Study of heating effect in multi-beam mask writing

Recently, Multi-Beam Mask Writer (MBMW) scheme is newly considered for next generation writing scheme. As the MBMW writing uses many multi-array bundle beams with small spot size, the fast writing and complex pattering is possible conceptually. The target dose level of MBMW is high around 100μC/cm2 and the target of total writing time is within 10 hours for next generation layout with complex and small node pattern. The risks of high dose writing are rising of blank temperature, chemical reaction with photo-resist and charging effects in blank. In addition, the fast writing can cause the rising of temperature in blank. The heating effect can be divided into local and global terms, and each effect of critical dimension (CD) and registration was analyzed by heating effect. In case of MBMW, the global heating is more critical than local heating. Therefore, we need to study about the global heating effect which can affect global registration in MBMW. In this paper, we study about the global heat distribution on mask blank in certain MBMW writing condition, and the directional deformation of blank which can affect global registration was analyzed by using Finite Element Method (FEM). We approach with two kinds of modified heat model and the FEM model was verified with analytical calculation. The temperature variation and deformation distribution were achieved with transient method with the writing conditions, in case of 100μC/cm2 of total dose, 50kV of acceleration voltage, 100% of chip density and 10 hour of total writing time. Therefore, we can consider the writing conditions according to mask specification in MBMW scheme.