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 an d 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 co nsidered for beam shapes of the exposure system. The effects of discharging due to electron beam induced conductivity are included in the analysis. Th e Poisson equation is solved for the potential distribution by using the si multaneous overrelaxation method. The iteration technique is used for the c onvergence of the potential. With the given potential distribution, beam de flection is calculated using the fourth order Runge-Kutta integration algor ithm. Comparison of the values of the surface potential obtained by simulat ions with experimental results by Pease' group at Stanford University show similar shapes between them. We also have applied this work to a SCALPEL ma sk with a thin silicon nitride membrane. This work will be helpful for the exact understanding and avoidance of charging effects, when an electron bea m is irradiating an insulator. (C) 2000 American Vacuum Society. [S0734-211 X(00)07506-X].