Toward better wireload models in the presence of obstacles

Wirelength estimation techniques typically contain a site density function that enumerates all possible path sites for each wirelength in an architecture and an occupation probability function that assigns a probability to each of these paths to be occupied by a wire. In this paper, we apply a generating polynomial technique to derive complete expressions for site density functions which take effects of layout region aspect ratio and the presence of obstacles into account. The effect of an obstacle is separated into two parts: the terminal redistribution effect and the blockage effect. The layout region aspect ratio and the obstacle area are observed to have a much larger effect on the wirelength distribution than the obstacle's aspect ratio and location. Accordingly, we suggest that these two parameters be included as indices of lookup tables in wireload models. Our results apply to a priori wirelength estimation schemes in chip planning tools to improve parasitic estimation accuracy and timing closure; this is particularly relevant for system-on-chip designs where IP blocks are combined with row-based layout.