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Electron dephasing process is important and interesting in disordered conductors. In general three-dimensional (3D) disordered metals, the electron-electron (e-e) scattering is negligibly weak compared with the electron-phonon (e-ph) scattering. Thus, the theoretical prediction concerning the e-e scattering rate 1/τee as a function of temperature T in 3D disordered conductor has not been fully tested so far, though it was proposed four decades ago. In the frame of free-electron-like model, the e-ph relaxation rate 1/τep is proportional to carrier concentration n, while the small-and large-energy-transfer e-e scattering rate obey the laws 1/τeeS ∝ n-4/3 and 1/τeeL ∝ n-2/3, respectively. In other words, e-e scattering may dominate the dephasing processes in 3D disordered metals with sufficient low carrier concentrations. In the present work, we systematically investigate the electronic transport properties of amorphous indium gallium zinc oxide (a-IGZO) prepared by the radio frequency sputtering method. The carrier concentrations of the highly degenerate IGZO films are all ～ 5×1019 cm-3, which are 3-4 orders of magnitude lower than those of typical metals. Our thick films (～ 800 nm) are 3D systems with respect to weak-localization (WL) effect and e-e scattering. X-ray diffraction patterns of the films indicate that our films are all amorphous. For each film, the resistivity increases with the increase of the temperature in the high temperature region (T ≥ 200 K) and the carrier concentration is almost invariable in the whole measured temperature range. This indicates that the films possess metal-like transport properties. By comparing the low-field magnetoconductivity versus magnetic field data σ (B) with that from the 3D WL theory, we extract the electron dephasing rate 1/τφ at different temperatures in the low temperature region. It is found that 1/τφ varies linearly with T3/2 for each film. The T3/2 behavior of 1/τφ can be quantitatively described by the 3D small-energy-transfer e-e scattering theory. The e-ph scattering rate 1/τep and large-energy-transfer e-e scattering rate 1/τeeL are negligibly weak in this low-carrier-concentration conductor. Thus, we can observe the T3/2 behavior of 1/τφ.
[1] Altshuler B L, Aronov A G, Khmelnitsky D E 1982 J. Phys. C 15 7367
[2] Lee P A, Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287
[3] Lin J J, Bird J P 2002 J. Phys. Condens. Matter 14 R501
[4] Rammer J, Schmid A 1986 Phys. Rev. B 34 1352
[5] Zhong Y L, Lin J J 1998 Phys. Rev. Lett. 80 588
[6] Fukuyama H, Abrahams E 1983 Phys. Rev. B 27 5976
[7] Schmid A 1974 Z. Phys. 271 251
[8] Sergeev A, Mitin V 2000 Phys. Rev. B 61 6041
[9] Lang W J, Li Z Q 2014 Appl. Phys. Lett. 105 042110
[10] Yang Y, Liu X D, Li Z Q 2016 EPL 114 37002
[11] Zhang Y J, Li Z Q, Lin J J 2013 EPL 103 47002
[12] Nomura K, Ohta H, Takagi A, Kamiya T, Hirano M, Hosono H 2004 Nature 432 488
[13] Kamiya T, Nomura K, Hosono H 2010 Sci. Technol. Adv. Mater. 11 044305
[14] Yabuta H, Sano M, Abe K, Aiba T, Den T, Kumomi H, Hosono H 2006 Appl. Phys. Lett. 89 112123
[15] Kamiya T, Nomura K, Hosono H 2009 J. Disp. Technol. 5 273
[16] Makise K, Hidaka K, Ezaki S, Asano T, Shinozaki B, Tomai S, Nakamura H 2014 J. Appl. Phys. 116 153703
[17] Takagi A, Nomura K, Ohta H, Yanagi H, Kamiya T, Hirano M, Hosono H 2005 Thin Solid Films 486 38
[18] Ziman J M 1960 Electron and Phonons (Oxford: Clarendon Press) p364
[19] Lien C C, Wu C Y, Li Z Q, Lin J J 2011 J. Appl. Phys. 110 063706
[20] Kawabata A 1980 J. Phys. Soc. Jpn. 49 628
[21] Kawabata A 1980 Solid State Commun. 34 431
[22] Fukuyama H, Hoshino K 1981 J. Phys. Soc. Jpn. 50 2131
[23] Fehr Y, May T S, Rosenbaum R 1986 Phy. Rev. B 33 6631
[24] Wu C Y, Lin J J 1994 Phys. Rev. B 50 385
[25] Baxter D V, Richter R, Trudeau M L, Cochrane R W, Strom-Olsen J O 1989 J. Phys. Paris 50 1673
[26] Bergmann G 2010 Int. J. Mod. Phys. B 24 2015
[27] Lany S, Zunger A 2007 Phys. Rev. Lett. 98 045501
[28] Zhong Y L, Sergeev A, Chen C D, Lin J J 2010 Phys. Rev. Lett. 104 206803
[29] Yoshikawa T, Yagi T, Oka N, Jia J, Yamashita Y, Hattori K, Shigesato Y 2013 Appl. Phys. Express 6 021101
[30] Nomura K, Kamiya T, Ohta H, Uruga T, Hirano M, Hosono H 2007 Phys. Rev. B 75 035212
[31] Cui B, Zeng L, Keane D, Bedzyk M J, Buchholz D B, Chang R P H, Yu Xinge, Smith J, Marks T J, Xia Y, Facchetti A F, Medvedeva J E, Grayson M 2016 J. Phys. Chem. C 120 7467
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[1] Altshuler B L, Aronov A G, Khmelnitsky D E 1982 J. Phys. C 15 7367
[2] Lee P A, Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287
[3] Lin J J, Bird J P 2002 J. Phys. Condens. Matter 14 R501
[4] Rammer J, Schmid A 1986 Phys. Rev. B 34 1352
[5] Zhong Y L, Lin J J 1998 Phys. Rev. Lett. 80 588
[6] Fukuyama H, Abrahams E 1983 Phys. Rev. B 27 5976
[7] Schmid A 1974 Z. Phys. 271 251
[8] Sergeev A, Mitin V 2000 Phys. Rev. B 61 6041
[9] Lang W J, Li Z Q 2014 Appl. Phys. Lett. 105 042110
[10] Yang Y, Liu X D, Li Z Q 2016 EPL 114 37002
[11] Zhang Y J, Li Z Q, Lin J J 2013 EPL 103 47002
[12] Nomura K, Ohta H, Takagi A, Kamiya T, Hirano M, Hosono H 2004 Nature 432 488
[13] Kamiya T, Nomura K, Hosono H 2010 Sci. Technol. Adv. Mater. 11 044305
[14] Yabuta H, Sano M, Abe K, Aiba T, Den T, Kumomi H, Hosono H 2006 Appl. Phys. Lett. 89 112123
[15] Kamiya T, Nomura K, Hosono H 2009 J. Disp. Technol. 5 273
[16] Makise K, Hidaka K, Ezaki S, Asano T, Shinozaki B, Tomai S, Nakamura H 2014 J. Appl. Phys. 116 153703
[17] Takagi A, Nomura K, Ohta H, Yanagi H, Kamiya T, Hirano M, Hosono H 2005 Thin Solid Films 486 38
[18] Ziman J M 1960 Electron and Phonons (Oxford: Clarendon Press) p364
[19] Lien C C, Wu C Y, Li Z Q, Lin J J 2011 J. Appl. Phys. 110 063706
[20] Kawabata A 1980 J. Phys. Soc. Jpn. 49 628
[21] Kawabata A 1980 Solid State Commun. 34 431
[22] Fukuyama H, Hoshino K 1981 J. Phys. Soc. Jpn. 50 2131
[23] Fehr Y, May T S, Rosenbaum R 1986 Phy. Rev. B 33 6631
[24] Wu C Y, Lin J J 1994 Phys. Rev. B 50 385
[25] Baxter D V, Richter R, Trudeau M L, Cochrane R W, Strom-Olsen J O 1989 J. Phys. Paris 50 1673
[26] Bergmann G 2010 Int. J. Mod. Phys. B 24 2015
[27] Lany S, Zunger A 2007 Phys. Rev. Lett. 98 045501
[28] Zhong Y L, Sergeev A, Chen C D, Lin J J 2010 Phys. Rev. Lett. 104 206803
[29] Yoshikawa T, Yagi T, Oka N, Jia J, Yamashita Y, Hattori K, Shigesato Y 2013 Appl. Phys. Express 6 021101
[30] Nomura K, Kamiya T, Ohta H, Uruga T, Hirano M, Hosono H 2007 Phys. Rev. B 75 035212
[31] Cui B, Zeng L, Keane D, Bedzyk M J, Buchholz D B, Chang R P H, Yu Xinge, Smith J, Marks T J, Xia Y, Facchetti A F, Medvedeva J E, Grayson M 2016 J. Phys. Chem. C 120 7467
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