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利用射频磁控溅射技术在MgO (001)单晶基片上沉积了一系列Ba0.94La0.06SnO3薄膜, 并对薄膜的结构和电输运性质进行了系统研究. 所有薄膜均表现出简并半导体 (金属) 导电特性: 在
$T > {T_{\min }}$ 的高温区 (${T_{\min }}$ 为电阻最小值对应的温度), 薄膜的电阻率随温度的升高而升高, 并且与温度的平方呈线性关系. 在$T < {T_{\min }}$ 的低温区域, 薄膜的电阻率随温度降低而上升, 并且电阻率随$ \ln T $ 呈线性变化, 均匀无序系统中的电子-电子相互作用、弱局域效应以及Kondo效应均不能解释这种现象. 经过定量分析, 发现电阻率在低温下$ \ln T $ 的依赖关系源于颗粒间电子的库仑相互作用. 同时, 在Ba0.94La0.06SnO3薄膜中也观察到霍尔系数$ {R_{\text{H}}} $ 与$ \ln T $ 呈线性关系, 并且该线性关系也定量的符合金属颗粒体系中库仑相互作用的理论. 薄膜断面高分辨透射电子显微镜结果表明, 虽然薄膜整体呈现外延结构, 但其中存在诸多条状非晶区域, 这使得薄膜整体表现出类似金属颗粒膜的电输运性质. 本文的结果为金属颗粒系统中库仑相互作用对电导率和霍尔系数修正理论的正确性提供了有力的支持.A series of Ba0.94La0.06SnO3 thin films are deposited on MgO(001) single crystal substrates by RF magnetron sputtering method, and their structure and electrical transport properties are systematically investigated. All films reveal degenerate semiconductor (metal) characteristics in electrical transport properties. In the high-temperature region ($T > {T_{\min }}$ , where${T_{\min }}$ is the temperature at which the resistivity reaches a minimum value), the resistivity of each film increases with temperature, and exhibits a linear relationship with the square of the temperature. In the low-temperature region ($T < {T_{\min }}$ ), the resistivity increases with decreasing temperature and varies linearly with$ \ln T $ . This temperature dependent behavior of resistivity cannot be explained by the general electron-electron interaction or weak localization effects in homogeneous disordered conductors and nor by Kondo effect. After quantitative analysis, it is found that the$ \ln T $ behavior of resistivity at low temperatures can be explained by the electron-electron Coulomb interaction effect in the presence of granularity. In addition, it is found that the Hall coefficient$ {R_{\text{H}}} $ also varies linearly with$ \ln T $ for the Ba0.94La0.06SnO3 film, which also quantitatively accords with the theoretical prediction of the electron-electron Coulomb interaction effects in the granular metals. The results of cross-section high-resolution transmission electron microscope indicate that although the films have epitaxial structures as a whole, there are many strip-shaped amorphous regions in films, which makes the films have electrical transport properties similar to those of metal granular films. Our results provide strong support for the validity of the theory concerning the effects of Coulomb interaction on the conductivity and Hall coefficient in granular metals.-
Keywords:
- transparent conductive oxide /
- granular metals /
- electron-electron interaction effect /
- electrical transport properties
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图 1 退火时间为0, 1和2 h的BLSO薄膜的XRD
$\theta-2\theta $ 扫描图谱. 插图为退火2 h的 BLSO薄膜的 (111) 晶面的$ \phi $ 扫描图Fig. 1. XRD
$\theta-2\theta $ scan patters of BLSO films annealed in situ for 0, 1, and 2 h. The inset is the$ \phi $ -scan spectrum of (111) plane for the BLSO film annealed for 2 h.
图 2 (a) 退火时间为0, 1 和2 h 的BLSO薄膜的归一化电阻率
$\rho /\rho (300{\text{ K}})$ 与T (对数刻度) 的关系, 插图为$\rho /\rho (300{\text{ K}})$ 与${T^2}$ 的关系; (b) 归一化电导率$\sigma /\sigma (300{\text{ K}})$ 与${T^{1/2}}$ 的关系, 插图为$T = 2{\text{ K}}$ 时样品的磁电阻Fig. 2. (a) Normalized resistivity
$\rho /\rho (300{\text{ K}})$ varies as a function of T (logarithmic scale) for BLSO films annealed for 0, 1, and 2 h, inset is$\rho /\rho (300{\text{ K}})$ vs.${T^2}$ for the films; (b) normalized conductivity$\sigma /\sigma (300{\text{ K}})$ versus${T^{1/2}}$ , and the inset is the magnetoresistance of the samples at$T = 2{\text{ K}}$ .
图 4 薄膜的
$ {R_{\text{H}}} $ 与$ T $ (对数刻度) 的关系. 实心三角形是实验值, 实线是使用 (4) 式拟合得出的结果 (a) 退火0 h; (b) 退火1 h; (c) 退火2 hFig. 4. Temperature (logarithmic scale) dependence of
$ {R_{\text{H}}} $ for films. The solid triangles are experimental values, and the solid lines are least-squares fits to Eq. (4): (a) Annealed for 0 h; (b) annealed for 1 h; (c) annealed for 2 h.
图 5 (a) 退火1 h和 (b) 退火2 h的 BLSO薄膜的表面SEM图像; (c) 退火2 h薄膜的断面HRTEM形貌图; (d) 图 (c) 中虚线矩形区域的放大图
Fig. 5. SEM images for the surfaces of the BLSO films (a) annealed for 1 h and (b) annealed for 2 h; (c) cross-sectional HRTEM micrograph of the BLSO films annealed for 2 h; (d) the enlarged image of the dashed rectangular area in panel (c).
表 1 BLSO薄膜的相关参数, 其中tA是薄膜原位退火时间, t是薄膜的厚度,
$ {n^*} $ 是有效载流子浓度,$ {g_{\text{T}}} $ 是使用(3)式拟合电导率与温度关系得出的值,$ {c_{\text{d}}} $ 是使用(4)式拟合霍尔系数与温度关系得出的值Table 1. Relevant parameters for BLSO films, where tA is in-situ annealing time. t is the thickness of the films.
$ {n^*} $ is the mean value of carrier concentration,$ {g_{\text{T}}} $ is the value obtained by fitting the conductivity vs. temperature with Eq. (3),$ {c_{\text{d}}} $ is the value obtained by fitting the Hall coefficient vs. temperature with Eq. (4).Sample tA/h t/nm ρ(300 K)/(mΩ·m) ρ(2 K)/(mΩ·m) D/(cm2·s–1) $ {n^*} $/(1020 cm–3) $ {g_{\text{T}}} $ $ {c_{\text{d}}} $ No.1 0 800 0.3 0.33 0.09 1.20 1.53 0.81 No.2 1 800 0.19 0.21 0.142 1.35 1.89 0.31 No.3 2 500 0.084 0.079 0.037 1.44 6.15 0.75 
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[1] Luo X, Oh Y S, Sirenko A, Gao P, Tyson T A, Char K, Cheong S W 2012 Appl. Phys. Lett. 100 172112
Google Scholar
[2] Kim H J, Kim U, Kim T H, Mun H S, Jeon B G, Hong K T, Lee W J, Ju C, Kim K H, Char K 2012 Appl. Phys. Express 5 061102
Google Scholar
[3] Kim H J, Kim U, Kim T H, Kim J, Kim H M, Jeon B G, Lee W J, Mun H S, Hong K T, Yu J, Char K, Kim K H 2012 Phys. Rev. B 86 165205
Google Scholar
[4] Kim K H, Kim J, Kim T H, Lee W J, Jeon B G, Park J Y, Choi W S, Jeong D W, Lee S H, Yu J, Noh T W, Kim H J 2013 Phys. Rev. B 88 125204
Google Scholar
[5] Mizoguchi H, Eng H W, Woodward P M 2004 Inorg. Chem. 43 1667
Google Scholar
[6] Zhang W, Tang J, Ye J 2007 J. Mater. Res. 22 1859
Google Scholar
[7] Lee W J, Kim H J, Kang J, Jang D H, Kim T H, Lee J H, Kim K H 2017 Ann. Rev. Matter. Res. 47 391
Google Scholar
[8] Cui J M, Zhang Y Y, Wang J L, Zhao Z B, Huang H L, Zou W, Yang M M, Peng R R, Yan W S, Huang Q P, Fu Z P, Lu Y L 2019 Phys. Rev. B 100 165312
Google Scholar
[9] Feng Z X, Qin P X, Yang Y L, Yan H, Guo H X, Wang X N, Zhou X R, Han Y Y, Yi J B, Qi D C, Yu X J, Breese M B H, Zhang X, Wu H J, Chen H Y, Xiang H J, Jiang C B, Liu Z Q 2021 Acta Mater. 204 116516
Google Scholar
[10] Eom K, Paik H, Seo J, Campbell N, Tsymbal E Y, Oh S H, Rzchowski M S, Schlom D G, Eom C B 2022 Adv. Sci. 9 2105652
Google Scholar
[11] Lee W J, Kim H J, Sohn E, Kim T H, Park J Y, Park W, Jeong H, Lee T, Kim J H, Choi K Y, Kim K H 2016 Appl. Phys. Lett. 108 82105
Google Scholar
[12] Park C, Kim U, Ju C J, Park J S, Kim Y M, Char K 2014 Appl. Phys. Lett. 105 203503
Google Scholar
[13] Sanchela A V, Wei M, Zensyo H, Feng B, Lee J, Kim G, Jeen H, Ikuhara Y, Ohta H 2018 Appl. Phys. Lett. 112 232102
Google Scholar
[14] Prakash A, Dewey J, Yun H, Jeong J S, Mkhoyan K A, Jalan B 2015 J. Vac. Sci. Technol. A 33 60608
Google Scholar
[15] Lebens-Higgins Z, Scanlon D O, Paik H, Sallis S, Nie Y, Uchida M, Quackenbush N F, Wahila M J, Sterbinsky G E, Arena D A, Woicik J C, Schlom D G, Piper L F J 2016 Phys. Rev. Lett. 116 027602
Google Scholar
[16] Raghavan S, Schumann T, Kim H, Zhang J Y, Cain T A, Stemmer S 2016 APL Mater. 4 016106
Google Scholar
[17] Prakash A, Xu P, Faghaninia A, Shukla S, Ager J W, Lo C S, Jalan B 2017 Nat. Commun. 8 15167
Google Scholar
[18] Prakash A, Xu P, Wu X, Haugstad G, Wang X J, Jalan B 2017 J. Mater. Chem. C 5 5730
Google Scholar
[19] Ganguly K, Prakash A, Jalan B, Leighton C 2017 APL Mater. 5 056102
Google Scholar
[20] Mountstevens E H, Attfield J P, Redfern S A T 2003 J. Phys. Condensed Matter 15 8315
Google Scholar
[21] Shannon R D 1976 Acta Cryst. A 32 751
Google Scholar
[22] Liu Q Z, Liu J J, Li B, Li H, Zhu G P, Dai K, Liu Z L, Zhang P, Dai J M 2012 Appl. Phys. Lett. 101 241901
Google Scholar
[23] Hadjarab B, Bouguelia A, Trari M 2007 J. Phys. D Appl. Phys. 40 5833
Google Scholar
[24] Hadjarab B, Bouguelia A, Benchettara A, Trari M 2008 J. Alloys Compd. 461 360
Google Scholar
[25] Yasukawa M, Kono T, Ueda K, Yanagi H, Hosono H 2010 Mater. Sci. Eng. B 173 29
Google Scholar
[26] Echternach P M, Gershenson M E, Bozler H M 1993 Phys. Rev. B 47 13659
Google Scholar
[27] Yeh S S, Lin J J, Jing X, Zhang D 2005 Phys. Rev. B 72 024204
Google Scholar
[28] II’In K S, Ptitsina N G, Sergeev A V, Gol Tsman G N, Gershenzon E M, Karasik B S, Pechen E V, Krasnosvobodtsev S I 1998 Phys. Rev. B 57 15623
Google Scholar
[29] Gao Z H, Wang Z X, Hou D Y, Liu X D, Li Z Q 2022 J. Appl. Phys. 131 065109
Google Scholar
[30] Altshuler B L, Khmel’Nitzkii D, Larkin A I, Lee P A 1980 Phys. Rev. B 22 5142
Google Scholar
[31] Altshuler B L, Aronov A G, Lee P A 1980 Phys. Rev. Lett. 44 1288
Google Scholar
[32] Abrahams E, Anderson P W, Licciardello D C, Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
Google Scholar
[33] Lee P A, Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287
Google Scholar
[34] Fukuyama H, Hoshino K 1981 J. Phys. Soc. Jpn. 50 2131
Google Scholar
[35] Kawabata A 1980 Solid State Commun. 34 431
Google Scholar
[36] Kawabata A 1980 J. Phys. Soc. Jpn. 49 628
Google Scholar
[37] Wu C Y, Lin J J 1994 Phys. Rev. B 50 385
Google Scholar
[38] Lin J J 2000 Physica B 279 191
Google Scholar
[39] Lin J J, Bird J P 2002 J. Phys. Condensed Matter 14 R501
Google Scholar
[40] Kondo J 1964 Prog. Theor. Phys. 32 37
Google Scholar
[41] Hewson A C 1997 The Kondo Problem to Heavy Fermions (Cambridge: Cambridge University Press) pp38–47
[42] Xue H X, Hong Y P, Li C J, Meng J C, Li Y C, Liu K J, Liu M R, Jiang W M, Zhang Z, He L, Dou R F, Xiong C M, Nie J C 2018 Phys. Rev. B 98 085305
Google Scholar
[43] Das S, Rastogi A, Wu L J, Zheng J C, Hossain Z, Zhu Y M, Budhani R C 2014 Phys. Rev. B. 90 081107
Google Scholar
[44] Lee M, Williams J R, Zhang S P, Frisbie C D, Goldhaber-Gordon D 2011 Phys. Rev. Lett. 107 256601
Google Scholar
[45] Beloborodov I S, Efetov K B, Lopatin A V, Vinokur V M 2003 Phys. Rev. Lett. 91 246801
Google Scholar
[46] Efetov K B, Tschersich A 2003 Phys. Rev. B 67 174205
Google Scholar
[47] Beloborodov I S, Lopatin A V, Vinokur V M, Efetov K B 2007 Rev. Mod. Phys. 79 469
Google Scholar
[48] Kharitonov M Y, Efetov K B 2007 Phys. Rev. Lett. 99 056803
Google Scholar
[49] Kharitonov M Y, Efetov K B 2008 Phys. Rev. B 77 045116
Google Scholar
[50] Zhang Y J, Li Z Q, Lin J J 2011 Phys. Rev. B 84 052202
Google Scholar
[51] Wu Y N, Wei Y F, Li Z Q, Lin J J 2015 Phys. Rev. B 91 104201
Google Scholar
[52] Rotkina L, Oh S, Eckstein J N, Rotkin S V 2005 Phys. Rev. B 72 233407
Google Scholar
[53] Achatz P, Gajewski W, Bustarret E, Marcenat C, Piquerel R, Chapelier C, Dubouchet T, Williams O A, Haenen K, Garrido J A, Stutzmann M 2009 Phys. Rev. B 79 201203
Google Scholar
[54] Sun Y C, Yeh S S, Lin J J 2010 Phys. Rev. B 82 054203
Google Scholar
[55] Sachser R, Porrati F, Schwalb C H, Huth M 2011 Phys. Rev. Lett. 107 206803
Google Scholar
[56] Yang Y, Zhang Y J, Liu X D, Li Z Q 2012 Appl. Phys. Lett. 100 262101
Google Scholar
[57] Zheng B, He Z H, Li Z Q 2019 Phys. Status Solidi Rapid Res. Lett. 13 1900123
Google Scholar
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