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.