Calculation of surface potential and beam deflection due to charging effects in electron beam lithography

In this article, we describe the analysis procedures of charging effects and calculation results of surface potential and beam deflection in electron beam lithography. Monte Carlo simulation is performed to obtain the charge distribution in e beam resist. A focused (Gaussian) and a flood beam are considered for beam shapes of the exposure system. The effects of discharging due to electron beam induced conductivity are included in the analysis. The Poisson equation is solved for the potential distribution by using the simultaneous overrelaxation method. The iteration technique is used for the convergence of the potential. With the given potential distribution, beam deflection is calculated using the fourth order Runge-Kutta integration algorithm. Comparison of the values of the surface potential obtained by simulations with experimental results by Pease' group at Stanford University show similar shapes between them. We also have applied this work to a SCALPEL mask with a thin silicon nitride membrane. This work will be helpful for the exact understanding and avoidance of charging effects, when an electron beam is irradiating an insulator. (C) 2000 American Vacuum Society. [S0734-211X(00)07506-X].