Accurate Small Signal Simulation of Superconductor Interconnects in SPICE

Superconductor electronics is gaining traction as the increasing density of integration of recent and future digital circuits pushes the limits of available simulation models. Designers often make assumptions in the behavioral models of circuit elements when simulating circuits. For instance high-frequency effects have been neglected so far in the design of superconductor digital circuits, while much has been done in the past to model them. Indeed these effects had little influence on the accuracy of digital circuits simulations until recently. The increase in clock frequency, combined with longer paths between cells and higher yield requirements for large scale circuits fabrication, has led to the need of more accurate models, including in particular high frequency effects such as quasi-particle losses. To do so, this work uses a state-space model that describes the circuit under study with internal state variables and a set of first-order differential equations. We extract the state-space model while analytically enforcing the DC requirements of superconductors that are required to account for flux-trapping. The model accurately traps flux at DC, and given the model is fitted with enough poles, the high-frequency effects are also accurate relative to the reference model. The high-frequency effects have been investigated on a practical circuit: a long-distance Passive Transmission Line (PTL) designed for the high-density MIT Lincoln Labs SFQ5ee process. Results obtained in the time domain allow to observe the effects of dispersion of pulses traveling on long paths of PTLs. Indeed the energy of voltage pulses is sufficient to break Cooper pairs for the highest clock frequencies.