This paper quantitatively analyzes thermal gradient of SoC and proposes a thermal flattening procedure. First, the impact of dominant parameters, such as area occupancy of memory/logic block, power density, and floorplan on thermal gradient are studied quantitatively. Temperature difference is also evaluated from timing and reliability standpoints. Important results obtained here are 1) the maximum temperature difference increases with higher memory area occupancy and 2) the difference is very floorplan sensitive. Then, we propose a procedure to amend thermal gradient. A slight floorplan modification using the proposed procedure improves on-chip thermal gradient significantly.

In this paper, we propose a methodology for calculating on-chip temperature gradient and leakage power distributions. It considers the interdependence between leakage power and local temperature using a general circuit simulator as a differential equation solver. The proposed methodology can be utilized in the early stages of the design cycle as well as in the final verification phase. Simulation results proved that consideration of the temperature dependence of the leakage power is critically important for achieving reliable physical designs since the conventional temperature analysis that ignores the interdependence underestimates leakage power considerably and may overlook potential thermal runaway.

With the recent advance of process technology shrinking, process parameter variation has become one of the major issues in SoC designs, especially for timing convergence. Recently, Statistical Static Timing Analysis (SSTA) has been proposed as a promising solution to consider the process parameter variation but it has not been widely used yet. For estimating the delay yield, designers have to know and understand the accuracy of SSTA. However, the accuracy has not been thoroughly studied from a practical point of view. This paper proposes two metrics to measure the pessimism/optimism of SSTA; the first corresponds to yield estimation error, and the second examines delay estimation error. We apply the metrics for a problem which has been widely discussed in SSTA community, that is, normal-distribution approximation of max operation. We also apply the proposed metrics for benchmark circuits and discuss about a potential problem originating from normal-distribution approximation. Our metrics indicate that the appropriateness of the approximation depends on not only given input distributions but also the target yield of the product, which is an important message for SSTA users.

Process variation is becoming a primal concern in timing closure of LSI (Large Scale Integrated Circuit) with the progress of process technology scaling. To overcome this problem, SSTA (Statistical Static Timing Analysis) has been intensively studied since it is expected to be one of the most efficient ways for performance estimation. In this paper, we study variation of output transition-time. We firstly clarify that the transition-time variation can not be expressed accurately by a conventional first-order sensitivity-based approach in the case that the input transition-time is slow and the output load is small. We secondly reveal quadratic dependence of the output transition-time to operating margin in voltage. We finally propose a procedure through which the estimation of output transition-time becomes continuously accurate in wide range of input transition-time and output load combinations.