Reduction in beam positioning error by modification of dynamic responses in electron beam direct writing system

Abstract

The dynamic responses of the electron beam direct writing system (EB direct writing system) are analyzed using the finite element method (FEM). The equipment is found to have a column swing vibration mode around 160 Hz. The column swing is caused by a bending vibration in the upper plate of the chamber. This vibration is initiated by the movement of the stage drive within the chamber. When column swing occurs, the resulting change in angle of the beam line creates a positioning error. FEM is also used to calculate the relative rotation angle of the column top to the stage surface. The maximum amplitude occurring after stage movement has stopped is 0.208 μrad. Since the distance between the upper plate of the chamber and the stage surface is 79 mm, the beam positioning error is 0.208 μrad×79 mm=16.4 nm. This error can be lessened by stiffening the upper plate. Utilizing cross ribs on this plate, the relative rotation angle can be lessened to 0.073 μrad. Thus, beam positioning error can be reduced to 0.073 μrad×79 mm=5.8 nm. Further, the increase in equipment weight is only 2%.