Three-dimensional tomography of single charge inside dielectric materials using electrostatic force microscopy
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Three-dimensional tomography of single charge inside dielectric materials using electrostatic force microscopy Clement Riedel1,2, Richard Arinero1, Angel Alegria2, Juan Colmenero2 and Juan Jose Saenz2,3 1
Institut d'Electronique du Sud, Université Montpellier 2, Montpellier, France Donostia International Physics Center, Universidad del pais vasco, San Sebastian, Spain 3 Universidad Autonoma de Madrid, Moving Light and Electron, Madrid, Spain 2
ABSTRACT In this contribution, we report on a numerical study demonstrating how to realize Electrostatic Force Microscopy (EFM) tomography. Based on the Equivalent Charge Method, both force and force gradient between a buried object (or trapped charges) and the Atomic Force Microscope tip are calculated. The main idea is to scan the sample at different tip sample distances and obtain the position and charge value of the object using reconstruction algorithms. The quantitative analysis here presented is a first step toward tomography for samples presenting “dilute” point charges creating non correlated signals by the interpretation of EFM signals. Lateral resolution, sensitivity (i.e. ability to detect an object), performance and limitations of EFM are also discussed in the paper. INTRODUCTION Among existing fine-scale tomography techniques, no one is able to provide electrical information of buried objects or trapped charges in dielectrics. Electrostatic Force Microscopy (EFM) may represent a solution to overcome this constraint. EFM allows characterizing electric and dielectric properties with tens nanometer spatial resolution. It has notably been used to observe and measure, respectively, single charge decay [1] and dielectric constant of insulating thin layers [2], and has also been applied for the first time to investigate polymer dynamics [3]. Moreover, it has been recently predicted theoretically that EFM should be a good candidate for subsurface characterization [4]. The aim of this work is to demonstrate the capabilities of EFM tomography, i.e. to obtain quantitative dielectric 3D information or subsurface trapped charges imaging. We first give a brief and rigorous introduction about how to tune an AFM in order to measure electrostatic force and force gradient signals. We then present a numerical study that demonstrates how to realize EFM tomography. The simulation of the Equivalent Charge Method permits to calculate both force and force gradient between a buried object and the microscope tip. The main idea is to scan the sample at different tip sample distances and obtain the position and charge value of the object using reconstruction algorithms. The lateral resolution, sensitivity (i.e. ability to detect an object) and particularities of EFM are then studied and discussed. ELECTROSTATIC FORCE MICROSCOPY OF DIELECTRICS AND EQUIVALENT CHARGE METHOD In the case of a thin dielectric film sample deposited on a conductive substrate, when a DC voltage V DC is applied to the probe (with the sample holder grounded), the electrostatic
1 ∂C (V DC − VCP )2 . VCP is the cont
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