Quantitative Charge Imaging of Silicon Nanocrystals by Atomic Force Microscopy
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Quantitative Charge Imaging of Silicon Nanocrystals by Atomic Force Microscopy Tao Feng and Harry A. Atwater1 Department of Applied Physics, California Institute of Technology, Pasadena, CA 91125, U.S.A. 1 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A. ABSTRACT Quantitative understanding of charging and discharging of Si nanocrystals in SiO2 films on Si substrate is essential to their application in floating gate nonvolatile memory devices. Charge imaging by atomic force microscopy (AFM) or electrostatic force microscopy (EFM) can provide qualitative information on such system, while a further step is needed. We have developed a generalized method of images, which can solve Poisson equation for multiple dielectric layers, to simulate the charge imaging of Si nanocrystals by non-contact mode AFM under different sample geometries. Simulated images can be compared with experimental images thoroughly to estimate the total amount and distributions of trapped charges, which is also useful in the study of time evolution of charges or dissipation problems. INTRODUCTION Spatial confinement of charges in nanometer-scale structures has great potential of application in novel electronic devices such as Si nanocrystal-based memories [1]. To study the local properties of these spatially confined charges and their effects in device operation, atomic force microscopy (AFM) [2] and electrostatic force microscopy (EFM) [3] have been used in charge deposition and detection [4-7]. To estimate the total amount of localized charges and to understand the charge distribution and dynamics, a quantitative charge imaging method is always demanded. This work is still far from completion due to the complex factors involved, especially, tip-sample interactions. Models for non-contact mode and tapping mode have been developed to calculate van der Waals force or contact force [8]. However, an accurate description and calculation of electrostatic force is important since it plays a key role in the charge imaging. In our model, the tip of AFM is approximated as a grounded metallic sphere, excited to oscillate like a harmonic oscillator close to its resonant frequency. The interactions between tip and sample include van der Waals force and electrostatic force. With the assumption that oscillation amplitude is much smaller than tip-sample distance, it can be proved the AFM feedback system adjusts the tip height to maintain a constant force gradient, which can be calculated based on experimental parameters. Thus in the simulation, the solution of equation ∂Fz ∂z total
=
∂Fz ∂z van
+ der Waals
∂Fz ∂z electrosta tic
=
Const
(1)
determines the tip position above the scanned region. The electrostatic force arises from the interaction between the charges of the sample and induced charges at the surface of the conducting tip. Using the method of images, it can be regarded that the interaction is between
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sample charges and image charges in the tip, and
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