The beam delivery modeling and error sources analysis of beam stabilization system for lithography

Abstract

Beam stabilization system is one of the most important units for lithography, which can accomplish displacement and pointing detection and control and includes beam measurement unit(BMU) and beam steering unit(BSU). Our group has set up a beam stabilization system and verified preliminarily beam stabilization algorithm of precise control beam position and angle. In the article, we establish beam delivery mathematic model and analyze the system inherent error. This shows that the reason why image rotation effect arises at the output plane of beam stabilization is the fast steering mirror (FSM) rotation of BSU in the process of beam stabilization. Two FSMs rotation around 45 o axis of FSM make the most contribution to image rotation which rotates 1.414 mrad as two FSMs rotation angle difference changes 1 mrad. It is found that error sources include three key points: FSM accuracy; measurement noise and beam translation by passing through of beam splitters changing as the ambient temperature changing. FSM accuracy leads to the maximum 13.2μm displacement error and 24.49μrad angle error. Measurement inaccuracy as a result of 5μm measurement noise results in the maximum 0.126mm displacement error and 57.2μrad angle error. Beam translation errors can be negligible if temperature is unchanged. We have achieved beam stability of about 15.5μrad for angle and 28μm for displacement (both 1σ) after correcting 2mm initial displacement deviation and 5mrad initial angle deviation with regard to the system rebuilt due to practical requirements.