| Signal integrity, crosstalk and delay are addressed for VLSI interconnects by using existing interconnect models and models that are developed in this dissertation. Two spectral domain criteria (ratio of attenuation constant to phase constant and wavelength) have been used for proper interconnect model comparison and selection. The ratio of attenuation constant to phase constant, first used here in the context of VLSI, provides a quantitative measure to determine how losses influence the operation regime (Transmission Line or Circuit Theory) of an interconnect. It is concluded that for local VLSI interconnects driven with large output resistances (R{dollar}rmsb{lcub}out{rcub}{dollar} {dollar}>{dollar} 100 {dollar}Omega){dollar} drivers, lumped element models are sufficient for lengths less than 1 cm and rise times greater than 500 ps.; Approximate expressions for the ramp response and delay of the interconnect is derived using Pade approximations. Specifically (0,1) Pade approximation is used for the case where the output resistance of the driver is much larger than the magnitude of the characteristic impedance of the interconnect. A second-order approximation is derived for the case where the output resistance of the driver is smaller than the magnitude of the characteristic impedance of the interconnect. The errors introduced by these approximations are shown to be negligible.; Analytical expressions for the backward and forward crosstalk under strong coupling theory are derived and compared to the commonly used weak coupling approximation. The important transition from weak to strong coupling, which has never been shown before, is demonstrated and their differences are established both in time and frequency domains. It is clearly shown that the weak coupling approximation fails for extremely high frequencies, for very long and for very inhomogeneous lines i.e., for t{dollar}rmsb{lcub}r{rcub}{dollar} {dollar}<{dollar} {dollar}rmvert Tsb{lcub}even{rcub} - Tsb{lcub}odd{rcub}vert, where vert Tsb{lcub}even{rcub} - Tsb{lcub}odd{rcub}vert{dollar} is the difference between the propagation times of the two modes.; Finally a new and interesting interaction between the coupled interconnects is shown to exist where the response resembles the response of coupled pendula. The implication of this new interaction, first described in this thesis, for the VLSI interconnects is that for the arbitrarily terminated interconnects the crosstalk voltages can get as large as the input voltages. For the matched interconnects, however, the crosstalk voltages can only reach 25% of the input signal. |
