PIERS ONLINE, VOL. 3, NO. 3, 2007 300 Hybrid Numerical Simulation of Electrostatic Force Microscopes Considering Charge Distribution U. B. Bala, M. Greiff, and W. Mathis Institute of Electromagnetic Theory Leibniz University of Hannover, Germany Abstract— The electrostatic force microscope (EFM) is an important tool for imaging and characterizing material surfaces. In this paper a hybrid numerical approach for the simulation of the EFM considering charge distribution inside the sample under investigtion is presented. In the simulation model electrical part is considered. In this paper first a basic knowledge on the EFM and then the numerical model of the EFM considering volume charge distribution are presented. At last several numerical simulation results of the EFM in 3D are pesented. DOI: 10.2529/PIERS060908081435 1. INTRODUCTION A significant progress in nanotechnology has been observed over the last few years. This progress has also been influenced by the development of new high resolution measurement instruments. Due to the rapid miniaturization of integrated devices into the mesoscopic regime and the increasing interest in very small structures, these instruments have become very important. An interesting example is the atomic force microscope (AFM). Based on the design of the scanning tunneling microscope (STM), the first AFM was developed in 1986 by G. Binnig and his coworkers in col- laboration between IBM and Standford university. Since then a new era of topographical imaging, as well as for measuring force-separation interactions between a probe and substrate began. The AFM’s ability to scan surfaces with nearly atomic resolution and its versatility make it one of the most important measurement devices in nanotechnics. If the sample under investigation holds a charge distribution and the distance between the AFM tip and the sample is kept large then all other interaction forces except the electrostatic force can be neglected. This special working mode of the AFM is known as electrostatic force microscope (EFM) which can be used for scanning electric field with nearly atomic resolution. The EFM has many materials-related applications including measuring the surface potential or contact potential, detecting charges on surfaces or nanocrystals etc. In this paper a 3D model of the EFM is presented considering charge distribution inside the sample. Several numerical methods are proposed to calculate the electric eld more efficiently. 2. WORKING PRINCIPLE AND MODEL OF THE EFM For the EFM the interaction force would be the electrostatic force between the biased atomically sharp tip and the sample. In addition the Van der Waals force between the tip and the sample are always present. The Van der Waals force and the electrostatic force have two different dom- inant regions. The Van der Waals force is proportional to 1/r 6 where as the elctrostatic force is proportional to 1/r 2 . Thus when the tip is close to the sample the Van der Waals force is dominat and when the tip is moved away from the sample the electrostatic force is dominant. The scanning of the EFM is usually done in two steps. First the topography of the sample is done by tapping scanning mode which is also known as “intermittent-contact” (IC) mode. In this case the Van der Waals force plays a signifiant role. Second using this topgraphical information a constant tip-sample distance is maintained while scanning where the electrostatic force is dominat, a technique which is known as “lift scanning” [1]. In this technique it is assumed that the influence of all short-range forces can be neglected and only the electrostatic force plays the vital role for imaging. To detect the electrostatic force a voltage is applied between the cantilever tip and the sample. The cantilever oscillates near its resonance frequency which changes in response to any additional force gradient. Changes in cantilever resonant frequency can be detected using phase detection, frequency modula- tion, amplitude modulation etc. A diode laser is focused on the back of the reflective cantilever and the reflected light is collected by a position sensitive detector (PSD). This usually consists of two closely spaced photodiodes. Any angular displacement of the cantilever results in one photodiode