Computational electromagnetics and the rational design of new dielectric heterostructures

Progress in Materials Science - Tập 48 - Trang 373-456 - 2003
C. Brosseau1,2, A. Beroual3
1Laboratoire d'Électronique et Systèmes de Télécommunications, Université de Bretagne Occidentale, B.P. 809, 6 avenue Le Gorgeu, 29285 Brest Cedex, France
2Département de Physique, Université de Bretagne Occidentale, Brest, France
3Centre de Génie Électrique de Lyon, École Centrale de Lyon, B.P. 163, 36 avenue Guy de Collongue, 69131 Ecully Cedex, France

Tài liệu tham khảo

Landauer, 1978, 2 Landauer, 1952, J. Appl. Phys, 23, 779, 10.1063/1.1702301 1992 Bergman, 1992, 147 Nan, 1993, Prog. Mater. Sci., 37, 1, 10.1016/0079-6425(93)90004-5 Hori, 1973, J Math Phys, 14, 514, 10.1063/1.1666347 Hori, 1974, J. Math. Phys, 15, 2177, 10.1063/1.1666599 Hori, 1975, J. Math. Phys, 16, 1722 Torquato, 1991, Appl. Mech. Rev., 44, 37, 10.1115/1.3119494 Cule, 1999, J. Appl. Phys, 86, 3428, 10.1063/1.371225 Torquato, 1986, Phys. Rev. B, 33, 6428, 10.1103/PhysRevB.33.6428 Yeong, 1998, Phys. Rev. E, 57, 495, 10.1103/PhysRevE.57.495 Sheenan, 2001, J. Appl. Phys, 89, 53, 10.1063/1.1327609 Hale, 1974, J. Mater. Sci., 11, 2105, 10.1007/BF02403361 Newnham, 1986, Annu. Rev. Mater. Sci., 16, 47, 10.1146/annurev.ms.16.080186.000403 Donnet, 1993 Medalia, 1978, Rubber Chem. Technol, 51, 437, 10.5254/1.3535748 Wang, 1978, Rubber Chem. Technol, 71, 520, 10.5254/1.3538492 Jonscher, 1977, Nature (London), 267, 673, 10.1038/267673a0 Jonscher, 1987 Jonscher, 1996 Jonscher, 1992, IEEE Trans. Elec. Insul, 27, 407, 10.1109/14.142701 Jonscher, 1999, J. Phys. D: Appl. Phys., 32, R57, 10.1088/0022-3727/32/14/201 Dyre, 1993, Phys. Rev. B, 48, 12511, 10.1103/PhysRevB.48.12511 Dyre, 2000, Rev. Mod. Phys, 72, 873, 10.1103/RevModPhys.72.873 Erman, 1997 Treloar, 1975 Steeman PM. PhD thesis, Technische Universiteit Delft, Delft, The Netherlands, 1992. For an analytic approach to the interfacial polarization in heterogeneous systems; Fu, 1993, Phys. Rev. B, 47, 13818, 10.1103/PhysRevB.47.13818 Hanai, 1960, Kolloid, Z., 171, 23, 10.1007/BF01520320 Sareni, 1996, J. Appl. Phys, 80, 1688, 10.1063/1.362969 Sareni, 1996, J. Appl. Phys, 80, 4560, 10.1063/1.363438 Sareni, 1997, J. Appl. Phys, 81, 2375, 10.1063/1.364276 Boudida, 1998, J. Appl. Phys, 83, 425, 10.1063/1.366725 Beroual, 1969, J. Phys. D: Appl. Phys, 33, 2000 Brosseau, 2001, J. Phys. D: Appl. Phys, 34, 1, 10.1088/0022-3727/34/5/307 Brosseau, 2000, J. Appl. Phys, 88, 7278, 10.1063/1.1321779 Beroual, 2001, IEEE Trans. Dielectrics EI, 8, 921, 10.1109/94.971447 McPhedran, 1978, Proc. R. Soc. London Ser. A, 359, 45, 10.1098/rspa.1978.0031 McKenzie, 1978, ibid, 362, 211 Nicorovici, 1945, Phys. Rev. E, 54, 1996 McPhedran, 1997, Physica A, 290, 173, 10.1016/S0378-4371(97)00078-2 Shen, 1990, J. Appl. Phys, 67, 7071, 10.1063/1.345056 Liu, 1993, Model Simul Mater Sci Engin, 1, 723, 10.1088/0965-0393/1/5/012 Ghosh, 1994, IEEE Trans. Dielec. Insul, 1, 975, 10.1109/94.368637 Cukier, 1990, Phys. Rev. B, 42, 5342, 10.1103/PhysRevB.42.5342 Sheu, 1990, Phys. Rev. B, 42, 1431, 10.1103/PhysRevB.42.1431 Lam, 1986, J. Appl. Phys, 60, 4230, 10.1063/1.337460 Schwartz, 1989, Physica A (Amsterdam), 157, 230, 10.1016/0378-4371(89)90307-5 Schwartz, 1989, Phys. Rev. B, 39, 11965, 10.1103/PhysRevB.39.11965 Sheng, 1986 Ma, 2000, Phys. Rev. B, 6, 962, 10.1103/PhysRevB.61.962 Pekonen, 1999, J. Electromagn. Waves Applicat, 13, 67, 10.1163/156939399X01618 Kärkkäinen, 2000, IEEE Trans. Geosci. Remote Sensing, 38, 1303, 10.1109/36.843023 Sihvola, 1999 Sihvola, 1989, IEEE Trans. Geosci. Remote Sensing, 27, 403, 10.1109/36.29560 Sihvola, 1989, J. Electromag. Waves Appl, 3, 37, 10.1163/156939389X00043 Ishimaru, 1997 Tsang, 1980, J. Appl. Phys, 51, 3465, 10.1063/1.328200 Tateiba, 1987, Radio Sci., 22, 881, 10.1029/RS022i006p00881 Kunz, 1993 Taflove, 1995 1986 Dal Maso, 1995 Berthier, 1994, J. Phys. I, 4, 303, 10.1051/jp1:1994139 Luciano, 2000, Int. J. Appl. Electromagn. Mech, 11, 163, 10.3233/JAE-2000-179 Bruno, 1994 Bergman, 1978, Phys. Rep, 43, 377, 10.1016/0370-1573(78)90009-1 Bergman, 1976, Phys. Rev. B, 14, 4304, 10.1103/PhysRevB.14.4304 Bergman, 1989, Phys. Rev. B, 39, 4598, 10.1103/PhysRevB.39.4598 Bergman, 1992, Phys. Rev. B, 45, 13262, 10.1103/PhysRevB.45.13262 Bergman, 1980, Phys. Rev. Lett., 44, 1285, 10.1103/PhysRevLett.44.1285 Bergman, 1982, Ann. Phys, 138, 78, 10.1016/0003-4916(82)90176-2 See also Bergman DJ, Siam DJ. J Appl Math, 53, 78, and Bergman DJ. J Phys C 1982;12:4947 1979 Stroud, 1975, Phys. Rev. B, 12, 3368, 10.1103/PhysRevB.12.3368 Stroud, 1978, Phys. Rev. B, 17, 1602, 10.1103/PhysRevB.17.1602 Yee, 1966, IEEE Trans. Antennas Prop., AP-14, 303 Maloney, 1992, IEEE Trans. Antennas Prop, 40, 38, 10.1109/8.123351 Beggs, 1992, IEEE Trans. Antennas Prop., 40, 49, 10.1109/8.123352 Taflove, 1970, IEEE Trans. Microw.ave Theory Tech., 23, 623, 10.1109/TMTT.1975.1128640 Shlager, 1995, IEEE Antennas Propag. Mag, 37, 39, 10.1109/74.414731 Shlager, 1995, IEEE Antennas Propag. Mag., 37, 39, 10.1109/74.414731 Greengard, 1997, Acta Numerica, 63, 229, 10.1017/S0962492900002725 It is worth observing that using the FMM proposed in this article, to solve an electrostatic problem with the boundary element method, reduces the computational costs and the memory requirements from O(N2) to O(N), where N is the number of unknowns. See also Greengard L, Rokhlin V, Anderson C, Greengard C, Greengard L. Lecture notes in mathematics the rapid evaluation of potential fields in three dimensions. Boston: MIT Press; 1988 Liu, 1997, Microwave Opt. Technol. Lett., 15, 158, 10.1002/(SICI)1098-2760(19970620)15:3<158::AID-MOP11>3.0.CO;2-3 Scaife, 1998 Doyle, 1978, J. Appl. Phys, 49, 795, 10.1063/1.324659 Smith, 1998, Mol. Phys, 95, 449, 10.1080/00268979809483179 Torquato, 2001 Day, 1978, Phys. Rev. Lett., 84, 2000 Roberts, 1996, Phys. Rev. E, 54, 2313, 10.1103/PhysRevE.54.2313 Roberts, 1995, Phys. Rev. E, 51, 4141, 10.1103/PhysRevE.51.4141 Brown, 1955, J. Chem. Phys., 23, 1514, 10.1063/1.1742339 Brown, 1965, Trans. Soc. Rheol., 9, 357, 10.1122/1.549016 The first material specific (third-order upper) bound was established by Prager: Prager S. Physica, 1963;29:129. Calculation of structural parameters for third-order bounds was first discussed by Weissberg in the context of hard spheres and gradient fields from solutions to single-body electrostatic problems: Weissberg HL. J Appl Phys 1963;34:2636. Zhuck, 1994, Phys. Rev. B, 50, 15636, 10.1103/PhysRevB.50.15636 Tsang, 1981, Radio Sci., 16, 303, 10.1029/RS016i003p00303 Morse, 1953 Romanov, 1994 Matheron, 1975 Adler, 1981 Cowan, 1998 Tikhonov, 1977 Kantorovich, 1982 Baker, 1977 Savary, 1999, Acta Stereol, 18, 297 Jeulin, 1997, J. Phys. I France, 7, 1123, 10.1051/jp1:1997103 Serra, 1982 Winkler, 1995 Carpenter, 1998, J. Appl. Phys, 84, 5843, 10.1063/1.368898 Jackson, 2000, Phys, 68, 307 2000 Faraday, 1857, Philos. Trans. R. Soc. London, 147, 145, 10.1098/rstl.1857.0011 Lakhtakia, 1996 Maxwell, 1881 Chew, 1990 Stratton, 1941 Binns, 1992 Landau, 1984 Jackson, 1975 Meredith, 1962 Van Beek, 1967 Mossotti, 1850, Memorie di matematica e di fisica della Società Italiana delle Scienze, residente in Modena, 24, 6353 Lorenz, 1880, Ann. Phys. Chem. (Leipzig), 11, 70, 10.1002/andp.18802470905 Lord Rayleigh (Strutt JWS) Phil Mag 1892;34:481. The analytical study undertaken by Rayleigh, in principle, would yield an exact value for the effective permittivity of the regular lattice of inclusions within the matrix, but his analytical calculation was not carried out far enough since it involves the calculation of certain static lattice sums, and his numerical study was cut short by the need of heavy computation. Following Rayleigh's method, McPhedran and co-workers [21], and Doyle [47] computed the effective permittivity to high accuracy for the simple-body-centered-, and face-centered-cubic lattices. Clausius, 1893 Maxwell Garnett, 1904, Philos. Trans. R. Soc. London, 203, 385, 10.1098/rsta.1904.0024 Wiener, 1912, Abh. Sächs. Akad. Wiss. Leipzig Math.—Naturwiss. Kl, 32, 509 Lorentz, 1916 Fricke, 1924, Phys. Rev., 24, 575, 10.1103/PhysRev.24.575 Fricke, 1953, J. Chem. Phys, 57, 934, 10.1021/j150510a018 Lichteneker, 1926, Physik Z., 27, 115 Brosseau, 1994, J. Appl. Phys, 75, 672, 10.1063/1.355815 Zachri, 1998, J. Phys. D: Appl. Phys, 31, 1589, 10.1088/0022-3727/31/13/013 Goncharenko, 2000, Opt. Commun., 174, 19, 10.1016/S0030-4018(99)00695-1 Bruggeman, 1935, Ann. Phys. Lpz, 24, 636, 10.1002/andp.19354160705 Biot, 1806, Mem. Inst. France, 7, 301 Van de Hulst, 1957 Milton, 1980, Appl. Phys. Lett., 37, 300, 10.1063/1.91895 Milton, 1981, J. Appl. Phys, 52, 5286, 10.1063/1.329385 McPhedran, 1981, Appl. Phys. A, 26, 207, 10.1007/BF00617840 Ghosh, 1991, Phys. Rev. B, 44, 7330, 10.1103/PhysRevB.44.7330 Hinsen, 1992, Phys. Rev. B, 46, 12955, 10.1103/PhysRevB.46.12955 McLachlan, 1989, Solid State Commun., 72, 831, 10.1016/0038-1098(89)90919-8 Hwang, 1999, J. Electroceram, 3, 7, 10.1023/A:1009998114205 McLachlan, 2000, J. Electroceram, 5, 37, 10.1023/A:1009989427283 McLachlan, 1990, J. Am. Ceram. Soc., 73, 2187, 10.1111/j.1151-2916.1990.tb07576.x Brosseau, 2001, J. Appl. Phys, 89, 4532, 10.1063/1.1343521 Brosseau, 2002, J. Appl. Phys., 90, 3197, 10.1063/1.1447307 Sen, 1981, Geophysics, 46, 781, 10.1190/1.1441215 Soukoulis, 1994, Phys. Rev. B, 49, 3800, 10.1103/PhysRevB.49.3800 Beran, 1965, Nuovo Cimento, 38, 771, 10.1007/BF02748596 Beran, 1968 Hashin, 1962, J. Appl. Phys, 33, 3125, 10.1063/1.1728579 Schulgasser, 1976, J. Appl. Phys, 47, 424, 10.1063/1.322664 Milton, 1980, J. Mech. Phys. Solids, 30, 177, 10.1016/0022-5096(82)90022-9 Milton, 1990, Commun. Pure Appl. Math, 43, 63, 10.1002/cpa.3160430104 Sawicz, 1995, J. Appl. Phys, 78, 7240, 10.1063/1.360436 Corson, 1974, J. Appl. Phys, 45, 3159, 10.1063/1.1663741 Broadbent, 1957, Proc. Cam. Phil. Soc., 53, 629, 10.1017/S0305004100032680 Stauffer, 1994 Kirkpatrick, 1973, Rev. Mod. Phys, 454, 574, 10.1103/RevModPhys.45.574 Kirkpatrick, 1971, Phys. Rev. Lett., 27, 1722, 10.1103/PhysRevLett.27.1722 Clerc, 1990, Adv. Phys, 39, 191, 10.1080/00018739000101501 Isichenko, 1992, Rev. Mod. Phys, 64, 961, 10.1103/RevModPhys.64.961 Sahimi, 1994 Anderson PW. In Balian R, Maynard R, Toulouse G, editors. Ill-condensed matter. Amsterdam: North-Holland; 1979. Hori, 1977, J. Phys. C, 10, 229, 10.1088/0022-3719/10/2/009 Kawamoto, 1982 Miyasakara, 1982, J. Mat. Sci., 17, 1610, 10.1007/BF00540785 Yacubowitz, 1986, Polym. Eng. Sci., 26, 1568, 10.1002/pen.760262207 1994 Carmona, 1980, J. Phys. Lett., 41, L531, 10.1051/jphyslet:019800041022053100 Carmona, 1981, Rev. Chim. Min, 18, 498 Lagarkov, 1998, Phys. Rev. B, 53, 6319 Lagarkov, 1997, Physica A, 241, 58, 10.1016/S0378-4371(97)00059-9 Boissonade, 1983, J. Phys. A, 16, 2777, 10.1088/0305-4470/16/12/023 Celzard, 1998, Phys. Rev. B, 53, 6209, 10.1103/PhysRevB.53.6209 Garboczi, 1995, Phys. Rev. E, 52, 819, 10.1103/PhysRevE.52.819 Balberg, 1984, Phys. Rev. B, 30, 3933, 10.1103/PhysRevB.30.3933 Balberg, 1984, Phys. Rev. Lett., 52, 1465, 10.1103/PhysRevLett.52.1465 Balberg, 1987, Philos. Mag. B, 56, 991, 10.1080/13642818708215336 Browning, 1998, J. Appl. Phys, 84, 6109, 10.1063/1.368925 Garboczi, 1995, Phys. Rev. E, 52, 819, 10.1103/PhysRevE.52.819 Lagarkov, 1998, J. Appl. Phys, 84, 3806, 10.1063/1.368559 Carmona, 1987, Phys. Rev. B, 35, 3284, 10.1103/PhysRevB.35.3284 Ravier, 2001, Carbon, 39, 314, 10.1016/S0008-6223(00)00242-6 Houze, 1975, Appl. Phys. Lett., 69, 1996 Brosseau, 1997, J. Appl. Phys, 81, 882, 10.1063/1.364173 Boulic, 1998, J. Phys. D: Appl. Phys, 31, 1904, 10.1088/0022-3727/31/15/020 Brosseau, 2001, J. Appl. Phys, 89, 8297, 10.1063/1.1371938 Tao, 1990, Phys. Rev. B, 41, 2417, 10.1103/PhysRevB.41.2417 Zhang, 2000, Physica B, 293, 16, 10.1016/S0921-4526(00)00525-1 Harrington, 1982 Harrington, 1967, IEE Proc, 55, 136, 10.1109/PROC.1967.5433 Wang, 1991 Mur, 1985, IEEE Trans. Magn, 21, 2188, 10.1109/TMAG.1985.1064256 Zienkiewicz, 1994 Mackerle, 1999, Model. Simul. Mater. Sci. Eng, 7, 107, 10.1088/0965-0393/7/1/008 There is a vast literature on the FEM in the context of engineering. It is also worth noting that FEM softwares with flexible mesh generators, robust equation solvers and versatile post-processors have become available in recent years. For a general introduction, the reader is refered to Strang G, Fix GJ. An analysis of the finite element method. Englewoods Cliffs: Prentice-Hall; 1973. Other important books are: Bathe KJ, Wilson EL. Numerical methods in finite element analysis. Englewoods Cliffs: Prentice-Hall; 1976, Jin J. The finite element in electromagnetics, New York: Wiley; 1993), Sylvester PP, Ferrari RL. Finite elements for electrical engineers. 2nd ed. New York: Cambridge University Press; 1991, Johnson C. Numerical solution of partial differential equations by the finite element method, Cambridge: Cambridge University Press; 1987, and Hughes TJR. The finite element method. Englewood Cliffs, New Jersey: Prentice-Hall; 1987. Stölzle, 1991, J. Phys. I France, 2, 401, 10.1051/jp1:1992153 Coverdale, 1995, Comput. Mater. Sci., 3, 465, 10.1016/0927-0256(95)00005-B Coverdale, 1994, J. Mater. Sci., 29, 4984, 10.1007/BF01151088 Weiland, 1984, Part. Accel., 15, 245 Bossavit, 1998 Bossavit, 1993 Finlaysson, 1972 Brebbia, 1980 Tuncer E. PhD thesis, Chalmers University of Technology, Gothenburg, Sweden; 2001 Tuncer, 2001, J. Appl. Phys, 89, 8092, 10.1063/1.1372363 Batchelor, 1974, Ann. Rev. Fluid Mech, 6, 227, 10.1146/annurev.fl.06.010174.001303 Schulgasser, 1992, Int. Commun. Heat Mass Transfer, 19, 639, 10.1016/0735-1933(92)90047-L Gillespie, 1978, Appl. Opt, 17, 989, 10.1364/AO.17.000989 Bohren, 1986, J. Atmos. Sci., 43, 68 Calame, 1996, J. Appl. Phys, 80, 3992, 10.1063/1.363357 Steeman, 1992, Colloid Polym. Sci., 270, 1069, 10.1007/BF00652870 Jones, 2000, Water Resour. Res., 36, 2821, 10.1029/2000WR900198 Gu, 1997, J. Phys. D: Appl. Phys, 30, 1523, 10.1088/0022-3727/30/10/020 Frommer, 1992, Angew. Chem., Int. Ed. Engl, 31, 1298, 10.1002/anie.199212981 Lewis, 1994, IEEE Trans. Dielec. Insul, 1, 812, 10.1109/94.326653 Foster, 1989, Crit. Rev. Biomed. Eng., 17, 25 Peters, 2001, Electromagnetics, 21, 545, 10.1080/027263401752246199 Polk, 1986 Stroud, 1989, J. Opt. Soc. Am. B, 6, 778, 10.1364/JOSAB.6.000778 Stroud, 1988, Phys. Rev. B, 37, 8719, 10.1103/PhysRevB.37.8719 Zeng, 1988, Phys. Rev. B, 38, 10970, 10.1103/PhysRevB.38.10970 Agarwal, 1988, Phys. Rev. A, 38, 5678, 10.1103/PhysRevA.38.5678 Ponte Castaneda, 1992, Philos. Trans. R. Soc. London Ser. A, 340, 531, 10.1098/rsta.1992.0079 Ponte Castaneda, 1997, Philos. Trans. R. Soc. London Ser. A, 453, 793, 10.1098/rspa.1997.0044 Ponte Castaneda, 1998, Adv. Appl. Mech, 34, 171, 10.1016/S0065-2156(08)70321-1 Ponte Castaneda, 1991, J. Mech. Phys. Solids, 39, 45, 10.1016/0022-5096(91)90030-R Ponte Castaneda, 1999, Philos. Trans. R. Soc. London, Ser. A, 455, 1799, 10.1098/rspa.1999.0380 Pellegrini, 2001, Phys. Rev. B, 64, 134211, 10.1103/PhysRevB.64.134211 Sipe, 1992, Phys. Rev. A, 46, 1614, 10.1103/PhysRevA.46.1614 Yablonovitch, 1987, Phys. Rev. Lett., 58, 2059, 10.1103/PhysRevLett.58.2059 John, 1987, Phys. Rev. Lett., 58, 2486, 10.1103/PhysRevLett.58.2486 In the mid 1980s, Drexler introduced the term “nanotechnology“ to describe atomically precise molecular manufacturing systems and their products. Within the past two decades, a variety of terms sharing the prefix “nano-“ (from the Greek root nanos, or dwarf), such as nanoparticle, nanomaterial, nanophase, nanomachine and nanostructured, have emerged to describe certain materials, technologies, and even businesses. See Drexler KE. Proc Natl Acad Sci USA 1981;78:5275, Drexler KE. Engines of creation: the coming era of nanotechnology. New York: Anchor Press; 1986, and Drexler KE. Nanosystems: molecular machinery, manufacturing, and computation. New York: Wiley; 1992. The excitement in the field of nanotechnology has led to a sea-change in our perception of what nanodevices can do, for example, Roco MC, Williams RS, Alivisatos P, editors. Nanotechnology research directions. Dordrecht, The Netherlands: Kluwer; 2000. Most current information in this rapidly progressing area can be found on the web pages, for example, http://www.foresight.com and http://www.zyvex.com. Talbot P, Brosseau C, Konn AM. J Magn Magn Mater 2002;249:483. See also Brosseau C, Ben Youssef J, Talbot P, Konn AM. [in press]. Bichurin, 2001, Phys. Rev. B, 64, 094409, 10.1103/PhysRevB.64.094409 Prinz, 1998, Science, 282, 1660, 10.1126/science.282.5394.1660 Joachim, 2000, Nature, 408, 541, 10.1038/35046000 Trau, 1996, Science, 272, 706, 10.1126/science.272.5262.706 Veselago, 1968, Sov. Phys. Usp, 10, 509, 10.1070/PU1968v010n04ABEH003699 Pendry, 1996, Phys. Rev. Lett., 76, 4773, 10.1103/PhysRevLett.76.4773 Walser, 2001, Phys. Rev. Lett., 87, 119701, 10.1103/PhysRevLett.87.119701 Pendry, 1998, J. Phys. Conden. Matter, 10, 4785, 10.1088/0953-8984/10/22/007 Pendry, 1999, IEEE Trans. Microwave Theory Tech., 47, 2075, 10.1109/22.798002 Smith, 1999, Appl. Phys. Lett., 75, 1425, 10.1063/1.124714 Smith, 2000, Phys.Rev. Lett., 84, 4184, 10.1103/PhysRevLett.84.4184 Yaghjian, 1980, Proc. IEEE, 68, 248, 10.1109/PROC.1980.11620 Yaghjian, 1985, Am J. Phys, 53, 859, 10.1119/1.14352 Bottcher, 1952