Protection of extreme ultraviolet lithography masks. I. Thermophoretic protection factors at low pressure for diffusing nanoscale particles

Model calculations are presented for thermophoretic protection of an extreme ultraviolet (EUV) mask placed face down in an EUV mask inspection tool. The protection factors, defined as the ratio of challenge particles to deposited particles, are calculated for a variety of test conditions (temperature gradient, gas type, particle density, and particle position) for a reticle bathed in clean gas from a facing showerhead. Thermophoretic protection (in combination with gravity) provides robust protection for particle sizes greater than ∼20 nm. However, for particle sizes less than ∼20 nm, protection falters quickly and is severely degraded for highly diffusing 10 nm particles that are of concern for mask contamination. Estimates are made for the required level of particle protection in both EUV mask inspection and EUV projection lithography. When compared with these estimates for the required protection, it is clear that thermophoresis alone cannot successfully defend against particles smaller than ∼20 nm, and must be augmented or replaced by another approach. Initial calculations are presented that suggest a cross-cutting gas flow, in combination with thermophoresis and a face-down mask orientation, can successfully protect mask surfaces from particle deposition for particles with 10 nm diameter or greater, motivating more detailed calculations of flow-based mask protection in a companion paper Part II.