Analytical modeling of particle stopping distance at low pressure to evaluate protection schemes for extreme ultraviolet lithography masks

We developed an analytical model that predicts the distance, particles can travel towards the critical surface of an extreme ultraviolet lithography mask as a function of their initial velocity and all forces (gravity, drag, thermophoresis, and electrophoresis) acting on the particles. To avoid gravitational settling of particles onto the mask, its critical surface is facing down. The model shows that at the low pressure level (50 mTorr), drag force is the dominating force to decelerate particles. Thermophoresis can add additional protection. Electrophoresis can be very effective, however, all particles must be unipolarly charged to make use of the Coulomb force.