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

Christof Asbach, Heinz Fissan, Jung Hyeun Kim, Se Jin Yook, David Y.H. Pui

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 (10-500 mTorr, 1.3-66.7 Pa) 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 (∼ t12 and ∼ P12) 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 300 nm is unlikely, whereas smaller particles might still be deposited. When a temperature gradient of 10 Kcm is established adjacent to the critical surface to make use of thermophoresis, the deposition of all particles down to 30 nm becomes quite unlikely for pressure levels of 50 mTorr and above.

Original languageEnglish (US)
Pages (from-to)47-53
Number of pages7
JournalJournal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures
Volume25
Issue number1
DOIs
StatePublished - 2007

Bibliographical note

Funding Information:
This research is supported by Intel Corporation. The financial and technical support is gratefully acknowledged. The authors would like to thank Kevin Orvek for very fruitful discussions. FIG. 1. Wafer surface scans. Particles injected through a small pinhole at high velocity towards the wafer without thermal gradient (left). Particles hit the surface; some particles bounced off and started to diffuse; diffusional deposition around the center spot can be seen. When a thermal gradient of 10 K ∕ cm was used (right), no diffusional deposition occurred. FIG. 2. Direction of diffusional, gravitational, and thermophoretic motions in the model. Worst case assumed, i.e., diffusion drives particles only up towards the critical surface FIG. 3. Schematic of the diffusional displacement, gravitational settling, and combined thermophoretic and gravitational settling over time at a given pressure. FIG. 4. Dimensionless time ( t ∕ τ ) cross (a) and distance x cross (b) after which diffusional displacement and gravitational settling are equal, as a function of pressure P for particle diameters of 10, 30, 60, 100, 300, and 500 nm . Forces considered for gravitational settling are gravity and drag force. FIG. 5. Dimensionless time ( t ∕ τ ) cross (a) and distance x cross (b) after which diffusional displacement and the combined thermophoretic and gravitational settling ( grad T = 10 K ∕ cm ) are equal, as a function of pressure P for particle diameters 10, 30, 60, 100, 300, and 500 nm . Forces considered for thermophoretic settling are thermophoresis, gravity, and drag force. FIG. 6. Ratio of crossing distance without thermophoresis ( x cross , g ) and with thermophoresis ( x cross , t , at grad T = 10 K ∕ cm ) as function of pressure P for particle diameters 10, 30, 60, 100, 300, and 500 nm .

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