Charging of substrates irradiated by particle beams

A simple dynamical model for studying the charging of substrates irradiated by particle beams is developed. The charging potential for positive ion beams can be as large as the beam voltage. For negative ion beams, the charging potential is significantly lower and is governed by the secondary electrons. A closed form expression derived for the charging voltage in the case of negative ion beams agrees well with our numerical work. The results are consistent with observations on charging of isolated substrates during ion implantation with positive and negative ion beams.