Statistical methodology to identify optimal placement of on-chip process monitors for predicting fmax

In previous literatures, many approaches use ring oscillators or other process monitors to correlate the chip's maximum operating frequency (F max ). But none of them focus on the placement of these on-chip process monitors (OPMs) on a chip. The placement will greatly influence the accuracy of a prediction model. In this paper, we first propose a simulation framework to sample a chip's F max and it's OPM result. These samples are used to develop our methodology of OPM placement and to verify the effectiveness of an OPM placement. Then, a model-fitting framework is presented to correlate the OPMs' result to chip's F max . Finally, we propose a methodology to idenify optimal placement of OPM for predicting F max . The experiments demonstrate the effectiveness of our methodology in both simulation and silicon data.