Low-temperature electrical transport properties of La doped BaSnO<sub>3</sub> films

Yang Jian; Gao Kuang-Hong; Li Zhi-Qing

doi:10.7498/aps.72.20231082

Abstract

A series of Ba_0.94La_0.06SnO₃ 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 Ba_0.94La_0.06SnO₃ 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:

Authors and contacts

Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, School of Science, Tianjin University, Tianjin 300350, China

Corresponding author: Li Zhi-Qing, zhiqingli@tju.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12174282).

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References

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[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
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[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
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[54]	Sun Y C, Yeh S S, Lin J J 2010 Phys. Rev. B 82 054203 Google Scholar
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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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 $T = 2{\text{ K}}$.

DownLoad: Full-Size Img PowerPoint

图 3 退火0, 1和2 h (插图) 的BLSO 薄膜在零磁场下的$ \Delta \sigma $与T (对数刻度)的关系, 实线是(3) 式拟合的结果

Figure 3. At zero magnetic field, $ \Delta \sigma $ vs. T (logarithmic scale) for BLSO films annealed for 0, 1 and 2 h (inset), the solid lines are the fitting results using Eq. (3).

DownLoad: Full-Size Img PowerPoint

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 h

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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).

DownLoad: Full-Size Img PowerPoint

表 1 BLSO薄膜的相关参数, 其中t_A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 t_A 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	t_A/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

DownLoad: CSV

[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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Low-temperature electrical transport properties of La doped BaSnO₃ films

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Low-temperature electrical transport properties of La doped BaSnO3 films

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Low-temperature electrical transport properties of La doped BaSnO₃ films