Electron-electron interaction induced beam displacement in a multiple electron beam system

We have studied electron-electron (e-e) interaction induced beam displacement in multiple electron beam systems both experimentally and using trajectory simulation. A prototype 32-beam lithography system was used to record the beam displacements on chrome mask plates and the latter were directly measured by electron microscopy. Both experimental data and simulation results of demagnifying columns were consistent with a demagnification of the electron beam array with increasing current. While the simulation matched qualitatively the experimental data well, it predicted a smaller effect than measured. The overall demagnification was underestimated by 20%–30%. In an attempt to understand the underlying physical reason, we used a phenomenological model for the e-e induced beam displacement to fit the acquired data. The analysis suggested that the trajectory simulation underestimated the defocusing lens effect of the interacting electrons by about 1.5. The parametric expression derived from this model may be used to correct for global space charge effects during multi-electron beam lithography.