We performed electron counting statistics to measure the thermoelectric effect in a nanometer-scale silicon dot. To separate the 100-nm-long dot from a silicon nanowire, we used an electrostatically created 30-nm-long energy barrier. By measuring current through a nearby sensor, we observed the random motion of single electrons between the dot and silicon nanowire. The statistics of single-electron motion provides us with information on temperature and voltage at the dot. Under the detailed balance assumption, we determined the temperature difference and the Seebeck voltage between the dot and silicon nanowire. The validity of our analysis was confirmed by observing the energy-barrier height dependence of the Seebeck coefficient. Furthermore, by counting the electrons leaving the dot, a minute output power on the order of sub-zeptowatt from the dot to the silicon nanowire was estimated.

1.
E.
Pop
, “
Energy dissipation and transport in nanoscale devices
,”
Nano Res.
3
,
147
(
2010
).
2.
B.
Sothmann
,
R.
Sánchez
, and
A. N.
Jordan
, “
Thermoelectric energy harvesting with quantum dots
,”
Nanotechnology
26
,
032001
(
2015
).
3.
G.
Benenti
,
G.
Casati
,
K.
Saito
, and
R. S.
Whitney
, “
Fundamental aspects of steady-state conversion of heat to work at the nanoscale
,”
Phys. Rep.
694
,
1–124
(
2017
).
4.
S.
Dorsch
,
A.
Svilans
,
M.
Josefsson
,
B.
Goldozian
,
M.
Kumar
,
C.
Thelander
,
A.
Wacker
, and
A.
Burke
, “
Heat driven transport in serial double quantum dot devices
,”
Nano Lett.
21
,
988
994
(
2021
).
5.
G.
Jaliel
,
R. K.
Puddy
,
R.
Sanchez
,
A. N.
Jordan
,
B.
Sothmann
,
I.
Farrer
,
J. P.
Griffiths
,
D. A.
Ritchie
, and
C. G.
Smith
, “
Experimental realization of a quantum dot energy harvester
,”
Phys. Rev. Lett.
123
,
117701
(
2019
).
6.
M.
Josefsson
,
A.
Svilans
,
A. M.
Burke
,
E. A.
Hoffmann
,
S.
Fahlvik
,
C.
Thelander
,
M.
Leijnse
, and
H.
Linke
, “
A quantum-dot heat engine operating close to the thermodynamic efficiency limits
,”
Nat. Nanotechnol.
13
,
920
(
2018
).
7.
H.
Thierschmann
,
R.
Saanchez
,
B.
Sothmann
,
F.
Arnold
,
C.
Heyn
,
W.
Hansen
,
H.
Buhmann
, and
L. W.
Molenkamp
, “
Three-terminal energy harvester with coupled quantum dots
,”
Nat. Nanotechnol.
10
,
854
(
2015
).
8.
F.
Hartmann
,
P.
Pfeffer
,
S.
H€ofling
,
M.
Kamp
, and
L.
Worschech
, “
Voltage fluctuation to current converter with Coulomb-coupled quantum dots
,”
Phys. Rev. Lett.
114
,
146805
(
2015
).
9.
B.
Roche
,
P.
Roulleau
,
T.
Jullien
,
Y.
Jompol
,
I.
Farrer
,
D. A.
Ritchie
, and
D. C.
Glattli
, “
Harvesting dissipated energy with a mesoscopic ratchet
,”
Nat. Commun.
6
,
6738
(
2015
).
10.
J. V.
Koski
,
A.
Kutvonen
,
I. M.
Khaymovich
,
T.
Ala-Nissila
, and
J. P.
Pekola
, “
On-chip Maxwell's demon as an information-powered refrigerator
,”
Phys. Rev. Lett.
115
,
260602
(
2015
).
11.
U.
Seifert
, “
Stochastic thermodynamics, fluctuation theorems and molecular machines
,”
Rep. Prog. Phys.
75
,
126001
(
2012
).
12.
S.
Ciliberto
, “
Experiments in Stochastic thermodynamics: Short history and perspectives
,”
Phys. Rev. X
7
,
021051
(
2017
).
13.
S.
Ito
and
T.
Sagawa
, “
Maxwell's demon in biochemical signal transduction with feedback loop
,”
Nat. Commun.
6
,
7498
(
2015
).
14.
A. C.
Barato
and
U.
Seifert
, “
Cost and precision of Brownian clocks
,”
Phys. Rev. X
6
,
041053
(
2016
).
15.
J. P.
Pekola
, “
Towards quantum thermodynamics in electronic circuits
,”
Nat. Phys.
11
,
118
(
2015
).
16.
H.
Tajima
and
K.
Funo
, “
Superconducting-like heat current: Effective cancellation of current-dissipation trade-off by quantum coherence
,”
Phys. Rev. Lett.
127
,
190604
(
2021
).
17.
S.
Gustavsson
,
R.
Leturcq
,
B.
Simovič
,
R.
Schleser
,
T.
Ihn
,
P.
Studerus
,
K.
Ensslin
,
D. C.
Driscoll
, and
A. C.
Gossard
, “
Counting statistics of single electron transport in a quantum dot
,”
Phys. Rev. Lett.
96
,
076605
(
2006
).
18.
T.
Fujisawa
,
T.
Hayashi
,
R.
Tomita
, and
Y.
Hirayama
, “
Bidirectional counting of single electrons
,”
Science
312
,
1634
(
2006
).
19.
C.
Flindt
,
C.
Fricke
,
F.
Hohls
,
T.
Novotný
,
K.
Netočný
,
T.
Brandes
, and
R. J.
Haug
, “
Universal oscillations in counting statistics
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
10116
(
2009
).
20.
V. F.
Maisi
,
D.
Kambly
,
C.
Flindt
, and
J. P.
Pekola
, “
Full counting statistics of Andreev tunneling
,”
Phys. Rev. Lett.
112
,
036801
(
2014
).
21.
V. F.
Maisi
,
A.
Hofmann
,
M.
Röösli
,
J.
Basset
,
C.
Reichl
,
W.
Wegscheider
,
T.
Ihn
, and
K.
Ensslin
, “
Spin-orbit coupling at the level of a single electron
,”
Phys. Rev. Lett.
116
,
136803
(
2016
).
22.
A.
Hofmann
,
V. F.
Maisi
,
C.
Gold
,
T.
Krähenmann
,
C.
Rössler
,
J.
Basset
,
P.
Märki
,
C.
Reichl
,
W.
Wegscheider
,
K.
Ensslin
, and
T.
Ihn
, “
Measuring the degeneracy of discrete energy levels using a GaAs/AlGaAs quantum dot
,”
Phys. Rev. Lett.
117
,
206803
(
2016
).
23.
A.
Hofmann
,
V. F.
Maisi
,
T.
Krähenmann
,
C.
Reichl
,
W.
Wegscheider
,
K.
Ensslin
, and
T.
Ihn
, “
Anisotropy and suppression of spin-orbit interaction in a GaAs double quantum dot
,”
Phys. Rev. Lett.
119
,
176807
(
2017
).
24.
S.
Matsuo
,
K.
Kuroyama
,
S.
Yabunaka
,
S. R.
Valentin
,
A.
Ludwig
,
A. D.
Wieck
, and
S.
Tarucha
, “
Full counting statistics of spin-flip and spin-conserving charge transitions in Pauli-spin blockade
,”
Phys. Rev. Res.
2
,
033120
(
2020
).
25.
J. V.
Koski
,
T.
Sagawa
,
O.-P.
Saira
,
Y.
Yoon
,
A.
Kutvonen
,
P.
Solinas
,
M.
Möttönen
,
T.
Ala-Nissila
, and
J. P.
Pekola
, “
Distribution of entropy production in a single-electron box
,”
Nat. Phys.
9
,
644
(
2013
).
26.
O.-P.
Saira
,
Y.
Yoon
,
T.
Tanttu
,
M.
Möttönen
,
D. V.
Averin
, and
J. P.
Pekola
, “
Test of the Jarzynski and Crooks fluctuation relations in an electronic system
,”
Phys. Rev. Lett.
109
,
180601
(
2012
).
27.
B.
Küng
,
C.
Rössler
,
M.
Beck
,
M.
Marthaler
,
D. S.
Golubev
,
Y.
Utsumi
,
T.
Ihn
, and
K.
Ensslin
, “
Irreversibility on the level of single-electron tunneling
,”
Phys. Rev. X
2
,
011001
(
2012
).
28.
K.
Chida
,
S.
Desai
,
K.
Nishiguchi
, and
A.
Fujiwara
, “
Power generator driven by Maxwell's demon
,”
Nat. Commun.
8
,
15310
(
2017
).
29.
J. V.
Koski
,
V. F.
Maisi
,
J. P.
Pekola
, and
D. V.
Averin
, “
Experimental realization of a Szilard engine with a single electron
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
13786
(
2014
).
30.
J. V.
Koski
,
V. F.
Maisi
,
T.
Sagawa
, and
J. P.
Pekola
, “
Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon
,”
Phys. Rev. Lett.
113
,
030601
(
2014
).
31.
R.
Sánchez
and
M.
Büttiker
, “
Optimal energy quanta to current conversion
,”
Phys. Rev. B
83
,
085428
(
2011
).
32.
R.
Sánchez
and
M.
Büttiker
, “
Detection of single-electron heat transfer statistics
,”
Europhys. Lett.
100
,
47008
(
2012
).
33.
R.
Sánchez
,
B.
Sothmann
,
A. N.
Jordan
, and
M.
Büttiker
, “
Correlations of heat and charge currents in quantum-dot thermoelectric engines
,”
New J. Phys.
15
,
125001
(
2013
).
34.
Z. A. K.
Durrani
, “
Seebeck coefficient of one electron
,”
J. Appl. Phys.
115
,
094508
(
2014
).
35.
C.
McConnell
and
A.
Nazir
, “
Strong coupling in thermoelectric nanojunctions: A reaction coordinate framework
,”
New J. Phys.
24
,
025002
(
2022
).
36.
K.
Nishiguchi
,
C.
Koechlin
,
Y.
Ono
,
A.
Fujiwara
,
H.
Inokawa
, and
H.
Yamaguchi
, “
Single-electron-resolution electrometer based on field-effect transistor
,”
Jpn. J. Appl. Phys.
47
,
8305
(
2008
).
37.
K.
Nishiguchi
,
Y.
Ono
, and
A.
Fujiwara
, “
Single-electron thermal noise
,”
Nanotechnology
25
,
275201
(
2014
);
[PubMed]
P. A.
Carles
,
K.
Nishiguchi
, and
A.
Fujiwara
, “
Deviation from the law of energy equipartition in a small dynamic-random-access memory
,”
Jpn. J. Appl. Phys.
54
,
06FG03
(
2015
).
38.
K.
Chida
,
K.
Nishiguchi
,
G.
Yamahata
,
H.
Tanaka
, and
A.
Fujiwara
, “
Thermal noise suppression in nano-scale Si field-effect transistors by feedback control based on single-electron detection
,”
Appl. Phys. Lett.
107
,
073110
(
2015
).
39.
N.
Freitas
,
J.-C.
Delvenne
, and
M.
Esposito
, “
Stochastic thermodynamics of nonlinear electronic circuits: A realistic framework for computing around kT
,”
Phys. Rev. X
11
,
031064
(
2021
).
40.
S.
Datta
,
Lessons From Nanoelectronics: A New Perspective on Transport
(
World Scientific Publishing Company
,
2012
), Vol.
1
.
41.
R.
Kim
,
S.
Datta
, and
M. S.
Lundstrom
, “
Influence of dimensionality on thermoelectric device performance
,”
J. Appl. Phys.
105
,
034506
(
2009
).
42.
M. S.
Lundstrom
and
C.
Jeong
,
Near-Equilibrium Transport: Fundamentals and Applications
(
World Scientific Publishing Company
,
2012
).
43.
K.
Nishiguchi
,
Y.
Ono
, and
A.
Fujiwara
, “
Single-electron counting statistics of shot noise in nanowire Si metal-oxide-semiconductor field-effect transistors
,”
Appl. Phys. Lett.
98
,
193502
(
2011
).
44.
D. V.
Averin
and
J. P.
Pekola
, “
Statistics of the dissipated energy in driven single-electron transitions
,”
Europhys. Lett.
96
,
67004
(
2011
).
45.
J. P.
Pekola
and
O.-P.
Saira
, “
Work, free energy and dissipation in voltage driven single-electron transitions
,”
J. Low Temp. Phys.
169
,
70
(
2012
).
46.
A.
Hofmann
,
V. F.
Maisi
,
J.
Basset
,
C.
Reichl
,
W.
Wegscheider
,
T.
Ihn
,
K.
Ensslin
, and
C.
Jarzynski
, “
Heat dissipation and fluctuations in a driven quantum dot
,”
Phys. Status Solidi B
254
,
1600546
(
2017
).
47.
N.
Shiraishi
, “
Time-symmetric current and its fluctuation response relation around nonequilibrium stalling stationary state
,”
Phys. Rev. Lett.
129
,
020602
(
2022
).
48.
C.
Maes
, “
Frenesy: Time-symmetric dynamical activity in nonequilibria
,”
Phys. Rep.
850
,
1–33
(
2020
).
49.
T.
Ruokola
and
T.
Ojanen
, “
Single-electron heat diode: Asymmetric heat transport between electronic reservoirs through Coulomb islands
,”
Phys. Rev. B
83
,
241404(R)
(
2011
).
50.
T.
Ruokola
and
T.
Ojanen
, “
Theory of single-electron heat engines coupled to electromagnetic environments
,”
Phys. Rev. B
86
,
035454
(
2012
).
51.
J. M.
Horowitz
and
M.
Esposito
, “
Thermodynamics with continuous information flow
,”
Phys. Rev. X
4
,
031015
(
2014
).
52.
R.
Sánchez
,
H.
Thierschmann
, and
L. W.
Molenkamp
, “
Single-electron thermal devices coupled to a mesoscopic gate
,”
New J. Phys.
19
,
113040
(
2017
).
53.
J.
Yang
,
C.
Elouard
,
J.
Splettstoesser
,
B.
Sothmann
,
R.
Sánchez
, and
A. N.
Jordan
, “
Thermal transistor and thermometer based on Coulomb-coupled conductors
,”
Phys. Rev. B
100
,
045418
(
2019
).
54.
P. A.
Erdman
,
B.
Bhandari
,
R.
Fazio
,
J. P.
Pekola
, and
F.
Taddei
, “
Absorption refrigerators based on Coulomb-coupled single-electron systems
,”
Phys. Rev. B
98
,
045433
(
2018
).
55.
S. F.
Svensson
,
E. A.
Hoffmann
,
N.
Nakpathomkun
,
P. M.
Wu
,
H. Q.
Xu
,
H. A.
Nilsson
,
D.
Sánchez
,
V.
Kashcheyevs
, and
H.
Linke
, “
Nonlinear thermovoltage and thermocurrent in quantum dots
,”
New J. Phys.
15
,
105011
(
2013
).
56.
K.
Yamamoto
and
N.
Hatano
, “
Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime
,”
Phys. Rev. B
92
,
042165
(
2015
).
57.
D.
Sánchez
and
R.
López
, “
Nonlinear phenomena in quantum thermoelectrics and heat
,”
C. R. Phys.
17
,
1060
(
2016
).
58.
R.
Wang
,
C.
Wang
,
J.
Lu
, and
J.
Jiang
, “
Inelastic thermoelectric transport and fluctuations in mesoscopic systems
,”
Adv. Phys. X
7
,
2082317
(
2022
).
59.
A. I.
Boukai
,
Y.
Bunimovich
,
J.
Tahir-Kheli
,
J.
Yu
,
W. A.
Goddard
 III
, and
J. R.
Heath
, “
Silicon nanowires as efficient thermoelectric materials
,”
Nature
451
,
168
(
2008
).
60.
R.
Chen
,
J.
Lee
,
W.
Lee
, and
D.
Li
, “
Thermoelectrics of nanowires
,”
Chem. Rev.
119
,
9260
(
2019
).
61.
T.
Takahashi
,
N.
Beppu
,
K.
Chen
,
S.
Oda
, and
K.
Uchida
, “
Self-heating effects and analog performance optimization of fin-type field-effect transistors
,”
Jpn. J. Appl. Phys.
52
,
04CC03
(
2013
).
You do not currently have access to this content.