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.
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机译：通过使用现有的互连模型和本文开发的模型，可以解决VLSI互连的信号完整性，串扰和延迟。两个光谱域标准（衰减常数与相位常数和波长之比）已用于正确的互连模型比较和选择。首先在VLSI中使用的衰减常数与相位常数之比提供了一种定量方法，以确定损耗如何影响互连的工作方式（传输线或电路理论）。结论是，对于以大输出电阻（R {dollar} rmsb {lcub} out {rcub} {dollar} {dollar}> {dollar} 100 {dollar} Omega} {dollar}驱动器驱动的本地VLSI互连，集总元件模型长度小于1厘米，上升时间大于500 ps足够了；使用Pade逼近可以得出互连的斜坡响应和延迟的近似表达式。具体地，在驱动器的输出电阻远大于互连的特征阻抗的大小的情况下，使用（0,1）Pade近似。对于驱动器的输出电阻小于互连的特征阻抗的大小的情况，可以得出二阶近似值。这些近似值引入的误差被证明是可以忽略的。推导了强耦合理论下的反向和正向串扰的解析表达式，并将其与常用的弱耦合近似进行了比较。证明了从弱耦合到强耦合的重要过渡，这一点以前从未显示过，并且它们的时差在时域和频域均已确定。清楚地表明，对于极高的频率，很长的线和非常不均匀的线，即t {dollar} rmsb {lcub} r {rcub} {dollar} {dollar} <{dollar} {dollar } rmvert Tsb {lcub} even {rcub}-Tsb {lcub} odd {rcub} vert，其中vert Tsb {lcub} even {rcub}-Tsb {lcub} odd {rcub} vert {dollar}是传播之间的差异两种模式的时间。最终，在耦合的互连之间存在新的有趣的交互，其中响应类似于耦合的摆的响应。本文首先描述的这种新交互作用对于VLSI互连的含义是，对于任意端接的互连，串扰电压可以与输入电压一样大。但是，对于匹配的互连，串扰电压只能达到输入信号的25％。
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