Rapid method to account for process variation in full-chip capacitance extraction

Full-chip capacitance extraction programs based on lookup techniques, such as HILEX/CUP [1], can be enhanced to rigorously account for process variations in the dimensions of very large scale integration interconnect wires with only modest additional computational effort. HILEX/CUP extracts interconnect capacitance from layout using analytical models with. reasonable accuracy. These extracted capacitances are strictly valid only for the nominal interconnect dimensions; the networked nature of capacitive relationships in dense, complex interconnect structures precludes simple extrapolations of capacitance with dimensional changes. However, the derivatives, with respect to linewidth variation of the analytical models, can be accumulated along with the capacitance itself for each interacting pair of nodes. A numerically computed derivative with respect to metal and dielectric layer thickness variation can also be accumulated, Each node pair's extracted capacitance and its gradient with respect to linewidth and thickness variation on each metal and dielectric layer can be stored in a file. Thus, instead of storing a scalar value for each extracted capacitance, a vector of 3I + 1 values will be stored for capacitance and its gradient, where I is the number of metal layers. Subsequently, this gradient information can he used during circuit simulation in conjunction with any arbitrary vector of interconnect process variations to perform sensitivity analysis of circuit performance.