The current state of the art of electrostatic force microscopy (EFM) is presented. The principles of EFM operation and the interpretation of the obtained local voltage and capacitance data are discussed. In order to show the capabilities of the EFM method, typical results for semiconducting nanostructures and lasers are presented and discussed. Improvements to EFM and complementary electrical methods using scanning microscopy demonstrate the continuing interest in electrical probing at the nanoscale range.

With the model of equivalent charge distribution, we calculated the exact electrostatic force acting on the real ͑conical͒ tip of an atomic force microscope. This model applies to a conductive tip in front of a conductive plane. We compared the equivalent charge model with several analytic models used to date to approximate the electrostatic forces and discussed their degree of validity. We estimated the contribution of the cantilever to the total force and showed, on the basis of theoretical calculations and experimental results, that the contribution of cantilever may constitute the essential part of the electrostatic force in the range of distances used in electrostatic force microscopy in the air.

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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...