FEM simulation of charging effect during SEM metrology

SEM metrology is widely used in microelectronics to control patterns dimensions after many processes, especially patterning. Process control is achieved by verifying that experimental dimensions match targeted ones. However SEM metrology may give erroneous measurements if strong charging occurs. Charging effect impacts on the SEM image contrast and introduces artefacts. This article intends to report on the modeling of the physical phenomena occurring when the electron gun scans a sample and how charging effect occurs. For this, charge dynamics are modeled by taking into account the drift kinetics and the diffusion of electrons. The corresponding Partial Differential Equation system is solved using FEniCS open software. First, we show that when only top view measurement are modeled, the typical contrast of SEM pictures can not be predicted. Second, cross section views are modeled. This time, the expected contrast behavior is obtained. Finally, a full 3D simulation is presented.