Stochastic Power/Ground Supply Voltage Prediction and Optimization Via Analytical Placement

Abstract

Abstract-Leakage power is one of the most critical issues for ultradeep submicrometer technology. Subthreshold leakage depends nearly exponentially on linewidth, and consequently, variation in linewidth translates to a large leakage variation. A significant fraction of variation in the linewidth occurs due to systematic variations involving focus and pitch. In this paper, we propose a new leakage-estimation methodology that accounts for focus-dependent variation in the linewidth. Our approach computes the pitch of each device in the design and uses it along with defocus information to predict the linewidth of the device. Once the linewidths of the devices in a cell are calculated, the cell leakage is computed to be the sum of leakages of all off-devices in the cell; device leakages are found from a linewidth-leakage table that is precharacterized with SPICE simulations. The presented methodology significantly improves the leakage estimation and can be used in existing leakage-reduction techniques to improve their efficacy. To demonstrate the use of our approach for leakage reduction, we modify the previously proposed linewidth-biasing technique of Gupta et al. to consider the systematic variations in linewidth and further optimize the leakage power. Our method reduces the leakage spread between worst and best process corners by up to 62% compared with the conventional corner-based analysis. Defocus awareness improves the leakage reduction from linewidth-biasing by up to 7%.

Walking pads: Fast power-supply pad-placement optimization

“…To find the proper virtual force for local balance, we first observe that there is a similarity between the 2D PDN on-chip voltage field and a 2D electrostatic voltage field. The steady state equation of a voltage field can be regarded as the finite-difference version of the 2D Poisson equation [5,13]:…”

Fast algorithms for power grid analysis based on effective resistance

“…In this section, the voltage at an arbitrary node within a power distribution network is determined when one power supply and multiple current loads exist within a grid, as shown 00 00 00 00 11 in Fig. 4.…”

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