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Positronium diffusion in porous methylsilsesquioxanethin films |
Dong Xi-Jie(董锡杰)a)b), Hu Yi-Fan(胡一帆) b)†, and Wu Yu-Ying(吴玉莹)a)b) |
a Wuhan High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China; b School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract Depth profiled positronium (Ps) annihilation lifetime spectroscopy (PALS) is an extremely useful probe of the pore characteristics in nanoporous low-dielectric (low-k) constant thin films. PALS has also been considered as a potential probe to investigate diffusion barrier integrity and the structural changes of porous low-k films during their integration with Cu. Hence, it is essential to understand the diffusion behaviour of positronium/Cu atoms in the films. In this work, based on the fact that porous materials possess characteristics of statistical self-similarity, a fractal model, the Menger sponge model, has been applied to simulate the structure of a promising dielectric, porous methylsilsesquioxane (MSQ) films. The diffusion behaviour of Ps out of the fractal model and into the surrounding vacuum is studied by means of the diffusion equation and traditional advective--diffusive theory. Predictive results from our model show good agreement with measurement data.
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Received: 07 October 2008
Revised: 13 August 2009
Accepted manuscript online:
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PACS:
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78.70.Bj
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(Positron annihilation)
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66.30.Ny
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(Chemical interdiffusion; diffusion barriers)
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66.30.Pa
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(Diffusion in nanoscale solids)
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77.22.Ch
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(Permittivity (dielectric function))
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77.55.+f
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78.66.Qn
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(Polymers; organic compounds)
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Fund: Project supported by the National
Natural Science Foundation of China (Grant No. 60476011). |
Cite this article:
Dong Xi-Jie(董锡杰), Hu Yi-Fan(胡一帆), and Wu Yu-Ying(吴玉莹) Positronium diffusion in porous methylsilsesquioxanethin films 2010 Chin. Phys. B 19 013601
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