Designs and methodologies for post-silicon timing characterization
Timing analysis is a key sign-off step in the design of today's chips, but technology scaling introduces many sources of variability and uncertainty that are difficult to model and predict. The result of these uncertainties is a degradation in our ability to predict the performance of fabricated chips, i.e., a lack of model-to-hardware matching. The prediction of circuit performance is the result of a complex hierarchy of models ranging from the basic MOSFET device model to full-chip models of important performance metrics including power, frequency of operation, etc. The assessment of the quality of such models is an important activity, but it is becoming harder and more complex with rising levels of variability and the increase in the number of systematic effects observed in modern CMOS processes. The purpose of this research is (i) to introduce special-purpose test structures that specifically focus on ensuring the accuracy of gate timing models, and (ii) to introduce methods that analyze the extracted information, in the form of path delay measurements, using the proposed test structures. The certification of digital design correctness (the so-called signoff) is based largely on the results of performing Static Timing Analysis (STA), which, in turn, is based entirely on the gate timing models. The proposed test structures compare favorably to alternative approaches; they are far easier to measure than direct delay measurement, and they are much more general than simple ring-oscillator structures. Furthermore, the structures are specified at a high level, allowing them to be synthesized using a standard ASIC place-and-route flow, thus capturing the local layout systematic effects which can sometimes be lost by simpler (e.g., ring oscillator) structures. For the silicon timing analysis, we propose methods that deduce segment delays from the path delay measurements. These estimated segment delays using our methods can be directly compared with the timing models. Therefore, it will be easy to identify the cause of timing mismatches. Deducing segment delays from path delays, however, is not an easy problem. The difficulties associated with deconvolving segment delays from measured path delays come from insufficient sampling points. To overcome this limitation, we first group the segments based on certain characteristics of segments, and adapt Moore-Penrose pseudo-inverse method to approximately solve the segment delays. Secondly, we used equality-constrained least squares methods, which enable us to find a unique and optimized solution of segment delays from underdetermined systems. We also propose another improved test structure that has a built-in test pattern generator, and hence does not require ATPG (Automatic Test Pattern Generation). It is a self-timed circuit, and this feature makes the test structure run as fast as it can. Therefore, measurements can be made under high speed switching conditions. Finally, we can study dynamic effects such as timing effects of different levels of switching activities and voltage drop with the new test structure.