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Traditionally, electrical noise is considered as an interference source for low level measurements. Shot noise is the current fluctuation caused by the discreteness of electrons. In a mesoscopic system, shot noise is sensitive to the interaction of charge carriers. Since the 20th century, it has been found that the shot noise measurement can provide the information about quantum fluctuations, which cannot be measured with traditional transport measurement method. It is usually difficult to measure weak noise signal at ultra- low temperature due to technical difficulties. It is necessary to mount a cryogenic preamplifier close to the sample to improve signal-to-noise ratio and to increase the bandwidth. Therefore, the ultra-low background noise and the power consumption of the amplifier should be used. In this report we present a shot noise measurement system at dilution refrigerator temperatures. We also introduce and analyze the noise model of our shot noise measurement system. With customized high electron mobility transistors, we make a series of ultra-low noise cryogenic preamplifiers. All the electronic components of the amplifier are packed into a shielding box, which makes the installation of the cryogenic amplifier more convenient. The amplifier is mounted on the 4 K stage of a dry dilution refrigerator and the total power consumption is less than 0.754 mW. The gains and the background noises of the amplifiers are calibrated with the Johnson-Nyquist noise of the combination of a superconducting resistor and a normal resistor at various temperatures. The measured input referred noise voltage can be as low as 0.25 nV/√Hz. In this report, the performance of the system is demonstrated by the shot noise measurement of an Al/AlOx/Al tunnel junction at various temperatures. Above the superconducting transition temperature of aluminum, the measured Fano factor of the system is very close to 1, which is in a good agreement with the theory prediction.
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Keywords:
- dilution refrigerator /
- low noise amplifier /
- shot noise /
- tunneling junction
[1] Landauer R 1998 Nature 392 658Google Scholar
[2] Schottky W 1918 Ann. Phys. 57 541
[3] Beenakker C, Schönenberger C 2003 Phys. Today 56 37
[4] Blanter Y M, Büttiker M 2000 Phys. Rep. 336 1Google Scholar
[5] Lesovik G B 1989 JETP Lett. 49 513
[6] Buttiker M 1990 Phys. Rev. Lett. 65 2901Google Scholar
[7] Beenakker C W J, Büttiker M 1992 Phys. Rev. B 46 1889Google Scholar
[8] Reznikov M, Heiblum M, Shtrikman H, Mahalu D 1995 Phys. Rev. Lett. 75 3340Google Scholar
[9] Kumar A, Saminadayar L, Glattli D C 1996 Phys. Rev. Lett. 76 2778Google Scholar
[10] Picciotto R D, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D 1997 Nature 389 162Google Scholar
[11] Saminadayar L, Glattli D C, Jin Y, Etienne B 1997 Phys. Rev. Lett. 79 2526Google Scholar
[12] Reznikov M, de Picciotto R, Griffiths T G, Heiblum M, Umansky V 1999 Nature 399 238Google Scholar
[13] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045Google Scholar
[14] Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083Google Scholar
[15] Zhang H, Liu C X, Gazibegovic S, Xu D, Logan J A, Wang G, van Loo N, Bommer J D S, de Moor M W A, Car D, Op Het Veld R L M, van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrom C J, Bakkers E, Sarma S D, Kouwenhoven L P 2018 Nature 556 74Google Scholar
[16] Armitage N P, Mele E J, Vishwanath A 2018 Rev. Mod. Phys. 90 015001Google Scholar
[17] Sbierski B, Pohl G, Bergholtz E J, Brouwer P W 2014 Phys. Rev. Lett. 113 026602Google Scholar
[18] Trescher M, Sbierski B, Brouwer P W, Bergholtz E J 2015 Phys. Rev. B 91 115135Google Scholar
[19] Matveeva P G, Aristov D N, Meidan D, Gutman D B 2017 Phys. Rev. B 96 165406Google Scholar
[20] Yang Y L, Bai C X, Xu X G, Jiang Y 2018 Nanotechnology 29 074002Google Scholar
[21] Golub A, Horovitz B 2011 Phys. Rev. B 83 153415Google Scholar
[22] Bolech C J, Demler E 2007 Phys. Rev. Lett. 98 237002Google Scholar
[23] Soller H, Komnik A 2014 Physica E 63 99Google Scholar
[24] Bolech C J, Demler E 2008 Physica B 403 994Google Scholar
[25] Akhmerov A R, Dahlhaus J P, Hassler F, Wimmer M, Beenakker C W 2011 Phys. Rev. Lett. 106 057001Google Scholar
[26] Lü H F, Guo Z, Ke S S, Guo Y, Zhang H W 2015 J. Appl. Phys. 117 164312Google Scholar
[27] DiCarlo L, Zhang Y, McClure D T, Marcus C M, Pfeiffer L N, West K W 2006 Rev. Sci. Instrum. 77 073906Google Scholar
[28] Hashisaka M, Nakamura S, Yamauchi Y, Kasai S, Kobayashi K, Ono T 2008 Phys. Status Solidi C 5 182Google Scholar
[29] Arakawa T, Nishihara Y, Maeda M, Norimoto S, Kobayashi K 2013 Appl. Phys. Lett. 103 172104Google Scholar
[30] Robinson A M, Talyanskii V I 2004 Rev. Sci. Instrum. 75 3169Google Scholar
[31] Ronen Y, Cohen Y, Kang J H, Haim A, Rieder M T, Heiblum M, Mahalu D, Shtrikman H 2016 Proc. Natl Acad. Sci. USA 113 1743Google Scholar
[32] 陈文豪, 杜磊, 庄奕琪, 包军林, 何亮, 陈华, 孙鹏, 王婷岚 2011 60 050704Google Scholar
Chen W H, Du L, Zhuang Y Q, Bao J L, He L, Chen H, Sun P, Wang T L 2011 Acta Phys. Sin. 60 050704Google Scholar
[33] Yang W H, Wei J 2018 Chin. Phys. B 27 060702Google Scholar
[34] Dong Q, Liang Y X, Ferry D, Cavanna A, Gennser U, Couraud L, Jin Y 2014 Appl. Phys. Lett. 105 013504Google Scholar
[35] Hashisaka M, Yamauchi Y, Nakamura S, Kasai S, Kobayashi K, Ono T 2008 J. Phys.: Conf. Ser. 109 012013Google Scholar
[36] Dicarlo L, Williams J R, Zhang Y, McClure D T, Marcus C M 2008 Phys. Rev. Lett. 100 156801Google Scholar
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表 1 不同课题组及公司的低温放大器功耗和本底电压噪声对比
Table 1. Comparison of power consumption and background noises of different cryogenic amplifiers made by different groups and companies.
表 2 不同架构的低温放大器参数对比
Table 2. Comparison of our home-made cryogenic amplifiers.
放大器架构 HEMT类型 增益/倍 功耗/mW 带宽 1/f噪声的拐角 等效输入电压噪声/nV·Hz–1/2 共源极 + 源极跟随 ATF33143 15.8 3.568 10 Hz—20 MHz 300 kHz 0.45 共源极 定制* 10 0.754 10 Hz—1 MHz 3 kHz 0.25 共源共栅 + 源极跟随 定制* 25 3 500 Hz—20 MHz 30 kHz 0.17 注: *表示由法国国家科学院纳米科学与技术中心金勇课题组提供的HEMT 表 3 不同温度下, 拟合得到的Fano因子
Table 3. Fano factors are obtained by fitting the test data at different temperature.
T/K 4 6 8 10 12 14 16 F 0.94827 0.95085 0.95115 0.98194 0.97113 0.99088 0.96408 -
[1] Landauer R 1998 Nature 392 658Google Scholar
[2] Schottky W 1918 Ann. Phys. 57 541
[3] Beenakker C, Schönenberger C 2003 Phys. Today 56 37
[4] Blanter Y M, Büttiker M 2000 Phys. Rep. 336 1Google Scholar
[5] Lesovik G B 1989 JETP Lett. 49 513
[6] Buttiker M 1990 Phys. Rev. Lett. 65 2901Google Scholar
[7] Beenakker C W J, Büttiker M 1992 Phys. Rev. B 46 1889Google Scholar
[8] Reznikov M, Heiblum M, Shtrikman H, Mahalu D 1995 Phys. Rev. Lett. 75 3340Google Scholar
[9] Kumar A, Saminadayar L, Glattli D C 1996 Phys. Rev. Lett. 76 2778Google Scholar
[10] Picciotto R D, Reznikov M, Heiblum M, Umansky V, Bunin G, Mahalu D 1997 Nature 389 162Google Scholar
[11] Saminadayar L, Glattli D C, Jin Y, Etienne B 1997 Phys. Rev. Lett. 79 2526Google Scholar
[12] Reznikov M, de Picciotto R, Griffiths T G, Heiblum M, Umansky V 1999 Nature 399 238Google Scholar
[13] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045Google Scholar
[14] Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083Google Scholar
[15] Zhang H, Liu C X, Gazibegovic S, Xu D, Logan J A, Wang G, van Loo N, Bommer J D S, de Moor M W A, Car D, Op Het Veld R L M, van Veldhoven P J, Koelling S, Verheijen M A, Pendharkar M, Pennachio D J, Shojaei B, Lee J S, Palmstrom C J, Bakkers E, Sarma S D, Kouwenhoven L P 2018 Nature 556 74Google Scholar
[16] Armitage N P, Mele E J, Vishwanath A 2018 Rev. Mod. Phys. 90 015001Google Scholar
[17] Sbierski B, Pohl G, Bergholtz E J, Brouwer P W 2014 Phys. Rev. Lett. 113 026602Google Scholar
[18] Trescher M, Sbierski B, Brouwer P W, Bergholtz E J 2015 Phys. Rev. B 91 115135Google Scholar
[19] Matveeva P G, Aristov D N, Meidan D, Gutman D B 2017 Phys. Rev. B 96 165406Google Scholar
[20] Yang Y L, Bai C X, Xu X G, Jiang Y 2018 Nanotechnology 29 074002Google Scholar
[21] Golub A, Horovitz B 2011 Phys. Rev. B 83 153415Google Scholar
[22] Bolech C J, Demler E 2007 Phys. Rev. Lett. 98 237002Google Scholar
[23] Soller H, Komnik A 2014 Physica E 63 99Google Scholar
[24] Bolech C J, Demler E 2008 Physica B 403 994Google Scholar
[25] Akhmerov A R, Dahlhaus J P, Hassler F, Wimmer M, Beenakker C W 2011 Phys. Rev. Lett. 106 057001Google Scholar
[26] Lü H F, Guo Z, Ke S S, Guo Y, Zhang H W 2015 J. Appl. Phys. 117 164312Google Scholar
[27] DiCarlo L, Zhang Y, McClure D T, Marcus C M, Pfeiffer L N, West K W 2006 Rev. Sci. Instrum. 77 073906Google Scholar
[28] Hashisaka M, Nakamura S, Yamauchi Y, Kasai S, Kobayashi K, Ono T 2008 Phys. Status Solidi C 5 182Google Scholar
[29] Arakawa T, Nishihara Y, Maeda M, Norimoto S, Kobayashi K 2013 Appl. Phys. Lett. 103 172104Google Scholar
[30] Robinson A M, Talyanskii V I 2004 Rev. Sci. Instrum. 75 3169Google Scholar
[31] Ronen Y, Cohen Y, Kang J H, Haim A, Rieder M T, Heiblum M, Mahalu D, Shtrikman H 2016 Proc. Natl Acad. Sci. USA 113 1743Google Scholar
[32] 陈文豪, 杜磊, 庄奕琪, 包军林, 何亮, 陈华, 孙鹏, 王婷岚 2011 60 050704Google Scholar
Chen W H, Du L, Zhuang Y Q, Bao J L, He L, Chen H, Sun P, Wang T L 2011 Acta Phys. Sin. 60 050704Google Scholar
[33] Yang W H, Wei J 2018 Chin. Phys. B 27 060702Google Scholar
[34] Dong Q, Liang Y X, Ferry D, Cavanna A, Gennser U, Couraud L, Jin Y 2014 Appl. Phys. Lett. 105 013504Google Scholar
[35] Hashisaka M, Yamauchi Y, Nakamura S, Kasai S, Kobayashi K, Ono T 2008 J. Phys.: Conf. Ser. 109 012013Google Scholar
[36] Dicarlo L, Williams J R, Zhang Y, McClure D T, Marcus C M 2008 Phys. Rev. Lett. 100 156801Google Scholar
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