This paper aimed at identifying the error sources that occur in dimensional measurements performed using atomic force microscopy. In particular, a set of characterization techniques for errors quantification is presented. The discussion on error sources is organized in four main categories: scanning system, tip-surface interaction, environment, and data processing. The discussed errors include scaling effects, squareness errors, hysteresis, creep, tip convolution, and thermal drift. A mathematical model of the measurement system is eventually described, as a reference basis for errors characterization, with an applicative example on a reference silicon grating.

1.
De Chiffre
,
L.
,
Kunzmann
,
H.
,
Peggs
,
G. N.
, and
Lucca
,
D. A.
, 2003, “
Surfaces in Precision Engineering, Microengineering and Nanotechnology
,”
CIRP Ann.
0007-8506,
52
(
2
), pp.
561
577
.
2.
Bruzzone
,
A. A. G.
,
Costa
,
H. L.
,
Lonardo
,
P. M.
, and
Lucca
,
D. A.
, 2008, “
Advances in Engineered Surfaces for Functional Performance
,”
CIRP Ann.
0007-8506,
57
(
2
), pp.
750
769
.
3.
Kawasegi
,
N.
,
Takano
,
N.
,
Oka
,
D.
,
Morita
,
N.
,
Yamada
,
S.
,
Kanda
,
K.
,
Takano
,
S.
,
Obata
,
T.
, and
Ashida
,
K.
, 2006, “
Nanomachining of Silicon Surface Using Atomic Force Microscope With Diamond Tip
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
128
(
3
), pp.
723
729
.
4.
Uppal
,
N.
, and
Shiakolas
,
P. S.
, 2009, “
Process Sensitivity Analysis and Resolution Prediction for the Two Photon Polymerization of Micro/Nano Structures
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
131
(
5
), p.
051018
.
5.
Marinello
,
F.
,
Savio
,
E.
,
Bariani
,
P.
, and
Carmignato
,
S.
, 2009, “
Coordinate Metrology Using Scanning Probe Microscopes (SPMs)
,”
Meas. Sci. Technol.
0957-0233,
20
(
8
), p.
084002
.
6.
Danzebrink
,
H. U.
,
Koenders
,
L.
,
Wilkening
,
G.
,
Yacoot
,
A.
, and
Kunzmann
,
H.
, 2006, “
Advances in Scanning Force Microscopy for Dimensional Metrology
,”
CIRP Ann.
0007-8506,
55
(
2
), pp.
841
878
.
7.
Dixson
,
R.
,
Koning
,
R.
,
Fu
,
J.
,
Vorburger
,
T.
, and
Renegar
,
B.
, 2000, “
Accurate Dimensional Metrology With Atomic Force Microscopy
,”
Proc. SPIE
0277-786X
3998
, pp.
362
368
.
8.
Misumi
,
I.
,
Gonda
,
S.
,
Huang
,
Q.
,
Keem
,
T.
,
Kurosawa
,
T.
,
Fujii
,
A.
,
Hisata
,
N.
,
Yamagishi
,
T.
,
Fujimoto
,
H.
,
Enjoji
,
K.
,
Aya
,
S.
, and
Sumitani
,
H.
, 2005, “
Sub-Hundred Nanometre Pitch Measurements Using an AFM With Differential Laser Interferometers for Designing Usable Lateral Scales
,”
Meas. Sci. Technol.
0957-0233,
16
, pp.
2080
2090
.
9.
Tocha
,
E.
,
Schönherr
,
H.
, and
Vancso
,
J. G.
, 2006, “
Quantitative Nanotribology by AFM: A Novel Universal Calibration Platform
,”
Langmuir
0743-7463,
22
(
5
), pp.
2340
2350
.
10.
Shegaonkar
,
A. C.
, and
Salapaka
,
S. M.
, 2007, “
Feedback Based Simultaneous Correction of Imaging Artifacts Due to Geometrical and Mechanical Cross-Talk and Tip-Sample Stick in Atomic Force Microscopy
,”
Rev. Sci. Instrum.
0034-6748,
78
(
10
), p.
103706
.
11.
Marinello
,
F.
,
Bariani
,
P.
,
De Chiffre
,
L.
, and
Savio
,
E.
, 2007, “
Fast Technique for AFM Vertical Drift Compensation
,”
Meas. Sci. Technol.
0957-0233,
18
(
3
), pp.
689
696
.
12.
Griffith
,
J. E.
, and
Grigg
,
D. A.
, 1993, “
Dimensional Metrology With Scanning Probe Microscopes
,”
J. Appl. Phys.
0021-8979,
74
(
9
), pp.
R83
R109
.
13.
Leang
,
K. K.
, and
Devasia
,
S.
, 2007, “
Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
15
(
5
), pp.
927
935
.
14.
Croft
,
D.
,
Shed
,
G.
, and
Devasia
,
S.
, 2001, “
Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
123
(
1
), pp.
35
43
.
15.
Edwards
,
H.
, and
McGlothlin
,
R.
, 1998, “
Vertical Metrology Using Scanning Probe Microscopes: Imaging Distortions and Measurement Repeatability
,”
J. Appl. Phys.
0021-8979,
83
(
8
), pp.
3952
3971
.
16.
Kühle
,
A.
,
Sorensen
,
A. H.
,
Zandbergen
,
J. B.
, and
Bohr
,
J.
, 1998, “
Contrast Artifacts in Tapping Tip Atomic Force Microscopy
,”
Appl. Phys. A
0947-8396,
66
, pp.
S329
S332
.
17.
Villarrubia
,
J. S.
, 1997, “
Algorithms for Scanned Probe Microscope Image Simulation, Surface Reconstruction, and Tip Estimation
,”
J. Res. Natl. Inst. Stand. Technol.
1044-677X,
102
(
4
), pp.
425
454
.
18.
Orji
,
N. G.
,
Vorburger
,
T. V.
,
Fu
,
J.
,
Dixson
,
R. G.
,
Nguyen
,
C. V.
, and
Raja
,
J.
, 2005, “
Line Edge Roughness Metrology Using Atomic Force Microscopes
,”
Meas. Sci. Technol.
0957-0233,
16
, pp.
2147
2154
.
19.
Frost
,
F.
,
Hirsch
,
D.
,
Schindler
,
A.
, and
Rauschenbach
,
B.
, 2001, “
AFM Tip Calibration Using Nanometer-Sized Structures Induced by Ion Beam Sputtering
,”
Proc. SPIE
0277-786X,
4449
, pp.
225
234
.
20.
Wang
,
Y.
, and
Chen
,
X.
, 2007, “
Carbon Nanotubes: A Promising Standard for Quantitative Evaluation of AFM Tip Apex Geometry
,”
Ultramicroscopy
0304-3991,
107
(
4–5
), pp.
293
298
.
21.
Mokaberi
,
B.
, and
Requicha
,
A. A. G.
, 2004, “
Towards Automatic Nanomanipulation: Drift Compensation in Scanning Probe Microscopes
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
416
421
.
22.
Savio
,
E.
,
Marinello
,
F.
,
Bariani
,
P.
, and
Carmignato
,
S.
, 2007, “
Feature-oriented Measurement Strategy in Atomic Force Microscopy
,”
CIRP Ann.
0007-8506,
56
(
1
), pp.
557
560
.
23.
Tsuji
,
T.
,
Kobari
,
K.
,
Ide
,
S.
, and
Yamanaka
,
K.
, 2007, “
Suppression of Spurious Vibration of Cantilever in Atomic Force Microscopy by Enhancement of Bending Rigidity of Cantilever Chip Substrate
,”
Rev. Sci. Instrum.
0034-6748,
78
(
10
), pp.
103703
.
24.
Balasubramanian
,
A.
,
Jun
,
M. B. G.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
, 2008, “
A Submicron Multiaxis Positioning Stage for Micro- and Nanoscale Manufacturing Processes
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
130
(
3
), p.
031112
.
25.
Sader
,
J. E.
,
Chon
,
J. W. M.
, and
Mulvaney
,
P.
, 1999, “
Calibration of Rectangular Atomic Force Microscope Cantilevers
,”
Rev. Sci. Instrum.
0034-6748,
70
(
10
), pp.
3967
3969
.
26.
Song
,
Y.
, and
Bhushan
,
B.
, 2008, “
Atomic Force Microscopy Dynamic Modes: Modeling and Applications
,”
J. Phys.: Condens. Matter
0953-8984,
20
, p.
225012
.
27.
Gainutdinov
,
R. V.
, and
Arutyunov
,
P. A.
, 2001, “
Artifacts in Atomic Force Microscopy
,”
Russian Microelectronics
,
30
(
4
), pp.
219
224
.
28.
Velegol
,
S. B.
, 2004,
Atomic Force Microscopy Imaging Artifacts
(
Dekker Encyclopedia of Nanoscience and Nanotechnology
),
J. A.
Schwarz
,
C. I.
Contescu
, and
K.
Putyera
, eds.,
CRC
,
Boca Raton, FL
, Vol.
1
, pp.
143
153
.
29.
Marinello
,
F.
, 2007, “
Atomic Force Microscopy in Nanometrology: Modeling and Enhancement of the Instrument
,” Ph.D. thesis, University of Padova and Technical University of Denmark, Padova, Italy and Lyngby, Denmark.
30.
Marinello
,
F.
, and
Savio
,
E.
, 2007, “
Use of Cylindrical Artifacts for AFM vertical calibration
,”
Meas. Sci. Technol.
0957-0233,
18
(
2
), pp.
462
468
.
31.
Garnaes
,
J.
,
Kofod
,
N.
,
Kühle
,
A.
,
Nielsen
,
C.
,
Dirscherl
,
K.
, and
Blunt
,
L.
, 2003, “
Calibration of Step Heights and Roughness Measurements With Atomic Force Microscopes
,”
Precis. Eng.
0141-6359,
27
(
1
), pp.
91
98
.
32.
Garnaes
,
J.
,
Kule
,
A.
,
Nielsen
,
L.
, and
Borsetto
,
F.
, 2004, “
True Three-Dimensional Calibration of Closed Loop Scanning Probe Microscopes
,”
Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro- and Nanometer Range
,
G.
Wilkening
and
L.
Koenders
, eds.,
Wiley-VCH
,
Berlin
, pp.
193
204
.
33.
Hansen
,
H. N.
,
Carneiro
,
K.
,
Haitjema
,
H.
, and
De Chiffre
,
L.
, 2006, “
Dimensional Micro and Nano Metrology
,”
CIRP Ann.
0007-8506,
55
(
2
), pp.
721
743
.
34.
Dixson
,
R. G.
,
Allen
,
R. A.
,
Guthrie
,
W. F.
, and
Cresswell
,
M. W.
, 2005, “
Traceable Calibration of Critical-Dimension Atomic Force Microscope Linewidth Measurements With Nanometer Uncertainty
,”
J. Vac. Sci. Technol. B
1071-1023,
23
(
6
), pp.
3028
3032
.
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