We report a method to characterize the potential barrier of a dynamic quantum dot by measuring the barrier height and determining the curvature. We show that the loading statistics and hence accuracy of electron transfer through the dynamic quantum dot depend significantly on these parameters, and hence our method provides a detailed characterization of device performance. This method takes a further step towards tunable barrier shapes, which would greatly increase the accuracy of single electron sources, allowing the single electron current to be useful for quantum sensing, quantum information, and metrology. We apply our method to the case of a tunable-barrier single-electron pump, an exemplary device that shows promise as a source of hot single electron wavepackets.

1.
M. D.
Blumenthal
,
B.
Kaestner
,
L.
Li
,
S.
Giblin
,
T. J. B. M.
Janssen
,
M.
Pepper
,
D.
Anderson
,
G.
Jones
, and
D. A.
Ritchie
,
Nat. Phys.
3
,
343
(
2007
).
2.
S. P.
Giblin
,
A.
Fujiwara
,
G.
Yamahata
,
M.-H.
Bae
,
N.
Kim
,
A.
Rossi
,
M.
Möttönen
, and
M.
Kataoka
,
Metrologia
56
,
044004
(
2019
).
3.
S. P.
Giblin
,
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
,
Nat. Commun.
3
,
930
(
2012
).
4.
M.-H.
Bae
,
Y.-H.
Ahn
,
M.
Seo
,
Y.
Chung
,
J. D.
Fletcher
,
S. P.
Giblin
,
M.
Kataoka
, and
N.
Kim
,
Metrologia
52
,
195
(
2015
).
5.
G.
Yamahata
,
S. P.
Giblin
,
M.
Kataoka
,
T.
Karasawa
, and
A.
Fujiwara
,
Appl. Phys. Lett.
109
,
013101
(
2016
).
6.
R.
Zhao
,
A.
Rossi
,
S. P.
Giblin
,
J. D.
Fletcher
,
F. E.
Hudson
,
M.
Möttönen
,
M.
Kataoka
, and
A. S.
Dzurak
,
Phys. Rev. Appl.
8
,
044021
(
2017
).
7.
A.
Rossi
,
T.
Tanttu
,
K. Y.
Tan
,
I.
Isakka
,
R.
Zhao
,
K. W.
Chan
,
G. C.
Tettamanzi
,
S.
Rogge
,
A. S.
Dzurak
, and
M.
Möttönen
,
Nano Lett.
14
,
3405
(
2014
).
8.
F.
Stein
,
H.
Scherer
,
T.
Gerster
,
R.
Behr
,
M.
Götz
,
E.
Pesel
,
C.
Leicht
,
N.
Ubbelohde
,
T.
Weimann
,
K.
Pierz
,
H. W.
Schumacher
, and
F.
Hohls
,
Metrologia
54
,
S1
S8
(
2017
).
9.
N.
Johnson
,
J. D.
Fletcher
,
D.
Humphreys
,
P.
See
,
J.
Griffiths
,
G.
Jones
,
I.
Farrer
,
D.
Ritchie
,
M.
Pepper
,
T.
Janssen
, and
M.
Kataoka
,
Appl. Phys. Lett.
110
,
102105
(
2017
).
10.
G.
Yamahata
,
S.
Ryu
,
N.
Johnson
,
H.-S.
Sim
,
A.
Fujiwara
, and
M.
Kataoka
, e-print arXiv:1903.07802.
11.
J.
Waldie
,
P.
See
,
V.
Kashcheyevs
,
J. P.
Griffiths
,
I.
Farrer
,
G. A. C.
Jones
,
D. A.
Ritchie
,
T. J. B. M.
Janssen
, and
M.
Kataoka
,
Phys. Rev. B
92
,
125305
(
2015
).
12.
E.
Bocquillon
,
F. D.
Parmentier
,
C.
Grenier
,
J.-M.
Berroir
,
P.
Degiovanni
,
D. C.
Glattli
,
B.
Plaçais
,
A.
Cavanna
,
Y.
Jin
, and
G.
Fève
,
Phys. Rev. Lett.
108
,
196803
(
2012
).
13.
N. M.
Zimmerman
and
M. W.
Keller
,
Meas. Sci. Technol.
14
,
1237
(
2003
).
14.
S. P.
Giblin
,
M.-H.
Bae
,
N.
Kim
,
Y.-H.
Ahn
, and
M.
Kataoka
,
Metrologia
54
,
299
(
2017
).
15.
H.
Scherer
and
H. W.
Schumacher
,
Ann. Phys.
531
,
1800371
(
2019
).
16.
N.-H.
Kaneko
,
IEEJ Trans. Electr. Electron. Eng.
12
,
627
(
2017
).
17.
C.
Bäuerle
,
D. C.
Glattli
,
T.
Meunier
,
F.
Portier
,
P.
Roche
,
P.
Roulleau
,
S.
Takada
, and
X.
Waintal
,
Rep. Prog. Phys.
81
,
056503
(
2018
).
18.
J. D.
Fletcher
,
P.
See
,
H.
Howe
,
M.
Pepper
,
S. P.
Giblin
,
J. P.
Griffiths
,
G. A. C.
Jones
,
I.
Farrer
,
D. A.
Ritchie
,
T. J. B. M.
Janssen
, and
M.
Kataoka
,
Phys. Rev. Lett.
111
,
216807
(
2013
).
19.
J. D.
Fletcher
,
N.
Johnson
,
E.
Locane
,
P.
See
,
J. P.
Griffiths
,
I.
Farrer
,
D. A.
Ritchie
,
P. W.
Brouwer
,
V.
Kashcheyevs
, and
M.
Kataoka
, e-print arXiv:1901.10985.
20.
V.
Kashcheyevs
and
B.
Kaestner
,
Phys. Rev. Lett.
104
,
186805
(
2010
).
21.
A.
Fujiwara
,
G.
Yamahata
, and
K.
Nishiguchi
, in
Nanoscale Silicon Devices
(
CRC Press
,
2016
), Chap. 9.
22.
B.
Kaestner
and
V.
Kashcheyevs
,
Rep. Prog. Phys.
78
,
103901
(
2015
).
23.
N.
Johnson
,
C.
Emary
,
S.
Ryu
,
H.-S.
Sim
,
P.
See
,
J. D.
Fletcher
,
J. P.
Griffiths
,
G. A. C.
Jones
,
I.
Farrer
,
D. A.
Ritchie
,
M.
Pepper
,
T. J. B. M.
Janssen
, and
M.
Kataoka
,
Phys. Rev. Lett.
121
,
137703
(
2018
).
24.
G.
Yamahata
,
K.
Nishiguchi
, and
A.
Fujiwara
,
Phys. Rev. B
89
,
165302
(
2014
).
25.
A.
Fujiwara
,
K.
Nishiguchi
, and
Y.
Ono
,
Appl. Phys. Lett.
92
,
042102
(
2008
).
26.
N.
Johnson
,
G.
Yamahata
, and
A.
Fujiwara
, “
Observation of cooling in a dynamic quantum dot
” (unpublished).
27.
M.
Kataoka
,
J. D.
Fletcher
,
P.
See
,
S. P.
Giblin
,
T. J. B. M.
Janssen
,
J. P.
Griffiths
,
G. A. C.
Jones
,
I.
Farrer
, and
D. A.
Ritchie
,
Phys. Rev. Lett.
106
,
126801
(
2011
).
28.
B.
Kaestner
,
V.
Kashcheyevs
,
G.
Hein
,
K.
Pierz
,
U.
Siegner
, and
H. W.
Schumacher
,
Appl. Phys. Lett.
92
,
192106
(
2008
).
29.
M. W.
Cole
and
R. H.
Good
, Jr.
,
Phys. Rev. A
18
,
1085
(
1978
).
30.
H.
Grabert
and
U.
Weiss
,
Phys. Rev. Lett.
53
,
1787
(
1984
).
31.

We note that this solution only gives a linear dependence on Vexit in the subject of the interior exponent, and that some references, including 2 and 22 use an alternative construction of δn.

32.
V.
Kashcheyevs
and
J.
Timoshenko
, in Proceedings of the
29th Conference on Precision Electromagnetic Measurements (CPEM)
(
2014
), p.
536
.
33.
A. O.
Caldeira
and
A. J.
Leggett
,
Phys. Rev. Lett.
46
,
211
(
1981
).
34.
P. G.
Wolynes
,
Phys. Rev. Lett.
47
,
968
(
1981
).
35.
G.
Yamahata
,
K.
Nishiguchi
, and
A.
Fujiwara
,
Appl. Phys. Lett.
98
,
222104
(
2011
).
36.

We note there was a discontinuity seen around T = 32 K, arising from a thermal cycle occurring to the device. On remeasuring the device, it was found δ1 was unchanged (ensuring consistency and generality of results) but the position in Vexit had slightly shifted by 14 mV. This has been accounted for in this analysis by offsetting curves for T < 32 K. Note that the curves of Figs. 1(c), 1(d), 2(a), and 3(a) are also offset.

37.

In the analysis of Fig. 3(b), low temperature data was excluded from the fit owing to instability of the curve position in Vexit, which we speculate is due to a changing channel conductance.40 

38.

The error bars plotted in Fig. 3(b) are the Type A (statistical) uncertainty, and these are used in the fit. The limit of our measurement resolution, and hence Type A uncertainty, is approximately 0.2 pA, which corresponds to ln(ln(Ip/ef))6, and points below this are not used in the fit. To show the crossover to the tunneling regime, we extend the fit curve in to this region.

39.
P.
Hanggi
,
H.
Grabert
,
G.-L.
Ingold
, and
U.
Weiss
,
Phys. Rev. Lett.
55
,
761
(
1985
).
40.
A.
Fujiwara
,
Y.
Takahashi
,
H.
Namatsu
,
K.
Kurihara
, and
K.
Murase
,
Jpn. J. Appl. Phys., Part 1
37
,
3257
(
1998
).
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