Sensitivity analysis of the electrostatic force distance curve using Sobol’s method and design of experiments

Previous studies have demonstrated that the electrostatic force distance curve (EFDC) is a relevant way of probing injected charge in 3D. However, the EFDC needs a thorough investigation to be accurately analyzed and to provide information about charge localization. Interpreting the EFDC in terms of charge distribution is not straightforward from an experimental point of view. In this paper, a sensitivity analysis of the EFDC is studied using buried electrodes as a first approximation. In particular, the influence of input factors such as the electrode width, depth and applied potential are investigated. To reach this goal, the EFDC is fitted to a law described by four parameters, called logistic law, and the influence of the electrode parameters on the law parameters has been investigated. Then, two methods are applied—Sobol's method and the factorial design of experiment—to quantify the effect of each factor on each parameter of the logistic law. Complementary results are obtained from both methods, demonstrating that the EFDC is not the result of the superposition of the contribution of each electrode parameter, but that it exhibits a strong contribution from electrode parameter interaction. Furthermore, thanks to these results, a matricial model has been developed to predict EFDCs for any combination of electrode characteristics. A good correlation is observed with the experiments, and this is promising for charge investigation using an EFDC.