Handling inverted temperature dependence in static timing analysis

Abstract

In digital circuit design, it is typically assumed that cell delay increases with decreasing voltage and increasing temperature. This assumption is the basis of the cornering approach with cell libraries in static timing analysis (STA). However, this assumption breaks down at low supply voltages because cell delay can decrease with increasing temperature. This phenomenon is caused by a competition between mobility and threshold voltage to dominate cell delay. We refer to this phenomenon as the inverted temperature dependence (ITD). Due to ITD, it becomes very difficult to analytically determine the temperatures that maximize or minimize the delay of a cell or a path. As such, ITD has profound consequences for STA: (1) ITD essentially invalidates the approach of defining corners by independently varying voltage and temperature; (2) ITD makes it more difficult to find short paths, leading to difficulties in detecting hold time violations; and (3) the effect of ITD will worsen as supply voltages decrease and threshold voltage variations increase. This article analyzes the consequences of ITD in STA and proposes a proper handling of ITD in an industrial sign-off STA tool. To the best of our knowledge, this article is the first such work.