Anomalies in thickness measurements of graphene and few layer graphite crystals
by tapping mode atomic force microscopy
P. Nemes-Incze1, *, Z. Osváth1, K. Kamarás2, L.P. Biró1
1 Research Institute for Technical Physics and Materials Science, Hungarian Academy of
Sciences, H-1525 Budapest, P.O. Box 49, Hungary
2 Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences,
H-1525 Budapest, P.O. Box 49, Hungary
Atomic Force Microscopy (AFM) in the tapping (intermittent contact) mode is a
commonly used tool to measure the thickness of graphene and few layer graphene (FLG)
flakes on silicon oxide surfaces. It is a convenient tool to quickly determine the thickness
of individual FLG films. However, reports from literature show a large variation of the
measured thickness of graphene layers. This paper is focused on the imaging mechanism
of tapping mode AFM (TAFM) when measuring graphene and FLG thickness and we
show that at certain measurement parameters significant deviations can be introduced in
the measured thickness of FLG flakes. An increase of as much as 1 nm can be observed
in the measured height of FLG crystallites, when using an improperly chosen range of
free amplitude values of the tapping cantilever. We present comparative Raman
spectroscopy and TAFM measurements on selected single and multilayer graphene films,
based on which we suggest ways to correctly measure graphene and FLG thickness using
Graphene, as a the building block of graphite has been theoretically investigated since the
1940s . Until 2004, when Novoselov et al. successfully identified graphene  and
other 2D crystals  in a simple tabletop experiment, it was assumed that 2D crystals
were thermodynamically unstable and could not exist under ambient conditions [4, 5].
The discovery that such samples can be produced has led to a wealth of scientific
investigation [6, 7, 8, 9, 10, 11], due to the very promising electronic  and mechanical
properties of graphene, furthermore due to it’s resistance to mechanical and chemical
stress and it's high crystallinity .
Today, the most successful method to prepare graphene samples is mechanical
exfoliation of graphite onto oxidised Si wafers . The thickness of few layer graphite
(FLG) films is estimated by optical microscopy [13, 14], after which the thickness of the
thinnest crystallites is measured by AFM. Much like other scanning probe techniques,
AFM is not free of measurement artefacts. With AFM being such a widely employed tool
to inspect the thickness of FLG crystals, we believe that a detailed investigation of the
* Corresponding author. Fax: +36-1-3922226
email address: firstname.lastname@example.org, URL: www.nanotechnology.hu (Peter Nemes-Incze)
possible sources of errors in the AFM measurement of FLG thickness is of great
importance. When measuring features of the order of magnitude of one atomic layer and
changing material properties, effects of lesser importance under other circumstances (like
homogeneous samples), may play a crucial role in distorting topography images. Indeed
various groups reported different thickness measurements for graphene layers, with
thicknesses ranging from 0.35 nm to 1 nm, relative to the SiO2 substrate. Novoselov et al.
measured platelet thicknesses of 1-1.6 nm . Gupta et al. have measured an instrumental
offset induced by the AFM, of 0.33 nm, ie. 0.7 nm height for a single layer . Other
authors have also reported varying step heights for FLG supported on silicon oxide [23,
15, 16]. This variation in the thickness of the single graphene layers may be attributed to
the change in the tip – sample interaction as the tapping tip scans over the surface.
Observations of distortions in the thickness of nanoparticles, measured with TAFM, are
well known. Anomalous nanoparticle height measurements, dependent on the free
amplitude of the cantilever and material properties of the sample, were reported earlier
[17, 18, 19].
It is generally accepted that folded regions in the graphene give the most reliable
measurement of thickness , however such folded regions are not always available in
every experiment. Furthermore, samples of good quality should not contain such regions,
leaving no option, but to check the thickness relative to the oxide surface. Recently
Raman scattering [20, 21, 22] and Rayleigh scattering  have been shown to be useful
tools in determining the number of graphene layers in a given sample, and other optical
techniques are showing promise [13, 14, 24]. However AFM is still being used frequently
to determine, or confirm the thickness of FLG layers obtained by other techniques [23,
25]. Our investigations shed light on some of the precautions that must be considered,
when estimating FLG film thicknesses using TAFM.
The fact that the thickness of graphene films measured by different groups has a certain
deviation suggests that the data obtained are dependent on either the measurement
conditions, sample preparations procedures or other laboratory conditions. In this paper,
we investigate the dependence on scanning parameters of the measured thickness of one
and multilayer graphene films on silicon oxide surfaces, using TAFM. We show that the
instrumental offset in the thickness is greatly influenced by the free amplitude of the
tapping cantilever. Differences of as much as 1 nm can be observed in the measured
height of the very same graphene platelet. We have compared Raman spectroscopy,
TAFM and contact mode AFM (CAFM) measurements on selected FLG crystals. We
present experimental evidence that the most important factors in distorting topography
data, in TAFM may be the improperly chosen free amplitude of the cantilever and the
Graphene samples have been prepared by mechanical exfoliation . HOPG (SPI-1 grade,
purchased from SPI Supplies) was rubbed against a silicon wafer covered by a 300 nm
layer of silicon oxide. Graphene and few layer graphite crystals were identified using
optical microscopy according to the procedure described in .
A Multimode Nanoscope SPM, from Veeco with a IIIa controller, was used in tapping
mode and contact mode to characterise the FLG samples, under ambient conditions.
Silicon scanning tips used in tapping mode were purchased from Nanosensors (model:
PPP-NCHR), with tip radiuses smaller than 10 nm (force constant ~42 N/m, resonance
frequency in the range of 300 kHz). The cantilever drive frequency was chosen in such a
way as to be 5% smaller then the resonance frequency. The free amplitudes of the TAFM
tips used were determined from amplitude – distance curves. Raman spectra were
recorded on selected graphene films, using a Renishaw 1000 MB Raman microscope.
The excitation source was the 488 nm line of an Ar+ laser with incident power in the mW
range in order to avoid excessive heating of the sample, using a laser spot with a diameter
of 2 µm.
Results and Discussion
TAFM images are not purely topographic, but depend on the material properties of the
sample and the interaction forces between the tip and the sample. Measurements with
TAFM, at constant amplitude show a surface of constant damping of the cantilever
We have studied various FLG crystals, by TAFM. During these measurements we have
noticed inconsistencies in the measured thickness, relative to the oxide layer. That is to
say, the thickness measured over a given FLG crystal was not always the same and in
some cases we have even observed random switching of the FLG thickness in the same
image. It is known that the free amplitude and setpoint of the TAFM cantilever can have
significant influence on the imaged topography [17, 18, 19, 26]. As the amplitude of the
cantilever is the main signal, based on which, the topography is mapped, we have
investigated the influence of the cantilever free amplitude on the measured thickness of
FLG crystals. In doing so, we have measured the thickness of various flakes, using a
range of free amplitude settings, keeping the setpoint of the cantilever amplitude at a
constant value. The results of such a measurement can be seen in Figure 1. Two FLG
crystals were measured simultaneously, one overlapping the other. The free amplitude
was varied from 16 nm to 30 nm. For each free amplitude setting a complete AFM image
was acquired and the step heights in three regions were evaluated (marked by white
squares): crystal C1 – oxide; crystal C2 – oxide and C2 overlapping C1. Starting with the
16 nm free amplitude and keeping the setpoint constant, we have observed that at 26 nm
free amplitude, the thickness measured on top of the oxide surface decreases almost
instantly, by about 0.8–1 nm. However, the thickness measured at the overlapping region
of FLG C2 (green triangles) stays constant. This shows, in accordance with reports from
literature that a more reliable measure of thickness is the step height relative to another
graphite substrate. The effect described here was checked on various FLG crystals, using
different scanning tips. In each case, the effect could be observed, to a greater or minor
degree, with deviations in the thickness measured at low free amplitudes.
The presence of two “stable” thickness values hints at the existence of a bistability in the
measurement system. To further investigate the phenomenon, we have measured
amplitude – distance (AD) curves on a FLG surface and the neighbouring oxide substrate,
using a range of free amplitudes. The curves were obtained by reducing the tip sample
distance from a value larger than the free amplitude to a minimal separation, where the
amplitude was reduced to about 10% of the free amplitude. The amplitude was not
reduced to zero because in this manner the reproducibility of the AD curves was poor
A typical AD curve is plotted on Figure 2a., recorded on an FLG surface, at 25.8 nm free
amplitude. The striking feature of the amplitude curve is that at the amplitude value of 16
nm a jump can be observed. In this region, two different piezo displacement values
correspond to the same amplitude, the difference being about 1 nm. This is important
because the feedback electronics of the AFM works correctly only for a linear signal. If
the measurement setpoint is selected in such a way as to coincide with the jump in
amplitude, the feedback electronics may produce random switching from one
displacement value to the other . Since the height signal is derived from the piezo
displacement signal, random switching in height occurs. This behaviour is presented in
Figure 2b-c on a FLG film. In one case Fig. 2b. the imaging is stable on silicon oxide,
while in Fig.2c. stable imaging is achieved over the FLG.
Changes in topography of such a magnitude (~1 nm) have been reported previously by
Kühle et al.  on Cu clusters supported on a silicon oxide substrate. The origin of this
change in topography, as reported by the authors, is a jump in the amplitude response of
the cantilever, with changing tip – sample separation, as seen on Fig. 2a. Anczykowski et
al, using time resolved numerical simulation of the tapping tip  pointed out that the
jump in amplitude marks a change in the sign of the tip sample interaction force. When
the tip starts to approach the sample, the amplitude decreases linearly. In this regime,
long range attractive forces are responsible for the oscillation damping. At a certain tip –
sample separation a jump occurs in the amplitude (see Fig. 2a). This jump marks the
onset of a region where, with further decreasing tip – sample distance, both long range
attractive and short range repulsive forces act on the tip, ie. the tip is in hard mechanical
contact with the sample. After the jump, the damping of the oscillation increases further,
but this time net repulsive forces characterise the tip sample interaction and the contact
time of the tip also produces a jump 
In the following paragraphs we will discuss the effect of this behaviour on topography,
by the example of a measurement on a FLG flake. In Figure 3. we have plotted the AD
curves on the FLG and oxide surface at three different free amplitude settings: 24 nm, 26
nm and 28.5 nm. The setpoint value is 15 nm in all cases. We can observe the presence of
net attractive and net repulsive regimes of interaction on both surfaces, with the effect
being more pronounced on the FLG. One important characteristic is worth pointing out:
at 24 nm amplitude the measurement setpoint is in the net attractive regime for both the
oxide and FLG surfaces. When we increase the free amplitude the curve shifts and at 26
nm the setpoint is at the instability point on the graphite. It is exactly at this free
amplitude that the TAFM image in Figure 2b was acquired. Because of the presence of
two piezo displacement values for a certain amplitude the feedback electronics can not
distinguish between these two, as it needs a linear signal to work with. Therefore random
switching of the step height on the FLG surface can be seen, similar to the effect
observed by Kühle et al. [19, 26]. Increasing the free amplitude further, the setpoint on
both the oxide and FLG surface will be in the net repulsive region. Plotting the step
height dependence on the FLG as a function of free amplitude we obtain the graph in Fig.
4. The plot shows a steep decrease in the step height at around 26 nm amplitude, from 4.5
nm to 2.25 nm. This falls within the range of the piezo displacement jump, when
transition occurs into the region where repulsive interactions become dominant (see Fig.
2a). Considering the information on Figure 1c that at free amplitudes of 26 nm and higher
the step height measured above the oxide and flake C1 correspond, we can say that a
more precise measure of the step height can be obtained, when measuring in the repulsive
regime on both oxide and FLG.
To crosscheck our data and to support the claim that the measured height (thickness) of
FLG crystals is influenced by the selected free amplitude, we have performed Raman
scattering experiments on graphene and FLG crystals having different numbers of layers.
FLG flakes of 1-5 layers were proven to exhibit characteristic Raman signatures .
We have carefully investigated graphene and FLG flakes (2, 3, 5, 10 layers) by TAFM at
different free amplitude settings and Raman spectroscopy, using a 488 nm laser. The
Raman spectra of single, bilayer and trilayer graphite are displayed in Figure 5. The
distinct characteristics  of the 2D peak of graphene and bilayer graphite at ~2700 cm-
1 are clearly identifiable. The Raman spectra of trilayer graphite are also clearly
distinguishable from the bulk signal. TAFM images and linecuts of the same FLG flakes
used to acquire the Raman spectra are shown in Figure 6. Topography images acquired in
the repulsive regime, at high free amplitude settings on both FLG and oxide surfaces fit
the Raman data well. Furthermore, the images measured using low free amplitudes show
a much larger thickness value (see Fig. 6). Where possible, we measured the thickness of
folded regions (like in the case of Fig. 1a). Such observations further support the claim
that in order to gain reliable thickness data, one needs to be using a setpoint where the tip
scans in the net repulsive regime on both the oxide and FLG surfaces. It is worth
mentioning that true, single layer graphene crystals were frequently measured to be
around 1 nm thick using free amplitudes below the sharp drop in thickness.
In the example of the FLG layer in Fig 2b, further decreasing the free amplitude shifts the
setpoint to a region where the damping is of attractive type on both surfaces, this time
with the instabilities in topography appearing on the oxide (see Fig. 2c). In this case a
thickness of 3.5 nm is measured (see Fig. 4), which is still different from the more precise
thickness of 2.3 nm (about 7 layers). This goes to show that the damping of the amplitude
due to attractive forces is of a different value for the two surfaces. Attractive forces acting
on the sample have various components: electrostatic, Van der Waals, capillary or
chemical forces. On mica and graphite surfaces one of the strongest contributions to the
attractive force comes from the capillary forces, as demonstrated by Ouyang et al. .
This comes as no surprise, since under ambient conditions a thin water layer is present on
most surfaces. Due to the strong hysteretic nature of the capillary force, its contribution to
oscillation damping is large . According to our observations, at small free amplitude
values, the tip does not even enter the repulsive regime and no jump in amplitude will
occur. This is in accordance with the measurements and simulation studies of Zitzler et al.
, who have also demonstrated experimentally that the free amplitude at which a jump
in the AD curves occurs is strongly dependent on the ambient relative humidity, further
proof of the fact that capillary forces have a key role to play in cantilever damping.
On surfaces with changing material properties, due to differences in wettability, or more
generally speaking gradients in the attractive forces, TAFM measurements of topography
are not reliable . Therefore, as seen in our experimental results, it is advised that the
TAFM measurements on graphene be carried out with great care and measurement
setpoints be chosen in the repulsive interaction regime, where the damping of the
cantilever is largely due to the topography of the sample. Before measurements amplitude
distance curves should be acquired on both the graphene and oxide surface and the
measurement setpoint chosen accordingly.
In our measurements of FLG flakes, the difference in height comes from the fact that the
repulsive region sets in at different free amplitude for the graphite and oxide. As the
amplitude setpoint crosses the jump in the AD curve unstable imaging is observed on
both the FLG and oxide. However, the shift of the critical amplitude at which the
repulsive regime sets in and its dependence on the nature of the attractive forces is still
not fully understood. Further research in this direction is on the way.
We have also performed CAFM measurements on our FLG samples, which further
confirm our findings. However, we found that the difference in lateral forces on the FLG
and support can introduce deviations in the thickness measured using contact mode. This
is illustrated by Figure 7, where we present TAFM and CAFM measurements on the
same FLG flake. The thickness of 2 nm (6 layers) measured at high free amplitudes in
tapping mode, correlates reasonably well with the thickness measured using contact mode.
However, we have observed a difference in the thickness measured by CAFM when
changing the direction of scanning (no such effect was observed using TAFM). This
suggests that differences in lateral forces on the FLG and oxide surfaces (for example
friction) play a non negligible role in influencing the CAFM cantilever bending, resulting
in differences in measured thickness. Such forces are negligible in TAFM.
While performing TAFM measurements on graphene and FLG flakes on silicon oxide
substrates, special care needs to be taken to obtain more precise flake thickness data. The
change in FLG thickness described in this paper, is in the order of 1 nm, which is a very
large error, when working with topography changes of less then one nanometre.
Where possible, the measurements should be performed in the repulsive regime on both
oxide and FLG surface. Either the free amplitude or measurement setpoint should be
chosen in such a way as to obtain this condition. Usually the setpoint is chosen in such a
way as to be as near as possible to the free amplitude in order to minimise the forces
acting on the tip and sample, but as we have seen, this may not be the correct setting. We
believe that the variation of the reported thickness of graphene among different research
groups is largely due to the unreliability of TAFM measurements in the attractive regime.
It is worth noting here that during our measurements at high free amplitude and low
setpoint settings, no damage to either the sample or tip were encountered.
Our work sheds some light on how a more precise estimate of the number of layers in a
FLG crystal can be obtained. However the number of layers should be compared to data
obtained by other methods as well, to support the AFM data. Furthermore additional
experimental work and computer simulation needs to be done, to determine the cause of
the shift in the instability point on the AD curves and the nature of the attractive forces on
The present work was financially supported by Hungarian Scientific Research Fund
OTKA-NKTH K67793, OTKA-NKTH NI67702 and and OTKA-NKTH 67842 grants.
Figure 1. a) Image of two overlapping FLG films on SiO2 (colour bar associated to height: 10
nm) b) Zoomed in region from image 1a (colour bar associated to height: 3 nm), averaged line cuts
and thickness measurements were taken in the regions marked by squares, C1 and C2 representing
each FLG film. In fig. c), each point represents the thickness of the crystal C1 (black squares) and
C2 (red circles) with respect to the oxide substrate, as a function of free amplitude. The thickness of
crystal C2 overlapping C1 with changing free amplitude is also plotted (green triangles).
Figure 2a. The damping of the cantilever oscillation as
a function of piezo displacement, recorded by
approaching the tip towards the sample. The curve was
taken on the surface of the FLG flake presented on Fig.
Figure 2c. TAFM image on the FLG flake, when
the instability point passes through the setpoint
amplitude on the oxide. In this case, unstable
imaging occurs on the oxide surface as shown by
crossing is experienced at free amplitudes around 21 nm.
Figure 2b. TAFM image of a FLG flake,
imaged at a setpoint of 15 nm, near the
bistability point in the AD curve. Random
switching from one thickness to the other
occurs. This is more evident at the top and
middle part of the image (as shown by
arrows), where a thickness jump occurs
between scan lines and during the
acquisition of a scan line.
Figure 3. AD curves on the FLG (a) and oxide (b) surface at different free amplitudes (24, 26,
28.5 nm). Dashed line at 15 nm amplitude shows the setpoint used during measurements. At
26 nm free amplitude the setpoint crosses the jump in amplitude. For the oxide surface such a
Figure 4. Step height as a function of free amplitude, measured on the
FLG flake presented in Fig. 2b. Two jumps in height can be observed:
the jump at ~25 nm marks the transition of from the attractive to the
repulsive regime on FLG and the one at ~21 nm the transition from
attractive to repulsive on the oxide surface.
Figure 5. Raman spectra of graphite having 1, 2, 3
and >10 layers (scaled to have similar height of the 2D
peak). For each sample we show the height measured by
TAFM, at high free amplitudes. These values correlate
well with Raman spectra. The four components of the
2D peak in bilayer graphite are plotted.
Figure 6. TAFM images of the regions where the Raman spectra in Fig. 5 have been acquired, for
single layer (a, b); bilayer (c, d); three layer (e, f) flakes (each image is 2.5 µm x 2.5 µm). The images
were acquired using a constant amplitude setpoint and two different free amplitudes, one higher (a, c, e)
and another one lower (b, d, f) than the amplitude at which unstable imaging occurs on the FLG. In the
first case (a, c, e) the setpoint is in the repulsive regime for both oxide and FLG, while in the latter case
(b, d, f) imaging is in the attractive regime for FLG. Averaged linecuts (inside the black markers) taken
on each image show the increase in thickness when measurements are not performed in the repulsive
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