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2009, 113, 15476–15479 Published on Web 08/12/2009
Study of Charge Diffusion at the Carbon Nanotube-SiO2 Interface by Electrostatic Force Microscopy Yingran He,† Hock Guan Ong,‡ Yang Zhao,‡ Sailing He,† Lain-Jong Li,‡ and Junling Wang*,‡ Centre for Optical and Electromagnetic Research, Zhejiang UniVersity, Hangzhou, China 310058, and School of Materials Science and Engineering, Nanyang Technological UniVersity, Singapore 639798 ReceiVed: June 19, 2009; ReVised Manuscript ReceiVed: August 02, 2009
Hysteresis behavior is observed in the transfer characteristic of most carbon-nanotube-based field effect transistors, and charges trapped at the carbon nanotube-dielectric interface are believed to be the cause. We have studied charge injection and dissipation around the interface of carbon nanotubes and SiO2 at different temperatures using an electrostatic force microscope. Numerical simulations were performed to extract the charge diffusion coefficients on the SiO2 surface under ambient conditions at different temperatures, and a critical temperature of ∼150 °C is observed. The activation energy of charge diffusion changes from ∼0.43 to ∼0.98 eV above this temperature, which is attributed to the change of surface chemistry. A more accurate model taking into consideration the electrostatic interaction among charges is used subsequently, and the fitting results are significantly improved. It is noted that the two models lead to similar activation energies. I. Introduction Because of their good chemical stability and superior electrical and mechanical properties, carbon nanotubes (CNTs) are promising candidates for applications in nanoelectronics. CNT field effect transistors (CNT FETs) have been studied extensively since they were first reported a decade ago.1 However, hysteresis in the transfer characteristics between the forward and reverse gate bias sweeps exists in most CNT FETs. This is problematic for logic devices where a constant threshold voltage is needed for reliable performance. However, the two stable states of the channel conductivities could be utilized for nonvolatile memory applications. The data is written by applying a positive or negative gate bias and read by detecting the channel conductivity change.2 Thus, understanding the mechanism of the hysteresis behavior is important. Various groups have studied this phenomenon, and it has been observed that the amount of hysteresis depends on the environment and experimental parameters such as maximum gate bias, holding time, sweep rate, and temperature.3,4 Recent studies have suggested that charges injected from the CNT into the surrounding dielectrics play an important role. This is supported by the observation that positive gate bias increases the threshold voltage.2 If mobile charges preexisting in the gate dielectrics are the cause, the opposite sign hysteresis should be expected.5 It is also believed that the thin water layer at the interface affects the process significantly.2,6-8 In our previous report,9 we studied the charge injection from CNT onto SiO2 and the dissipation of injected charges around the CNT using electrostatic force microscopy (EFM) over a range of temperatures. In this paper, we report our numerical simulations of the charge dissipation process and extract precisely the charge diffusion coefficients on the SiO2 surface at different temperatures. A critical temperature is observed, and the activation energy changes significantly above it. The results clearly demonstrate the effect of * To whom correspondence should be addressed. Phone: (+65) 6316 8920. E-mail:
[email protected]. † Zhejiang University. ‡ Nanyang Technological University.
10.1021/jp905779f CCC: $40.75
surface chemistry on the charge trapping and dissipation processes at the CNT-SiO2 interface. II. Experimental Methods The experimental setup has been reported before9 and is schematically shown in Figure 1a. (For detailed experimental conditions, please refer to the Supporting Information.) A DC bias of -5 V is applied to electrode B, while the Si back gate is grounded and electrode A left floating. Electrons are injected from the CNT onto the SiO2 surface around it under this condition. The DC bias is applied for 10 min before electrode B is grounded. EFM is then used to scan a section of the CNT channel. We use the Asylum Research MFP-3D system with Olympus (OMCLAC240TM) Pt coated cantilevers for the experiments. The tip curvature radius is ∼15 nm, the spring constant is 2 N/m, the resonance frequency is ∼70 kHz, and the cantilever length is 240 µm. EFM is a dual-pass technique. The first scan captures the topography under tapping mode, and the second scan (the interleave scan) is done at a distance (30 nm in this study) from the surface with a DC bias applied to the tip (3 V in this study). The electrostatic force between the tip and the sample alters the tip resonance frequency, changing the phase and amplitude signals. The phase shift, which is related to the force (F) through the equation ∆φ ) -arcsin[(Q/k)(dF/dz)],10 is recorded as the tip scans along the surface. Q is the quality factor, and k is the spring constant of the cantilever. The value of the phase shift is proportional to the charge density. III. Results and Discussion Figure 1b shows the EFM image at 30 °C right after electrode B is grounded. Negative charges on the surface give rise to an attractive force on the tip (biased at 3 V), leading to bright contrast in the image.9 Thus, the brighter regions around the CNT correspond to higher charge density on the SiO2 surface. Figure 1c displays the contrast variation along the line indicated in Figure 2009 American Chemical Society
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Figure 1. (a) Schematic of the experimental setup. (b) EFM image measured during the discharging process with a tip bias of 3 V. The bright region along the CNT represents negative charges on the SiO2 surface. (c) Cross section profiles of the discharging images, indicating that charges diffuse back to the CNT and the peak moves to the right.
1b, which is ∼40 µm away from electrode B, at different times during the discharging process. It reveals the diffusion of the electrons back into the CNT and the formation of a charge density peak. Lines taken at different locations within the channel show similar behavior. x represents the distance away from the CNT, as shown in Figure 1b. A set of data was collected from 30 to 180 °C using the same setup. Fick’s second law, which governs the diffusion of particles, is employed to extract diffusion coefficients of the injected charges on the SiO2 surface from the experimental data. In our simulation, we only consider the direction perpendicular to the CNT. In other words, we treat the diffusion of injected charges in a onedimensional space. We assume that the diffusion coefficient is independent of density. Therefore, Fick’s second law is reduced to (∂c/∂t) ) D(∂2c/∂x2), where D is the diffusion coefficient and c
is the density of charges. We define the boundaries at the CNT (x ) 0 µm) and a point 10 µm from the CNT (x ) 10 µm), as indicated in Figure 1c. At x ) 0 µm, the CNT acts as a sink for charges, since it is grounded during the discharging process. We assume the diffusion current sinking into the CNT, jd ) -D(dc/ dx), is proportional to the charge density at this point, c(x)0). The other boundary (x ) 10 µm) is chosen because the charge density at this point is negligible, as observed in Figure 1c. Thus, the boundary conditions are summarized as the following:
x ) 0 µm, x ) 10 µm,
dc ) koutc dx c)0
D
Figure 2. Fitting of the experimental results using Fick’s second law at (a) 110 °C, (b) 130 °C, (c) 150 °C, and (d) 170 °C.
(1) (2)
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Figure 3. Plot of ln D vs 1/T showing a transition point at 150 °C, above which the activation energy changes from ∼0.43 to ∼0.98 eV. This is attributed to the transition where water molecules are removed from the SiO2 surface, leaving behind the silanol groups.
where kout is the proportional constant to be determined in the simulation. During the experiments, it is impossible to capture the exact initial discharge curve due to equipment limitation. Thus, the cross section line of the first captured image (∼2 s after the bias is turned off) is used as the initial density profile (t ) 0 min) for the simulation. The numerical calculation is done with
Letters Matlab version 7.5 for experimental results obtained between 110 and 180 °C (see the Supporting Information for the code). Figure 2 shows the simulated discharging curves (in lines) in comparison with the experimental results (in dots) for four temperatures: (a) 110 °C, (b) 130 °C, (c) 150 °C, and (d) 170 °C. Following the least-squares method, we obtain the values of kout ) 0.35, 1.3, 2.3, and 22.5 (µm/min) and D ) 0.25, 0.48, 0.85, and 3.16 (µm2/min), at the above temperatures, respectively. In order to calculate the activation energy of the charge diffusion process, i.e., the trap depth, we follow the general relation D ) D0 exp(-Ea/kbT). The gradient of the ln D vs 1/T plot reveals the activation energy. Unlike what was reported previously,9 it is noted that a transition occurs at ∼150 °C, revealing two distinct regions. It is shown in Figure 3 that the activation energy is ∼0.43 eV below 150 °C, which increases to ∼0.98 eV above 150 °C. It has been reported by different groups11,12 that a critical temperature exists in the region of 150-190 °C, above which water molecules are removed, exposing the silanol groups on the surface of SiO2. Thus, we conclude from our results that the activation energy of charge diffusion on the SiO2 surface is greatly reduced by the presence of water. The higher activation energy associated with the silanol groups suggests that, even though the hysteresis behavior can be reduced by removing the water layer, charges trapped by the silanol groups will induce hysteresis behavior that will persist for a much longer time. We note in Figure 2 that the simulated curves do not fit experimental results well at a distance further away from the CNT. Considering that the particles are electrons with negative
Figure 4. (a) Cross section profile of the discharging image at 180 °C (in dots) and fitting curve with the first model (lines). (b) Cross section profiles of the discharging image at 180 °C (in dots) and fitting curve with the second model (lines). (c) Plots of ln D vs 1/T from 110 to 180 °C. Top, the first model; bottom, the second model.
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charge, we add an electrostatic interaction term to the charge particle movement model. Both diffusion current bjd and drift current bje should be taken into account.
charge diffusion almost doubles its low temperature value. We attribute the difference to different trap depths of electrons by silanol groups and water layers on the SiO2 surface, respectively.
∂c ) -∇ · (bj d + bj e) ∂t be) ) -∇ · (-D∇c + σE σ be ) D∇2c ∇·D εrε0 σ )D∇2c c εrε0
Acknowledgment. We acknowledge the support from Nanyang Technological University and the Ministry of Education of Singapore under project numbers AcRF RG30/06 and ARC 16/08.
(3)
b e are the conductivity, electric field intensity and σ, b Ee, and D electric displacement intensity, respectively. By defining γ ≡ σ/εrε0, it is used as an additional variable parameter in the simulation. The boundary condition at x ) 0 is redefined as jd + je ) -D(dc/dx) + σEe ) kout′c and Ee is proportional to charge density at x ) 0. Thus, boundary condition D(dc/dx) ) kout′′c at x ) 0 is still applicable. The other boundary condition, c ) 0 at x ) 10 µm, remains unchanged. Following the least-squares method, we obtain the best fit to our experimental results by optimizing D, γ, and kout′′. The fitting quality is significantly improved. A comparison of the two models is shown in Figure 4a and b for experimental results obtained at 180 °C. The corresponding new D, γ, and kout′′ at this temperature are 3.1 µm2/min, 0.4 min-1, and 30 µm/min, respectively. We have also plotted ln D(c) vs 1/T from 110 to 180 °C in Figure 4c. The new results lead to activation energies of ∼0.46 and ∼0.91 eV for the two regions, respectively, which are similar to values obtained previously. IV. Conclusions In conclusion, we have obtained the diffusion coefficients of electrons on the SiO2 surface at different temperatures through simulations of the EFM images using two models. By taking into consideration the electrostatic interaction among electrons, fitting results are improved significantly. A critical temperature of ∼150 °C is observed, above which the activation energy of
Supporting Information Available: Detailed experimental conditions and Matlab code used for the simulations in this study. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Tans, S. J.; Verschueren, A. R. M.; Dekker, C. Nature (London) 1998, 393, 49–51. (2) Fuhrer, M. S.; Kim, B. M.; Drkop, T.; Brintlinger, T. Nano Lett. 2002, 2, 755–759. (3) Kim, W.; Javey, A.; Vermesh, O.; Wang, Q.; Li, Y.; Dai, H. Nano Lett. 2003, 3, 193–198. (4) Radosavljevic, M.; Freitag, M.; Thadani, K. V.; Johnson, A. T. Nano Lett. 2002, 2, 761–764. (5) Vanheusden, K.; Warren, W. L.; Devine, R. A. B.; Fleetwood, D. M.; Schwank, J. R.; Shaneyfelt, M. R.; Winokur, P. S.; Lemnios, Z. J. Nature 1997, 386, 587–589. (6) Robert-Peillard, A.; Rotkin, S. V. IEEE Trans. Nanotechnol. 2005, 4, 284–288. (7) Vijayaraghavan, A.; Kar, S.; Soldano, C.; Talapatra, S.; Nalamasu, O.; Ajayan, P. M. Appl. Phys. Lett. 2006, 89, 162108/1–162108/3. (8) Chua, L. L.; Zaumseil, J.; Chang, J. F.; Ou, C. W.; Ho, K. H.; Sirringhaus, H.; Friend, R. H. Nature (London) 2005, 434, 194–199. (9) Ong, H. G.; Cheah, J. W.; Chen, L.; Tangtang, H.; Xu, Y.; Li, B.; Zhang, H.; Li, L. J.; Wang, J. L. Appl. Phys. Lett. 2008, 93, 093509/1093509/3. (10) Sarid, D. Scanning Force Microscopy: With applications to Electric, Magnetic and Atomic Forces, revised edition; Oxford University Press, Inc: New York, 1994; Chapter 13, p 263. (11) Zhuravlev, L. T. Colloids Surf., A 2000, 173, 1–38. (12) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; Wiley-Interscience: New York, 1979; Chapter 7, p 866.
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