Study on physical model of resist surface charge in multi-beam mask writer and single variable-shaped beam writers

NuFlare Technology, Inc. has developed the charge effect correction (CEC) system, in which the predicted placement errors caused by resist surface charge effect are compensated. Due to good reproducibility of these exposure-dose-dependent and time-dependent behaviors, CEC has successfully improved image placement accuracy in single variable-shaped electron beam mask (EBM) writers. The physical mechanism of resist charging, however, has remained unclear. Considering large difference in beam current densities between EBM and multi-beam mask writers (MBM), it is concerning that unexpected charge phenomena occur. Therefore, it is required to reveal the mechanism and to show the resist charging is still predictable in MBM by a common charging model. In order to provide validity of CEC consistently with EBM and MBM, the surface charge densities caused in EBM writers and MBM-2000 were experimentally evaluated from those placement errors. The charge densities strongly depend on the resist thickness meanwhile they do not change significantly by the writers. Furthermore, equations to reproduce those experimental results are proposed in terms of a physical model, which takes into account low-energy secondary electrons drawn to resist surface by an already-existing surface charge and vertical flow of the charge in the resist.