Abstract
We present a comprehensible introduction to capacitive gate-based sensing, a technique for charge state readout of gate-defined semiconductor quantum dots. The objective of this chapter is to introduce the reader to the fundamental concepts necessary to understand the technique from a theoretical perspective and to be able to apply the method experimentally. We aimed to maintain a pedagogical tone with necessary rigour to keep it accessible and self-contained. We start by introducing the fundamentals of single-electron effects in single and double quantum dots i.e. Coulomb blockade. We use the constant interaction model and the effect of quantum confinement with a focus on explaining the electrical impedance of these systems under direct current excitation. We then explain how these properties are modified under the effect of an electrical excitation at high-frequency. More particularly, we focus on the appearance of a new component to the impedance, the so-called parametric capacitance when single-electrons tunnels back and forth between stable charge states because of the effect of the drive. We show how the parametric capacitance is composed by two physically distinct terms, the quantum capacitance and the tunneling capacitance, associated to adiabatic and non-adiabatic tunneling processes, respectively. In the second part of this chapter, we introduce the experimental technique. We show how embedding the devices in a high-Q lumped-element LC resonator can be used to probe the parametric capacitance of the system. We first present the fabrication technique of superconducting niobium nitride (NbN) spiral inductors and how these can be used in conjunction with the devices to construct high-Q resonators at radio-frequencies (rf). We show how the resonator can be characterized and optimized for optimum sensitivity of the charge state of the quantum dot system. Finally, we present an experimental demonstration of rf capacitive gate-based sensing utilizing a NbN inductor coupled to the gate of a silicon nanowire field effect transistor. Coulomb blockade manifest in these devices at milikelvin temperatures allowing probing their parametric capacitance when driven by an external high-frequency excitation. Based on the theoretical concepts in combination with the experiential demonstration presented, this chapter provides a pedagogical introduction to rf gated-based charge sensing.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Hanson, L.P. Kouwenhoven, J.R. Petta, S. Tarucha, L.M.K. Vandersypen, Rev. Mod. Phys. 79, 1217 (2007)
F.A. Zwanenburg, A.S. Dzurak, A. Morello, M.Y. Simmons, L.C.L. Hollenberg, G. Klimeck, S. Rogge, S.N. Coppersmith, M.A. Eriksson, Rev. Mod. Phys. 85, 961 (2013)
L. Fricke, M. Wulf, B. Kaestner, F. Hohls, P. Mirovsky, B. Mackrodt, R. Dolata, T. Weimann, K. Pierz, U. Siegner et al., Phys. Rev. Lett. 112, 226803 (2014)
T. Ihn, S. Gustavsson, U. Gasser, B. Küng, T. Müller, R. Schleser, M. Sigrist, I. Shorubalko, R. Leturcq, K. Ensslin, Solid State Commun. 149, 1419 (2009)
S. Gustavsson, R. Leturcq, T. Ihn, K. Ensslin, M. Reinwald, W. Wegscheider, Phys. Rev. B. 75, 075314 (2007)
D. McClure, L. DiCarlo, Y. Zhang, H.-A. Engel, C. Marcus, M. Hanson, A. Gossard, Phys. Rev. Lett. 98, 056801 (2007)
A. Rossi, T. Ferrus, D.A. Williams, Appl. Phys. Lett. 100, 133503 (2012)
D. Maradan, L. Casparis, T.-M. Liu, D.E.F. Biesinger, C.P. Scheller, D.M. Zumbühl, J.D. Zimmerman, A.C. Gossard, J. Low. Temp. Phys. 175, 784 (2014)
A. Mavalankar, S.J. Chorley, J. Griffiths, G.A.C. Jones, I. Farrer, D.A. Ritchie, C.G. Smith, Appl. Phys. Lett. 103, 133116 (2013)
I. Ahmed, A. Chatterjee, S. Barraud, J.J.L. Morton, J.A. Haigh, M.F. Gonzalez-Zalba, Commun. Phys. 1, 66 (2018a)
T.F. Watson, S.G.J. Philips, E. Kawakami, D.R. Ward, P. Scarlino, M. Veldhorst, D.E. Savage, M.G. Lagally, M. Friesen, S.N. Coppersmith, M.A. Eriksson, L.M.K. Vandersypen, Nature 555, 633 (2018)
F.H.L. Koppens, J.A. Folk, J.M. Elzerman, R. Hanson, L.H.W. Van Beveren, I.T. Vink, H.-P. Tranitz, W. Wegscheider, L.P. Kouwenhoven, L.M.K. Vandersypen, Science 309, 1346 (2005)
J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard, Science 309, 2180 (2005)
M. Veldhorst, H.G.J. Eenink, C.H. Yang, A.S. Dzurak, Nat. Commun. 8, 1766 (2017)
A. Morello, J.J. Pla, F.A. Zwanenburg, K.W. Chan, K.Y. Tan, H. Huebl, M. Mottonen, C.D. Nugroho, C. Yang, J.A. van Donkelaar, A.D.C. Alves, D.N. Jamieson, C.C. Escott, L.C.L. Hollenberg, R.G. Clark, A.S. Dzurak, Nature 467, 687 (2010)
K.D. Petersson, L.W. McFaul, M.D. Schroer, M. Jung, J.M. Taylor, A.A. Houck, J.R. Petta, Nature 490, 380 (2012)
A. Stockklauser, P. Scarlino, J.V. Koski, S. Gasparinetti, C.K. Andersen, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, A. Wallraff, Phys. Rev. X 7, 011030 (2017)
X. Mi, J.V. Cady, D.M. Zajac, P.W. Deelman, J.R. Petta, Science 355, 156 (2017)
N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U.C. Mendes, A. Blais, G. Scappucci, L.M.K. Vandersypen, Science 359, 1123 (2018)
X. Mi, M. Benito, S. Putz, D.M. Zajac, J.M. Taylor, G. Burkard, J.R. Petta, Nature 555, 599 (2018)
J.I. Colless, A.C. Mahoney, J.M. Hornibrook, A.C. Doherty, H. Lu, A.C. Gossard, D.J. Reilly, Phys. Rev. Lett. 110, 046805 (2013)
M.F. Gonzalez-Zalba, S. Barraud, A.J. Ferguson, A.C. Betz, Nat. Commun. 6, 6084 (2015)
M.G. House, T. Kobayashi, B. Weber, S.J. Hile, T.F. Watson, J. Van Der Heijden, S. Rogge, M.Y. Simmons, Nat. Commun. 6, 8848 (2015)
N. Ares, F.J. Schupp, A. Mavalankar, G. Rogers, J. Griffiths, G.A.C. Jones, I. Farrer, D.A. Ritchie, C.G. Smith, A. Cottet, G.A.D. Briggs, E.A. Laird, Phys. Rev. Appl. 5, 034011 (2016)
A. Crippa, R. Maurand, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, A.O. Orlov, P. Fay, R. Laviéville, S. Barraud, M. Vinet, M. Sanquer, S.D. Franceschi, X. Jehl, Nano Lett. 17, 1001 (2017)
I. Ahmed, J.A. Haigh, S. Schaal, S. Barraud, Y. Zhu, C.-M. Lee, M. Amado, J.W.A. Robinson, A. Rossi, J.J.L. Morton, M.F. Gonzalez-Zalba, Phys. Rev. Appl. 10, 014018 (2018b)
R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, D.E. Prober, Science 280, 1238 (1998)
R.C. Ashoori, H.L. Stormer, J.S. Weiner, L.N. Pfeiffer, S.J. Pearton, K.W. Baldwin, K.W. West, Phys. Rev. Lett. 68, 3088 (1992)
C. Ciccarelli, A.J. Ferguson, New J. Phys. 13, 093015 (2011)
F. Persson, C.M. Wilson, M. Sandberg, G. Johansson, P. Delsing, Nano Lett. 10, 953 (2010)
R. Mizuta, R.M. Otxoa, A.C. Betz, M.F. Gonzalez-Zalba, Phys. Rev. B 95, 045414 (2017)
D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986)
T.A. Fulton, G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987)
K. Barnham, D. Vvedensky, Low-Dimensional Semiconductor Structures: Fundamentals and Device Applications (Cambridge University Press, 2008)
S. Shin, J. Lee, H. Kang, J.B. Choi, S.-R.E. Yang, Y. Takahashi, D. Hasko, Nano lett. 11, 1591 (2011)
T. Ihn, Semiconductor Nanostructures (Oxford University Press, Oxford, 2010)
L.P. Kouwenhoven, D.G. Austing, S. Tarucha, Rep. Prog. Phys. 64, 701 (2001)
L.P. Kouwenhoven, C.M. Marcus, P.L. McEuen, S. Tarucha, R.M. Westervelt, N.S. Wingreen, Proc. NATO Adv. Study Inst., 105 (1997)
C.W.J. Beenakker, Phys. Rev. B, 44, 1646 (1991)
C. Wasshuber, H. Kosina, Superlattices Microstruct. 21, 37 (1997)
C.W.J. Beenakker, H. van Houten, in Solid State Physics, Vol. 44 (Elsevier, 1991), pp. 1–228
M.A. Kastner, Phys. Today 46, 24 (1993)
R.C. Ashoori, Nature 379, 413 (1996)
A. Cottet, C. Mora, T. Kontos, Phys. Rev. B 83, 121311 (2011)
I. Ahmed, Radio-Frequency Capacitive Gate-based Sensing for Silicon CMOS Quantum Electronics, Ph.D. thesis, University of Cambridge (2019)
D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)
J. Gorman, D.G. Hasko, D.A. Williams, Phys. Rev. Lett. 95, 090502 (2005)
W.G. Van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75, 1 (2002)
A.C. Betz, R. Wacquez, M. Vinet, X. Jehl, A.L. Saraiva, M. Sanquer, A.J. Ferguson, M.F. Gonzalez-Zalba, Nano Lett. 15, 4622 (2015)
F. Hofmann, T. Heinzel, D.A. Wharam, J.P. Kotthaus, G. Böhm, W. Klein, G. Tränkle, G. Weimann, Phys. Rev. B 51, 13872 (1995)
M.F. Gonzalez-Zalba, Single Donor Detection in Silicon Nanostructures, Ph.D. thesis, University of Cambridge (2013)
M. Larsson, Electron Transport in Quantum Dots Defined in Low-Dimensional Semiconductor Structures, Ph.D. thesis (2011)
A.K. Hüttel, S. Ludwig, H. Lorenz, K. Eberl, J.P. Kotthaus, Phys. Rev. B 72, 081310 (2005)
M. Pioro-Ladriere, M.R. Abolfath, P. Zawadzki, J. Lapointe, S.A. Studenikin, A.S. Sachrajda, P. Hawrylak, Phys. Rev. B 72, 125307 (2005)
M.F. González-Zalba, A. Saraiva, M. Calderón, D. Heiss, A.J. Koiller, B. Ferguson, Nano lett. 14, 5672 (2014)
S.J. Hile, M.G. House, E. Peretz, J. Verduijn, D. Widmann, T. Kobayashi, S. Rogge, M.Y. Simmons, Appl. Phys. Lett. 107, 093504 (2015)
https://iopscience.iop.org/article/10.1088/1367-2630/14/2/023050
A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, J. Huang, R.S. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, Nature 431, 162 (2004)
T. Frey, P. Leek, M. Beck, J. Faist, A. Wallraff, K. Ensslin, T. Ihn, M. Büttiker, Phys. Rev. B 86, 115303 (2012)
D. Kim, D.R. Ward, C.B. Simmons, J.K. Gamble, R. Blume-Kohout, E. Nielsen, D.E. Savage, M.G. Lagally, M. Friesen, M.A. Coppersmith, Eriksson, Nat. Nanotechnol. 10, 243 (2015)
M.F. Gonzalez-Zalba, S.N. Shevchenko, S. Barraud, J.R. Johansson, A.J. Ferguson, F. Nori, A.C. Betz, Nano Lett. 16, 1614 (2016)
M.A. Sillanpää, L. Roschier, P.J. Hakonen, App. Phys. Lett. 87, 092502 (2005)
T. Duty, G. Johansson, K. Bladh, D. Gunnarsson, C. Wilson, P. Delsing, Phys. Rev. Lett. 95, 206807 (2005)
D. Berns, W. Oliver, S. Valenzuela, A. Shytov, K. Berggren, L. Levitov, T. Orlando, Phys. Rev. Lett. 97, 150502 (2006)
C. Tahan, R. Joynt, Phys. Rev. B 89, 075302 (2014)
O. Astafiev, Y.A. Pashkin, Y. Nakamura, T. Yamamoto, J.-S. Tsai, Phys. Rev. Lett. 93, 267007 (2004)
K. Wang, C. Payette, Y. Dovzhenko, P. Deelman, J.R. Petta, Phys. Rev. Lett. 111, 046801 (2013)
P. Boross, G. Széchenyi, A. Pályi, Nanotechnology 27, 314002 (2016)
L. Roschier, P. Hakonen, K. Bladh, P. Delsing, K.W. Lehnert, L. Spietz, R.J. Schoelkopf, J. Appl. Phys. 95, 1274 (2004)
T. Müller, T. Choi, S. Hellmüller, K. Ensslin, T. Ihn, S. Schön, Rev. Sci. Inst. 84, 083902 (2013)
I. Ferain, C.A. Colinge, J.P. Colinge, Nature 479, 310 (2011)
Y.M. Niquet, D. Rideau, C. Tavernier, H. Jaouen, X. Blase, Phys. Rev. B 79, 245201 (2009)
D.J. Ibberson, L. Bourdet, J.C. Abadillo-Uriel, I. Ahmed, S. Barraud, M.J. Calderón, Y.M. Niquet, M.F. Gonzalez-Zalba, Appl. Phy. Lett. 113, 053104 (2018)
B. Voisin, V.H. Nguyen, J. Renard, X. Jehl, S. Barraud, F. Triozon, M. Vinet, I. Duchemin, Y.M. Niquet, S. de Franceschi, M. Sanquer, Nano Lett. 14, 2094 (2014)
H. Sellier, G.P. Lansbergen, J. Caro, S. Rogge, N. Collaert, I. Ferain, M. Jurczak, S. Biesemans, Appl. Phys. Lett. 90, 073502 (2007)
A.C. Betz, S. Barraud, Q. Wilmart, B. Placais, X. Jehl, M. Sanquer, M.F. Gonzalez-Zalba, Appl. Phys. Lett. 104, 043106 ( 2014)
Y. Nagamune, H. Sakaki, L.P. Kouwenhoven, L.C. Mur, C.J. P.M. Harmans, J. Motohisa, and H. Noge, Appl. Phys. Lett. 64, 2379 (1994)
J.C. Powder Diffraction Standards, on Joint committee on powder diffraction standards, 9 (1967)
S. Ran, L. Gao, J. Am. Ceram. Soc. 90, 2626 (2007)
D.K. Schroder, Semiconductor Material and Device Characterization (Wiley, New York, 2006)
T.R. Stevenson, F.A. Pellerano, C.M. Stahle, K. Aidala, R.J. Schoelkopf, Appl. Phys. Lett. 80, 3012 (2002)
J.M. Hornibrook, J.I. Colless, A.C. Mahoney, X.G. Croot, S. Blanvillain, H. Lu, A.C. Gossard, D.J. Reilly, Appl. Phys. Lett. 104, 103108 (2014)
G. Stojanovic, L.J. Zivanov, in International Conference on Microelectronics, Vol. 2 (IEEE, 2004), pp. 613–616
S.J. Chorley, J. Wabnig, Z.V. Penfold-Fitch, K.D. Petersson, J. Frake, C.G. Smith, M.R. Buitelaar, Phys. Rev. Lett. 108, 036802 (2012)
K.D. Petersson, C.G. Smith, D. Anderson, P. Atkinson, G.A.C. Jones, D.A. Ritchie, Nano Lett. 10, 2789 (2010)
H. Brenning, S. Kafanov, T. Duty, S. Kubatkin, P. Delsing, J. Appl. Phys. 100, 114321 (2006)
M. Veldhorst, C.H. Yang, J.C.C. Hwang, W. Huang, J.P. Dehollain, J.T. Muhonen, S. Simmons, A. Laucht, F.E. Hudson, K.M. Itoh, A. Morello, A.S. Dzurak, Nature 526, 410 (2015)
A. Aassime, G. Johansson, G. Wendin, R.J. Schoelkopf, P. Delsing, Phys. Rev. Lett. 86, 3376 (2001)
J. Stehlik, Y.-Y. Liu, C.M. Quintana, C. Eichler, T.R. Hartke, J.R. Petta, Phys. Rev. Applied 4, 014018 (2015)
https://journals.aps.org/prl/accepted/45074Y00Td815f8fb07c0695224d14d130011b382
A. West, B. Hensen, A. Jouan, T. Tanttu, H. Yang, C.A. Rossi, M.F. Gonzalez-Zalba, F. Hudson, A. Morello, D.J. Reilly, A.S. Dzurak, Nat. Nanotechnol. 14, 437–441 (2019)
M. Urdampilleta, D.J. Niegemann, E. Chanrion, B. Jadot, C. Spence, P.-A. Mortemousque, L. Hutin, B. Bertrand, S. Barraud, R. Maurand, X. Jehl, V.M. Ranceschi, S. De, T. Meunier, Nature Nanotechnol
G. Zheng, N. Samkharadze, M.L. Noordam, N. Kalhor, D. Brousse, A. Sammak, G. Scappucci, L.M.K. Vandersypen, arXiv preprint arXiv:1901.00687 (2019)
P. Pakkiam, A.V. Timofeev, M.G. House, M.R. Hogg, T. Kobayashi, M. Koch, S. Rogge, M.Y. Simmons, Phys. Rev. X 8, 041032 (2018)
M. Veldhorst, J.C.C. Hwang, C.H. Yang, A.W. Leenstra, B. de Ronde, J.P. Dehollain, J.T. Muhonen, F.E. Hudson, K.M. Itoh, A. Morello, A.S. Dzurak, Nat. Nanotechnol. 9, 981 (2014)
E. Kawakami, P. Scarlino, D.R. Ward, F.R. Braakman, D.E. Savage, M.G. Lagally, M. Friesen, S.N. Coppersmith, M.A. Eriksson, L.M.K. Vandersypen, Nat. Nano. 9, 666 (2014)
M.D. Stewart, N.M. Zimmerman, Appl. Sci. 6, 187 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Ahmed, I., Gonzalez-Zalba, M.F. (2020). Radio-Frequency Capacitive Gate-Based Charge Sensing for Semiconductor Quantum Dots. In: Zhu, Y. (eds) Micro and Nano Machined Electrometers. Springer, Singapore. https://doi.org/10.1007/978-981-13-3247-0_3
Download citation
DOI: https://doi.org/10.1007/978-981-13-3247-0_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-3246-3
Online ISBN: 978-981-13-3247-0
eBook Packages: EngineeringEngineering (R0)