Self-Compensating Design for Reduction of Timing and Leakage Sensitivity to Systematic Pattern-Dependent Variation

Abstract

Abstract-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 defocus condition compared to a design employing a conventional library for the benchmarks studied.

Improving the Quality of Delay-Based PUFs via Optical Proximity Correction

“…Since the sources of variation in lithography have both random and systematic components [16], the above method will effectively amplify both, which is undesired. Thus, to ensure that the amplified variation is mostly random, P-OPC approach should ideally be applied along with layout/design compensation methods [4], [29] that counteract systematic variation.…”

On improving the uniqueness of silicon-based physically unclonable functions via optical proximity correction

“…If the photoresist material is positive (negative) and the image intensity at a certain location is greater (lesser) than a specific threshold, the resist gets etched out. The post-etch image is called the resist or pattern image Ip and is often calculated as follows [12] Ip(x, y) = 1, if Ia(x, y) ≥ I th 0, otherwise (5) where I th is a constant intensity threshold. Process variations in this optical system are typically modeled by a combination of focus and dose variations [8]: Focus Variations: Focus variations (defocus) are essentially small changes in the distance between the projection lens and resist/wafer from the ideal setting (zero defocus).…”

“…Second, a PUF printed with the highest variability will clearly not conform well with the original design. To deal with the first problem, we use compensation methods to the PUF layout/design which counteract (balance out) systematic variation such as those discussed in [10,5]. This ensures that PUF responses are effectively determined by only random variation.…”