On error tolerance and Engineering Change with Partially Programmable Circuits

The growing size, density and complexity of modern VLSI chips are contributing to an increase in hardware faults and design errors in the silicon, decreasing manufacturing yield and increasing the design cycle. The use of Partially Programmable Circuits (PPCs) has been recently proposed for yield enhancement with very small overhead. This new circuit structure is obtained from conventional logic by replacing some subcircuits with programmable LUTs. The present paper lays the theoretical groundwork for evaluating PPCs with Quantified Boolean Formula (QBF) satisfiability. First, QBF models are constructed to calculate the fault tolerance and design error tolerance of a PPC, namely the percentages of faults and design errors that can be masked using LUT reconfigurations. Next, zero-cost Engineering Change Order (ECO) in PPCs is investigated. QBF formulations are given for performing ECOs, and for quantifying the ECO coverage of a PPC architecture. Experimental results are presented evaluating PPCs from [1], demonstrating the applicability and accuracy of the proposed formulations.