We propose an approach for the characterization of scanning thermal microscopy (SThM) probe response using a sample with silicon dioxide steps. The chessboard-like sample provides a series of nine surfaces made of the same material, with identical roughness, but consisting of different thicknesses of silica layers standing on a single silicon wafer. The nine regions have different effective thermal conductivities, allowing the calibration of SThM probes within a given set of surface conditions. A key benefit is the possibility of comparing the spatial resolution and the sensitivity to vertical inhomogeneities of the sample for different probes. A model is provided to determine the thermal contact area and contact thermal resistance from the experimental data. The results underline that ballistic heat conduction can be significant in crystalline substrates below the top thin films, especially for film thicknesses lower than 200 nm and effective thermal contact radius lower than 200 nm. They also highlight the sensitivity of SThM to ultrathin films, as well as the substrate below micrometric films under in-air conditions but not when in vacuum. This work advances quantitative nanometer-scale thermal metrology, where usual photothermal methods are more difficult to implement.
REFERENCES
1.
C.
Dames
, Annu. Rev. Heat Transfer
16
, 7
–49
(2013
). 2.
E.
Pop
, D. A.
Mann
, K. E.
Goodson
, and H.
Dai
, J. Appl. Phys.
101
(9
), 093710
(2007
). 3.
T.
Phan
, S.
Dilhaire
, V.
Quintard
, W.
Claeys
, and J.
Batsale
, Microelectron. J.
29
, 181
–190
(1998
). 4.
D. I.
Florescu
, V. M.
Asnin
, F. H.
Pollak
, R. J.
Molnar
, and C. E. C.
Wood
, J. Appl. Phys.
88
(6
), 3295
–3300
(2000
). 5.
Y.
Hu
, L.
Zeng
, A.
Minnich
, M. S.
Dresselhaus
, and G.
Chen
, Nat. Nanotech.
10
, 701
–706
(2015
).6.
S.
Gomès
, A.
Assy
, and P. O.
Chapuis
, Phys. Status Solidi A
212
(3
), 477
–494
(2015
). 7.
W.
Jeong
, S.
Hur
, E.
Meyhofer
, and P.
Reddy
, Nanoscale Microscale Thermophys. Eng.
19
(4
), 279
–302
(2015
). 8.
Y.
Zhang
, W.
Zhu
, F.
Hui
, M.
Lanza
, T.
Borca-Tasciuc
, and M.
Muñoz Rojo
, Adv. Funct. Mater.
30
(18
), 1900892
(2020
). 9.
F.
Menges
, H.
Riel
, A.
Stemmer
, C.
Dimitrakopoulos
, and B.
Gotsmann
, Phys. Rev. Lett.
111
(20
), 205901
(2013
). 10.
S.
Pailhès
, H.
Euchner
, V. M.
Giordano
, R.
Debord
, A.
Assy
, S.
Gomès
, A.
Bosak
, D.
Machon
, S.
Paschen
, and M.
De Boissieu
, Phys. Rev. Lett.
113
(2
), 025506
(2014
). 11.
P.
Newby
, B.
Canut
, J. M.
Bluet
, S.
Gomès
, M.
Isaiev
, R.
Burbelo
, K.
Termentzidis
, P.
Chantrenne
, L.
Frechette
, and V.
Lysenko
, J. Appl. Phys.
114
(1
), 014903
–014909
(2013
). 12.
S.
Gomès
, L.
David
, V.
Lysenko
, A.
Descamps
, T.
Nychyporuk
, and M.
Raynaud
, J. Phys. D Appl. Phys.
40
, 6677
–6683
(2007
). 13.
J. L.
Bosse
, M.
Timofeeva
, P. D.
Tovee
, B. J.
Robinson
, B. D.
Huey
, and O. V.
Kolosov
, J. Appl. Phys.
116
(13
), 134904
(2014
). 14.
A. M.
Massoud
, J. M.
Bluet
, V.
Lacatena
, M.
Haras
, J. F.
Robillard
, and P. O.
Chapuis
, Appl. Phys. Lett.
111
(6
), 063106
(2017
). 15.
E.
Puyoo
, S.
Grauby
, J. M.
Rampnoux
, E.
Rouvière
, and S.
Dilhaire
, J. Appl. Phys.
109
(2
), 024302
(2011
). 16.
JCGM 2012 International Vocabulary of Metrology, see www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf for “Basic and general concepts and associated terms (VIM).”
17.
A. A.
Wilson
and T.
Borca-Tasciuc
, Rev. Sci. Instrum.
88
, 074903
(2017
). 18.
B. D.
Iverson
, J. E.
Blendell
, and S. V.
Garimella
, Rev. Sci. Instrum.
81
, 036111
(2010
). 19.
S.
Lefevre
, S.
Volz
, J. B.
Saulnier
, C.
Fuentes
, and N.
Trannoy
, Rev. Sci. Instrum.
74
(4
), 2418
–2423
(2003
). 20.
E.
Guen
, P.-O.
Chapuis
, N. J.
Kaur
, P.
Klapetek
, and S.
Gomès
, “Impact of roughness on heat conduction involving nanocontacts
,” Appl. Phys. Lett.
(unpublished).21.
S.
Lefèvre
and S.
Volz
, Rev. Sci. Instrum.
76
(3
), 033701
(2005
). 22.
23.
L.
David
, S.
Gomès
, and M.
Raynaud
, J. Phys. D Appl. Phys.
40
, 4337
–4346
(2007
). 24.
25.
26.
T. P.
Nguyen
, L.
Thiery
, S.
Euphrasie
, S.
Gomès
, B.
Hay
, and P.
Vairac
, Rev. Sci. Instrum.
90
(11
), 114901
(2019
). 27.
R. B.
Dinwiddie
, R. J.
Pylkki
, and P. E.
West
, Therm. Conduct.
22
, 668
–668
(1993
).28.
P. S.
Dobson
, J. M.
Weaver
, and G.
Mills
, Sens. IEEE
2007
, 708
–711
(2007
).29.
M.
Hinz
, O.
Marti
, B.
Gotsmann
, M. A.
Lantz
, and U.
Dürig
, Appl. Phys. Lett.
92
(4
), 043122
(2008
). 30.
A.
Al Mohtar
, G.
Tessier
, R.
Ritasalo
, M.
Matvejeff
, J.
Stormonth-Darling
, P. S.
Dobson
, P. O.
Chapuis
, S.
Gomès
, and J. P.
Roger
, Thin Solid Films
642
, 157
–162
(2017
). 31.
M. M.
Yovanovich
, J. R.
Culham
, and P.
Teertstra
, IEEE Trans. Compon. Packag. Manuf. Technol. Part A
21
(1
), 168
–176
(1998
). 32.
J. R.
Dryden
, J. Heat Transfer
105
(2
), 408
(1983
). 33.
Y. S.
Muzychka
, M. R.
Sridhar
, M. M.
Yovanovich
, and V. W.
Antonetti
, J. Thermophys. Heat Transf.
13
(4
), 489
–494
(1999
).34.
F.
Menges
, H.
Riel
, A.
Stemmer
, C.
Dimitrakopoulos
, and B.
Gotsmann
, Phys. Rev. Lett.
111
, 205901
(2013
). 35.
The average mean free path Λsub can be determined by inverting the spectral kinetic expression of thermal conductivity , with where is the (polarization-dependent spectral) heat capacity and is the (polarization-dependent spectral) velocity of the phonons in the isotropic dispersion assumption. Depending on the fit of the dispersion curve, the value is close to 170–185 nm. Here, we take Λsub = 170 nm.
36.
G.
Wexler
, Proc. Phys. Soc.
89
(4
), 927
–941
(1966
). 37.
Y. V.
Sharvin
, Sov. Phys. JETP
21
, 655
(1965
).38.
B.
Nikolić
and P. B.
Allen
, Phys. Rev. B
60
(6
), 3963
(1999
). 39.
A.
Assy
, S.
Lefèvre
, P. O.
Chapuis
, and S.
Gomès
, J. Phys. D Appl. Phys.
47
(44
), 442001
(2014
). 40.
S.
Lefèvre
, J. B.
Saulnier
, C.
Fuentes
, and S.
Volz
, Superlattices Microstruct.
35
(3–6
), 283
–288
(2004
). 41.
S.
Lefèvre
, Ph.D. thesis
(University of Lyon
, 2004
).42.
E.
Guen
, Ph.D thesis
(University of Lyon
, 2020
).43.
P.
Tovee
, M.
Pumarol
, D.
Zeze
, K.
Kjoller
, and O.
Kolosov
, J. Appl. Phys.
112
(11
), 114317
(2012
). 44.
A.
Assy
and S.
Gomès
, Nanotechnology
26
(35
), 355401
(2015
). 45.
C. T.
Gibson
, G. S.
Watson
, and S.
Myhra
, Nanotechnology
7
(3
), 259
(1996
). 46.
M.
Chirtoc
, J.
Bodzenta
, and A.
Kaźmierczak-Bałata
, Int. J. Heat Mass Transfer
156
, 119860
(2020
). 47.
A.
Alkurdi,
E.
Guen
et al, “Resistive-thermometry scanning thermal microscopy: Combined experimental/numerical approaches for thermal studies of nano-objects
,” J. Phys. Cond. Mat.
(unpublished). 48.
J.
Bodzenta
, J.
Juszczyk
, A.
Kaźmierczak-Bałata
, P.
Firek
, A.
Fleming
, and M.
Chirtoc
, Int. J. Thermophys.
37
(7
), 73
(2016
). 49.
K.
Kim
, J.
Chung
, G.
Hwang
, O.
Kwon
, and J. S.
Lee
, ACS Nano
5
(11
), 8700
–8709
(2011
). 50.
J.
Spiece
, C.
Evangeli
, K.
Lulla
, A.
Robson
, B.
Robinson
, and O.
Kolosov
, J. Appl. Phys.
124
(1
), 015101
(2018
). © 2020 Author(s).
2020
Author(s)
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