Three-dimensional Integrated Circuit Design

Appendix A. Enumeration of Gate Pairs in a 3-D IC

The starting gates N^start used in the derivation of the interconnect length distribution for 3-D circuits in [123] are described in this appendix. Starting gates are these gates that can form manhattan hemispheres of radius l, where l is the interconnect length connecting two gates. For a 3-D circuit consisting of n planes, Nⁿ = N/n gates per plane. For those gates located close to the periphery of each plane, only partial manhattan hemispheres are formed. Consequently, the number of gates encircled by these partial manhattan hemispheres varies with the interconnect length:

Region I. l = 0 (A-1)

Region II.

(A-2)

Region III.

(A-3)

Region IV.

(A-4)

Region V.

(A-5)

Region VI.

(A-6)

Region VII. ...