

下载: 全尺寸图片幻灯片

图 5 褶皱状单层GeSe驱动力和激子转移速率随波长的变换规律

Fig. 5. The driving force and exciton transfer rate of wrinkled GeSe as a function of wavelength.

下载: 全尺寸图片幻灯片

表 1 理论计算所需参数

Table 1. Input parameters for calculations of monolayer GeSe.

GeSe E_f/GPa a/Å b/Å h/Å E_C/eV ν₁₍₃₎ ν₂₍₄₎ m_e m_h E_g/eV

Zigzag 66^[8] 3.96^[6] 4.16^[6] 2.62^[6] 3.1^[4] 0.42^[40]
(0.14) –0.43^[9]
(0.58) 0.31^[6]
(m₀) 0.38^[6]
(m₀) 1.16^[6]

Armchair 25^[8]

下载: 导出CSV

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[2]	Mak K F, Lee C, Hone J, Shan J, Heinz T F 2010 Phys. Rev. Lett. 105 136805 Google Scholar
[3]	Li L K, Yu Y J, Ye G J, Ge Q Q, Ou X D, Wu H, Feng D L, Chen X H, Zhang Y B 2014 Nat. Nanotechnol. 9 372 Google Scholar
[4]	Zhao H Q, Mao Y L, Mao X, Shi X, Xu C S, Wang C X, Zhang S M, Zhou D H 2018 Adv. Funct. Mater. 28 1704855 Google Scholar
[5]	Zhou X, Hu X Z, Jin B, Yu J, Liu K L, Li H Q, Zhai T Y 2018 Adv. Sci. 5 1800478 Google Scholar
[6]	Hu Y H, Zhang S L, Sun S F, Xie M Q, Cai B, Zeng H B 2015 Appl. Phys. Lett. 107 122107 Google Scholar
[7]	Xia C X, Du J, Huang X W, Xiao W B, Xiong W Q, Wang T X, Wei Z M, Jia Y, Shi J J, Li J B 2018 Phys. Rev. B 97 115416 Google Scholar
[8]	Xu Y F, Zhang H, Shao H Z, Ni G, Li J, Lu H L, Zhang R J, Peng Bo, Zhu Y Y, Zhu H Y, Soukoulis C M 2017 Phys. Rev. B 96 245421 Google Scholar
[9]	Kong X, Deng J K, Li L, Liu Y L, Ding X D, Sun J, Liu J Z 2018 Phys. Rev. B 98 184104 Google Scholar
[10]	Mao Y L, Xu C S, Yuan J M, Zhao H Q 2019 J. Mater. Chem. A 7 11265 Google Scholar
[11]	Lu Q L, Yang W H, Xiong F B, Lin H F, Zhuang Q Q 2020 Acta Phys. Sin. 69 196801 [卢群林, 杨伟煌, 熊飞兵, 林海峰, 庄芹芹 2020 物理学报 69 196801]Google Scholar Lu Q L, Yang W H, Xiong F B, Lin H F, Zhuang Q Q 2020 Acta Phys. Sin. 69 196801 Google Scholar
[12]	Muhammad Z, Li Y L, Abbas G, Usman M, Sun Z, Zhang Y, Lv Z Y, Wang Y, Zhao W S 2022 Adv. Electron. Mater. 8 2101112 Google Scholar
[13]	Huang L, Wu F G, Li J B 2016 J. Chem. Phys. 144 114708 Google Scholar
[14]	Li Z B, Liu X S, Wang X, Yang Y, Liu S C, Shi W, Li Y, Xing X B, Xue D J, Hu J S 2020 Phys. Chem. Chem. Phys. 22 914 Google Scholar
[15]	Zuo B Min, Yuan J M, Feng Z, Mao Y L 2019 Acta Phys. Sin. 68 113103 [左博敏, 袁健美, 冯志, 毛宇亮 2019 物理学报 68 113103]Google Scholar Zuo B Min, Yuan J M, Feng Z, Mao Y L 2019 Acta Phys. Sin. 68 113103 Google Scholar
[16]	Guo G X, Bi G 2018 Micro Nano Lett. 13 600 Google Scholar
[17]	Wang J J, Zhao Y F, Zheng J D, Wang X T, Deng X, Guan Z, Ma R R Zhong Ni, Yue F Y, Wei Z M, Xiang P H, Duan C G 2021 Phys. Chem. Chem. Phys. 23 26997 Google Scholar
[18]	Li Y, Ma K, Fan X, Liu F S, Li J Q, Xie H P 2020 Appl. Sur. Sci. 521 146256 Google Scholar
[19]	Feng J, Qian X F, Huang C W, Li J 2012 Nat. Photonics 6 866 Google Scholar
[20]	Li H, Contryman A W, Qian X F, Ardakani S Mo, Gong Y J, Wang X L, Weisse J M, Lee C H, Zhao J H, Ajayan P M, Li Ju, Manoharan H C, Zheng X L 2015 Nat. Commun. 6 7381 Google Scholar
[21]	San-Jose P, Parente V, Guinea F, Roldán R, Prada E 2016 Phys. Rev. X 6 031046
[22]	Lam N H, Nguyen P, Cho S, Kim J 2023 Surf. Sci. 730 122251 Google Scholar
[23]	Zheng J D, Zhao Y F, Bao Z Q, Shen Y H, Guan Z, Zhong N, Yue F Yu, Xiang P H, Duan C G 2022 2D Mater. 9 035005 Google Scholar
[24]	Harats M G, Kirchhof J N, Qiao M X, Greben K, Bolotin K I 2020 Nat. Photonics 14 324 Google Scholar
[25]	Lee J, Yun S J, Seo C, Cho K, Kim T S, An G H, Kang K, Lee H S, Kim J Y 2021 Nano Lett. 21 43 Google Scholar
[26]	Wang J W, Han M J, Wang Q, Ji Y Q, Zhang X, Shi R, Wu Z F, Zhang L, Amini A, Guo L, Wang N, Lin J H, Cheng C 2021 ACS Nano 15 6633 Google Scholar
[27]	Hao S J, Hao Y L, Li J, Wang K Y, Fan C, Zhang S W, Wei Y H, Hao G L 2024 Appl. Phys. Lett. 125 072102 Google Scholar
[28]	Dastgeer G, Afzal A M, Nazir G, Sarwar N 2021 Adv. Mater. Interfaces 8 2100705 Google Scholar
[29]	Song Q C, An M, Chen X D, Peng Z, Zang J F, Yang N 2016 Nanoscale 8 14943 Google Scholar
[30]	Ouyang G, Wang C X, Yang G W 2009 Chem. Rev. 109 4221 Google Scholar
[31]	Zhu Z M, Zhang A, Ouyang G, Yang G W 2011 Appl. Phys. Lett. 98 263112 Google Scholar
[32]	Dong J S, Zhao Y P, Ouyang G, Yang G W 2022 Appl. Phys. Lett. 120 080501 Google Scholar
[33]	Huang R 2005 J. Mech. Phys. Solids 53 63 Google Scholar
[34]	Jiang H Q, Khang D Y, Song J Z, Sun Y G, Huang Y G, Rogers J A 2007 Proc. Natl. Acad. Sci. 104 15607 Google Scholar
[35]	Khang D Y, Rogers J A, Lee H H 2009 Adv. Funct. Mater. 19 1526
[36]	Iguiñiz N, Frisenda R, Bratschitsch R, Gomez A C 2019 Adv. Mater. 31 1807150 Google Scholar
[37]	Guo Q L, Zhang M, Xue Z Y, Ye L, Wang G, Huang G S, Mei Y F, Wang X, Di Z F 2013 Appl. Phys. Lett. 103 264102 Google Scholar
[38]	Vellaa D, Bicoa J, Boudaoudb A, Romana B, Reis P M 2009 Proc. Natl. Acad. Sci. 106 10901 Google Scholar
[39]	Gomez A C, Roldan R, Cappelluti E, Buscema M, Guinea F, Zant H S J, Steele G A 2013 Nano Lett. 13 5361 Google Scholar
[40]	Jiang J W, Zhou Y P 2017 Parameterization of Stillinger-Weber Potential for Two-Dimensional Atomic Crystals DOI: 10.5772/intechopen.71929
[41]	Sun C Q 2007 Prog. Solid State Chem. 35 1 Google Scholar
[42]	Zhu Y F, Jiang Q 2016 Coordin. Chem. Rev. 326 1 Google Scholar
[43]	Marcus R A 1956 J. Chem. Phys. 24 966 Google Scholar
[44]	Wang J H, Ding T, Gao K M, Wang L F, Zhou P W, Wu K F 2021 Nat. Commun. 12 6333 Google Scholar
[45]	Ghosh R, Papnai B, Chen Y S, Yadav K, Sankar R, Hsieh Y P, Hofmann M, Chen Y F 2023 Adv. Mater. 35 2210746 Google Scholar
[46]	Garzona L V, Frisenda R, Gomez A C 2019 Nanoscale 11 12080 Google Scholar
[47]	Shang H X, Liang X, Deng F, Hu S L, Shen S P 2022 Int. J. Mech. Sci. 234 107685 Google Scholar
[48]	Shang H X, Dong H T, Wu Y H, Deng F, Liang X, Hu S L, Shen S P 2024 Phys. Rev. Lett. 132 116201 Google Scholar
[49]	Zhang Z, Zhao Y P, Ouyang G 2017 J. Phys. Chem. C 121 19296 Google Scholar
[50]	Furchi M M, Pospischil A, Libisch F, Burgdörfer J, Mueller T 2014 Nano Lett. 14 4785 Google Scholar
[51]	Lee C H, Lee G H, Zande A M, Chen W C, Li Y L, Han M Y, Cui X, Arefe G, Nuckolls C, Heinz T F, Guo J, Hone J, Kim P 2014 Nat. Nanotechnol. 9 676 Google Scholar
[52]	Cao G Y, Shang A X, Zhang C, Gong Y P, Li S J, Bao Q L, Li X F 2016 Nano Energy 30 260 Google Scholar

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褶皱状单层GeSe各向异性的能带漏斗效应