Semiconductor quantum dot (QD) devices experience a modulation of the band structure at the edge of lithographically defined gates due to mechanical strain. This modulation can play a prominent role in the device behavior at low temperatures, where QD devices operate. Here, we develop an electrical measurement of strain based on characteristics of tunnel junctions defined by aluminum and titanium gates. We measure relative differences in the tunnel barrier height due to strain consistent with experimentally measured coefficients of thermal expansion () that differ from the bulk values. Our results show that the bulk parameters commonly used for simulating strain in QD devices incorrectly capture the impact of strain. The method presented here provides a path forward toward exploring different gate materials and fabrication processes in silicon QDs in order to optimize strain.
REFERENCES
1.
D.
Berman
, N. B.
Zhitenev
, R. C.
Ashoori
, H. I.
Smith
, and M. R.
Melloch
, “Single-electron transistor as a charge sensor for semiconductor applications
,” J. Vac. Sci. Technol. B
15
, 2844
(1997
). 2.
N. M.
Zimmerman
and M. W.
Keller
, “Electrical metrology with single electrons
,” Meas. Sci. Technol.
14
, 1237
–1242
(2003
). 3.
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
, and A. S.
Dzurak
, “A two-qubit logic gate in silicon
,” Nature
526
, 410
–414
(2015
). 4.
J. R.
Petta
, A. C.
Johnson
, J. M.
Taylor
, E. A.
Laird
, A.
Yacoby
, M. D.
Lukin
, C. M.
Marcus
, M. P.
Hanson
, and A. C.
Gossard
, “Coherent manipulation of coupled electron spins in semiconductor quantum dots
,” Science
309
, 2180
–2184
(2005
). 5.
D.
Loss
and D. P.
DiVincenzo
, “Quantum computation with quantum dots
,” Phys. Rev. A
57
, 120
–126
(1998
). 6.
G.
Yamahata
, K.
Nishiguchi
, and A.
Fujiwara
, “Gigahertz single-trap electron pumps in silicon
,” Nat. Commun.
5
, 5038
(2014
). 7.
A.
Rossi
, T.
Tanttu
, K. Y.
Tan
, I.
Iisakka
, R.
Zhao
, K. W.
Chan
, G. C.
Tettamanzi
, S.
Rogge
, A. S.
Dzurak
, and M.
Möttönen
, “An accurate single-electron pump based on a highly tunable silicon quantum dot
,” Nano Lett.
14
, 3405
–3411
(2014
). 8.
S.
Giblin
, M.
Kataoka
, J.
Fletcher
, P.
See
, T.
Janssen
, J.
Griffiths
, G.
Jones
, I.
Farrer
, and D.
Ritchie
, “Towards a quantum representation of the ampere using single electron pumps
,” Nat. Commun.
3
, 930
(2012
). 9.
T.
Thorbeck
and N. M.
Zimmerman
, “Formation of strain-induced quantum dots in gated semiconductor nanostructures
,” AIP Adv.
5
, 087107
(2015
). 10.
J.
Park
, Y.
Ahn
, J. A.
Tilka
, K. C.
Sampson
, D. E.
Savage
, J. R.
Prance
, C. B.
Simmons
, M. G.
Lagally
, S. N.
Coppersmith
, M. A.
Eriksson
, M. V.
Holt
, and P. G.
Evans
, “Electrode-stress-induced nanoscale disorder in Si quantum electronic devices
,” APL Mater.
4
, 066102
(2016
). 11.
D.
Cooper
, T.
Denneulin
, N.
Bernier
, A.
Béché
, and J.-L.
Rouvière
, “Strain mapping of semiconductor specimens with nm-scale resolution in a transmission electron microscope
,” Micron
80
, 145
–165
(2016
). 12.
W.
Osborn
, L. H.
Friedman
, and M.
Vaudin
, “Strain measurement of 3D structured nanodevices by EBSD
,” Ultramicroscopy
184
, 88
–93
(2018
). 13.
M. D.
Vaudin
, W. A.
Osborn
, L. H.
Friedman
, J. M.
Gorham
, V.
Vartanian
, and R. F.
Cook
, “Designing a standard for strain mapping: HR-EBSD analysis of SiGe thin film structures on Si
,” Ultramicroscopy
148
, 94
–104
(2015
). 14.
S.
Di Fonzo
, W.
Jark
, S.
Lagomarsino
, C.
Giannini
, L.
De Caro
, A.
Cedola
, and M.
Müller
, “Non-destructive determination of local strain with 100-nanometre spatial resolution
,” Nature
403
, 638
–640
(2000
). 15.
P.
Hermann
, M.
Hecker
, D.
Chumakov
, M.
Weisheit
, J.
Rinderknecht
, A.
Shelaev
, P.
Dorozhkin
, and L. M.
Eng
, “Imaging and strain analysis of nano-scale SiGe structures by tip-enhanced Raman spectroscopy
,” Ultramicroscopy
111
, 1630
–1635
(2011
). 16.
R.
He
and P.
Yang
, “Giant piezoresistance effect in silicon nanowires
,” Nat. Nanotechnol.
1
, 42
–46
(2006
). 17.
D.
Gao
, Z.
Yang
, L.
Zheng
, and K.
Zheng
, “Piezoresistive effect of N-type 111-oriented Si nanowires under large tension/compression
,” Nanotechnology
28
, 095702
(2017
). 18.
J.
Mansir
, P.
Conti
, Z.
Zeng
, J. J.
Pla
, P.
Bertet
, M. W.
Swift
, C. G.
Van de Walle
, M. L. W.
Thewalt
, B.
Sklenard
, Y. M.
Niquet
, and J. J. L.
Morton
, “Linear hyperfine tuning of donor spins in silicon using hydrostatic strain
,” Phys. Rev. Lett.
120
, 167701
(2018
). 19.
J.
Bardeen
and W.
Shockley
, “Deformation potentials and mobilities in non-polar crystals
,” Phys. Rev.
80
, 72
–80
(1950
). 20.
F.
Stern
and W. E.
Howard
, “Properties of semiconductor surface inversion layers in the electric quantum limit
,” Phys. Rev.
163
, 816
–835
(1967
). 21.
M. V.
Fischetti
and S. E.
Laux
, “Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys
,” J. Appl. Phys.
80
, 2234
–2252
(1996
). 22.
I.
Balslev
, “The influence of high uniaxial stress on the indirect absorption edge in silicon
,” Solid State Commun.
3
, 213
–218
(1965
). 23.
S.
Riskaer
, “Determination of shear deformation potentials from the free-carrier piezobirefringence in germanium and silicon
,” Phys. Rev.
152
, 845
–849
(1966
). 24.
J. E.
Aubrey
, W.
Gubler
, T.
Henningsen
, and S. H.
Koenig
, “Piezoresistance and piezo-Hall-effect in n -type silicon
,” Phys. Rev.
130
, 1667
–1670
(1963
). 25.
J.-S.
Lim
, X.
Yang
, T.
Nishida
, and S. E.
Thompson
, “Measurement of conduction band deformation potential constants using gate direct tunneling current in N-type metal oxide semiconductor field effect transistors under mechanical stress
,” Appl. Phys. Lett.
89
, 073509
(2006
). 26.
A.
Shirkhorshidian
, J. K.
Gamble
, L.
Maurer
, S. M.
Carr
, J.
Dominguez
, G. A.
Ten Eyck
, J. R.
Wendt
, E.
Nielsen
, N. T.
Jacobson
, M. P.
Lilly
, and M. S.
Carroll
, “Spectroscopy of multielectrode tunnel barriers
,” Phys. Rev. Appl.
10
, 044003
(2018
). 27.
H. B.
Michaelson
, “The work function of the elements and its periodicity
,” J. Appl. Phys.
48
, 4729
–4733
(1977
). 28.
This difference in gate metal thickness was unintentionally caused by an error in the e-beam evaporator. We believe this thickness difference is not a significant factor in the results.
29.
We note that this discrimination is temperature dependent. Accessing lower temperatures could reveal disorder-induced modulation of the potential in a device which cannot be seen in measurements at higher temperatures. We do not know to what temperature ( K) our designation of weak disorder extends.
30.
J. G.
Simmons
, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film
,” J. Appl. Phys.
34
, 1793
–1803
(1963
). 31.
W. F.
Brinkman
, R. C.
Dynes
, and J. M.
Rowell
, “Tunneling conductance of asymmetrical barriers
,” J. Appl. Phys.
41
, 1915
–1921
(1970
). 32.
A.
Shirkhorshidian
, N. C.
Bishop
, J.
Dominguez
, R. K.
Grubbs
, J. R.
Wendt
, M. P.
Lilly
, and M. S.
Carroll
, “Transport spectroscopy of low disorder silicon tunnel barriers with and without Sb implants
,” Nanotechnology
26
, 205703
(2015
). 33.
K.
MacLean
, S.
Amasha
, I. P.
Radu
, D. M.
Zumbühl
, M. A.
Kastner
, M. P.
Hanson
, and A. C.
Gossard
, “Energy-dependent tunneling in a quantum dot
,” Phys. Rev. Lett.
98
, 036802
(2007
). 34.
X.
Gao
, D.
Mamaluy
, E.
Nielsen
, R. W.
Young
, A.
Shirkhorshidian
, M. P.
Lilly
, N. C.
Bishop
, M. S.
Carroll
, and R. P.
Muller
, “Efficient self-consistent quantum transport simulator for quantum devices
,” J. Appl. Phys.
115
, 133707
(2014
). 35.
S.
Rochette
, M.
Rudolph
, A.-M.
Roy
, M. J.
Curry
, G. A. T.
Eyck
, R. P.
Manginell
, J. R.
Wendt
, T.
Pluym
, S. M.
Carr
, D. R.
Ward
, M. P.
Lilly
, M. S.
Carroll
, and M.
Pioro-Ladrière
, “Quantum dots with split enhancement gate tunnel barrier control
,” Appl. Phys. Lett.
114
, 083101
(2019
). 36.
M. G.
Borselli
, K.
Eng
, R. S.
Ross
, T. M.
Hazard
, K. S.
Holabird
, B.
Huang
, A. A.
Kiselev
, P. W.
Deelman
, L. D.
Warren
, I.
Milosavljevic
, A. E.
Schmitz
, M.
Sokolich
, M. F.
Gyure
, and A. T.
Hunter
, “Undoped accumulation-mode Si/SiGe quantum dots
,” Nanotechnology
26
, 375202
(2015
). 37.
B.
Zhang
, X.
Li
, and D.
Li
, “Assessment of thermal expansion coefficient for pure metals
,” Calphad
43
, 7
–17
(2013
). 38.
W.
Fang
and C.-Y.
Lo
, “On the thermal expansion coefficients of thin films
,” Sens. Actuators A
84
, 310
–314
(2000
). 39.
F. C.
Nix
and D.
MacNair
, “The thermal expansion of pure metals: Copper, gold, aluminum, nickel, and iron
,” Phys. Rev.
60
, 597
–605
(1941
). 40.
M.
Wagner
, “Structure and thermodynamic properties of nanocrystalline metals
,” Phys. Rev. B
45
, 635
–639
(1992
). 41.
H. J.
Fecht
, “Intrinsic instability and entropy stabilization of grain boundaries
,” Phys. Rev. Lett.
65
, 610
–613
(1990
). 42.
J. A.
Thornton
and D.
Hoffman
, “Stress-related effects in thin films
,” Thin Solid Films
171
, 5
–31
(1989
). 2020
U.S. Government
You do not currently have access to this content.
