A modeling approach to charging in e‐beam columns

A fundamental requirement in e‐beam lithography is tight control of the electron beam position. Parasitic electrical fields due to charging in the beam environment are a common and often significant cause of position errors. It is difficult to generate controlled conditions to experimentally investigate the problem in a systematic manner. A modeling approach has therefore been taken to calculate the electrical fields generated by surface and space charges in the e‐beam column and their effect on the beam position error. A general expression for the effect of perturbing fields on the position error is derived. Perturbing electrical fields of surface charges and space charges generated by ions and secondary electrons are calculated as a function of key parameters (vacuum pressure, temperature, beam current, acceleration voltage, and dimensions) for cases of practical interest. Mechanisms for surface charging are included. From the results, critical areas are identified and conclusions are drawn regarding pr...