Modeling Techniques for the Formal Verification of Integrated Circuits at Transistor-Level: Performance vs. Precision Trade-offs

The behavior of any electronic system can be traced back to how its constituting components physically interact with each other. Such low-level interactions explain how specific states of a given circuit are physically possible. Some circuit states can be erroneous, e.g., applying a voltage stress greater than what some device can tolerate. It is of particular importance to know whether such errors can happen on a given circuit, so that required corrections can be made. Identifying errors requires some circuit modeling technique, and a way to explore the state space of the circuit model (which may be very large if at all finite). In this work, we show the limitations of classical verification techniques, and propose a new approach based on formal methods to overcome them. We propose new circuit semantics for transistor-level descriptions from (1) recalling and improving existing semantics, and (2) introducing novel alternate ones. We then demonstrate their usage in our verification framework—which makes use of a satisfiability modulo theories (SMT) solver—to verify specific electric properties of circuits. Specifically, we address the problem of the search for circuit transistors that are subject to electrical overstress (EOS). We draw interesting conclusions by comparing the presented circuit semantics, both formally and via experimental benchmarks.