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J. Phys. Chem. C 2009, 113, 204–207
Quantifying Surface Charge Density by Using an Electric Force Microscope with a Referential Structure Guicun Qi, Yanlian Yang, Hao Yan, Li Guan, Yibao Li, Xiaohui Qiu,* and Chen Wang* National Center for Nanoscience and Technology, Beijing 100190, People’s Republic of China ReceiVed: March 12, 2008; ReVised Manuscript ReceiVed: October 31, 2008
A comparative method was proposed to quantitatively measure the charge density on sample surfaces at the nanometer scale by using an electric force microscope (EFM). By introducing a millimeter-sized conductive sphere as a charge reference, whose surface charge density was proportional to the applied voltage, the electrostatic interaction between an EFM probe and the sphere could be calibrated as a function of charge density. Because the Coulombic force acting on the probe is proportional to the linear term of the phase shift (∆θ) versus tip voltage (Vt) characteristics, the charge density of an unknown sample could be derived by comparing the slopes of the characteristic curves measured on the studied sample with that obtained on the reference sphere whose absolute charge density had been known. The approach was applied to determine the charge density of a freshly cleaved mica surface. The comparative scheme avoids the complex influence from the irregular shape of EFM tips, providing a facile approach for quantitative analysis of the charge density on sample surfaces at the nanometer scale. I. Introduction The miniaturization of electronic devices demands precise information on the functionalities and electrostatic characteristics of nanosized structures.1-6 Since the past decade, the electric force microscope (EFM) has provided a powerful method to investigate the electrical properties, such as charge density and charge distribution, in various materials7-12 and devices.13-15 The capability of simultaneously performing topographical and electrical measurements enables EFM to directly investigate the electrostatics properties of self-assembled organic monolayers,16 surface potential variations in oxide bicrystals,17,18 as well as charge storage in nanoparticles.19-22 Recently, the application of EFM has been more focused on extracting quantitative information on the local dielectric constant, trapped charge, and work function of nanostructure materials. In many cases, to quantify the EFM signal is a nontrivial process because of the difficulties in simulating complex interactions between EFM probes and samples. Although models based on isolated point charges21,23 and parallel-plate geometry22,24 have been proposed and extended by taking the tip shape, particle geometry, and image charge effects in the substrate9,25,26 into consideration, a quantitative analysis of EFM data still calls for detailed knowledge of the tip geometry as well as the exact nature of the tip-sample interaction.9,27 In this paper, we propose a comparative method to measure the charge density on sample surfaces by using an EFM. The scheme uses a millimeter-sized conductive sphere as a charge reference to calibrate the electrostatic interaction between an EFM probe and the sphere, whose surface charge density is proportional to the voltages applied to it. By comparing the slopes of the phase shift (∆θ) versus tip voltage (Vt) characteristics measured on an unknown sample with that obtained on the reference sphere, the charge density of the studied sample could be directly derived without complex simulation that requires precise information about the irregular geometry of the * To whom correspondence should be addressed. E-mail:
[email protected] (X.Q.);
[email protected] (C.W.).
EFM probe. The approach provides a facile route to quantitatively analyze the charge density on sample surfaces at the nanometer scale. The detailed principle of the method is described as follows. Previous studies have shown that the total electrostatic forces acting on an EFM tip over a sample can be separated into two components: capacitive forces associated with the tip-sample capacitance and Coulombic forces due to the static charges and/ or multipoles on the sample surface.28 A generalized expression is given by28,29
1 F ) Ct′Vt2 + EsQt 2
(1)
Here, C ′t is the derivative of tip-sample capacitance with respect to tip-to-sample separation. Vt is the voltage applied to the tip. Qt is the effective charge on the tip. We expect Qt ) CtVt when a tip is located near a planar sample surface. Es represents the electric field at the tip location that is only created by the charges and/or multipoles on the sample surface. For a flat sample with uniform surface charge density δs, Es could be regarded as a constant in the vicinity of the sample surface and be written as Es ) g(s)δs, where g(s) is a factor related to the tip geometry. The force gradient F ′ acting on the tip can be approximated as
F′ )
∂F 1 ≈ C ″V 2 + g(s)δsCt′Vt ∂z 2 t t
(2)
At small oscillation amplitude, the phase shift of a cantilever is tan(∆θ) ≈ -(QF ′)/k, where Q and k are the quality factor and effective spring constant of the cantilever, respectively. Equation 2 could be further written as
tan(∆θ) ) -
Q 1 C ″V 2 + g(s)δsCt′Vt k 2 t t
(
)
(3)
Equation 3 suggests that the capacitive contribution, -QC ′′t / (2k), is determined by the characteristic tip capacitance. In contrast, the Coulombic component, -Qg(s)δsC ′t/k, is linearly proportional to the charge density δs of the sample surface and can be deduced by measuring the slope of the characteristic
10.1021/jp806667h CCC: $40.75 2009 American Chemical Society Published on Web 12/09/2008
Quantifying Surface Charge Density by EFM
Figure 1. Schematic of the experimental setup. A stainless steel sphere 5.01 mm in diameter supported on a PVC substrate is electrically connected via a thin copper wire to the bias channel of the EFM instrument.
curve of tan(∆θ) versus tip voltage (Vt). For a given tip and lift height, the value of -Qg(s)C ′t/k is expected to be a constant irrespective of sample species. Therefore, if we introduce a reference of known surface charge density, the charge density of a studied sample can be readily calculated by comparing the slopes of the tan(∆θ) versus tip voltage (Vt) characteristics measured on the reference and that on the sample.
J. Phys. Chem. C, Vol. 113, No. 1, 2009 205
Figure 2. Characteristic curves of tan(∆θ) vs the tip voltages (Vt) measured on the referential sphere with sphere voltage varying from -10 to 10 V. The experiments were performed at the conditions of lift height of 200 nm and tip voltage varying from -6 to 6 V.
II. Experimental Section The EFM measurements were performed with a Dimension 3100 atomic force microscope (Veeco Metrology Group, U.S.A.). EFM tips (MESP, Veeco) are highly doped Si cantilevers coated with Cr and Co with a nominal spring constant κ of 2.8 N/m and a resonance frequency of 75 kHz. The tip height is in the range of 10 to 15 µm. The topography and EFM phase images were obtained simultaneously by using the interleaving scan mode, i.e., each scan line is composed of two passes. The first pass is to get the topographic image with the feedback active in a standard tapping mode. In the pass, no voltage is applied to the tip; in the second pass, the topographic data is used to retrace the first pass and the tip is raised at a given height above the sample. In the pass, voltages varying from -6 to 6 V are applied to the tip with the feedback disabled. In our experiments, self-programmed software successively changed the dc voltages acting on the tip. Phase shift ∆θ is the difference between the phases of tip oscillation at tip bias of Vt and null. A stainless steel sphere 5.01 mm in diameter and with an rms roughness of 1.15 nm (see Figure 1 in the Supporting Information) was used in the experiment. To minimize the organic and inorganic contamination, the sphere was thoroughly rinsed in ethanol, acetone, and purified water by ultrasonic treatment. As schematically shown in Figure 1, the sphere was glued on a poly(vinyl chloride) (PVC) substrate to insulate from the EFM chuck base. A thin copper wire 5.0 µm in diameter was carefully soldered to the side of the sphere opposite to the tip scan area and electrically connected to the bias channel of the instrument. Measurement on the newly cleaved mica was performed using the same experimental conditions, especially lift height, as that used on the referential sphere. III. Results and Discussion The conductive sphere as shown in Figure 1 could be considered as an isolated capacitor, whose surface charge density could be calculated according to δs ) CsphereVsp/4πR2 ) ε0Vsp/ R. Here Csphere is the capacitance of the isolated sphere, Vsp is the voltage applied to the sphere, R is the radii of the sphere, and ε0 is the dielectric constant of air. Because the nominal
Figure 3. Coefficients of the Coulombic term (Kcou ) -Qg(s)δsC t′/k) (black line with solid black squares) and capacitive term (Kcap ) -QC ′′t /(2k)) (blue line with empty blue squares) vs sphere voltage (Vsp). The charge density on the sphere surface at the corresponding voltage is shown on the top axis. The voltage range applied to the sphere is from -10 to 10 V.
radius of an EFM tip is a few tens of nanometers, the sphere surface could be viewed as an infinite plane. The surface charge density δs of the sphere was varied by changing the voltages applied to the sphere. Figure 2 shows the characteristic curves of tan(∆θ) versus tip voltage (Vt) measured at various sphere voltages. The tip voltage Vt was varied from -6.00 to 6.00 V with step voltage of 1.00 V. And the sphere voltage Vsp was increased from -10.00 to 10.00 V. The curves became more linear with increasing sphere voltages because the contribution from the Coulombic term becomes more significant at larger sphere voltages. These results were consistent with the prediction in eq 3. By fitting the curves according to eq 3, the coefficients of the capacitive and Coulombic terms were obtained. Figure 3 plots the curves of the coefficients of the capacitive and Coulombic terms as a function of the sphere voltage Vsp. It is noticed that the coefficient of the capacitive term is nearly constant, irrespective of the sphere voltages Vsp. In contrast, the Coulombic term is proportional to the sphere voltage Vsp, indicating a linear dependence on the surface charge density δs of the reference sphere (see the simulation in the Supporting Information). The curve of the Coulombic coefficients versus the sphere voltage Vsp in Figure 3 is referred to as the calibration curve for subsequently calculating the surface charge density
206 J. Phys. Chem. C, Vol. 113, No. 1, 2009
Figure 4. Calibration curve of the Coulombic coefficient (Kcou ) -Qg(s)δsC ′t/k) vs sphere voltage (Vsp) measured on the reference sphere. Fitting the characteristic curves of tan(∆θ) vs the tip voltages (Vt) measured on a sample of freshly cleaved mica yields a Coulombic coefficient of 0.0578, which is marked as a star in the curve. The surface charge density δs on the mica surface is equivalent to that on the sphere surface induced by a sphere voltage of 14.3 V, which corresponds to the charge density of 3.2 × 107 e/cm2.
of unknown samples. For these samples, we could derive the coefficient of the Coulombic term in corresponding characteristic curves measured under the same experimental conditions as the sphere experiments. The charge density δs of the studied samples could be calculated by comparing the coefficient of the studied sample with the values of the referential sphere. The method was applied to characterize the charge density of mica. Freshly cleaved mica surface is a common substrate for studying the aggregation morphology, interaction mechanism, and binding theory of protein, DNA, and organic semiconductor materials.30-32 In the lamellar crystal structure of mica, one of every four Si4+ is substituted by Al3+ and causes a net negative charge structural surface that is compensated by potassium ions on the interface of mica layers. On freshly cleaved mica surface, high surface potential was observed and attributed to a loss or uneven charge distribution of potassium ion on two cleaved surfaces.33-35 The quantitative information on the charge distribution of the mica surface is important to reveal the detailed mechanism related to these surface assembling processes. The characteristic curve of tan(∆θ) versus the tip voltage Vt was measured on a newly cleaved mica surface under the same condition as that used in the reference experiment. Fitting the curve with eq 3 yielded a Coulombic coefficient of 0.0578. By referring to the calibration curve in Figure 4, the value (marked by a star in the curve) corresponds to the surface charge density of the reference sphere at a voltage of 14.3 V. The surface charge density on the freshly cleaved mica surface was then determined to be 3.2 × 107 e/cm2. The data is consistent with previous studies that showed the surface potential of mica immediately after cleavage was more than 10 V and might last for several hours in dry environments.35 The maximum surface charge density of mica was calculated to be 2.0 × 1014 e/cm2 based on the mica lattice structure; however, this value is sensitively dependent on the environmental condition, e.g., humidity. When exposed in ambient environment, the freshly cleaved mica surface would finally become neutral due to hydrated surface ions. This slow discharging process was also observed in our experiment as shown in Figure 5. The plot suggests that the charge density on the mica surface decreased with extended exposure time, which is in agreement with previous results.35
Qi et al.
Figure 5. Evolution of the coefficient of the Coulombic term (Kcou ) -Qg(s)δsC t′/k) obtained on a mica surface as a function of exposure time in ambient environment. The experiments were carried out at the conditions of lift scanning height of 50 nm and tip voltages varying from -4 to 4 V.
It should be mentioned that the surface charge on the studied samples might affect the charge distribution on the tip. Such effect is adverse to the measuring accuracy; however, the proposed comparative scheme is meaningful to further develop quantitative characterization based on EFM. IV. Conclusions In summary, we have proposed a comparative method to measure the surface charge density by using an EFM, based on referring to a millimeter-sized conductive sphere as a charge reference. This “nanoelectrometer” would be helpful for quantitatively studying the electric properties of sample surfaces at the nanometer scale. Acknowledgment. This work is supported by the National Basic Research Program of China (2007CB936800) and Chinese Academy of Sciences (KJCX2-YW-M04). Financial support from the National Science Foundation of China (90406019) is also gratefully acknowledged. Supporting Information Available: Atomic force microscopy (AFM) image of the sphere surface, section curves of topographic and EFM phase data, and simulation of the tip-sphere interaction. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Klein, L.; Williams, C. Appl. Phys. Lett. 2001, 79, 1828. (2) Bussmann, E.; Kim, D. J.; Williams, C. C. Appl. Phys. Lett. 2004, 85, 2538. (3) Parthasarathy, R.; Lin, X. M.; Elteto, K.; Rosenbaum, T. F.; Jaeger, H. M. Phys. ReV. Lett. 2004, 92, 076801. (4) Fan, H.; Yang, K.; Boye, D. M.; Sigmon, T.; Malloy, K. J.; Xu, H.; Lopez, G. P.; Brinker, C. J. Science 2004, 304, 567. (5) Likharev, K. K. Proc. IEEE 1999, 87, 606. (6) Nakakima, A.; Ito, Y.; Yokoyama, S. Appl. Phys. Lett. 2002, 81, 733. (7) Boer, E. A.; Bell, L. D.; Brongersma, M. L.; Atwater, H. A. J. Appl. Phys. 2001, 90, 2764. (8) Gordon, M. J.; Baron, T. Phys. ReV. B 2005, 72, 165420. (9) Me´lin, T.; Diesinger, H.; Deresmes, D.; Stie´venard, D. Phys. ReV. B 2004, 69, 035321. (10) Diesinger, H.; Me´lin, T.; Deresmes, D.; Stie´venard, D. Appl. Phys. Lett. 2004, 85, 3546. (11) Boer, E. A.; Brongersma, M. L.; Atwater, H. A.; Flagan, R. C.; Bell, L. D. Appl. Phys. Lett. 2001, 79, 791. (12) Boer, E. A.; Bell, L. D.; Brongersma, M. L.; Atwater, H. A. Appl. Phys. Lett. 2001, 78, 3133.
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