Self-compensating design for reduction of timing and leakage sensitivity to systematic pattern-dependent variation

Critical dimension (CD) variation caused by defocus is largely systematic with dense lines "smiling"" through focus while isolated lines frown." In this paper, we propose a new design methodology that allows explicit compensation of focus-dependent CD variation, in particular, either within a cell (self-compensated cells) or across cells in a critical path (self-compensated design). By creating iso and dense variants for each library cell, we can achieve designs that are more robust to focus variation. Optimization with a mixture of dense and iso cell variants is possible, both for area and leakage power in timing constraints (critical delay), with the latter an interesting complement to existing leakage-reduction techniques, such as dual-Vth. We implement both a heuristic and mixed-integer linear-programming (MILP) solution methods to address this optimization and experimentally compare their results. Results indicate that designing with a self-compensated cell library incurs 12% area penalty and 6% leakage increase over a baseline library while compensating for focus-dependent CD variation (i.e., the design meets timing constraints across a large range of focus variation). We observe 27% area penalty and 7% leakage increase at the worst case defocus condition using only single-pitch cells. The area penalty of circuits after using both the heuristic and MILP optimization approaches is reduced to 3% while maintaining timing. We also apply the optimization to leakage, which traditionally shows very large variability due to its exponential relationship with gate CD. We conclude that a mixed iso/dense library that is combined with a sensitivity-based optimization approach yields much better area/timing/leakage tradeoffs than using a self-compensated cell library alone. Selfcompensated designs show 25% less leakage power on average at the worst defoeus condition compared to a design employing a conventional library for the benchmarks studied.close3

Self-compensating design for reduction of timing and leakage sensitivity to systematic pattern dependent variation - art. no. 61560B

Focus is one of the major sources of linewidth variation. CD variation caused by defocus is largely systematic after the layout is finished. In particular, dense lines "smile" through focus while isolated lines "frown" in typical Bossung plots. This well-defined systematic behavior of focus-dependent CD variation allows us to develop a self-compensating design methodology. In this work, we propose a novel design methodology that allows explicit compensation of focus-dependent CD variation, either within a cell (self-compensated cells) or across cells in a critical path (self-compensated design). By creating iso and dense variants for each library cell, we can achieve designs that are more robust to focus variation. Optimization with a mixture of iso and dense cell variants is possible both for area and leakage power, with the latter providing an interesting complement to existing leakage reduction techniques such as dual-Vth. We implement both heuristic and Mixed-Integer Linear Programming (MILP) solution methods to address this optimization, and experimentally compare their results. Our results indicate that designing with a self-compensated cell library incurs ???12% area penalty and ???6% leakage increase over original layouts while compensating for focus-dependent CD variation (i.e., the design meets timing constraints across a large range of focus variation). We observe ???27% area penalty and ???7% leakage increase at the worst-case defocus condition using only single-pitch cells. The area penalty of circuits after using either the heuristic or MILP optimization approach is reduced to ???3% while maintaining timing. We also apply our optimizations to leakage, which traditionally shows very large variability due to its exponential relationship with gate CD. We conclude that a mixed iso/dense library combined with a sensitivity-based optimization approach yields much better area/timing/leakage tradeoffs than using a self-compensated cell library alone. Self-compensated design shows an average of 25% leakage reduction at the worst defocus condition for the benchmark designs that we have studied