A method for the automated extraction of the short-range part of the probe-surface interaction from force spectroscopy curves is presented. Our algorithm consists of two stages: the first stage determines a boundary that separates the region where the short-range interaction is dominantly acting on the probe and a second stage that finds the parameters to fit the interaction over the long-range region. We applied this method to force spectroscopy maps acquired over the Si(111)-(7×7) surface and found, as a result, a faint pattern on the short-range interaction for one of the probes used in the experiments, which would have probably been obviated using human-supervised fitting strategies.

1.
J.
Hwangbo
,
J.
Lee
,
A.
Dosovitskiy
,
D.
Bellicoso
,
V.
Tsounis
,
V.
Koltun
, and
M.
Hutter
, “
Learning agile and dynamic motor skills for legged robots
,”
Sci. Rob.
4
,
eaau5872
(
2019
).
2.
S.
Gu
,
E.
Holly
,
T.
Lillicrap
, and
S.
Levine
, “
Deep reinforcement learning for robotic manipulation with asynchronous off-policy updates
,” arXiv:1610.00633 (
2016
).
3.
S.
Thrun
, “
Robotic mapping: A survey
,”
Exploring Artificial Intelligence in the New Millennium
(
Morgan Kaufmann Publishers Inc
.,
San Francisco, CA, USA
,
2003
), pp.
1
35
.
4.
G. F.
Elsayed
,
S.
Shankar
,
B.
Cheung
,
N.
Papernot
,
A.
Kurakin
,
I.
Goodfellow
, and
J.
Sohl-Dickstein
, “
Adversarial examples that fool both computer vision and time-limited humans
,” arXiv:1802.08195 (
2018
).
5.
D.
Bahdanau
,
K.
Cho
, and
Y.
Bengio
, “
Neural machine translation by jointly learning to align and translate
,” arXiv:1409.0473 (
2014
).
6.
D.
Silver
,
A.
Huang
,
C. J.
Maddison
,
A.
Guez
,
L.
Sifre
,
G.
van den Driessche
,
J.
Schrittwieser
,
I.
Antonoglou
,
V.
Panneershelvam
,
M.
Lanctot
,
S.
Dieleman
,
D.
Grewe
,
J.
Nham
,
N.
Kalchbrenner
,
I.
Sutskever
,
T.
Lillicrap
,
M.
Leach
,
K.
Kavukcuoglu
,
T.
Graepel
, and
D.
Hassabis
, “
Mastering the game of go with deep neural networks and tree search
,”
Nature
529
,
484
489
(
2016
).
7.
K. J.
Bergen
,
P. A.
Johnson
,
M. V.
de Hoop
, and
G. C.
Beroza
, “
Machine learning for data-driven discovery in solid earth geoscience
,”
Science
363
,
eaau0323
(
2019
).
8.
J.
Zhang
,
H. S.
Naik
,
T.
Assefa
,
S.
Sarkar
,
R. V. C.
Reddy
,
A.
Singh
,
B.
Ganapathysubramanian
, and
A. K.
Singh
, “
Computer vision and machine learning for robust phenotyping in genome-wide studies
,”
Sci. Rep.
7
,
44048
(
2017
).
9.
Y.
Gurovich
,
Y.
Hanani
,
O.
Bar
,
G.
Nadav
,
N.
Fleischer
,
D.
Gelbman
,
L.
Basel-Salmon
,
P. M.
Krawitz
,
S. B.
Kamphausen
,
M.
Zenker
,
L. M.
Bird
, and
K. W.
Gripp
, “
Identifying facial phenotypes of genetic disorders using deep learning
,”
Nat. Med.
25
,
60
64
(
2019
).
10.
P.
Raccuglia
,
K. C.
Elbert
,
P. D. F.
Adler
,
C.
Falk
,
M. B.
Wenny
,
A.
Mollo
,
M.
Zeller
,
S. A.
Friedler
,
J.
Schrier
, and
A. J.
Norquist
, “
Machine-learning-assisted materials discovery using failed experiments
,”
Nature
533
,
73
76
(
2016
).
11.
J.
Ren
,
N. A.
Ahlgren
,
Y. Y.
Lu
,
J. A.
Fuhrman
, and
F.
Sun
, “
VirFinder: A novel k-mer based tool for identifying viral sequences from assembled metagenomic data
,”
Microbiome
5
,
69
(
2017
).
12.
M.
de Jong
,
W.
Chen
,
R.
Notestine
,
K.
Persson
,
G.
Ceder
,
A.
Jain
,
M.
Asta
, and
A.
Gamst
, “
A statistical learning framework for materials science: Application to elastic moduli of k-nary inorganic polycrystalline compounds
,”
Sci. Rep.
6
,
34256
(
2016
).
13.
L.
Ward
,
A.
Agrawal
,
A.
Choudhary
, and
C.
Wolverton
, “
A general-purpose machine learning framework for predicting properties of inorganic materials
,”
npj Comput. Mater.
2
,
16028
(
2016
).
14.
V.
Botu
and
R.
Ramprasad
, “
Adaptive machine learning framework to accelerate ab initio molecular dynamics
,”
Int. J. Quantum Chem.
115
,
1074
1083
(
2015
).
15.
L.
Ward
,
A.
Agrawal
,
A.
Choudhary
, and
C.
Wolverton
, “
A general-purpose machine learning framework for predicting properties of inorganic materials
,”
Comput. Mater.
2
,
16028
(
2016
).
16.
A.
Khorshidi
and
A. A.
Peterson
, “
Amp: A modular approach to machine learning in atomistic simulations
,”
Comput. Phys. Commun.
207
,
310
324
(
2016
).
17.
A. P.
Bartók
,
S.
De
,
C.
Poelking
,
N.
Bernstein
,
J. R.
Kermode
,
G.
Csányi
, and
M.
Ceriotti
, “
Machine learning unifies the modeling of materials and molecules
,”
Sci. Adv.
3
,
e1701816
(
2017
).
18.
R.
Gómez-Bombarelli
,
J.
Aguilera-Iparraguirre
,
T. D.
Hirzel
,
D.
Duvenaud
,
D.
Maclaurin
,
M. A.
Blood-Forsythe
,
H. S.
Chae
,
M.
Einzinger
,
D.-G.
Ha
,
T.
Wu
,
G.
Markopoulos
,
S.
Jeon
,
H.
Kang
,
H.
Miyazaki
,
M.
Numata
,
S.
Kim
,
W.
Huang
,
S. I.
Hong
,
M.
Baldo
,
R. P.
Adams
, and
A.
Aspuru-Guzik
, “
Design of efficient molecular organic light-emitting diodes by a high-throughput virtual screening and experimental approach
,”
Nat. Mater.
15
,
1120
1127
(
2016
).
19.
N. E.
Jackson
,
A. S.
Bowen
,
L. W.
Antony
,
M. A.
Webb
,
V.
Vishwanath
, and
J. J.
de Pablo
, “
Electronic structure at coarse-grained resolutions from supervised machine learning
,”
Sci. Adv.
5
,
eaav1190
(
2019
).
20.
B.
Alldritt
,
P.
Hapala
,
N.
Oinonen
,
F.
Urtev
,
O.
Krejci
,
F.
Federici Canova
,
J.
Kannala
,
F.
Schulz
,
P.
Liljeroth
, and
A. S.
Foster
, “
Automated structure discovery in atomic force microscopy
,”
Sci. Adv.
6
,
eaay6913
(
2020
).
21.
M.
Rashidi
and
R. A.
Wolkow
, “
Autonomous scanning probe microscopy in situ tip conditioning through machine learning
,”
ACS Nano
12
,
5185
5189
(
2018
).
22.
O.
Gordon
and
P.
Moriarty
, “
Machine learning at the (sub)atomic scale: Next generation scanning probe microscopy
,”
Mach. Learn.
1
,
023001
(
2020
).
23.
Noncontact Atomic Force Microscopy
, edited by
S.
Morita
,
R.
Wiesendanger
, and
E.
Meyer
(
Springer
,
2002
).
24.
Noncontact Atomic Force Microscopy
, edited by
S.
Morita
,
R.
Wiesendanger
, and
F. J.
Giessibl
(
Springer
,
2009
), Vol.
2
.
25.
Noncontact Atomic Force Microscopy
, edited by
S.
Morita
,
F. J.
Giessibl
, and
E.
Meyer
(
Springer
,
2015
), Vol.
3
.
26.
T. R.
Albrecht
,
P.
Grutter
,
D.
Horne
, and
D.
Rugar
,
J. Appl. Phys.
69
,
668
673
(
1991
).
27.
M. A.
Lantz
,
H. J.
Hug
,
R.
Hoffmann
,
P. J. A.
van Schendel
,
P.
Kappenberger
,
S.
Martin
,
A.
Baratoff
, and
H. J.
Guntherodt
, “
Quantitative measurement of short-range chemical bonding forces
,”
Science
291
,
2580
2583
(
2001
).
28.
M.
Abe
,
Y.
Sugimoto
,
O.
Custance
, and
S.
Morita
, “
Room-temperature reproducible spatial force spectroscopy using atom-tracking technique
,”
Appl. Phys. Lett.
87
,
173503
(
2005
).
29.
M.
Abe
,
Y.
Sugimoto
,
T.
Namikawa
,
K.
Morita
,
N.
Oyabu
, and
S.
Morita
, “
Drift-compensated data acquisition performed at room temperature with frequency modulation atomic force microscopy
,”
Appl. Phys. Lett.
90
,
203103
(
2007
).
30.
Y.
Sugimoto
,
T.
Namikawa
,
K.
Miki
,
M.
Abe
, and
S.
Morita
, “
Vertical and lateral force mapping on the Si(111)-(7 × 7) surface by dynamic force microscopy
,”
Phys. Rev. B
77
,
195424
(
2008
).
31.
M.
Ternes
,
C. P.
Lutz
,
C. F.
Hirjibehedin
,
F. J.
Giessibl
, and
A. J.
Heinrich
, “
The force needed to move an atom on a surface
,”
Science
319
,
1066
1069
(
2008
).
32.
R.
Pérez
,
M. C.
Payne
,
I.
Štich
, and
K.
Terakura
, “
Role of covalent tip-surface interactions in noncontact atomic force microscopy on reactive surfaces
,”
Phys. Rev. Lett.
78
,
678
681
(
1997
).
33.
L.
Gross
,
F.
Mohn
,
N.
Moll
,
P.
Liljeroth
, and
G.
Meyer
, “
The chemical structure of a molecule resolved by atomic force microscopy
,”
Science
325
,
1110
1114
(
2009
).
34.
F. J.
Giessibl
, “
Physical interpretation of frequency-modulation atomic force microscopy
,”
Phys. Rev. B
61
,
9968
9971
(
2000
).
35.
J. E.
Sader
and
S. P.
Jarvis
, “
Accurate formulas for interaction force and energy in frequency modulation force spectroscopy
,”
Appl. Phys. Lett.
84
,
1801
(
2004
).
36.
S.
Kuhn
, “
Discriminating short-range from van der waals forces using total force data in noncontact atomic force microscopy
,”
Phys. Rev. B
89
,
235417
(
2014
).
37.
A.
Sweetman
and
A.
Stannard
, “
Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces
,”
Beilstein J. Nanotechnol.
5
,
386
393
(
2014
).
38.
P.
Baldi
,
IEEE Trans. Neural Networks
6
,
182
195
(
1995
).
39.
S.
Ruder
, “
An overview of gradient descent optimization algorithms
,” CoRR abs/1609.04747, arXiv:1609.04747 (
2016
).
40.
N.
Otsu
, “
A threshold selection method from gray-level histograms
,”
IEEE Trans. Syst., Man, Cybern.
9
,
62
66
(
1979
).
41.

It is important that E1st contains two terms. Although Δf̃FIT should be calculated in the range of z>z̃0, it is uncertain whether z>z̃0 is the most likely value at the initial part of the first stage. In the first state, we set the initial value of z̃0 close to zMAX so that the second term dominates initially. This enables the first stage calculation to finish quickly. w0(z) has the effect of bringing z0 close to the sample surface.

42.
D. P.
Kingma
and
J.
Ba
, “
Adam: A method for stochastic optimization
,” CoRR abs/1412.6980, arXiv:1412.6980 (
2014
).
43.
See https://www.tensorflow.org/ for the Adam optimizer module in Python API.
44.
D.
Rugar
,
H. J.
Mamin
, and
P.
Guethner
,
Appl. Phys. Lett.
55
,
2588
2590
(
1989
).
45.
A.
Yurtsever
,
Y.
Sugimoto
,
H.
Tanaka
,
M.
Abe
,
S.
Morita
,
M.
Ondráček
,
P.
Pou
,
R.
Pérez
, and
P.
Jelínek
, “
Force mapping on a partially H-covered Si(111)-(7 × 7) surface: Influence of tip and surface reactivity
,”
Phys. Rev. B
87
,
155403
(
2013
).
46.
R.
Bechstein
,
C.
González
,
J.
Schütte
,
P.
Jelínek
,
R.
Pérez
, and
A.
Kühnle
, “
‘All-inclusive’ imaging of the rutile TiO2(110) surface using NC-AFM
,”
Nanotechnology
20
,
505703
(
2009
).
47.
J.
Welker
and
F. J.
Giessibl
, “
Revealing the angular symmetry of chemical bonds by atomic force microscopy
,”
Science
336
,
444
449
(
2012
).
48.
Y.
Sugimoto
,
P.
Pou
,
O.
Custance
,
P.
Jelinek
,
M.
Abe
,
R.
Perez
, and
S.
Morita
, “
Complex patterning by vertical interchange atom manipulation using atomic force microscopy
,”
Science
322
,
413
417
(
2008
).
49.
K.
Yamasue
,
M.
Abe
,
Y.
Sugimoto
, and
Y.
Cho
, “
Atomic-dipole-moment induced local surface potential on Si(111)-(7 × 7) surface studied by non-contact scanning nonlinear dielectric microscopy
,”
Appl. Phys. Lett.
105
,
121601
(
2014
).
50.
See https://pypi.org/project/errandpy/ for a basic usage to extract the short-range force.
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