Theoretical Study Of Influences Of Skin Effect On Copper Interconnect Reliability Design In Integrated Circuits

Along with the rising of signal frequencies in integrated circuits and thedeteriorating of heat dissipating conditions of multilevel interconnect structures, thereliability issues of interconnects transmitting pulse or alternate current signals arebecoming more and more serious. When the frequency exceeds a certain critical value,skin effect will occur in metal interconnects. However, traditional reliability researcheson interconnects transmitting high frequency signals are almost all done from theperspective of converting these signals into effective direct current ones, failing to takeinto account of the signals’ high frequency characteristics, especially the impacts of skineffect. Aimed at this unexplored research area, the thesis makes a groundbreaking studyof the influences of skin effect on the reliability design of copper interconnects inintegrated circuits, based on three aspects involving the extra heating effect generatedby skin effect, the variations of current densities in interconnects caused by skin effect,and the skin-effect-related high frequency losses of interconnects, providing atheoretical basis for the research in related fields.Firstly, the impacts of extra heating generated by skin effect on the self-consistentreliability design of copper interconnects are discussed. Incorporating the nonuniformskin current distribution, a simplified model for the effective skin current distributionarea on the cross-section of rectangular interconnects is derived, laying the ground forhigh-frequency resistance calculation and determining the actual effective currentdensity on the cross-section of rectangular interconnects. A one-dimensionaltemperature distribution for a typical two-level structure in copper interconnectreliability analyses is solved, showing the differences in temperature distributionsbetween the two-level interconnect structure including the via and a single interconnect.Using the simplified high-frequency resistance model derived, the impacts of skin effecton the temperature distribution are calculated, demonstrating the relationship betweenthe temperature distribution variations of the two-level interconnect structure and thefrequency. Then, the self-consistent method is improved to be suitable for the reliabilitydesign of copper interconnects with a unique double-failure characteristic. A suggestion is given that using the temperatures near the vias to calculate the lifetimes of copperinterconnects is more reasonable. Based on the thermal calculation results, theinfluences of skin effect on the maximum allowed specifications, such as the maximumallowed current density and temperature of interconnects in the self-consistent designare studied, pointing out that over optimistic results will be obtained if these influencesare ignored, and suggesting that a maximum allowed frequency specification must beconsidered in the high-frequency reliability design.After that, the current density variations around the vias of copper interconnectstructures caused by skin effect and the resulting reliability problems are studiedqualitatively and quantitatively, using three-dimensional finite element simulations.Since the skin current distribution is relevant to the positional relationships between theinterconnect structure and the ground, these relationships are mainly divided into threesituations. Through the simulation, the nonuniform current distributions caused bycurrent crowding effect in the corner areas around the via in direct current condition isdemonstrated graphically, and comparisons of the current distributions on three crucialsurface areas near the via determining the lifetime of the interconnect structure betweenhigh frequency and direct current situations are given. Then the relationship between theaverage current densities on the three surface areas and the frequency is calculated,showing how the mutual inductive coupling between the interconnects and the groundand the self-inductances of the interconnects influence the high-frequency currentdistributions, and revealing an important disparity of skin current distributions betweenthe corner area near the via and the straight interconnect limbs as frequency changes.The non-ignorable impacts of current density variations on the lifetime of the copperinterconnect structure as the frequency changes are elaborated quantitatively, and anappropriately design of the positional relation between interconnects and the ground issuggested to improve the interconnect reliability in high frequency conditions.Finally, the influences of frequency-related losses such as skin effect loss in seriesinterconnect system on the fast current estimations and the lifetime calculations in theinterconnect reliability design are discussed. A voltage transfer function model ofinterconnects is established, and the functions of skin effect, dielectric and resistivelosses on various sizes of interconnects are elaborated. The step responses of the seriessystem consisting of the previous level interconnect and the gate are obtained using Inverse Fourier Transform, showing the effects of the high frequency losses of theprevious level interconnect on the waveforms of the step response. Then, the impacts ofthe variations of the step response waveform on the accuracy of the fast currentestimation and the lifetime computation of the next level interconnect are demonstratedthrough further calculation, pointing out that the high frequency losses of interconnectsare not only signal integrity issues, they are also reliability problems; at the same time,the failing processes of interconnects in a series system are not entirely mutuallyindependent, and the influences of previous level interconnects on the next level mustbe taken into account when calculating the reliability of an interconnect system.