Characterization of Carbon Nanotubes on
Insulating Substrates using Electrostatic Force
Microscopy
T.S. Jespersen∗ , P.E. Lindelof∗ and J. Nygård∗
∗
Niels Bohr Institute, NanoScience Center, University of Copenhagen, Denmark
Abstract. We report on the use of electrostatic force microscopy (EFM) for the characterization
of carbon nanotubes (CNT) grown on insulating substrates. In contrast to traditional atomic force
microscopy (AFM) which relies on the van der Waals forces, EFM measures the long range
Coulomb interaction between a conducting cantilever and the nanotube. This makes large area scans
possible for rapid assessment of CNT samples and we present a statistical method of extracting the
CNT density.
The samples used for most carbon nanotube based electrical devices and for many
other studies of isolated CNT’s have the same structure as starting point[1]: A wafer
of doped silicon (Si) capped with a layer of insulating silicon dioxide (SiO2 ) onto which
a sub-monolayer of CNT’s is either deposited from a suspension of CNT’s in an organic
solvent[2] or grown directly on the substrate by chemical vapor deposition (CVD)[3].
Therefore, techniques for characterizing such samples are often required. Most often
atomic force microscopy (AFM) or scanning electron microscopy (SEM) is employed
but both methods have their drawbacks. The SEM is relatively fast but the resolution is
often limited by charge build-up in the insulating substrate and the sample may change
during imaging due to defects induced by the electron beam or deposition of hydrocarbons thus debilitating device performance. The AFM does not change the sample but
is relatively slow and limited to imaging only a small area (about 30µ m × 30µ m) if single walled CNT’s with diameters of 1-3nm are to be clearly resolved.
The slow imaging of an AFM is due to the short range of the van der Waals forces
exploited in imaging the topography of a surface. Thus high resolution and slow movement of the AFM tip is needed to not "miss" the CNT’s. Electrostatic force microscopy
(EFM), however, is a scanning probe technique similar to AFM, but relying on the long
range Coulomb interaction between the scanning tip and the sample. Here we emphasize
the usefulness of EFM for the characterization of the standard CNT samples described
above.
The EFM operation of a scanning probe microscope (Figure 1a) is a dual scan technique
where the topography of each scan line is first obtained by standard tapping mode AFM.
In the second scan the topographic data is used to retrace the first line with a constant
tip-sample separation h. In the second scan the cantilever is oscillated at its free resonant
frequency ω0 and the EFM signal is the phase difference between the driving force and
the actual oscillation of the tip. In the presence of a force F between the tip and the
Vs
SiO2
p++ Si
Height [nm]
4
(c)
2
0
-2
1
(d)
0,5
Phase shift [deg.]
h
(b)
[deg.]
(a)
0,0
-0,5
-1,0
0
-1,5
-1
0
2
4
6
8
Position [nm]
10
-6 -4 -2
0
2
4
6
8
10 12
Sample bias [V]
FIGURE 1. (a) Schematic illustration of the EFM measurement. (b) Topography (top) and EFM (bottom) of CVD-grown CNT’s. (c) Height profile (top) and EFM phase shift along the line in (b). (d) The
nanotube EFM signal ΦNT as a function of Vs . The solid line is a fit to a quadratic form ΦNT = aVs2 + b.
sample the phase difference (in radians) is given by[4, 5]
µ
¶
k
π Q
−1
ϕ = tan
≈ + F0
0
QF
2 k
(1)
where F 0 (z) = ∂ F(z)/∂ z is the force gradient. The standard convention of EFM is to use
Φ = ϕ − π /2 as the EFM signal. If a voltage Vs is applied between tip and sample and a
capacitive coupling between them is assumed then
Φ=
Q 00 2
C Vs ,
2k
(2)
where C00 is the second derivative of the tip-sample capacitance[5]. Usually an off-set
is chosen such that Φ = 0 at the naked substrate, and by considering the tip-sample
capacitances with and without a nanotube on the substrate, it can be shown that CNT’s
will always appear with at negative phase shift ΦNT [4]. Furthermore both metallic and
semiconducting CNT’s have relatively high conductances and both types appear in EFM
images [5].
All CNT samples discussed here are single walled CNT’s grown by CVD on highly
doped silicon substrates with 400nm oxide (for details on the growth, see ref. [6]).
The EFM measurements were performed using a Digital Instruments Dimension 3100
operated in air at room temperature and using conducting PtIr-coated cantilevers[7] with
resonant frequencies ω0 ∼ 60kHz, spring constants k ∼ 2.8N/m, and quality factors
Q ∼ 225.
Figure 1b shows topography and EFM of a typical sample (EFM parameters: Vs =
−5V, h = 60nm). With the chosen color scale the negative phase shift of the CNT’s
appear as dark lines in the EFM panel. The height profile and EFM along the dotted
line of panel b is shown in panel c. The diameter of the CNT’s are 1 − 3nm but since
EFM measures the long range Coulomb interaction the CNT’s appear with an effective
width of about 0.5µ m. This makes it possible to observe CNT’s in fast large area scans
where they do not show up in standard topography AFM. It is our experience that with
a resolution of a 512 × 1024 (lines × points per line) a standard topography AFM
image is limited to an area of approximately 10 × 10µ m if individual CNT’s are to
be clearly identified. With this resolution CNT’s can be clearly resolved in EFM scans
of 100µ m × 100µ m. Thus, for these samples the EFM technique is at least 100 times
(a)
(b)
(c)
FIGURE 2. (a) 100µ m × 100µ m EFM scan of CVD grown CNT’s and metal alignment marks. The
resolution of the corresponding topography (inset) is to low to resolve the CNT’s. (b) 12µ m × 12µ m
topography scan of the region marked in (a). (c) EFM image of CNT’s between metal electrodes. Electrode
distance, 5µ m
more time efficient than standard AFM in assessing the overall properties. Figure 1d
shows ΦNT as a function of Vs and the quadratic dependence expected for a capacitive
coupling (eq 2) is clearly observed. Below we show two cases where the properties of
EFM is used for: (i) Identification of special CNT structures with respect to predefined
alignment marks (in this case CNT loops for electrical devices) and (ii) for fast density
characterization of as-grown CNT samples using a statistical analysis of the EFM data.
In the process of making electrical devices we identify CNT’s with respect to predefined
alignment marks. For low density samples, or devices which require rare CNT structures
(e.g. crossing CNT’s or CNT loops), a large area may have to be scanned in order to
find an adequate structure, and this process can be very time consuming using standard
AFM. Figure 2a shows an example where EFM is used to identify CVD grown CNTloops in a 100µ m × 100µ m area with a grid of metal alignment marks made by e-beam
lithography. The inset shows the corresponding topographic image in which the tubes
are not resolved. However, for information about the diameter of the tubes we still rely
on standard AFM and Figure 2b shows a high resolution topography image of the area
marked in 2a. The final devices may also be examined by EFM if the electrode gap is
not to small. Figure 2c shows such an example.
The possibility of large area scans makes EFM ideal for rapid characterization of CNT
samples. Figure 3a,b,c show three 90µ m × 90µ m EFM images with a resolution of
512 × 1024 points of as-grown CNT samples. The samples have different tube densities
due to differences in the growth conditions. The histogram in Figure 3d shows the
measured phase shifts from Figure 3a and the inset shows the data along the dashed
line. For the specific experimental conditions the nanotubes appear with a phase shift of
ΦNT ∼ −1.2◦ with respect to the substrate. In order to estimate the tube density we find
the percentage of pixels with phase shifts below a cut-off value Φ0 = 31 ΦNT ≈ −0.4◦
chosen to ensure a safe CNT/substrate distinction. Correlating with the apparent width
of the CNT’s at this value (0.6µ m) the entire length of tubes in the image is found. In
the case of Figure 3a 1.02% of the pixels have phase shifts below Φ0 resulting in a total
length of tubes of 180µ m very close to the actual length (190µ m) found by measuring
(a)
10 m/cm2
Phase shift [deg.]
2.2 m/cm2
#Counts
(b)
0,6
(c)
78 m/cm2
(d)
(e)
(f)
0,0
-0,6
Substrate
-1,2
0
10
20
Distance [µm]
30
CNT's
x25
-1,0
-0,5
0,0
Phase Shift [deg.]
0,5
-1,0
-0,5
0,0
0,5
1,0
Phase Shift [deg.]
-1,0
-0,5
0,0
0,5
Phase Shift [deg.]
FIGURE 3. (a),(b),(c) 90µ m × 90µ m EFM images of CVD grown SWNT samples with varying tube
density. Images were measured with Vs = −5V and h = 60nm. (d),(e),(f) Histograms of measured phase
shift values from (a),(b),(c), respectively. Inset to (d) shows the EFM phase along the dashed line in (a).
directly the length of each NT in the image. This gives a density of 2.2m/cm2 on sample
a. On the higher density samples shown in Figure 3b,c the direct measurement is very
time consuming but the statistical approach above directly gives a rough idea of the
amount of tubes: 830µ m and 6300µ m for Figure 3b and c, respectively giving densities
of 10m/cm2 and 78m/cm2 .
In summary we have shown that EFM is a powerful technique for rapid characterization
of CNT’s on insulating substrates, however, the technique does have limitations: Unlike
AFM it cannot be used on conducting surfaces and it does not give information about
the tube diameter which is often desired and, to some extend, can be used to distinguish
between isolated tubes and ropes.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
S. Reich, et. al., Carbon Nanotubes, Wiley-Vch (2004).
See, e.g., J. Nygård, et. al., Appl. Phys. A, 69, 297 (1999).
J.H. Hafner, et. al., J. Phys. Chem. B, 105, 743 (2001).
C. Staii, et. al., Nano Lett., 4, 859 (2001).
M. Bockrath, et. al., Nano Lett., 2, 187 (2002).
T.S. Jespersen, et. al., (submitted)
SCM-PIT cantilevers from Veeco Instruments, www.veeco.com.