Observation of electric field gradients near field-emission cathode arrays

Liang, Yuncheng; Bonnell, Dawn A.; Goodhue, W. D.; Rathman, D.D.; Bozler, C.O.

doi:10.1063/1.113841

Cited by 18 publications

(20 citation statements)

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“…By fitting the log-log plots of the force gradients, the linear relation of log(FЈ) vs log͑L͒ means that the FЈ is proportional to the exponential of L, which is similar to that observed for the conical field emitter of submicrometer . 6 The parameters used in the calculation are close to that of the nanotubes arrays fabricated as described earlier. The anode voltage is 1 V and the cathode is grounded.…”

Section: Resultsmentioning

confidence: 99%

“…The electrostatic force microscopy ͑EFM͒ is a useful tool to give three-dimensional ͑3D͒ mapping of the electric field gradient as well as surface topography. 6 By using a conductive tip as a nanosize probe, the space field above the sample surface can be measured from the quantitative electrostatic force sensed by the cantilever. In this article, we will present our experimental and numerical studies on the local electric field at the surface of the nanotube thin film induced by a conductive tip.…”

Section: Introductionmentioning

confidence: 99%

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Probing local electric field distribution of nanotube arrays using electrostatic force microscopy

Zhang

et al. 2003

Journal of Applied Physics

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The local electric field distribution of nanotube arrays has been studied by using the electrostatic force microscopy ͑EFM͒ technique. The nanotube arrays were fabricated using the anodic alumina template method. Good electric contact has been proofed using contact mode conductive atomic force microscopy. The experiment shows that the EFM can provide a quantitative mapping tool to measure three-dimensional distribution of local electric field with resolution down to several nanometers. The finite difference method has been applied to calculate the electric field distribution near the surface of the nanotube array induced by a conductive tip. The results show that the field decays in a power law with exponent varies for nanotubes of different packing environments as the tip was lifted away from the top of nanotubes. The protrusion of nanotubes causes a much higher enhanced field than packing geometry. Medium packing density may enable the maximum collective emission current for such nanotube arrays of narrow diameter and height diversity.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probing local electric field distribution of nanotube arrays using electrostatic force microscopy

Zhang

et al. 2003

Journal of Applied Physics

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“…More precisely, this type of microscope is realized by applying a voltage on a conducting AFM tip. It is a good tool for imaging samples that present a gradient of electrical properties [3][4][5]. Variations of flexion of the cantilever holding the tip during a scan allow us to construct an electrical image [6] on inhomogeneous materials as well as on nanostructures (superlattices, nanoelectronics, etc.)…”

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confidence: 99%

Finite element simulations of the resolution in electrostatic force microscopy

Belaidi

Lebon²,

Girard

et al. 1998

Applied Physics A: Materials Science & Processing

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In this paper, we present simulation results for the electrostatic force between two conducting parts placed at different voltages: an atomic force microscope (AFM) sensor and a metallic sample. The sensor is composed of a cantilever supporting a conical tip terminated by a spherical apex. The simulations are based on the finite element method. For tip-sample distances (5-50 nm) and for an electrically homogeneous plane, the electrostatic force can be compared to the results obtained with the equivalent charge model and experiment. By scanning a plane with a potential step, the variation of the electrostatic force near the discontinuity gives the spatial resolution in electrostatic force microscopy (EFM). We establish then the relationships between the resolution, tipsample distance, and tip apex radius.The electrostatic force microscope results from one of many specializations of tip sensor in near-field microscopy [1, 2]. More precisely, this type of microscope is realized by applying a voltage on a conducting AFM tip. It is a good tool for imaging samples that present a gradient of electrical properties [3][4][5]. Variations of flexion of the cantilever holding the tip during a scan allow us to construct an electrical image [6] on inhomogeneous materials as well as on nanostructures (superlattices, nanoelectronics, etc.) [7][8][9]. In the simple case where the tip is in front of a conductive plane sample, we can deduce the force applied on the sensor by means of analytical expressions [10][11][12] or an equivalent charge model [13]. As soon as the geometry of the sample becomes complex (integrated circuits, dielectrics), the theoretical behavior of the system can be obtained by numerical methods such as the surface charge method [14], finite difference method [15], or finite element method [16].To determine the properties of the electrostatic force microscope in front of a sample with areas at different potentials, we propose to use the finite element method. In Sect. 1 we verify the results obtained by this numerical method in the simple case of a tip in front of a plane sample at constant potential [13]. In Sect. 2 we consider the response of the microscope near a potential step [17]. For this, we study the 3-dimensional tip-object system and determine the force applied on the tip by the finite element method and then we deduce the resolution for a potential step. Mathematical model The electrostatic problemThe problem consists in determining the interaction between an AFM sensor (tip + cantilever) and an infinite plane (both conducting). If the tip is long enough or the distance d between the tip and the sample is small, we can neglect the effect of the cantilever [18]. Then, the study is reduced to the calculation of the force exerted on a conical tip in front of a metallic plane. We treat the problem in 3-dimensional space because heterogeneities, as introduced in Sect. 2, cause the revolution symmetry to disappear. First, we must obtain the potential distribution in the space between the tip and the plan...

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“…Electrostatic force microscopy (EFM), [3][4][5][6][7][8][9] measures the long-range electrostatic interactions between a sample and a conducting probe when a voltage is applied between them. This methodology, with slight variations, has been applied to electric field distributions in devices, [10][11][12] electrostatics of self-assembled monolayers on surfaces, 13 studies of surface potential variations in oxide bicrystals, 14,15 static and dynamic properties of ferroelectric materials, [16][17][18][19][20][21] charge measurements in single nanostructures, [22][23][24] as well as observation of charge storage and leakage in various materials. [25][26][27] Although some quantitative measurements of surface charges have been reported, 7,13,22,[24][25][26][27][28][29] most applications of EFM have focused on the mapping of surface potential, which does not require a quantitative understanding of the tip-surface capacitance.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Noncontact Electrostatic Force Imaging of Nanocrystal Polarizability

et al. 2003

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A simple analytical model describing tip-surface interactions in an electrostatic force microscopy (EFM) experiment is proposed. Tip-surface capacitance is modeled as a sum of capacitances of cone, sphere, and plate with the substrate. Individual tips are calibrated according to this model by the choice of tip radius. Differences in EFM signal amplitude between probes are explained by differences in the sphere radii. Three tips with different sphere radii were used to detect EFM force gradients on an array of samples of dispersed Au nanoparticles with diameters ranging from 6 to 18 nm. The spatial distribution of the electric field created by an Au nanoparticle polarized by the inhomogeneous field of the tip is calculated analytically. The particle diameter and tip-surface separation dependence of the measured force gradient due to metal sphere polarization is compared to that predicted by the model. A statistically significant z-offset factor is introduced into the model to correct for the curvature mismatch between the model system and the actual tip. IntroductionSince the invention of scanning tunneling and atomic force microscopies, 1,2 various adaptations of the scanning probe technique have revolutionized the study of surfaces. Scanning probe methods allow the simultaneous mapping and correlation of surface topography and other physical properties. Electrostatic force microscopy (EFM), 3-9 measures the long-range electrostatic interactions between a sample and a conducting probe when a voltage is applied between them. This methodology, with slight variations, has been applied to electric field distributions in devices, 10-12 electrostatics of self-assembled monolayers on surfaces, 13 studies of surface potential variations in oxide bicrystals, 14,15 static and dynamic properties of ferroelectric materials, 16-21 charge measurements in single nanostructures, [22][23][24] as well as observation of charge storage and leakage in various materials. [25][26][27] Although some quantitative measurements of surface charges have been reported, 7,13,22,24-29 most applications of EFM have focused on the mapping of surface potential, which does not require a quantitative understanding of the tip-surface capacitance. However, surface potential does not uniquely determine the charge and polarizability distribution in the sample. To determine the distribution of static charges and polarizability, one must characterize the capacitive interactions between the surface and the probe. Because the EFM probe is in reality an irregular pyramid with a small rounded tip, there is no simple analytical solution. Hence, an approximate model must be used. A number of theoretical works exploring both analytical and numerical methods have addressed these issues, proposing different simplified geometries for the AFM probe, such as cone, sphere, parallel-plate, hyperboloid, as well as their various combinations. [30][31][32][33][34][35][36][37] Herein we develop the apparatus and modeling methodology to enable rigorous quantitative EFM int...

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Observation of electric field gradients near field-emission cathode arrays

Cited by 18 publications

References 1 publication

Probing local electric field distribution of nanotube arrays using electrostatic force microscopy

Probing local electric field distribution of nanotube arrays using electrostatic force microscopy

Finite element simulations of the resolution in electrostatic force microscopy

Quantitative Noncontact Electrostatic Force Imaging of Nanocrystal Polarizability

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