Simple theoretic approach to estimate the effect of gravity and thermophoresis on the diffusional nanoparticle contamination under low pressure conditions

Abstract

The problem of nanoparticle contamination on critical surfaces is becoming more and more important for the semiconductor industry. Under the low pressure conditions, as, e.g., prevalent in the extreme ultraviolet lithography (EUVL), generally two different deposition mechanisms need to be distinguished: impaction of high speed particles and diffusion of low speed particles. To protect EUVL photomasks from particle contamination, it is intended to maintain them facing down to make use of gravitational settling and to establish a temperature gradient below the mask surface to make use of thermophoresis. A simple theoretical approach to estimate the effect of gravity and thermophoresis on the diffusional nanoparticle deposition on downward facing surfaces, e.g., of EUVL photomasks, under low pressure conditions (10–500mTorr, 1.3–66.7Pa) is described in this article. The time dependent diffusional displacement of particles is compared with the gravitational and with the combined thermophoretic and gravitational settling. Initially, the diffusional displacement is always larger than the distance, particles have traveled due to gravity or gravity plus thermophoresis. Since thermophoresis and gravity move the particles away from the downward facing critical surface, while diffusion might cause a particle to move towards the surface, a certain risk exists that particles might deposit on the mask. Due to the different time and pressure dependencies of diffusional displacement (∼t1∕2 and ∼P1∕2) on the one side and gravitational and thermophoretic settlings (∼t and ∼P) on the other side, gravity and the combined effect of gravity and thermophoresis can overcome diffusion only after a certain time and distance. The approach presented here allows the estimation whether particle contamination is likely or not. The authors found that if only gravity is acting as a protecting force against diffusion, only the deposition of particles larger than 300nm is unlikely, whereas smaller particles might still be deposited. When a temperature gradient of 10K∕cm is established adjacent to the critical surface to make use of thermophoresis, the deposition of all particles down to 30nm becomes quite unlikely for pressure levels of 50mTorr and above.