Minimization of Abbe error on the LNE’s metrological AFM by alignment of
interferometer laser beams using a CCD camera
S. Ducourtieux, D. Ahamed, A. Delvallée
LNE – DMSI – Nanometrology, 29 avenue Roger Hennequin, 78197 Trappes - France
type Notation unity ui Rank
-positioning of the alignment setup on the metrological AFM A u1 µm 101 2
-positioning of the Zerodur prism on the metrological AFM B u2 µm 10
-positioning of AFM tip on the tip holder B u3 µm 2
of the tip holder on the metrological AFM head
-positioning of the metrological AFM head A u5 µm 11
inclination with respect to Abbe plan
Determination of the measurement axis of
the interferometer B u8 µm 300 1
positioning with micrometer screw B u9 µm 5
misalignment during the clamping step A u10 µm 15
B u11 µm 30 5
alignment B u12 µm 55.6 3
Camera pixel size calibration
B u13 µm 0,001
Fit of the beam profile for
thickness B u15 µm 50 4
Accuracy of the
spot position detection using the developed software B u16 µm 5.56
LNE’s metrological AFM:
In 2018, LNE’s metrological atomic force microscope (mAFM) performed its very first calibrations on standards developed at LNE (P600H60) in collaboration with C2N
(Centre for Nanoscience and Nanotechnology). It provides a French traceability route to the SI meter for dimensional measurement at nanometer scale for calibration of
standards commonly used in scanning probe and scanning electron microscopy. To measure in real time the position of the tip relative to the sample, the mAFM uses four
double path differential interferometers whose He-Ne laser sources are frequency-calibrated. The measurement uncertainty of the mAFM was evaluated using a model of the
metrology loop and a Monte Carlo approach and is estimated to +/- 2 nm and +/- 1 nm (k=2) for respectively P900H60 pitch and step height. The several studies conducted
show that the main source of uncertainty for the positioning of the instrument comes from Abbe error. It represents 75% of the combined uncertainty and originates from
residual misalignments of the interferometers (+/- 1 mm at k=2) combined with the parasitic rotations of the scanning stage (about 20 µrad in the worst case). In a
perspective of continuous improvement of the measurement uncertainty, a more precise method to align the interferometer beams with the tip had to be found.
(2D grating standard)
Interferometer Detail of the metrology loop and laser beam alignment to meet Abbe principle:
Reference prism (static)
Sample holder with
an adjustable thickness
Setup used for laser beam alignment:
Specific software developed under LabVIEW:
•Continuous acquisition of images.
•Pixel size calibration using the screen holder dimensions.
•Possible adjustment of the camera exposure to improve spot detection.
•Automatic display of crosshair to assist the beam alignment.
•Pattern recognition to detect the spots and precisely determine their positions.
•Gaussian profile fit on the detected pattern to increase the position determination
used to translate
Developed setup Setup mounted on the
Alignment achieved with an accuracy of 0,6 mm
spot: 7 mm
Theoretical alignment Alignment uncertainty
The main source of uncertainty is due to the
impossibility to observe the second spot on the
measurement arm of the interferometer. Some
unfavourable assumptions are necessary to
estimate its position leading to the 300 µm
uncertainty for this components.
Before alignment After rough alignment After fine alignment
Alignment of the
tip with the target
A specific protocol has been developed to reduce impact of Abbe error on the LNE’s mAFM by improving the accuracy of laser beam alignment. It uses
a specific setup and a CCD camera to visualize in the sample plane the tip position which is tracked by a target and the laser spots. A tool is then used
to translate and position the interferometer measurement axes with respect to the tip. With this protocol, the accuracy of laser beam alignment has
been improved from 4,5 mm to 0,6 mm and Abbe error reduced by a factor of 7 (the maximum parasitic rotations are still 20 µrad).
This alignment is limited by the lack of knowledge on the position of the secondary spots (dual path interferometer). Solutions are being studied to
overcome this limitation.
Spot arrangement in