PosterPDF Available

Validation of the French metrological Atomic Force Microscope for dimensional nanometrology applications

Authors:

Abstract

To provide traceable dimensional measurements at the nanometer scale, SPM users need to periodically calibrate their instruments. This calibration task is achieved thanks to reference standards like 1D or 2D gratings and/or step heights whose dimensional characteristics have been calibrated by a National Metrology Institute (or ISO/IEC accredited laboratory) using a reference instrument called a metrological Atomic Force Microscope (mAFM). In France, the National Metrology Institute (LNE) developed such an instrument to reach calibration capabilities for these reference standards and to promote the nanometrology activities at the national level. This instrument is fully home-made and directly traceable to the meter SI. This meter definition is ensured by the integration of four differential interferometers with calibrated laser sources which measure in real time the relative position of the sample with respect to the tip. The instrument is based on an immobile AFM head working in a origin detection mode. A three axes piezo-actuated flexure stage supports the sample and produces three translations with low parasitic rotations (±10 µrad). Displacement range reaches 60 μm along X and Y axes and 15 μm along Z axis. The adopted design allow specialising each element of the instrument in a very specific task that can be more easily optimised: for example the scanning stage only generates displacements whereas AFM head only measures the cantilever deflections. The instrument adopts many original technical solutions to drastically reduce drifts and thermal sources that could perturb the measurement. It also compensates in real time for air refractive index fluctuations linked to temperature, pressure and humidity variations which have a strong impact on the position measurement by interferometry. The development was also supported by a heavy task of experimental characterization, in parallel with the development of a virtual instrument and the use of statistical tools like Monte Carlo approach to evaluate all the possible error sources and uncertainty components. This instrument has now provided its first images on several samples of interest like dimensional standards or nanoparticles deposited on flat substrates in order to respectively measure pitch and step height value or their size distribution.
Sébastien Ducourtieux, Younes Boukellal and Paul Ceria
sebastien.ducourtieux@lne.fr
Validation of the French metrological Atomic Force
Microscope for dimensional nanometrology applications
MESURES ET RÉFÉRENCES
VECTEUR DE COMPÉTITIVITÉ
ET DE SÉCURITÉ
1 – Short introduction to the metrological Atomic Force
Microscope (mAFM)
2 – Estimation of the measurement uncertainty through
modelling and Monte Carlo approach
3 – Results for three different samples of interest
4 – Conclusion
2
Topics
21 septembre 2017
1 – Short introduction to the metrological Atomic Force
Microscope (mAFM)
2 – Estimation of the measurement uncertainty through
modelling and Monte Carlo approach
3 – Results for three different samples of interest
4 – Conclusion
3
Topics
21 septembre 2017
4
AFM and SEM traceability
Scanning Probe Microscope (SPM) Scanning Electron Microscope (SEM)
If you want to make your
measurements comparable and
traceable to the SI, you must
calibrate your instruments. Then
you need a standard.
2D grating whose pitch
and step height are
calibrated by a reference
instrument:
a metrological atomic
force microscope
(mAFM)
5
The mAFM
- AFM and mAFM have the same operating principle :
Laser
diode
Quad cell
photodiode
zkF
=
(
)
(
)
( ) ( )
+++
++
=
+++
++
=
DCBA
CADB
DCBA
CDBA
VVVV
VVVV
torsion
VVVV
VVVV
deflection
6
The mAFM
- AFM and mAFM have the same operating principle:
3D cloud of points
Laser
diode
Quad cell
photodiode
Each point has measured coordinates (x,y,z)
- But mAFM additionally has metrological capabilities :
-Its design is optimized for dimensional metrology applications
-It is traceable to the meter definition
-It delivers measurements with an uncertainty
-It integrates calibrated position sensors (laser interferometers)
7
LNE’s metrological Atomic Force Microscope (mAFM)
The LNE metrological Atomic Force
Microscope (mAFM): a reference
instrument traceable to SI meter
S. Ducourtieux and B. Poyet, Meas. Sci. Technol. 22 (2011) 094010
Traceability pyramid mAFM
standard
8
LNE’s metrological Atomic Force Microscope (mAFM)
AFM head
Metrology loop
XYZ scanning stage
Structural frame
9
mAFM metrology loop
x
y
z
The metrology loop is composed of 4 differential interferometers
(Renishaw), 2 Zerodur prisms (one linked to the tip, the other one to the
sample) and 8 mirrors.
S. Ducourtieux and B. Poyet, Meas. Sci. Technol. 22 (2011) 094010
Interferometry is used to
measure and control the
position in closed loop.
mAFM equipped with a dedicated AFM head
mAFM has been equipped with a new AFM head
to better control measurement uncertainties :
no heat source (very stable)
fiber super luminescent diode for detection of
cantilever deflection using optic beam lever
technique
quad cell photodiode replaced by a fiber optic
bundle made of 40000 fibers [1] : Y. Boukellal and al., Meas. Sci. Technol., 26 (2014), 015201
[2] : Y. Boukellal and al ., Meas. Sci. Technol., 26 (2015) 095403
[3] : Younes Boukellal, PhD thesis, July 2015 (ENS Cachan)
10
11
LNE’s metrological atomic force microscope (mAFM)
The LNE metrological Atomic Force
Microscope (mAFM): a reference
instrument traceable to SI meter
mAFM is now operational !
Measurement volume:
60 µm x 60 µm x 15 µm
Maximum sample size:
20 mm x 20 mm x 8 mm
Standard imaged by LNE’s mAFM
Scan size: 9 µm x 9 µm
12
LNE’s metrological atomic force microscope (mAFM)
The LNE metrological Atomic Force
Microscope (mAFM): a reference
instrument traceable to SI meter
mAFM is now operational !
Measurement volume:
60 µm x 60 µm x 15 µm
Maximum sample size:
20 mm x 20 mm x 8 mm
Standard imaged by LNE’s mAFM
Scan size: 9 µm x 9 µm
What is the measurement uncertainty on such standard ?
How do we have estimated this measurement uncertainty ?
Metrological validation of the instrument
Intensive characterization of the instrument (resolution, drift, noise, repeatability, K)
Original configuration for the interferometers with very good performances :
-low noise for position measurement in close loop at 1,5 MHz: 0,3 nm
-stability in position estimated to only few nanometers over one hour.
BUT it is difficult to feel how much sensitive the system is to factors like :
-Parasitic rotations, interferometer misalignment (Abbe error)
-Cosine error
-Non perfect geometry of the prisms (angles of the mirror, shapes and
roughness of the mirror)
-Positioning error
-Basic dilatations
-K
=> This is the reason why we came to a virtual representation of the
metrology system in order to better estimate the uncertainty budget of the
instrument and also to gain knowledge on its behavior.
13
1 – Short introduction to the metrological Atomic Force
Microscope (mAFM)
2 – Estimation of the measurement uncertainty through
modelling and Monte Carlo approach
3 – Results for three different samples of interest
4 – Conclusion
14
Topics
21 septembre 2017
Modelling of the mAFM metrology loop
[1] P. Ceria, PhD thesis, July 2017 (Université Toulouse 3 Paul Sabatier)
[2] P. Ceria et al., , Meas. Sci. Technol. 28 (2017), 034007
In Matlab and using object oriented programming, we have developed a virtual representation
(a model) of the metrology loop of the instruments with the 4 differential interferometers, the 16
beams, the 8 mirrors, the two prisms made of Zerodur.
The homogeneous coordinate formalism is used to translate and rotate each component of the
model and to introduce displacement, misalignment, drift, parasitic rotations K
We have a control over approximatively 140 parameters which can potentially influence the
measurement.
CAD drawing under Solidworks Model under Matlab
15
Modelling of the mAFM metrology loop
[1] P. Ceria, PhD thesis, July 2017 (Université Toulouse 3 Paul Sabatier)
[2] P. Ceria et al., , Meas. Sci. Technol. 28 (2017), 034007
General components :
Range of displacement
Measurement time
Interferometers:
Vacuum wavelength
Edlen correction
• Drift
Temperature, pressure and hygrometry
Dead path error
Resolution limit
• Noise
• Nonlinearity
Beam diameter
• K
Instrument geometry:
Prism shape
Shape and roughness of the mirrors
Parasitic rotations
Abbe error
Cosine error
Non orthogonality error
Thermal expansion
Thermal flexure of the structural frame
16
Link with experimental data
We feed the model with experimental data
Flatness and roughness measurement
using interferometric microscope*
Angular relations between the prism mirror
using the LNE angular platen and
using theodolite system*
*Performed by the Optic Group team from Soleil Synchrotron
Beam intensity profile
Stage Parasitic rotations
Instrument and room thermal stability
Model
17
Implemented statistical tools
[1] P. Ceria, PhD thesis, July 2017 (Université Toulouse 3 Paul Sabatier)
[2] P. Ceria et al., , Meas. Sci. Technol. 28 (2017), 034007
A Monte Carlo approach is used to evaluate the measurement uncertainties:
Complementary tools:
Morri’s plan is used to identify the most influential components by evaluating their
interactions two by two.
Sobol’ indices are used to evaluate the contribution of each parameter to the global
uncertainty.
Definition of the
model parameters
and associated
distribution laws
Random draw of
each parameter to
build the distribution
associated to each
parameter
A configuration (a set of
parameters) is injected
in the model to
evaluate the reached
position (XrYrZr)
105
times
Parallel computing on the
LNE’s cluster to reduce
calculation time
A target position (XYZ)
is defined
Analysis of the
output
distribution for
X-Xr, Y-Yr, Z-Zr
Determination of
the position
uncertainty
ux, uy, uz
18
Récuperer fichier
March 9th - 11th, 2016 19Nanoscale 2016
The results
XYZ positioning uncertainty (combined standard uncertainty) for the
instrument for the full range of displacement (60x60x15 µm3) is
about 8 nm.
Most influential parameters for the full range of displacement
(60x60x15 µm3) :
Parasitic rotations
Abbe offset
Sample thickness
Orthogonally error
Contribution to the global uncertainty in the actual configuration :
75 % coming from Abbe error (parasitic rotations, Abbe
offset and sample height)
24 % coming from the orthogonality error
Abbe error
20
1 – Short introduction to the metrological Atomic Force
Microscope (mAFM)
2 – Estimation of the measurement uncertainty through
modelling and Monte Carlo approach
3 – Results for three different samples of interest
4 – Conclusion
21
Topics
21 septembre 2017
22
Collaboration with C2N and Pollen Metrology
Centre for Nanoscience and
Nanotechnology
Christian Ulysse (christian.ulysse@c2n.upsaclay.fr)
Design and
manufacturing of
structures
Development of
structures and standards
for metrological
applications
Collaboration
23
Development of structures in collaboration with C2N
Standard P900H60:
Pitch : 900 nm
Step height : 60 nm
24
Development of structures in collaboration with C2N
Standard P140H20:
Pitch : 140 nm
Step height : 20 nm
25
Development of structures in collaboration with C2N
Crosses for repositioning:
Pitch : 15 µm
Depth : 30 nm
Modelling of AFM images
[1] P. Ceria, PhD thesis, July 2017 (Université Toulouse 3 Paul Sabatier)
[2] P. Ceria et al., , Meas. Sci. Technol. 28 (2017), 034007
Definition of the
model parameters
and associated
distribution laws
Random draw of
each parameter to
build the distribution
associated to each
parameter
A configuration (a set of
parameters) is injected
in the model to
evaluate the reached
position (XrYrZr)
A target position (XYZ)
is defined
Analysis of the
output
distribution for
X-Xr, Y-Yr, Z-Zr
Determination of
the position
uncertainty
ux, uy, uz
Scanning to get an image (1000 x 1000 pixels)
Virtual sample
Control of the parameters distribution over space and time
128 images of
the sample
Image
processing to
extract
dimensional
properties
Analysis of the
dimensional
property
distribution
Determination of
measurement
uncertainty for
the dimensional
properties
26
Measurement uncertainties evaluated for 3 scenarios:
Scenario 1:
first grating
Scenario 2:
second grating
Scenario 3:
population of nanoparticles
Image size: 10 x 10 µm² Image size: 1,4 x 1,4 µm² Image size: 2 x 2 µm²
2600 nanoparticles
analyzed
evaluated uncertainties are very low and need to be confirmed through a bilateral
comparison with another National Metrology Institute
measurement uncertainties will be increased to few nanometers in a first step
Pitch: 900 +/- 0,5 nm
Height: 60 +/- 0,25
Pitch : 140 +/- 0,15 nm
Height : 20 +/- 0,25
Mean diameter:
25,4 +/- 0,03 nm
27
1 – Short introduction to the metrological Atomic Force
Microscope (mAFM)
2 – Estimation of the measurement uncertainty through
modelling and Monte Carlo approach
3 – Results for three different samples of interest
4 – Conclusion
28
Topics
21 septembre 2017
- mAFM is now operational and able to produce some measurements with an
established uncertainty.
- We can offer :
dimensional measurement of structures with a high level of confidence,
standards (P900H60, P140H20),
calibration services,
Si substrates lithographed with crosses and letters for repositioning,
Si substrates with nanoparticles deposited on,
a unique package (standard + calibration + dedicated software) thanks
to the collaboration with C2N and Pollen Metrology.
- For more information, please contact M. Georges Favre: georges.favre@lne.fr
29
In conclusion
30
Thank you for your attention
ResearchGate has not been able to resolve any citations for this publication.
  • P Ceria
P. Ceria et al.,, Meas. Sci. Technol. 28 (2017), 034007