Fast-yet-accurate PVT simulation by combined direct and iterative methods

The operations and performances of deep-submicron integrated circuits are affected significantly by the variations of process parameters, power supply voltages and operating temperatures. Circuit simulation for all the combinations of process-voltage-temperature (PVT) conditions, known as PVT simulation, is emerging as a must not only for analog and RF circuit designs, but also for the designs of digital library cells and critical paths. With the number of PVT conditions in the range of hundreds and even thousands, existing solution of invoking a simulator repeatedly for all these PVT conditions is becoming extremely time consuming. This paper presents a new simulation approach capable of simulating hundreds and thousands PVT corners with the computational cost comparable to or even less than that of a few corner simulations, yet with the same simulation accuracy and robustness. The proposed approach is based on the combination of the LU-factorization based direct method and Krylov subspace based iterative methods to explore the common characteristics shared by a circuit under all PVT corners. The key novelty is a systematic method that uses as few LU based direct solving as possible for underlying linearized systems, and then solves the rest of linearized systems across the entire PVT linear system space using Krylov subspace based iterative methods with preconditioners computed from those LU factors.