For a metallic surface (Au) and highly doped (N) and (P) semiconductor surfaces (GaInAs) and for localised zones (2 Â 2 mm) we have measured using an electrostatic force microscope the variation of the gradient of the electrostatic force by the signal (phase of the oscillating movement of the metallised tip) as a function of the sample-tip potential difference (À 4 V to 4 V). In both cases the signal shows a quadratic variation with the sample-tip potential difference. The variation of the signal is of the order of magnitude of the theoretical predictions obtained by modelling the shape of the tip by a truncated cone a portion of a sphere.Using the parabolic curve that ®ts the experimental results, the value of the contact potential difference, corresponding to a zero value of the electrostatic force gradient, can be determined with an accuracy of 50 mV. The contact potential difference, measured between the metallised tip and the metal (Au), taken as a reference, allows the work function of the metal tip to be determined (5.25 eV). The values of the contact potential difference for the GaInAs (N) and (P) surfaces can be explained by the Fermi level pinning due to surface charges.The electrostatic force microscope (EFM) which is derived from the atomic force microscope (AFM) is sensitive to the electrostatic force between the metallised tip and the sample. This electrostatic force can be due to the presence of existing charges or to an applied bias between the tip and the sample.The interest of this new microscopy is its ability to image local voltages of working microelectronic structures [1, 2], charges on insulator surfaces [3] and to image the ferroelectric domains [4].The curve of the electrostatic force versus the potential difference between the tip and the sample allows measurement of the contact potential difference which is directly related to the work function difference. As for the Kelvin method [5], this also allows local potentiometry to be performed [6], or the dopant distribution to be mapped [7].The electrostatic force due to the effect of a potential difference between the tip and the surface of a metal or a highly doped semiconductor can be evaluated by an analytical model using a geometrical simulation of the tip shape and the cantilever [8,9].In this paper, we have used an EFM working in thè`t apping'' mode. The electrostatic force is separated from the van der Waals force by using a``lift'' method which allows ®rst the topography to be recorded using the van der Waals forces and then the surface topography to be followed at a distance constant equal or greater to 100 nm. At this distance, the tip is only sensitive to the electrostatic force.In the case of a metallic surface and of a highly doped semiconductor, we have calculated, using the geometrical shape of the tip, the electrostatic force as well as its gradient with the distance. We have done experiments by applying a bias to the Au contacts and the GaInAs (N) and (P) layers with the metallised tip grounded. For each sample, a 2 Â 2 mm ...