Error analysis and compensation method of focus detection in exposure apparatus

An original approach to measurement accuracy of a typical focus sensor in conventional integrated circuit lithographic equipment is introduced. Causes of measurement error in the focus sensor are theoretically analyzed and found to be generated mainly from interactions between imperfections of the optical system and the actual surface of processed wafers. We derive mathematical formulations describing these errors, which are confirmed by the experimental results performed by using an optical setup composed of the focus sensor and samples on which the wafer surface condition is reproduced. Furthermore, several novel techniques that are intended to reduce those measurement errors are successfully demonstrated.