Abstract

Several approaches to three-dimensional integration of conventional electronic circuits have been pursued recently. To determine whether the advantages of optical interconnections are negated by these advances, we compare the limitations of fully three-dimensional systems interconnected with optical, normally conducting, repeatered normally conducting, and superconducting interconnections by showing how system-level parameters such as signal delay, bandwidth, and number of computing elements are related. In particular, we show that the duty ratio of pulses transmitted on terminated transmission lines is an important optimization parameter that can be used to trade off signal delay and bandwidth so as to optimize applicable measures of performance or cost, such as minimum message delay in parallel computation.

© 1999 Optical Society of America

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References

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  1. IEEE, eds., Proceedings of the 45th Electronic Components and Technology Conference (ECTC) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).
  2. H. M. Ozaktas, J. W. Goodman, “The limitations of interconnections in providing communication between an array of points,” in Frontiers of Computing Systems Research, S. K. Tewksbury, ed. (Plenum, New York, 1991), Vol. 2, pp. 61–130.
    [CrossRef]
  3. H. M. Ozaktas, “A physical approach to communication limits in computation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1991).
  4. A. L. Rosenberg, “Three-dimensional VLSI: a case study,” J. Assoc. Comput. Mach. 30, 397–416 (1983).
    [CrossRef]
  5. F. T. Leighton, A. L. Rosenberg, “Three-dimensional circuit layouts,” J. Comput. Sys. Sci. 15, 793–813 (1986).
  6. M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.
  7. H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).
  8. H. M. Ozaktas, J. W. Goodman, “Lower bound for the communication volume required for an optically interconnected array of points,” J. Opt. Soc. Am. A 7, 2100–2106 (1990).
    [CrossRef]
  9. H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
    [CrossRef]
  10. H. M. Ozaktas, D. Mendlovic, “Multistage optical interconnection architectures with least possible growth of system size,” Opt. Lett. 18, 296–298 (1993).
    [CrossRef]
  11. K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
    [CrossRef]
  12. K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
    [CrossRef]
  13. H. M. Ozaktas, “Paradigms of connectivity for computer circuits and networks,” Opt. Eng. 31, 1563–1567 (1992).
    [CrossRef]
  14. H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
    [CrossRef]
  15. H. M. Ozaktas, “Toward an optimal foundation architecture for optoelectronic computing. Part I. Regularly interconnected device planes,” Appl. Opt. 36, 5682–5696 (1997).
    [CrossRef] [PubMed]
  16. H. M. Ozaktas, “Toward an optimal foundation architecture for optoelectronic computing, Part II. Physical construction and application platforms,” Appl. Opt. 36, 5697–5705 (1997).
    [CrossRef] [PubMed]
  17. H. B. Bakoglu, Circuits, Interconnections, and Packaging for VLSI (Addison-Wesley, Reading, Mass., 1990).
  18. W. Nakayama, “On the accomodation of coolant flow paths in high density packaging,” IEEE Trans. Component Hybrids Manuf. Technol. 13, 1040–1049 (1990).
    [CrossRef]
  19. W. Nakayama, “Heat-transfer engineering in systems integration—outlook for closer coupling of thermal and electrical designs of computers,” IEEE Trans. Components Packag. Manuf. Technol. Part A 18, 818–826 (1995).
    [CrossRef]

1997 (2)

1995 (2)

W. Nakayama, “Heat-transfer engineering in systems integration—outlook for closer coupling of thermal and electrical designs of computers,” IEEE Trans. Components Packag. Manuf. Technol. Part A 18, 818–826 (1995).
[CrossRef]

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

1993 (2)

H. M. Ozaktas, D. Mendlovic, “Multistage optical interconnection architectures with least possible growth of system size,” Opt. Lett. 18, 296–298 (1993).
[CrossRef]

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
[CrossRef]

1992 (2)

H. M. Ozaktas, “Paradigms of connectivity for computer circuits and networks,” Opt. Eng. 31, 1563–1567 (1992).
[CrossRef]

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

1991 (2)

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

1990 (2)

W. Nakayama, “On the accomodation of coolant flow paths in high density packaging,” IEEE Trans. Component Hybrids Manuf. Technol. 13, 1040–1049 (1990).
[CrossRef]

H. M. Ozaktas, J. W. Goodman, “Lower bound for the communication volume required for an optically interconnected array of points,” J. Opt. Soc. Am. A 7, 2100–2106 (1990).
[CrossRef]

1986 (1)

F. T. Leighton, A. L. Rosenberg, “Three-dimensional circuit layouts,” J. Comput. Sys. Sci. 15, 793–813 (1986).

1983 (1)

A. L. Rosenberg, “Three-dimensional VLSI: a case study,” J. Assoc. Comput. Mach. 30, 397–416 (1983).
[CrossRef]

Amitai, Y.

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

Bacon, D. D.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Bakoglu, H. B.

H. B. Bakoglu, Circuits, Interconnections, and Packaging for VLSI (Addison-Wesley, Reading, Mass., 1990).

Chirovsky, L. M. F.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Cunningham, J. E.

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
[CrossRef]

D’Asaro, L. A.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Dahringer, D.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Goodman, J. W.

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).

H. M. Ozaktas, J. W. Goodman, “Lower bound for the communication volume required for an optically interconnected array of points,” J. Opt. Soc. Am. A 7, 2100–2106 (1990).
[CrossRef]

H. M. Ozaktas, J. W. Goodman, “The limitations of interconnections in providing communication between an array of points,” in Frontiers of Computing Systems Research, S. K. Tewksbury, ed. (Plenum, New York, 1991), Vol. 2, pp. 61–130.
[CrossRef]

Goossen, K. W.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
[CrossRef]

Grinberg, J.

M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

Hui, S. P.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Jan, W. Y.

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
[CrossRef]

Kossives, D.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Leibenguth, R.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Leighton, F. T.

F. T. Leighton, A. L. Rosenberg, “Three-dimensional circuit layouts,” J. Comput. Sys. Sci. 15, 793–813 (1986).

Lentine, A. L.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Little, M. J.

M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

Mendlovic, D.

Miller, D. A. B.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Nakayama, W.

W. Nakayama, “Heat-transfer engineering in systems integration—outlook for closer coupling of thermal and electrical designs of computers,” IEEE Trans. Components Packag. Manuf. Technol. Part A 18, 818–826 (1995).
[CrossRef]

W. Nakayama, “On the accomodation of coolant flow paths in high density packaging,” IEEE Trans. Component Hybrids Manuf. Technol. 13, 1040–1049 (1990).
[CrossRef]

Oksuzoglu, H.

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

Ozaktas, H. M.

H. M. Ozaktas, “Toward an optimal foundation architecture for optoelectronic computing. Part I. Regularly interconnected device planes,” Appl. Opt. 36, 5682–5696 (1997).
[CrossRef] [PubMed]

H. M. Ozaktas, “Toward an optimal foundation architecture for optoelectronic computing, Part II. Physical construction and application platforms,” Appl. Opt. 36, 5697–5705 (1997).
[CrossRef] [PubMed]

H. M. Ozaktas, D. Mendlovic, “Multistage optical interconnection architectures with least possible growth of system size,” Opt. Lett. 18, 296–298 (1993).
[CrossRef]

H. M. Ozaktas, “Paradigms of connectivity for computer circuits and networks,” Opt. Eng. 31, 1563–1567 (1992).
[CrossRef]

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).

H. M. Ozaktas, J. W. Goodman, “Lower bound for the communication volume required for an optically interconnected array of points,” J. Opt. Soc. Am. A 7, 2100–2106 (1990).
[CrossRef]

H. M. Ozaktas, J. W. Goodman, “The limitations of interconnections in providing communication between an array of points,” in Frontiers of Computing Systems Research, S. K. Tewksbury, ed. (Plenum, New York, 1991), Vol. 2, pp. 61–130.
[CrossRef]

H. M. Ozaktas, “A physical approach to communication limits in computation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1991).

Pease, R. F. W.

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

Rosenberg, A. L.

F. T. Leighton, A. L. Rosenberg, “Three-dimensional circuit layouts,” J. Comput. Sys. Sci. 15, 793–813 (1986).

A. L. Rosenberg, “Three-dimensional VLSI: a case study,” J. Assoc. Comput. Mach. 30, 397–416 (1983).
[CrossRef]

Tseng, B.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Walker, J. A.

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

Appl. Opt. (2)

IEEE Photonics Technol. Lett. (2)

K. W. Goossen, J. E. Cunningham, W. Y. Jan, “GaAs 850 modulators solder-bonded to silicon,” IEEE Photonics Technol. Lett. 5, 776–778 (1993).
[CrossRef]

K. W. Goossen, J. A. Walker, L. A. D’Asaro, S. P. Hui, B. Tseng, R. Leibenguth, D. Kossives, D. D. Bacon, D. Dahringer, L. M. F. Chirovsky, A. L. Lentine, D. A. B. Miller, “GaAs MQW modulators integrated with silicon CMOS,” IEEE Photonics Technol. Lett. 7, 360–362 (1995).
[CrossRef]

IEEE Trans. Component Hybrids Manuf. Technol. (1)

W. Nakayama, “On the accomodation of coolant flow paths in high density packaging,” IEEE Trans. Component Hybrids Manuf. Technol. 13, 1040–1049 (1990).
[CrossRef]

IEEE Trans. Components Packag. Manuf. Technol. Part A (1)

W. Nakayama, “Heat-transfer engineering in systems integration—outlook for closer coupling of thermal and electrical designs of computers,” IEEE Trans. Components Packag. Manuf. Technol. Part A 18, 818–826 (1995).
[CrossRef]

Int. J. Electron. (1)

H. M. Ozaktas, H. Oksuzoglu, R. F. W. Pease, J. W. Goodman, “Effect on scaling of heat removal requirements inthree-dimensional systems,” Int. J. Electron. 73, 1227–1232 (1992).
[CrossRef]

J. Assoc. Comput. Mach. (1)

A. L. Rosenberg, “Three-dimensional VLSI: a case study,” J. Assoc. Comput. Mach. 30, 397–416 (1983).
[CrossRef]

J. Comput. Sys. Sci. (1)

F. T. Leighton, A. L. Rosenberg, “Three-dimensional circuit layouts,” J. Comput. Sys. Sci. 15, 793–813 (1986).

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “Comparison of system size for some optical interconnection architectures and the folded multi-facet architecture,” Opt. Commun. 82, 225–228 (1991).
[CrossRef]

H. M. Ozaktas, Y. Amitai, J. W. Goodman, “A three dimensional optical interconnection architecture with minimal growth rate of system size,” Opt. Commun.85, 1–4 (1991); errata 88, 569 (1992).

Opt. Eng. (1)

H. M. Ozaktas, “Paradigms of connectivity for computer circuits and networks,” Opt. Eng. 31, 1563–1567 (1992).
[CrossRef]

Opt. Lett. (1)

Other (5)

M. J. Little, J. Grinberg, “The 3-D computer: an integrated stack of WSI wafers,” in Wafer-Scale Integration (Kluwer, New York, 1988), Chap. 8.

IEEE, eds., Proceedings of the 45th Electronic Components and Technology Conference (ECTC) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).

H. M. Ozaktas, J. W. Goodman, “The limitations of interconnections in providing communication between an array of points,” in Frontiers of Computing Systems Research, S. K. Tewksbury, ed. (Plenum, New York, 1991), Vol. 2, pp. 61–130.
[CrossRef]

H. M. Ozaktas, “A physical approach to communication limits in computation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1991).

H. B. Bakoglu, Circuits, Interconnections, and Packaging for VLSI (Addison-Wesley, Reading, Mass., 1990).

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Figures (5)

Fig. 1
Fig. 1

Comparison of optical (solid curve), normally conducting (dashed curve), repeatered (dotted–dashed curve), and superconducting interconnections (dotted curve). We take k = 5, p = 0.8, Q = 10 W/cm2 and assume d d, T d, and T r to be small enough to have no effect.

Fig. 2
Fig. 2

Comparison of optical (solid curve), normally conducting (long-dashed curve), repeatered (long–short-dashed curve), and superconducting interconnections (short-dashed curve). We take k = 5, p = 0.8, Q = 10 W/cm2 and assume d d, T d, and T r to be small enough to have no effect. (a) B = 10 Mbit/s. (b) B = 100 Mbit/s. (c) B = 1 Gbit/s. (d) B = 10 Gbit/s.

Fig. 3
Fig. 3

Comparison of optical (solid curve), normally conducting (long-dashed curve), repeatered (long–short-dashed curve), and superconducting interconnections (short-dashed curve). Similar assumptions are made as in the previous figures. (a) B = 100 Mbit/s, V = 0.1 V; (b) B = 100 Mbit/s, V = 0.01 V; (c) B = 10 Gbit/s, V = 0.1 V; (d) B = 10 Gbit/s, V = 0.01 V.

Fig. 4
Fig. 4

Comparison of optical (solid curve), normally conducting (dashed curve), repeatered (dotted–dashed curve), and superconducting interconnections (dotted curve) when S = B is maximized. Similar assumptions are made as in the previous figures, but T d = 100 ps. (a) Optimum duty ratio. (b) Resulting S = B versus N.

Fig. 5
Fig. 5

Comparison of optical (solid curve), normally conducting (long-dashed curve), repeatered (long–short-dashed curve), and superconducting interconnections (short-dashed curve) when τ L is minimized. Similar assumptions are made as in the previous figures, but T d = 100 ps. (a) Optimum duty ratio for L = 10. (b) Resulting τ L -1 versus N for L = 10. (c) Optimum duty ratio for L = 100. (d) Resulting τ L -1 versus N for L = 100.

Tables (4)

Tables Icon

Table 1 Optical Interconnection Modela when T l T dT p

Tables Icon

Table 2 Normally Conducting Interconnection Modela when T dT l

Tables Icon

Table 3 Repeatered Interconnection Modela

Tables Icon

Table 4 Superconducting Interconnection Model when T dT p (T dT l in the Unterminated Case)a

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

3=Nd3=maxdd3N, kχr¯W2Nd, kEB/Q3/2N3/2.
=N1/3d=maxddN1/3, kχκ1/2WNp/2, kEB/Q1/2.
τ=maxTp, T,  T=maxTl, Td.
Tr=T.
1S=1cmaxddN1/3, kχκ1/2fλNp/2, kEB/Q1/2N1/2,χ=max1, BTd.
T=16ρkr¯N2/3,
BNp=16ρ-1kκ-1,
T=16ρl2W2,
d2V2kκNp-1/3BQ.
QN3/2d21rx 2V2rdgrdr+rxN1/3 2V2vTgrdrB,
Qd2N1/3k2V2κrx3p-2d+2V2vTrx3p-1zB,
d3p-12V2vT3p-2kκN1/3BQ,
d=min2V2kκNp-1/3BQ,2V2vT3p-2kκN1/3BQ13p-1.
SNp/2=4R0C0ρ1/2-1kχκ-1/2,χ=max1, BR0C0,
d=min2V2kκNp-1/3BQ, 8V2ρR0C0/μ1/2Q1/2×χ1/4kκ3/4N3p/4-1/3B1/2.
SNp/2=v4λpkχκ-1/2,χ=max1, BTd.
1S=1vmaxddN1/3, kχκ1/24λpNp/2,k2V2/μ TdB/Q1/2N1/2,χ=max1, BTd.
SHB1/2=constant.
HS  Np-1/2B1/2,
HB=constant.
HS  Np/4,
τL=τ+LB=1S+LB.

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