DP-fill: A dynamic programming approach to X-filling for minimizing peak test power in scan tests

At-speed testing is crucial to catch small delay defects that occur during the manufacture of high performance digital chips. Launch-Off-Capture (LOC) and Launch-Off-Shift (LOS) are two prevalently used schemes for this purpose. LOS scheme achieves higher fault coverage while consuming lesser test time over LOC scheme, but dissipates higher power during the capture phase of the at-speed test. Excessive IR-drop during capture phase on the power grid causes false delay failures leading to significant yield reduction that is unwarranted. As reported in literature, an intelligent filling of don´t care bits (X-filling) in test cubes has yielded significant power reduction. Given that the tests output by automatic test pattern generation (ATPG) tools for big circuits have large number of don´t care bits, the X-filling technique is very effective for them. Assuming that the design for testability (DFT) scheme preserves the state of the combinational logic between capture phases of successive patterns, this paper maps the problem of optimal X-filling for peak power minimization during LOS scheme to a variant of interval coloring problem and proposes a dynamic programming (DP) algorithm for the same along with a theoretical proof for its optimality. To the best of our knowledge, this is the first ever reported X-filling algorithm that is optimal. The proposed algorithm when experimented on ITC99 benchmarks produced peak power savings of up to 34% over the best known low power X-filling algorithm for LOS testing. Interestingly, it is observed that the power savings increase with the size of the circuit.