Analytical and statistical modeling of nanoparticle contamination of critical surfaces under low pressure conditions
Final Report Abstract
Deposition of particles on critical surfaces can be a major concern, e.g. in clean manufacturing of semiconductors. In Extreme Ultraviolet Lithography (EUVL), a prominent successor to optical lithography to produce the next generation of computer processor chips, photomasks have to be protected against particulate contaminants. These masks are maintained facing down during chip manufacturing, which occurs under low pressure conditions (10 Pa). In order to protect these masks, the processes causing particle motion and consequenfly deposifion need to be understood. The aim of this project was to develop an analytical-statistical model that can be easily solved, and delivers accurate estimates of the deposition probability of particles on inverse surfaces under low pressure conditions, e.g. to mimic an EUVL photomask during scanning operation. Two main driving mechanisms are considered, diffusion and inertia. If the surface is facing down, gravity always acts against the deposition. A thermal gradient can furthermore be assumed underneath the critical surface in order to thermophoretically repel particles and protect the surface. The model follows a decoupled approach for the two sources of motion, i.e. equations for inertial and diffusional motion are solved separately and results merged. The model is designed such that it can be solved using common spreadsheet software, i.e. no major computational resources are required. The model showed that it is very likely that particles traveling at a high initial velocity are deposited on the surface, even in presence of a protective thermal gradient, because thermophoresis is a rather weak force. However, if particles travel at low or no inifial velocity, and diffusion is the main driving mechanism, then thermophoresis (considered thermal gradient 10 K/cm) can be very efficient in preventing particle deposition. With an initial distance of 10 mm between particle and surface, the deposition probability of particles <100 nm is at least three orders of magnitude lower if a thermal gradient (10 K/cm) is applied. If a deposition probability of 0.1% is considered as tolerable, the surface is safe against all particles with an initial distance of 10 mm or more, except for particles of >150 nm, traveling at an initial velocity of >10m/s. The deposifion probability increases with decreasing inifial distance between particle and surface. If the initial distance is only 1 mm, then particles of >150nm are already deposited if initially traveling at >1 m/s and particles below 30 nm are deposited with a probability of more than 0.1%. In EUVL, however, 30 nm is considered as the critical particle size. Experiments were conducted using a vacuum chamber with a dual stage particle injection system that allows for particle injection at known velocity into a quiescent space. The vacuum chamber can be equipped with witness wafers at a known distance from the particle injection port. The wafer surfaces are scanned in order to detect the number of added particles. With the known number of injected particles, the deposifion ratio can be determined and compared to the modeled deposifion probability. After several inifial problems with the experimental system, conclusive results were flnally obtained. The experiments will be completed after the termination ofthe project and results published soon. Within this project, the obtained results were published in two papers in Applied Physics Letters and presented at altogether six international conferences.
Publications
- C. Asbach, B, Stahlmecke, H. Fissan, T.A.J. Kuhlbusch, J. Wang, D.Y.H. Pui: Nanoparticle deposition on inverse surfaces under low pressure, Annual AAAR conference, Orlando, FL, USA, October 23'^ 2008
- C. Asbach, B. Stahlmecke. H. Fissan, T.A.J. Kuhlbusch, J. Wang, D.Y.H. Pui (2008): Analytical-statistical model to accurately estimate nanoparticle deposition on inverted surfaces at low pressure, Applied Physics Letters 92:064107
- C. Asbach, B::Stahlmecke,',H. Fissan, T.A.J. Kuhlbusch, J, Wang, D.Y.H, Pui: Nanoparticle deposition on inverse surfaces under low pressure, European- Aerosol Conference,-Thessalonikii Greece, August 24th-29'", 2008
- C. Asbach, H. Fissan, J, Wang, D.Y.H. Pui: An Approach to Analytically Model Diffusional Nanoparticle Deposition under Low Pressure Conditions, Annual AAAR conference, Reno, NV, September 28th, 2007
- C. Asbach, H. Fissan, J. Wang, D.Y.H. Pui: Analytical Modeling of Diffusional Nanoparticle Deposition under Low Pressure Conditions, European Aerosol Conference, Salzburg, Austria, September 10th, 2007
- C. Asbach, H. Fissan, T.A.J. Kuhlbusch, J. Wang, D.Y.H. Pul (2008): Model for the combination of diffusional and inertial particle deposition on inverse surfaces at low pressure. Applied Physics Letters 93:054104
- C. Asbach, J. Wang;;H. Fissan, D.Y.H. Pui (2007): Analytical Model to Estimate Diffusional Nanoparticle Contamination on EUVL Photomasks, 0^ international EUVL Symposium, Sapporo; Japan, October 28-31, 2007
