A self-similarity model for dielectric constant of porous ultra low-k dielectrics

Journal of Physics D: Applied Physics

Volumn 40, Issue 17, 2007, Pages 5377-5382

  Tang, Yanni ^a   Yu, Boming ^a   Hu, Yifan ^a   Cai, Jianchao ^a   Feng, Yongjin ^a   Xu, Peng ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MODULI; NANOPORES; PERMITTIVITY; PORE SIZE; POROUS MATERIALS; THERMAL CONDUCTIVITY;

MIXTURE RULE TECHNIQUE; MODEL PREDICTIONS; POROUS ULTRA LOW-K DIELECTRICS; SELF-SIMILARITY MODEL; SIERPINSKI CARPET APPROXIMATION;

DIELECTRIC MATERIALS;

EID: 34548699870     PISSN: 00223727     EISSN: 13616463     Source Type: Journal    
DOI: 10.1088/0022-3727/40/17/055     Document Type: Article

References (31)

1. Kresge C T, Leonowicz M E, Roth W J, Vartuli J C and Beck J S 1992 Ordered mesoporous molecular sieves synthesized by a liquid-crystal template mechanism Nature 359 710
2. Asefa T, MacLachlan M J, Coombs N and Ozin G A 1999 Periodic mesoporous organosilicas with organic groups inside the channel walls Nature 402 867
3. Corma A 1997 From microporous to mesoporous molecular sieve materials and their use in catalysis Chem. Rev. 97 2373
4. Zhao D Y, Feng J L, Huo Q S, Melosh N, Fredrickson G H, Chnelka B and Stucky G D 1998 Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores Science 279 548
5. Zhao D, Sun J, Li Q and Stucky G D 2000 Morphological control of highly ordered mesoporous silica SBA-15 Chem. Mater. 12 275
6. Kim H C, Wilds J B, Kreller C R, Volksen W, Brock P J, Lee V Y, Magbitang T, Hedrick J L, Hawker C J and Miller R D 2002 Fabrication of multi layered nanoporous poly(methyl silsesquioxane) Adv. Mater. 14 1637
7. Torquato S 2002 Random Heterogeneous Material, Microstructure and Macroscopic Properties (Berlin: Springer)
8. Sahimi M 2003 Heterogeneous Materials (Berlin: Springer)
9. Murray C, Flannery C, Streiter I, Schulz S E, Baklanov M R, Mogilnikov K P, Himcinschi C, Friedrich M, Zahn D R T and Gessner T 2002 Comparison of techniques to characterise the density, porosity and elastic modulus of porous low-k SiO[2] xerogel films Microelectron. Eng. 60 133
10. Baklanov M R and Mogilnikov K P 2002 Non-destructive characterisation of porous low-k dielectric films Microelectron. Eng. 64 335
11. Lakhtakia A (ed) 1996 Selected Papers on Linear Optical Composite Materials (Bellingham, WA: SPIE)
12. Ward L 1995 The Optical Constants of Bulk Materials and Films 2nd edn (Bristol, UK: Hilger) chapter 8
13. Maxwell Garnett J C 1904 Phil. Trans. R. Soc. Lond. A 203 385
14. Bruggeman D A G 1935 Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen Ann. Phys. Lpz. 24 636
15. Lichtenecker K 1926 Kolloid-Beih. 23 285
16. Landauer R 1978 Electric transport and optical properties of inhomogeneous media AIP Conf. Proc. 40 2
17. Kingery W D, Bowen H K and Uhlmann D R 1976 Introduction to Ceramics 2nd edn (New York: Wiley) chapter 18 p 948
18. Li H R 1990 Introduction to Dielectric Physics (Chengdu: Chengdu University of Science and Technology Press) p 330 (in Chinese)
19. Azzam R M and Bashara N M 1977 Ellipsometry and Polarized Light (Amsterdam: Elsevier)
20. Aiichiro N, Lingsong B, Kalia R K and Priya V 1993 Structural correlations in porous silica: molecular dynamics simulation on a parallel computer Phys. Rev. Lett. 71 85
21. Beckers J V L and de Leeuw S W 2001 Fractal structure and specific surface of nanoporous silica Int. J. Inorg. Mater. 3 175
22. Mandelbrot B B 1982 The Fractal Geometry of Nature (New York: Freeman) p 23
23. Cha H J, Hedrick J, DiPietro R A, Blume T, Beyers R and Yoon D Y 1996 Structures and dielectric properties of thin polyimide films with nano-foam morphology Appl. Phys. Lett. 68 1930
24. Feder J 1988 Fractals (New York: Plenum) pp 7-30, 184-92
25. Hyeon-Lee J, Rhee J, Yim J H, Jeong H D and Gidley D W 2005 Properties of nanoporous organosilicate hybrid thin films with a bimodal pore size distribution Polym. Int. 54 772
26. Yu B M and Li J H 2001 Some fractal characters of porous media Fractals 9 365
27. Shamiryan D, Abell T, Iacopi F and Maex K 2004 Low-k dielectric materials Mater. Today (January)
28. Feng Y J, Yu B M, Zou M Q and Zhang D M 2004 A generalized model for the effective thermal conductivity of porous media based on self-similarity J. Phys. D: Appl. Phys. 37 3030
29. Jin-Heong Y, Mikhail R B, David W G, Huagen P, Hyun-Dam J and Lyong S P 2004 Pore structure of modified cyclic silsesquioxane thin films made porous using a cyclodextrins-based porogen J. Phys. Chem. B 108 8953
30. Yu B M and Yao K L 1988 Critical percolation probabilities for site problem on Sierpinski carpets Z. Phys. B: Condens. Matter 70 209
31. 2 aerogel film as a novel intermetal dielectric J. Appl. Phys. 82 1299