Journal of Surface Engineered Materials and Advanced Technology, 2013, 3, 29-35
http://dx.doi.org/10.4236/jsemat.2013.34A1004 Published Online October 2013 (http://www.scirp.org/journal/jsemat)
29
The Use of Light Diffracted from Grating Etched onto
the Backside Surface of an Atomic Force Microscope
Cantilever Increases the Force Sensitivity
Sergey K. Sekatskii*, Mounir Mensi, Andrey G. Mikhaylov, Giovanni Dietler
Laboratoire de Physique de la Matière Vivante, IPSB, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Swit-
zerland.
Received June 19th, 2013; revised July 22nd, 2013; accepted August 3rd, 2013
Copyright © 2013 Sergey K. Sekatskii et al. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
A reflecting diffraction grating has been etched onto the backside of a standard cantilever for atomic force microscopy,
and the diffracted light has been used to monitor the angular position of the cantilever. It is shown experimentally that
for small angles of incidence and for large reflection angles, the force sensitivity can be improved by few times when an
appropriate detection scheme based on the position sensitive (duolateral) detector is used. The first demonstration was
performed with a one micron period amplitude diffraction grating onto the backside of an Al-coated cantilever etched
by a focused ion beam milling for the experiments in air and an analogous 600 nm-period grating for the experiments in
air and in water.
Keywords: Atomic Force Microscopy; Force Measurement Sensitivity; Diffraction Grating
1. Introduction
Atomic Force Microscopy nowadays is an extremely use-
ful and broadly used instrument to investigate the topog-
raphy of different samples with a (sub) nanometer spatial
resolution and to measure interaction forces with pico-
Newton sensitivity [1]. In practice, the overwhelming
majority of the instruments are based on measuring the
deflection angle of the laser beam reflected from the can-
tilever’s backside, see Figure 1. The physical principle
of this approach is that one measures as precisely as pos-
sible the reflection angle

, which is changing because
the lever bends under the action of the interaction force
between the tip and the substrate. In Figure 1, a typical
experimental situation is shown: without grating, a mir-
ror-like reflection of the laser beam occurs and under the
action of the interaction force, which changes the angle
between the cantilever and the sample (initially equal to
15˚ on the Figure 1) on the d

value, the angles
change all of the same amount, namely 0
ddd

  .
The aim of this Note is to attract the attention on the
fact that the sensitivity of the detection scheme to change
of

or 0

can be essentially increased if a diffraction
grating is present on the cantilever’s backside (see Fig-
ure 1). Different types of diffraction gratings can be used
(see below), but here the simplest case of a flat regular
grating is first considered. Let l be the grating period,
n—the order of the diffraction,

—the wavelength of
the laser light, then the condition for an intensity maxi-
mum of the reflected beam reads [2]:


0
sin sinn

  (1)
Here 0

is the incidence angle of the laser beam with
respect to the normal to the grating surface. The purpose
of this setup is to measure

in the far zone in order to
determine 0

as precisely as possible (for the reason-
able cantilever bending one evidently has that the change
of this angle is the same as the change of angle

;
0
dd



). Hence the derivative 0 dd

 or dd


should be as large as possible. From (1), it follows that
0
0
cos d
dcos




 (2)
This means that if one selects the angles 0

0˚,


90˚,
that is the normal incidence and the oblique reflection,
one will obtain a large gain in sensitivity: a small change
of

or 0

will lead to a much larger change in

.
*Corresponding author.

The Use of Light Diffracted from Grating Etched onto the Backside Surface of an
Atomic Force Microscope Cantilever Increases the Force Sensitivity
30
15˚



0


Figure 1. Schematic of a proposed detection scheme based
on the reflection of light from the diffraction grating on the
cantilever backside and its detection by the position-sensi-
tive detector (PD).
Therefore, the detection sensitivity can be improved up
to a factor of ten-twenty (and potentially much more),
because angles

in the range

70˚ - 80˚ are suffi-
cient.
As we have discovered in a course of work, a similar
idea has been already put forward in a Japanese patent
filed 18.10.1994 (in Japanese) [3] but, to the best of our
knowledge, here we present its first experimental realiza-
tion and also clarify some hitherto non-discussed impor-
tant issues, first of all the necessity to use other than the
most common in the field of split photodetector to detect
the reflected light, for obtaining real improvements re-
lated with this approach. This latter aspect has also been
tested experimentally using an appropriate lateral effect
photodetector, see below.
2. Results and Discussion
In practice, the method at hand does not bring a real im-
provement of sensitivity when using a flat regular dif-
fraction grating in conjunction with a standard AFM split
detector (two or four quadrants photodiode) to detect the
deflection signal. The problem is that the sensitivity of
this detection scheme is proportional to the angular di-
vergence of the reflected laser beam [1,4]. Assuming that
the distance L between lever and detector is large and
that the laser light spot on the lever is much smaller than
the spot size a on the detector, then one can estimate the
sensitivity

of detection proportional to PL a


,
where P is the laser power. However, the angular diver-
gence of the reflected beam and the spot size a are ampli-
fied by the same factor 0
cos cos

 , thus cancelling the
suggested increase of the sensitivity. The same conclu-
sion holds with respect to the proposal to use a cylindri-
cal reflector glued onto the cantilever to improve the an-
gular sensitivity [5].
Different approaches how to overcome this limitation
are discussed below. Now we would like just to note that
even if a flat diffraction grating is used, the sensitivity
increase of the proposed method can be still obtained in
practice if a lateral effect detector (duo-lateral detector)
is exploited [4]. This is due to the circumstance that to
realize the high sensitivity for such a detector it is neces-
sary that the light to be detected exposes almost the
whole active surface of detector for which, given the
fixed detector-cantilever distance, the enlarged angular
spread of diffracted-reflected light in comparison with
that mirror-like reflected, is really important [4]. Note
also that the theoretically estimated minimum detected
angle for the duo-lateral detector is a factor 2π2.5
smaller than that of a split detector [4].
Duo-lateral detector is not common in AFM field, so
its use for our experimental demonstration required pre-
paration of special cantilever holder and electronics.
These results, as well as the data obtained in a proof-of-
the-concept experiment using a standard two-quadrants
photodiode detector, are presented here. In all cases,
aluminum coated silicon levers CSC38 cantilevers from
MicroMash, Tartu, Estonia, with the length 250 µm, width
35 µm, thickness 1 µm and typical spring constant 0.08
N/m, coating thickness 30 nm, were used.
In the first experiment we used an amplitude diffrac-
tion grating with a period of 1 micron etched into the
backside of the AFM cantilever by the Focused Ion
Beam (FIB) (see Figure 2). The grating consisted in 500
nm wide aluminum-free grooves alternating with 500
nm-wide aluminum strips. This experiment has been
performed in air. Laser beam (CW He-Ne, 5 mW) was
focused onto the end part of the cantilever beam by a
small lens with a focal distance of 15 mm and a typical
spot size of approximately 20 - 40 µm. The reflected
light was detected by a two-quadrant photodiode whose
signal was amplified by a differential amplifier. The
sample was a standard 0.17 mm thick microscopy cover
glass mounted onto a NIS-70 scanner (Nanonics, Israel),
and a triangular HV signal was applied to the scanner to
realize the periodical engagement/disengagement of the
contact between the tip and sample. Scan ranges from 8
to 35 microns were used, and approach/retraction curves
were recorded by a PC using a customarily written Lab-
View program. The experiment was designed in order to
be able to compare alternatively the mirror reflection
with the diffracted reflection from the grating on the
same sample. Different incidence angles 0

were tested,
but below we report the results obtained for 0


18˚,


70˚, where the direct comparison is possible. This
incidence angle was easy to control by observing the n =
−1 order diffraction beam, which for our case was very
close to the auto-collimation condition: 0



 if
0


18.4˚.
This first experiment was designed to remove the in-

The Use of Light Diffracted from Grating Etched onto the Backside Surface of an
Atomic Force Microscope Cantilever Increases the Force Sensitivity
31
Figure 2. SEM images of the grating formed at the backside surface of CSC38 AFM lever by the focused ion beam etching
method. Up: 1 micron-period grating, down: 600 nm-period grating.
fluence of the PL a

 factor in order to test the effect
of 0 dd

 itself. For this, we vary the focusing condi-
tions and adjusted the position of a focused laser spot
with respect to the cantilever in such a manner that the
powers and sizes of the laser light spots “grating-re-
flected” and “mirror-reflected” from the cantilever were
as close to each other as possible. (The typical laser po-
wer in both reflected spots was around 0.5 - 0.8 mW and
sizes agrat, amirr, measured at a distance of 10 cm from
the cantilever, were 8 - 12 mm). Then the photodiode
with the diameter of 25 mm was placed at a distance 2 -
3 cm from the cantilever and approach-contraction
curves were recorded cyclically “measurement of the
grating reflection-measurement of the mirror reflection,
etc”. with an appropriate readjusting of the laser with
respect to the cantilever but without changing the po-
sition of cantilever and sample to be sure in the re-
producibility of the data; see the results of our testing
in Figure 3.
The experimentally measured ratio of the signal am-
plitudes is equal to approximately 2.2, while the theo-
retical value is cos18˚/cos70˚ = 2.8. In our opinion, there
is a reasonably good agreement between the prediction
and the experiment and one can consider the results as a
proof of the principle of the proposed approach. A better
coincidence is hardly possible given the uncertainties

The Use of Light Diffracted from Grating Etched onto the Backside Surface of an
Atomic Force Microscope Cantilever Increases the Force Sensitivity
32
Figure 3. Approach/contract curves recorded for the grat-
ing (up) and mirror (bottom) reflections from the cantile-
ver. The continuous z-coordinate (recalculated from the
time using the calibrated scanning rate) is used and the
moments of the change of the scanning direction are not
shown.
related with the measurement of experimental parameters
involved (first of all, the reflected light spot sizes and,
obviously, the distribution of the light intensity through-
out the spot is not as homogeneous as required for a pre-
cise comparison).
It was not a problem to work with the larger grating
reflection angles, up to

80˚, but the quantitative
comparison of corresponding approach curves with those
obtained for the mirror reflection in the same conditions
was not possible because the parameters of two reflected
beams differed too much.
Similar experiment was aimed at proving the method
under liquids in order to assess its sensitivity for single
molecule force spectroscopy experiments, see e.g. re-
views [6-8]. For this, a Nanoscope AFM head (Brucker
Corp., USA) with the built-in two-quadrant photodiode
and laser diode (wavelength 650 nm) was used.
A liquid cell modified with an additional metal-coated
prism to reflect the grating-reflected light (Figure 4) was
prepared for this experiment. Hence, signals caused by a
light beam diffracted from the grating and mirror-like
reflected from it were both measured just by a slight re-
adjustment of the position of the mirror and of the photo-
diode without any other change of the set up. An addi-
tional complication of this experiment was caused by the
index of refraction of water (n = 1.33) that reduces the
wavelength to ca. 489 nm necessitating the use of grat-
photodiode
z -piezo
.
I
..
I
..
I
..
I
.
.
I
.
laser light
mirror
liquid
liquid container
Figure 4. Experimental setup demonstrating the applicabil-
ity of the proposed method in liquids (not to scale). Liquid
container equipped with a protective ring and containing a
mica sheet as a sample is installed onto the z-piezo and can
be moved independently from the PMMA plate with a 90˚
metal-coated glass prism and AFM tip holder both glued
onto it. From the backside, PMMA plate contains a hole for
injection/extraction of the liquid (not shown). The same
mirror can be adjusted to direct the signal either of a grat-
ing-diffracted light (as shown; the SEM photo of the 600
nm-period diffraction light is presented in grating used is
presented in the insert) or of a mirror-like reflected light to
the photodiode. An example of the disengagement (contrac-
tion) curve recorded for the diffracted the bottom part of
the figure.

The Use of Light Diffracted from Grating Etched onto the Backside Surface of an
Atomic Force Microscope Cantilever Increases the Force Sensitivity
33
ings with a period essentially smaller than 1 micron. A
600 nm period grating was selected for this experiment,
but it turned out that the fabrication of this grating re-
quires the highest possible resolution of the FIB etching
process which was possible only on smaller area (Figure
2) limiting the efficiency of grating reflection. Using this
grating and the liquid cell, approach/retraction curves of
the AFM tip on a mica surface showing the characteristic
adhesion forces of a few hundreds of pN have been suc-
cessfully recorded in water. In the best cases, the slope of
the linear part of these approach curves recorded for the
first order grating reflection attains roughly the same va-
lue as for the mirror-like reflection, which is quite good
given all the negative factors discussed above.
In a next series of experiments, both 1 micron- and
600 nm-period gratings etched onto the cantilever back-
side were tested in air exploiting the detection of dif-
fracted light by high linearity position sensing detector
SL5-1 (duo-lateral photodiode) of UDT Sensors Inc.,
USA, with the size of an active area 5 × 1 mm. This
photodiode was used together with the customarily pre-
pared amplifier recommended for these purposes by
many sources, e.g. by Hamamatsu Company [9]. Espe-
cially convincing results were obtained when detecting
the reflection of a He-Ne laser beam from 600-nm period
grating. This grating supports only one single n = −1
order of diffraction provided an incidence angle 0

3.1˚.
Correspondingly, using an incidence angle 0


3.3˚ one
gets a diffracted beam at the angle

85˚ (at the angle

80˚ for 0

4.0˚) which gives the value of 0
cos
cos


equal to 11.5 (respectively to 5.7). Experimentally, for
such a configuration we observed effective reflection
even for the aforementioned large diffraction angles (up
to 1.5 mW of light power has been measured for a beam
diffracted at the angle of 80˚ when the laser was focused
with a lens with a focal distance of 25 mm), and almost
whole surface of the active area of duo-lateral photodi-
ode has been exposed to light for cantilever-detector dis-
tance about 30 mm. These experimental results hold
much promise for an application of such scheme in real
single molecule force spectroscopy experiment which
preparation is currently underway in our laboratory; for
this field cf. e.g. our publications [10,11].
3. Conclusions and Further Suggestions
To conclude, we would like to stress again that an idea to
use a diffraction grating etched onto the reflective back-
side surface of an AFM cantilever to improve the force
sensitivity of the instrument has been for the first time
successfully experimentally tested in both air and liquid
environments, using both standards for the field split
photodetector and lateral effect detector. In our opinion,
such a testing does create interesting opportunities for
further use of this approach for AFM researches in prac-
tically important areas.
The perspectives of the method can be drastically im-
proved when more complicated specially designed grat-
ings are formed onto the backside of the cantilever. Dif-
ferent opportunities can be envisaged and they will be
considered elsewhere in details. As an example, one can
use focusing concave gratings, which nowadays are broad-
ly applied not only for spectrometry [2] but also in laser
resonators [12], as spectral multiplexers/demultiplexers
in optical networks, see e.g. [13]. For these gratings, the
effect of an increased of angular sensitivity is decoupled
from the initial angular divergence of the light source.
Note also that for the quite practical Rowland circle radii
of approximately 2 cm (cf. [13]), spot sizes on the canti-
lever of approximately 30 microns, and the depth of the
profiling of the cantilever are necessary to realize the re-
quired concavity amounts to the value of only

20 nm.
This is smaller than the typical thickness of the reflecting
metal coating deposited onto the backside of a cantilever,
and thus the possibility to prepare these gratings seems
evident. Even more promising is the possibility to use a
specially designed non-fully periodic sub-wavelength
gratings enabling the focusing of an incident light with
high reflectivity (see the recent paper [14] and references
therein).
A few other possibilities to improve the presented ap-
proach also deserved to be mentioned here. In order to
increase further the angle

, one can imagine to detect
the opposite diffraction spot as it is indicated in Figure 1,
which has an angle


that can approach the maximal
value of 90˚ being not obstructed by the sample surface.
(This supposes that the photodiode is placed on the side
of the chip carrying the lever: at present this is not a vi-
able solution because the chip is obstructing the light
beam, but necessary modifications of chip design should
not pose serious problems).
If desirable, known methods to increase the reflectivity
(for example, using special forms of grating grooves [2])
can be also used. Multiple diffracted beams from an ap-
propriately designed grating could be simultaneously re-
corded and cross-measurement data could be used for
improving the precision of the force and position deter-
mination.
Note also that the grating reflected beam is far away
from a mirror-like reflection and it is practically not in-
fluenced by the reflection from the sample (this has been
tested experimentally), while for the mirror-reflected
beam the latter is an important source of noise and in
ambiguity when using metallic or other well-reflecting
substrates. Correspondingly, very narrow cantilevers with

The Use of Light Diffracted from Grating Etched onto the Backside Surface of an
Atomic Force Microscope Cantilever Increases the Force Sensitivity
34
Figure 5. 720 nm-period grating etched onto the backside of
the ultra-short USNMCB-5 MHz cantilever, NanoWorld AG,
Neuchatel, Switzerland, specially designed for high speed
AFM applications and having the sizes 10 × 5 microns.
widths down to 0.5 - 1 micron or even less could be used,
again because the substrate reflected beam does not dis-
turb the measurements. These narrow cantilevers would
enable us to decrease drastically the spring constant,
which is important for many applications, especially for
very high speed imaging. Such a possibility is illustrated
in Figure 5, where 720 nm-period grating etched onto
the backside of the ultra-short USNMCB-5 MHz canti-
lever, NanoWorld AG, Neuchatel, Switzerland, specially
designed for high speed AFM applications and having
the sizes 10 × 5 microns, is presented. Efficient enough
grating-like reflection of focused He-Ne laser beam from
this cantilever (up to 0.4 mW of reflected light power for
a laser beam focused with a lens with the focal distance
of 15 mm) has been observed experimentally.
To conclude, we would like to mention a few papers
where using of diffraction grating in combination with
AFM was reported [15-18]. However, in these works a
grating has been explored as an interferometer: a photo-
diode, placed in a certain position, measures a light inten-
sity, which changes together with the change of the dis-
tance grating—photodiode due to the interference be-
tween the light beam directly passed via the grating (or
mirror-reflected by it) and the light beam corresponding
to certain (usually n = 1) diffraction order in reflection or
transmission. No effect of the increase of the angular/
force sensitivity considered in our note was used.
4. Acknowledgements
The authors thank M. Pavius and S. Clabecq, EPFL, for
the focused ion beam etching preparation of diffraction
gratings and M. Burri, NanoWorld AG, for a kind gift of
USNMCB-5 MHz ultra-small cantilevers. The financial
support of Swiss National Science Foundation (grant No.
200021-137711) is gratefully acknowledged.
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