Electric force microscopy of individually charged nanoparticles on conductors: An analytical model for quantitative charge imaging

We address in this paper the issue of quantitative charge imaging of individually charged semiconductor nanoparticles on conductive substrates by electric force microscopy (EFM). An analytical model is proposed for arbitrary tip and nanoparticle geometries to determine the amount of stored charges from the ratio $\mathcal{R}$ between the nanoparticle charge and capacitive force gradients. The quantitative character of the model is validated by extensive numerical calculations of EFM signals using various nanoparticle shapes, sizes, and aspect ratios, and different EFM tip geometries.