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有机半导体中极化子运动的同位素效应

刘璇 高腾 解士杰

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有机半导体中极化子运动的同位素效应

刘璇, 高腾, 解士杰

Isotope effect of carrier transport in organic semiconductors

Liu Xuan, Gao Teng, Xie Shi-Jie
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  • 针对近年来实验发现的有机半导体电磁光现象中的同位素效应, 基于强电声耦合的紧束缚模型, 利用非绝热近似分别研究了小分子晶体和聚合物链内的极化子的运动, 并通过引入有效质量, 解释了同种材料中迁移率与基团质量的关系. 结果表明氢元素的氘化或碳13元素的存在都会降低有机材料迁移率, 且同位素效应的大小与电声耦合的大小有关. 在同位素取代浓度不变时, 同位素的分布不影响整个器件的迁移率. 本文讨论了各种可能的同位素效应并对其物理机理进行了分析, 为利用同位素效应调控有机器件性能提供理论支持.
    Isotopic substitution can effectively tune the device performances of organic semiconductors. According to the experimental results of isotope effects in electric, light and magnetic process in organic semiconductors, we adopt the tight-binding model with strong electron-phonon coupling to study the isotope effects on carrier transport. We try to give a quantificational explanation and show the physical origin of isotope effects on mobility in organic semiconductors in this work. Using polaron transport dynamics with diabatic approach, we simulate the carrier transport in an array of small molecule crystals under weak bias. Because of strong electron-phonon coupling in organic materials, an injected electron will induce lattice distortion, and the carriers are no longer free electrons or holes, but elementary excitations such as solitons, polarons or bipolarons. Our simulation results indicate that the existence of deuterium and 13C element will reduce the mobility of organic material, which means that the isotopic substitution can be utilized to manifest organic device performance. Besides, we also find that the isotope effect on mobility will increase with electron-phonon coupling increasing. This suggests that both the mass of lattice groups and electron-phonon coupling should be taken into account to understand the isotope effects in organic semiconductors. With the consideration of that, we derive the effective mass of polaron based on the continuum model, and verify that effective mass can successfully describe the isotope effect on mobility. The effective mass of carrier can be measured to represent the property of a material, which can tell us whether we need the isotopic substitution in organic layer to improve the device performance. Then we present the microcosmic movement of a polaron at the moment when it encounters isotopic substituted molecules. We come to the conclusion that the isotopic distribution will affect the instantaneous speed of the carrier, but has little effect on the mobility of the whole device when the substituted concentration remains constant. In conclusion, after simulating various possible isotope effects in materials, analyzing its physical mechanism and comparing calculation results in experiment, we provide a theoretical foundation for describing the isotope effects on mobility, which can be a basis of improving the performances of organic semiconductor devices.
      通信作者: 解士杰, xsj@sdu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11974212)和山东省自然科学基金重大基础研究项目(批准号: ZR2019ZD43)资助的课题
      Corresponding author: Xie Shi-Jie, xsj@sdu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11974212) and the Key Basic Research Program of the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019ZD43)
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    Nguyen T D, Hukic-Markosian G, Wang F, Wojcik L, Li X G, Ehrenfreund E, Vardeny Z V 2010 Nat. Mater. 9 345Google Scholar

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    Li L W, Li T Y, Arras M M L, Bonnesen P V, Peng X F, Li W, Hong K L 2020 Polymer 193 122375Google Scholar

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    White R P, Lipson J E G, Higgins J S 2010 Macromolecules 43 4287Google Scholar

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    Jiang J W, Lan J, Wang J S, Li B W 2010 J. Appl. Phys. 107 054314Google Scholar

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    Chang D, Li T, Li L, Jakowski J, Huang J, Keum J K, Lee B, Bonnesen P V, Zhou M, Garashchuk S, Sumpter B G, Hong K 2018 Macromolecules 51 9393Google Scholar

    [14]

    Shi C, Zhang X, Yu C H, Yao Y F, Zhang W 2018 Nat. Commun. 9 481Google Scholar

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    Jakowski J, Huang J, Garashchuk S, Luo Y, Hong K, Keum J, Sumpter B G 2017 J. Phys. Chem. Lett. 8 4333Google Scholar

    [16]

    Jiang Y, Peng Q, Geng H, Ma H, Shuai Z 2015 Phys. Chem. Chem. Phys. 17 3273Google Scholar

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    Tong C C, Hwang K C 2007 J. Phys. Chem. C 111 3490Google Scholar

    [18]

    Shao M, Keum J, Chen J, He Y, Chen W, Browning J F, Jakowski J, Sumpter B G, Ivanov I N, Ma Y Z, Rouleau C M, Smith S C, Geohegan D B, Hong K, Xiao K 2014 Nat. Commun. 5 3180Google Scholar

    [19]

    Fratini S, Nikolka M, Salleo A, Schweicher G, Sirringhaus H 2020 Nat. Mater. 19 491Google Scholar

    [20]

    Ren X, Bruzek M J, Hanifi D A, Schulzetenberg A, Wu Y, Kim C H, Zhang Z, Johns J E, Salleo A, Fratini S, Troisi A, Douglas C J, Frisbie C D 2017 Adv. Electron. Mater. 3 1700018Google Scholar

    [21]

    Jiang Y, Geng H, Shi W, Peng Q, Zheng X, Shuai Z 2014 J. Phys. Chem. Lett. 5 2267Google Scholar

    [22]

    Jiang Y, Geng H, Li W, Shuai Z 2019 J. Chem. Theory Comput. 15 1477Google Scholar

    [23]

    Low F E, Pines D 1953 Phys. Rev. 91 193Google Scholar

    [24]

    Li W, Ren J, Shuai Z 2020 J. Phys. Chem. Lett. 11 4930Google Scholar

    [25]

    Liu X, Gao K, Fu J, Li Y, Wei J, Xie S 2006 Phys. Rev. B 74 172301Google Scholar

    [26]

    Troisi A, Orlandi G 2006 Phys. Rev. Lett. 96 086601Google Scholar

    [27]

    Johansson A A, Stafström S 2004 Phys. Rev. B 69 235205Google Scholar

    [28]

    Brankin R W, Gladwell I, Shampine L F http://www.netlib.org [2019-11-3]

    [29]

    Köhler A, Bässler H 2015 Electronic Processes in Organic Semiconductors: An Introduction (Weinheim: Wiley-VCH) pp193–292

    [30]

    Takayama H, Linliu Y R, Maki K 1980 Phys. Rev. B 21 2388Google Scholar

    [31]

    Miyata A, Mitioglu A, Plochocka P, Portugall O, Wang J T W, Stranks S D, Snaith H J, Nicholas R J 2015 Nat. Phys. 11 582Google Scholar

    [32]

    Zhong M, Zeng W, Tang H, Wang L X, Liu F S, Tang B, Liu Q J 2019 Sol. Energy 190 617Google Scholar

  • 图 1  无机材料(inorganic materials, IM)与有机材料(organic materials, OM)中的同位素对迁移率影响示意图

    Fig. 1.  Schematic diagram of isotope effects on mobility in inorganic materials (IM) and organic materials (OM).

    图 2  红荧烯与聚乙炔材料极化子迁移率随分子质量的变化(内插图为Ren等[20]对红荧烯材料计算结果)

    Fig. 2.  Mobility changes with molecular mass for rubrene and polyacetylene. Inset: results of calculation for rubrene from Ren et al. [20].

    图 3  同位素效应随电声耦合的变化

    Fig. 3.  Variation of isotope effect (IE) with electron-phonon coupling.

    图 4  瞬时迁移率的同位素效应 (a) 单分子同位素取代; (b) 多分子同位素连续取代, 取代起始位置均为第125格点; (c)多分子同位素不连续取代. 图(a)和图(c)中圆点表示同位素取代分子所在位置, 取代分子中H与C元素均被取代

    Fig. 4.  Isotope effects on instantaneous mobility: (a) Isotopic substitution of one molecule; (b) isotopic substitution of continuous molecules, the initial position of all the substitution is on the 125th site; (c) isotopic substitution of discontinuous molecules. The dots in panels (a) and (c) indicate the locations of molecules in which both hydrogen and carbon are substituted.

    图 5  极化子平均迁移率及同位素效应与同位素浓度的关系

    Fig. 5.  Avergae mobility and isotope effects depend on substituted concentration.

  • [1]

    Root S E, Savagatrup S, Printz A D, Rodriquez D, Lipomi D J 2017 Chem. Rev. 117 6467Google Scholar

    [2]

    Taniguchi T, Fukui K, Asahi R, Urabe Y, Ikemoto A, Nakamoto J, Inada Y, Yamao T, Hotta S 2017 Synth. Met. 227 162Google Scholar

    [3]

    de Jong M P 2016 Open Physics 14 337Google Scholar

    [4]

    Groves C 2017 Rep. Prog. Phys. 80 37Google Scholar

    [5]

    Danos A, MacQueen R W, Cheng Y Y, Dvorak M, Darwish T A, McCamey D R, Schmidt T W 2015 J. Phys. Chem. Lett. 6 3061Google Scholar

    [6]

    Stoltzfus D M, Joshi G, Popli H, Jamali S, Kavand M, Milster S, Grunbaum T, Bange S, Nahlawi A, Teferi M Y, Atwood SI, Leung A E, Darwish T A, Malissa H, Burn P L, Lupton J M, Boehme C 2020 J. Mater. Chem. C 8 2764Google Scholar

    [7]

    Wang P, Wang F F, Chen Y, Niu Q, Lu L, Wang H M, Gao X C, Wei B, Wu H W, Caic X, Zou D C 2013 J. Mater. Chem. C 1 4821Google Scholar

    [8]

    Nguyen T D, Hukic-Markosian G, Wang F, Wojcik L, Li X G, Ehrenfreund E, Vardeny Z V 2010 Nat. Mater. 9 345Google Scholar

    [9]

    Li L W, Li T Y, Arras M M L, Bonnesen P V, Peng X F, Li W, Hong K L 2020 Polymer 193 122375Google Scholar

    [10]

    Bartell L S, Roskos R R 1966 J. Chem. Phys. 44 457Google Scholar

    [11]

    White R P, Lipson J E G, Higgins J S 2010 Macromolecules 43 4287Google Scholar

    [12]

    Jiang J W, Lan J, Wang J S, Li B W 2010 J. Appl. Phys. 107 054314Google Scholar

    [13]

    Chang D, Li T, Li L, Jakowski J, Huang J, Keum J K, Lee B, Bonnesen P V, Zhou M, Garashchuk S, Sumpter B G, Hong K 2018 Macromolecules 51 9393Google Scholar

    [14]

    Shi C, Zhang X, Yu C H, Yao Y F, Zhang W 2018 Nat. Commun. 9 481Google Scholar

    [15]

    Jakowski J, Huang J, Garashchuk S, Luo Y, Hong K, Keum J, Sumpter B G 2017 J. Phys. Chem. Lett. 8 4333Google Scholar

    [16]

    Jiang Y, Peng Q, Geng H, Ma H, Shuai Z 2015 Phys. Chem. Chem. Phys. 17 3273Google Scholar

    [17]

    Tong C C, Hwang K C 2007 J. Phys. Chem. C 111 3490Google Scholar

    [18]

    Shao M, Keum J, Chen J, He Y, Chen W, Browning J F, Jakowski J, Sumpter B G, Ivanov I N, Ma Y Z, Rouleau C M, Smith S C, Geohegan D B, Hong K, Xiao K 2014 Nat. Commun. 5 3180Google Scholar

    [19]

    Fratini S, Nikolka M, Salleo A, Schweicher G, Sirringhaus H 2020 Nat. Mater. 19 491Google Scholar

    [20]

    Ren X, Bruzek M J, Hanifi D A, Schulzetenberg A, Wu Y, Kim C H, Zhang Z, Johns J E, Salleo A, Fratini S, Troisi A, Douglas C J, Frisbie C D 2017 Adv. Electron. Mater. 3 1700018Google Scholar

    [21]

    Jiang Y, Geng H, Shi W, Peng Q, Zheng X, Shuai Z 2014 J. Phys. Chem. Lett. 5 2267Google Scholar

    [22]

    Jiang Y, Geng H, Li W, Shuai Z 2019 J. Chem. Theory Comput. 15 1477Google Scholar

    [23]

    Low F E, Pines D 1953 Phys. Rev. 91 193Google Scholar

    [24]

    Li W, Ren J, Shuai Z 2020 J. Phys. Chem. Lett. 11 4930Google Scholar

    [25]

    Liu X, Gao K, Fu J, Li Y, Wei J, Xie S 2006 Phys. Rev. B 74 172301Google Scholar

    [26]

    Troisi A, Orlandi G 2006 Phys. Rev. Lett. 96 086601Google Scholar

    [27]

    Johansson A A, Stafström S 2004 Phys. Rev. B 69 235205Google Scholar

    [28]

    Brankin R W, Gladwell I, Shampine L F http://www.netlib.org [2019-11-3]

    [29]

    Köhler A, Bässler H 2015 Electronic Processes in Organic Semiconductors: An Introduction (Weinheim: Wiley-VCH) pp193–292

    [30]

    Takayama H, Linliu Y R, Maki K 1980 Phys. Rev. B 21 2388Google Scholar

    [31]

    Miyata A, Mitioglu A, Plochocka P, Portugall O, Wang J T W, Stranks S D, Snaith H J, Nicholas R J 2015 Nat. Phys. 11 582Google Scholar

    [32]

    Zhong M, Zeng W, Tang H, Wang L X, Liu F S, Tang B, Liu Q J 2019 Sol. Energy 190 617Google Scholar

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出版历程
  • 收稿日期:  2020-05-25
  • 修回日期:  2020-08-18
  • 上网日期:  2020-12-03
  • 刊出日期:  2020-12-20

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