NANO LETTERS
Charge Trapping in Carbon Nanotube Loops Demonstrated by Electrostatic Force Microscopy
2005 Vol. 5, No. 9 1838-1841
Thomas Sand Jespersen* and Jesper Nygård Niels Bohr Institute, Nano-Science Center, UniVersity of Copenhagen, UniVersitetsparken 5, DK-2100 Copenhagen, Denmark Received March 29, 2005; Revised Manuscript Received May 26, 2005
ABSTRACT Electronic devices made from carbon nanotubes (CNTs) can be greatly affected by substrate charges, which, for instance, induce strong hysteresis in CNT field effect transistors. In this work, electrostatic force microscopy (EFM) is employed to investigate single-walled nanotubes grown by chemical vapor deposition on SiO2 substrates. We demonstrate the use of this technique to gain quantitative information on the substrate charges. It is found that charge pools with densities around 10-8 C/cm2 can be trapped inside nanotube loops for extended periods of time, showing that nanotubes can act as confining barriers for substrate charges. The trapped charges can be removed by scanning probe manipulation.
The electronic interaction between carbon nanotubes (CNTs) and local charges plays a vital role for applications of carbon nanotubes in molecular electronics. Carbon nanotube field effect transistors (FETs) exhibit hysteric behavior upon sweeping the back gate due to rearrangements of charges in the substrate or in adsorbed water molecules that locally gate the semiconducting nanotube.1-3 This hysteresis can be exploited in CNT-based memory elements1,2 but must be eliminated for reproducible operation of the CNT FETs in electronic circuitry. Also, applications of carbon nanotubes as the active element in nanoscale sensors for chemical compounds4,5 exploit the high sensitivity of nanotube FETs to local charges in the environment.6 In the previously reported studies of these effects, the role of the charges has been elucidated by monitoring the change in conductance of CNT FETs upon changing the nanotube environment. In this letter we report on the use of electrostatic force microscopy (EFM) to investigate the interaction of surface charges on SiO2 with carbon nanotubes. We find that tubes strongly influence the dynamics of surface charges and that charges can be trapped on regions of the substrate fenced by nanotubes. The nanotubes studied in the this work were grown by chemical vapor deposition (CVD) using methane as the carbon feedstock. Substrates of highly p-doped Si capped with 400 nm SiO2 were prepared with catalyst by dipping for 10 s into a solution of 1 mg/mL Fe(NO3)3‚9H2O in 2-propanol, followed by 5 s in n-hexane and air-drying.7 The substrates were placed in a tube oven that was flushed with Ar during heating to 950 °C. Then the Ar was replaced by 10.1021/nl0505997 CCC: $30.25 Published on Web 06/17/2005
© 2005 American Chemical Society
Figure 1. (a) Schematic illustration of the EFM measurement. (b) EFM image of long CVD-grown nanotubes forming loops. Enhanced EFM phase shift Φl is observed from the interior of some of the loops. Arrows point to pairs of similar loops formed on the same CNT of which only one exhibit enhanced Φl. (c) EFM image of CNT loop and coil from a different spot on the sample. (d) EFM image from a different sample showing many loops. (e) Phase difference over the bare substrate as a function of Vs2 for z ) 60 nm (0) and lift height z for Vs ) -10 V (b). The data have been fitted to theory, see text. Scale bars for all images are 10 µm, intermediate lift heights are z ) 60 nm, and Vs ) -6 V.
H2 (0.25 L/min) for 10 min to reduce the iron catalyst particles. Tubes were grown by changing to a methane flow (0.75 L/min) for 5 min. Figure 1b,c,d shows EFM images of the growth product attained with a Digital Instruments Dimension 3100 operated in air at room temperature. Carbon nanotubes appear as dark
lines for reasons described below. As seen in Figure 1, the grown CNTs are extremely long (up to ∼100 µm) and form loops and coils, as also reported in ref 8 for long CVD grown CNTs.9 An example of a nanotube coil formed at the end of a CNT is shown in Figure 1c. We use conducting PtIr coated cantilevers10 with resonant frequencies ω0∼60 kHz, spring constants k∼2.8N/m, and quality factors Q∼225. The EFM operation of the scanning probe microscope (Figure 1a) is a dual scan technique where the topography of a scan line is first obtained by standard tapping mode atomic force microscopy (AFM). In the second scan the topographic data are used to retrace the first scan while the tip keeps a constant height z above the surface. During the second scan the tip is oscillated at its free resonant frequency ω0 and the phase difference between the driving force and the observed oscillation of the tip is measured. In the presence of a force F between the tip and the sample, the phase difference (in radians) is given by (refs 11,12) φ ) tan-1
(QF′k ) ≈ π2 + QkF′
(1)
where F′(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 C′′Vs2 2k
(2)
where C′′ is the second derivative of the tip-sample capacitance.12 The Φ∝Vs2 dependence is clearly seen in Figure 1e for the measurement over the bare substrate.13 By considering the capacitances between tip and sample with and without a nanotube on the surface, it can be shown that when the offset is chosen such that zero corresponds to the measured Φ over the bare substrate, nanotubes will always appear with a negative phase shift ΦNT regardless of their band structure.12 As seen in Figure 1b,c, a pronounced EFM signal Φl is observed in the interior of some of the loops. This reflects that the tip experiences a force gradient over the substrate enclosed by a nanotube loop different from when it is outside a loop. This force cannot be attributed to a mere capacitive coupling to the nanotubes since it is often observed that in two loops made from the same tube and of similar geometries only one exhibits the contrast in the interior. Such cases are marked by the arrows in Figure 1b. Figure 2a shows the phase shift along a line through a nanotube coil with radius r ∼ 2 µm (Figure 2b). Sharp peaks ΦNT are observed when the tip passes a nanotube, and the enhanced phase difference Φl in the interior of the coil is clearly observed. Figure 2c shows how Φl and ΦNT from Figure 2a depend on the potential difference Vs between tip and substrate. The relation ΦNT ∝ Vs2 expected for a capacitive coupling to the carbon nanotubes is clearly observed, but for the interior of the loop we find Φl ∝ Vs, indicating different physical origins for the two forces. We ascribe Φl to static charges trapped in Nano Lett., Vol. 5, No. 9, 2005
Figure 2. (a) EFM phase shift with Vs ) -5 V through a nanotube loop along the line in (b) for Vs ) -5 V. x ) 0 µm corresponds to the top of the line. The two edges of the loop are seen as sharp peaks with phase shift ΦNT, and the trapped charges give rise to shift Φl from the interior of the loop. (c) The phase shifts Φl and ΦNT from (a) as a function of sample bias. The measured points are averages from ∼15 scans along the line shown in (b). A linear fit to Φl and a quadratic fit to ΦNT are shown as solid lines. (d) Phase shifts Φl for the loop shown in (e) and (f) [AFM and EFM, respectively] as a function of lift height for Vs ) -5 V (9) and Vs ) -10 V (0). The solid lines are fits to powers az-3 + b. Scale bars in (b) and (e) are 5 µm and (b), (f) are measured with Vs ) -5 V and z ) 60 nm.
the interior of the nanotube loops. If a charge Qs rests on the substrate, image charges qt ) AQs and qb ) (1 - A)Qs will be induced in the tip and back gate, respectively. The parameter A ∈ [0,1] describes the division of the image charges between tip and substrate. With a capacitance Ctb between tip and backgate the total charge on the tip is Qt ) qt + CtbVs, and the force on the tip can be approximated by (refs 14,15) F(z) ≈
-Qs(AQs+CtbVs) 2
4π0z
1 - Ctb′Vs2 2
(3)
Here we have neglected the van der Waals forces, which are negligible for z > 10 nm.16 The force gradient entering eq 1 is then
F′ )
[
]
AQs2 QsVs Ctb 1 ∂Ctb 1 + - Ctb′′Vs2 2 z 3 2 ∂z 2 2π0z 2π0z
(4)
The last term is canceled by the offset of our measurement. Thus, for the static charge contribution F′ depends linearly on Vs as we measure inside the loop. To estimate the charge density in the loop we must determine the capacitances called for in eq 4. From the slope of the linear fit in Figure 1e (2.8 × 10-3 rad/V2) and eq 2 we find 7.0 × 10-5 F/m2 for the second derivative. This, however, corresponds to the entire cantilever-substrate capacitance, but at these heights only about one-third of this is due to the tip of the cantilever, 1839
which is the part sensitive to the charge.17 Thus, approximating the tip as a circular disk of radius R and the tip-substrate system as a parallel plate capacitor with z ) 60 nm air and t ) 400 nm SiO2 with dielectric constant s ) 3.9, we estimate11
C′′tb )
2πR20
F ) 2.3 × 10-5 2 (z+t/s) m 3
(5)
and from this we find C′tb ) -1/2C′′tb(z + t/s) ) - 1.9 × 10-12 F/m and Ctb ) - C′tb(z + t/s) ) 3.1 × 10-19 F. In this approximation the tip acts as a circular disk with effective radius r ≈ 40 nm, in reasonable agreement with the observation that CNTs appear in EFM measurements with widths of about 200 nm, which is close to 2R (Figure 2a). In Figure 1e we also plot the z-dependence, and fitting the data to eq 5 (solid line) we find again effectively R ≈ 40 nm, identical to the estimate from the voltage dependence. Using these capacitances in eq 4 and relating the measured phase shifts to F′ by eq 1, we use the slope of the line in Figure 2c to calculate Qs ≈ - 7.7 × 10-19 C. The sign of the charge is inferred by noting that conducting objects (e.g., CNTs), which attract the tip, appear with a negative phase shift and negative Φl is measured with Vs negative, i.e., with a positive charge on the tip. Thus the loop charge Qs must be negative. This charge is situated within an area πR2, which gives an average charge density of 2.2 × 10-8 C/cm2, i.e., the coil in Figure 2b contains a charge of about -17500e (e ) elemental charge). With a similar analysis it is found that the r ∼ 1 µm loops in Figure 1b contain between 1500e and 3500e each, corresponding to densities around 0.8-1.8 × 10-8 C/cm2. Studies of charges induced on sapphire substrates by corona discharge from an SPM tip18 yield densities of 2 × 10-8 C/cm2, close to our measured value. The third term of eq 4 gives the Vs independent phase shift due to the charges on the surface. Using our calculated Qs, we find a value of 0.1 × A deg., which is consistent with the fact that we do not observe a phase shift for Vs ) 0 V if 0 < A < 0.1. Figure 2d shows the height dependence of Φl for Vs ) - 5 V and Vs ) - 10 V for the loop shown in Figure 2e,f. Assuming the Coulomb interaction to dominate the z-dependence, we have fitted the data to the function az-3 + b, i.e., the first term of eq 4.19 The fit gives charge densities of 9.9 × 10-10 C/cm2 and 1.8 × 10-9 C/cm2 for the Vs ) - 5 V and Vs ) -10 V respectively. Using the Vs dependence as above, we find a charge density in the loop of ∼2.4 × 10-8 C/cm2, i.e., an order of magnitude larger. We expect the estimate from the z-dependence to be the less accurate since the relative scales of the tip-sample-substrate system change when changing z, and this will influence the interaction of the charges with the tip. Further evidence that Φl is indeed due to charges on the substrate is provided by AFM manipulation. Figure 3c shows an AFM image of two loops formed on the same nanotube, which initially each hold ∼6500e trapped in their interior as seen on the EFM image (panel a). By touching the substrate in the interior of the lower loop with the grounded 1840
Figure 3. (a) EFM image of two loops formed on the same nanotube, each trapping charges as seen by the phase difference measured in their interior. (b) EFM image of same area as (a) after touching the interior of the lower loop by the grounded AFM-tip. (c) Topographic image of the nanotube shown in (a) and (b). (d-f) AFM and EFM images of nanotube coil before (d),(f) and after (e),(g) the coil is broken by AFM manipulation. All measurements are performed with z ) 60 nm and Vs ) -6 V. Scale bars are 2 µm.
AFM-tip the loop is discharged as observed on the subsequent EFM-image (panel b). It was not possible to recharge the loop by applying voltages of ( 20 V to the tip while touching the substrate. The disappearance of the loop force unambiguously shows that Φl is not due to a geometric effect. Furthermore, since the entire loop is discharged by just touching the middle of the loop and the observation that the charges are uniformly distributed within the loops suggests that the charges are relatively mobile on the surface and not trapped deeply in the substrate. In panels d-g a similar series of images is shown where the charges (∼3000e) are removed by cutting a nanotube coil using the AFM tip in contact mode to ensure that the surface was indeed touched when removing the charges. Only a fraction of all loops have trapped charges as seen from Figure 1b which shows loops both with and without charges, and Figure 1d which shows 22 loops on a sample from a different batch, none of which show trapped charges. Altogether, trapped charges have been observed in samples from 2 out of the 8 separate growth runs which produced samples with loops. However, there is a large variation between different areas on the samples. Trapped charges have been observed in loops with diameters from 2 to 4 µm. We have not observed significant trapped charges in regions fenced by CNTs in other geometrical configurations than closed loops or coils. We speculate that the charges stem from ions introduced during the sample preparation, e.g., from the iron nitrate used as catalyst for the CVD growth or other impurities.3 The CNT may deplete neighboring regions of the substrate from free charges, effectively making the region in the interior an isolated island where charges can reside. Alternatively, the CNT loops could themselves be negatively charged and thus trap charges through the Coulomb interaction. In the latter case, however, the static Nano Lett., Vol. 5, No. 9, 2005
charges should contribute a large linear component to the Vs dependence of ΦNT (Figure 2c), which is not observed. It it also possible that the hydrophobic CNTs enclose a thin layer of surface-adsorbed water molecules which can trap charges. Reference 3 estimates local charge densities up to 10-5 C/cm2 in the proximity of CNT-FETs, and it is suggested that this is due to charge trapping in surface bound water molecules. This indicates that the smaller densities of around 10-8 C/cm2 found in the present study could indeed be enabled by the presence of a water layer. Tribological effects where charges are induced on the substrate by the scanning cantilever can be ruled out since scanning does not recharge loops that were once discharged, as in Figure 3a. In the lower loop of Figure 3a, charges did not reappear after 12 h. Further work where charge is deliberately injected during the experiments could aid in resolving the issue. In conclusion, we have used EFM to quantitatively address the interaction between surface charges and carbon nanotubes. We find that surface charges can be effectively trapped on the substrate in regions enclosed by CNTs. The charges can be removed by AFM manipulation. Static charges are responsible for the hysteretic behavior of CNT FETs that play a key role in CNT memories, sensors, and logic circuits. References 1, 2, and 3 find that charge traps of only a few e can significantly affect the conductance of CNT FETs, suggesting that the charge pools with around 103e found here would have a significant impact on CNT devices. In particular, the behavior of the CNT loop devices might be different from those of ordinary CNT devices. Furthermore, we have shown that EFM provides a powerful tool for rapid characterization of large area CNT samples, and the present work shows how to identify contributions from static charges in such data. Acknowledgment. We acknowledge P.E. Lindelof for discussions.
Nano Lett., Vol. 5, No. 9, 2005
References (1) Fuhrer, M. S.; Kim, B. M.; Durkop, T.; Brintlinger, T. Nano Lett. 2002, 2, 755. (2) Radosavljevic´, M.; Freitag, M.; Thadani, K. V.; Johnson, A. T. Nano Lett. 2002, 2, 761. (3) Kim, W.; Javey, A.; Vermesh, O.; Wang, Q.; Li, Y.; Dai, H. Nano Lett. 2003, 3, 193. (4) Kong, J.; Franklin, N.; Zhou, C.; Chapline, M.; Peng, S.; Cho, K.; Dai, H. Science 2000, 287, 622. (5) Collings, P. G.; Bradley, K.; Ishigami, M.; Zettl, A. Science 2000, 287, 1801. (6) Kru¨ger, M.; Buitelaar, M. R.; Nussbaumer, T.; Scho¨nenberger C.; Forro´, L. Appl. Phys. Lett. 2001, 78, 1291. (7) Hafner, J. H.; Cheung, C.-L.; Oosterkamp, T. H.; Lieber, C. M. J. Phys. Chem. B 2001, 105, 743. (8) Kim, W.; Chio, H. C.; Shim, M.; Li, Y.; Wang, D.; Dai, H. Nano Lett. 2002, 2, 703. (9) These as-grown loop structures are different from the closed CNT rings that can be formed during chemical processing of pregrown CNTs. See: Martel, R. et. al. Science 1999, 398, 299 and Sano, M. et. al. Science 2001, 293, 1299. (10) SCM-PIT cantilevers from Veeco Instruments, www.veeco.com. (11) Staii, C.; Johnson, A. T.; Pinto, N. J. Nano Lett. 2004, 4, 859. (12) Bockrath, M.; Markovic, N.; Shepard, A.; Tinkham, M.; Gurevich, L.; Kouwenhoven, L. P.; Wu, M. W.; Sohn, L. L. Nano Lett. 2002, 2, 187. (13) For the Vs dependence in Figure 1e, the offset is chosen such that Φ ) 0° corresponds to the phase-shift for Vs ) 0 V. For the z-dependence the offset is arbitrary. (14) Terris, B. D.; Stern, J. E.; Rugar, D.; Mamin, H. J. Phys. ReV. Lett. 1989, 63, 2669. (15) Scho¨nenberger, C.; Alvarado, S. F. Phys. ReV. Lett. 1990, 65, 3162. (16) Guggisberg, M.; Bammerlin, M.; Loppacher, C.; Pfeiffer, O.; Abdurixit, A.; Barwich, V.; Bennewitz, R.; Baratoff, A.; Meyer, E.; Gu¨ntherodt, H. J. Phys. ReV. B 2000, 61, 11151. (17) Colchero, J.; Gil, A.; Baro´, A. M. Phys. ReV. B 2001, 64, 245403. Note that the cantilever used in this study have length half of that of our experiment (225 µm). Other cantilever parameters are similar. The effective cantilever-substrate separation is z + t/s ) 160 nm. (18) Stern, J. E.; Terris, B. D.; Mamin, H. J.; Rugar, D. Appl. Phys. Lett. 1988, 53, 2717. (19) The fit remains the same if the entire expression eq 4 is used.
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