Abstract.
The
realization of the quantum metrology triangle offers a great breakthrough in
metrology. Moreover, it will aid in the refinement of fundamental constants,
namely the elementary charge and the Planck constant. Currently, there are no
commercially available fundamental current sources, unlike those for frequency
and voltage. We review single electron devices designs, which are suitable as
a current standard for the quantum metrology triangle. Quantum dot
semiconductor electron pumps offer a best combination of ampacity and accuracy.
The main component of such devices is a single-dimensional wire, on which is
turned into a series of quantum dots with electrostatic gates. Different are
fabrication technology concepts are compared. Top-down fabrication offers
excellent placement control, however requires expensive equipment. Bottom-up
fabrication allows nanowire mass production, with a possibility of different
doping zones in-situ. The main drawback is the transfer of the nanowires to a
substrate and the subsequent integration into the measurement circuit.
Key words:
single
electron devices, electron pump, one-dimensional structures, nanowire, current
standard, high resolution lithography.
References
[1]
Kononogov
S.A., Konstantinov M.Yu., Khruschov.
About some methods of mass standard redetermination. Izmeritel'naya tekhnika
- Measurement technique, 2006, N4, pp.3-7 (In Russian)
[2] Zimmerman, Neil
M., and Mark W. Keller. "Electrical metrology with single electrons."
Measurement Science and Technology 14.8 (2003): 1237.
[3] Piquemal,
François, et al. "Fundamental electrical standards and the quantum
metrological triangle." Comptes Rendus Physique 5.8 (2004):
857-879.
[4] Likharev, K. K.,
and A. B. Zorin. "Theory of the Bloch-wave oscillations in small Josephson
junctions." Journal of Low Temperature Physics 59.3-4
(1985): 347-382.
[5] Bordé, Christian J. "Base units of the SI, fundamental
constants and modern quantum physics." Philosophical Transactions of
the Royal Society of London A: Mathematical, Physical and Engineering Sciences
363.1834 (2005): 2177-2201.
[6] Pekola, Jukka P., et al. "Single-electron current sources:
Toward a refined definition of the ampere." Reviews of Modern Physics
85.4 (2013): 1421.
[7] Geerligs, L. J., et al. "Frequency-locked turnstile device for
single electrons." Physical review letters 64.22 (1990): 2691.
[8] Averin, D. V.,
and A. A. Odintsov. "Macroscopic quantum tunneling of the electric charge
in small tunnel junctions." Physics Letters A 140.5 (1989):
251-257.
[9] Averin, D. V., A.
A. Odintsov, and S. V. Vyshenskii. "Ultimate accuracy of
single‐electron dc current standards." Journal of applied
physics 73.3 (1993): 1297-1308.
[10]
Zorin, A. B., et al. "Coulomb blockade and
cotunneling in single electron circuits with on-chip resistors: towards the
implementation of r-pump." arXiv preprint cond-mat/9912032 (1999).
[11]
Blumenthal, M. D., et al. "Gigahertz
quantized charge pumping." Nature Physics 3.5 (2007): 343-347.
[12]
Hu, Yongjie, et al. "A Ge/Si heterostructure
nanowire-based double quantum dot with integrated charge sensor."
Nature
nanotechnology 2.10 (2007): 622-625.
[13]
Kouwenhoven, L. P., et al. "Quantized
current in a quantum-dot turnstile using oscillating tunnel barriers." Physical
Review Letters 67.12 (1991): 1626.
[14]
Kouwenhoven, L. P., et al. "Quantized
current in a quantum dot turnstile." Zeitschrift für Physik B
Condensed Matter 85.3 (1991): 381-388.
[15]
Kouwenhoven, L. P., A. T. Johnson, N. C. Van der
Vaart, A. Van der Enden, C. J. P. M. Harmans, and C. T. Foxon. "Quantized
current in a quantum dot turnstile." Zeitschrift für Physik B
Condensed Matter 85, no. 3 (1991): 381-388.
[16]
Giblin, S. P., M. Kataoka, J. D. Fletcher, P. See, T.
J. B. M. Janssen, J. P. Griffiths, G. A. C. Jones, I. Farrer, and D. A.
Ritchie. "Towards a quantum representation of the ampere using single
electron pumps." Nature communications 3 (2012): 930.
[17]
Yamahata, Gento, Katsuhiko Nishiguchi, and Akira
Fujiwara. "Gigahertz single-trap electron pumps in silicon."
Nature
communications 5 (2014).
[18]
Janssen, T. J. B. M., and A. Hartland. "Accuracy
of quantized single-electron current in a one-dimensional channel."
Physica
B: Condensed Matter 284 (2000): 1790-1791.
[19]
Hobbs, Richard G., Nikolay Petkov, and Justin D.
Holmes. "Semiconductor nanowire fabrication by bottom-up and top-down
paradigms." Chemistry of Materials 24, no. 11 (2012):
1975-1991.
[20]
Santos, A., M. J. Deen, and L. F. Marsal.
"Low-cost fabrication technologies for nanostructures: state-of-the-art
and potential." Nanotechnology 26, no. 4 (2015): 042001.
[21]
Lu, Cheng, and R. H. Lipson. "Interference
lithography: a powerful tool for fabricating periodic structures."
Laser
& Photonics Reviews 4, no. 4 (2010): 568-580.
[22]
Do, Yun Seon, Jung Ho Park, Bo Yeon Hwang,
Sung‐Min Lee, Byeong‐Kwon Ju, and Kyung Cheol Choi. "Plasmonic
Color Filter and its Fabrication for Large‐Area Applications."
Advanced
Optical Materials 1, no. 2 (2013): 133-138.
[23]
French, Roger H., and Hoang V. Tran. "Immersion
lithography: photomask and wafer-level materials." Annual Review
of Materials Research 39 (2009): 93-126.
[24]
Kemp, Kevin, and Stefan Wurm. "EUV
lithography." Comptes Rendus Physique 7, no. 8 (2006): 875-886.
[25]
Maldonado, Juan R., and Martin Peckerar. "X-ray
lithography: Some history, current status and future prospects." Microelectronic
Engineering 161 (2016): 87-93.
[26]
Yang, Joel KW, Bryan Cord, Huigao Duan, Karl K.
Berggren, Joseph Klingfus, Sung-Wook Nam, Ki-Bum Kim, and Michael J. Rooks.
"Understanding of hydrogen silsesquioxane electron resist for
sub-5-nm-half-pitch lithography." (2009).
[27]
Manfrinato, Vitor R., Lin Lee Cheong, Huigao
Duan, Donald Winston, Henry I. Smith, and Karl K. Berggren. "Sub-5keV
electron-beam lithography in hydrogen silsesquioxane resist." Microelectronic
Engineering 88, no. 10 (2011): 3070-3074.
[28]
Sim, Jae Hwan, Sung-Il Lee, Hae-Jeong Lee, Richard
Kasica, Hyun-Mi Kim, Christopher L. Soles, Ki-Bum Kim, and Do Y. Yoon.
"Novel Organosilicate Polymer Resists for High Resolution E-Beam
Lithography." Chemistry of Materials 22, no. 10 (2010):
3021-3023.
[29]
Pain, Laurent, Serge Tedesco, and Christophe
Constancias. "Direct write lithography: the global solution for R&D
and manufacturing." Comptes Rendus Physique 7, no. 8 (2006):
910-923.
[30]
Lee, Hyo-Sung, Byung-Sung Kim, Hyun-Mi Kim,
Jung-Sub Wi, Sung-Wook Nam, Kyung-Bae Jin, Ki-Bum Kim, and Yoshihiro Arai.
"Electron beam projection nanopatterning using crystal lattice images
obtained from high resolution transmission electron microscopy." In SPIE
OPTO: Integrated Optoelectronic Devices, pp. 72221B-72221B. International
Society for Optics and Photonics, 2009.
[31]
Sidorkin, V., E. van Veldhoven, and E. van der Drift.
"van der; Alkemade, P.; Salemink, H.; Maas, D." J. Vac. Sci.
Technol.,
B 27 (2009): 25.
[32]
Winston, Donald, Vitor R. Manfrinato, Samuel M.
Nicaise, Lin Lee Cheong, Huigao Duan, David Ferranti, Jeff Marshman et al.
"Neon
ion beam lithography (NIBL)." Nano letters 11, no. 10 (2011):
4343-4347.
[33]
Lieber, Charles M., and Zhong Lin Wang.
"Functional nanowires." MRS bulletin 32, no. 02 (2007):
99-108.
[34]
Fuhrer, Andreas, Carina Fasth, and Lars Samuelson.
"Single electron pumping in InAs nanowire double quantum dots."
Applied
Physics Letters 91, no. 5 (2007): 052109.
[35]
d’Hollosy, S., M. Jung, A. Baumgartner, V. A. Guzenko,
M. H. Madsen, J. Nygard, and C. Schönenberger. "Gigahertz quantized
charge pumping in bottom-gate-defined InAs nanowire quantum dots."
Nano
letters 15, no. 7 (2015): 4585-4590.
[36]
Holmes, Justin D., Keith P. Johnston, R. Christopher
Doty, and Brian A. Korgel. "Control of thickness and orientation of
solution-grown silicon nanowires." Science 287, no. 5457
(2000): 1471-1473.
[37]
Dayeh, Shadi A., and S. T. Picraux. "Direct
observation of nanoscale size effects in Ge semiconductor nanowire
growth." Nano letters 10, no. 10 (2010): 4032-4039.
[38]
Lu, Wei, Jie Xiang, Brian P. Timko, Yue Wu, and
Charles M. Lieber. "One-dimensional hole gas in germanium/silicon nanowire
heterostructures." Proceedings of the National Academy of Sciences of
the United States of America 102, no. 29 (2005): 10046-10051.
[39]
Yuan, Fang-Wei, and
Hsing-Yu Tuan. "Supercritical fluid− solid growth of
single-crystalline silicon nanowires: An example of metal-free growth in an
organic solvent." Crystal Growth & Design 10, no. 11
(2010): 4741-4745.
[40]
Tuan, Hsing-Yu, Doh C. Lee, Tobias Hanrath, and Brian
A. Korgel. "Germanium nanowire synthesis: An example of solid-phase seeded
growth with nickel nanocrystals." Chemistry of materials 17,
no. 23 (2005): 5705-5711.
[41]
Heitsch, Andrew T.,
Dayne D. Fanfair, Hsing-Yu Tuan, and Brian A. Korgel. "solution−
liquid− solid (SLS) growth of silicon nanowires."
Journal of the American Chemical Society
130, no. 16 (2008): 5436-5437.
[42]
Lensch-Falk, Jessica L., Eric R. Hemesath, Francisco J.
Lopez, and Lincoln J. Lauhon. "Vapor-solid-solid synthesis of Ge nanowires
from vapor-phase-deposited manganese germanide seeds." Journal
of the American Chemical Society 129, no. 35 (2007): 10670-10671.
[43]
Bierman, Matthew J., YK Albert Lau, Alexander V. Kvit,
Andrew L. Schmitt, and Song Jin. "Dislocation-driven nanowire
growth and Eshelby twist." Science 320, no. 5879 (2008): 1060-1063.
[44]
Koch, R. H., and A. Hartstein. "Evidence for
resonant tunneling of electrons via sodium ions in silicon dioxide."
Physical
review letters 54, no. 16 (1985): 1848.