Process variability, in addition to wide temperature and supply voltage variation ranges, severely degrades the fabrication outcome (yield) of digital cells as for the fulfillment of performance specification bounds. This paper presents the application of mathematical optimization to the design of standard cells that are robust to process variations even in worst-case operating conditions. The method attains the optimal sizing of individual transistors in the cell for maximizing the statistical yield referring to leakage power and propagation delay bounds, with local and global process variations specified by industrial process development kits (PDKs). The approach is demonstrated for a 40 nm low-power standard threshold voltage Complementary Metal Oxide Semiconductor (CMOS) technology, for an intended operating temperature range [À40°C, 125°C] and supply voltage range [0.95 V, 1.05 V]. The reported optimization results show a yield improvement from an initial 50% to 99.9%, and Simulation Program with Integrated Circuit Emphasis (SPICE)-level Monte Carlo analysis confirmed the estimated yield of the obtained circuits.slow corners for such devices. However, digital corners account for global variation, not including local variations effects, which are critical in the present scenario [24]. Also, digital corners are not design-specific, which is necessary to determine the impact of variation. Such characteristics limit the accuracy of the digital corners and cannot be considered as accurate indicators of performance variation bounds [25]. In order to achieve effective variation-aware design, we must thoughtfully account both the statistical inter-die and intra-die variations, and the operating condition fluctuations.As a result, statistical optimization for yield has become a crucial task in IC design, and because the specifications of an IC usually have challenging trade-offs, requiring multidimensional, multiobjective optimization, the role of mathematical techniques for circuit analysis and yield optimization has become essential to obtain solutions that satisfy the requested performance in the least time effort [6][7][8][9]14]. Transistor level designs like standard cells are most susceptible to parametric yield issues caused by process/operating variations [10,11,13,16,17,23] and are the scope of this work. Several design time transistor sizing algorithms have been proposed in literature to optimize the delay and/or power variations. In [27], authors report an approach for the variation-tolerant gate sizing incorporating statistical timing model. The proposed approach formulates a statistical objective and timing constraints and solves the resulting nonlinear optimization. However, this seems computationally difficult and therefore does not fit to complex circuits. Other techniques proposed in [28][29][30]36] rely on the notion of capturing the delay distribution by performing the statistical static timing analysis instead of static timing analysis. Later, gate sizing is carried out using either nonlinear prog...