Outline Motivation and Contributions Related Works ILP Formulation

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Presentation transcript:

Co-optimization of Memory BIST Grouping, Test Scheduling, and Logic Placement Andrew B. Kahng and Ilgweon Kang VLSI CAD LABORATORY, UC San Diego Design, Automation & Test in Europe March 26th, 2014

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Memory BIST Architecture Motivation Memory built-in self-test (MBIST) Essential DFT technique in modern SOCs MBIST design impacts chip resources and quality of test solution Physical optimizations of MBIST logic: not well-studied MEM BIST TAP Memory BIST Architecture

Challenges and Contributions Challenge: Multiple optimization criteria Minimize test time Minimize number of BIST controllers Minimize wirelength between BIST logic and memories Our work: Three-stage heuristic Memory partitioning : FM in a weighted hypergraph model Test scheduling : Integer Linear Program (ILP) formulation MBIST logic placement : min-weight maximum matching

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Related Works Test scheduling Reduction of test time is a fundamental goal in DFT Typical: scheduling as rectangle packing Also typical: scheduling as ILP Design optimizations for memory BIST controllers Most works focus on architectural and testing aspects Chien et al. [2009] propose a memory BIST design optimization ILP for clustering of memories to controllers Studies physical design aspects Various simplifications: all of a cluster is tested in parallel, no two clusters tested simultaneously, …

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Test time with one solution Improved test time is possible ILP Formulation Objective: Minimize test end time Subject to: Upper bound on test power Logical constraints capture parallel and serial testing scenarios power time MEM4 MEM2 MEM1 MEM3 MEM8 MEM6 MEM5 MEM9 MEM7 Test power limit Test time with one solution MBIST1 MBIST2 MEM3 power MEM8 MEM6 MEM5 MEM9 MEM7 MEM1 MEM2 MEM4 time Test power limit Improved test time is possible Reduced test time MBIST1 MBIST2

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Overall Flow Input: Memories, Constraints Memory Partitioning with Hypergraph (MLPart [1], FM-style) (2) Test Scheduling with ILP formulation (CPLEX [2], logical constraints) (3) Placement of BIST Logic for each Partition ([3], Min-Weight Max-Cardinality Matching) Output: Memory BIST Groups, Test Schedules, BIST Logic Placements [1] MLPart. http://vlsicad.ucsd.edu/GSRC/bookshelf/Slots/Partitioning/MLPart [2] IBM ILOG CPLEX Optimizer. http://www.ilog.com/products/cplex [3] Hungarian algorithm source code. http://www.informatik.uni-freiburg.de/~stachnis/index.html

Memory Partitioning Divide memories into k partitions using MLPart MLPart: Min-cut hypergraph partitioner based on multilevel FM k = number of BIST controllers Hypergraph: vertices = memories; hyperedge weights reflect test time implications of grouping Reduced test time if memories with same shape and depth in same group MEM Hyperedges: The same shape, depth and test power, respectively Edges: Distances < D1, < avg(D1, D2) and < D2, respectively (where D1 < D2) Example Hypergraph

Test Scheduling Solve ILP formulation Minimize test time, subject to power constraint ILP solver: CPLEX Optimizer 12.5.1 Additional partition (BIST controller) for better test time Obtain alternative test scheduling solution with extra BIST controller {1 BIST controller, 2 BIST controllers} per each partition MEM BIST1 Est. Test Time 1000 MEM BIST1 BIST2 Est. Test Time 900 Solution with one BIST controller Solution with two BIST controllers

Memory BIST Logic Placement To minimize wirelength between each BIST and memories Min-weight maximum-cardinality matching in a bipartite graph Apply Hungarian algorithm Cost: Diameter from a grid to all memories in a group Forbidden grids (intersection with memories) MEM MEM MEM MEM MEM MEM MEM MEM BIST placement solution MEM Possible grids for BIST logic placement Memories in the same BIST group

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Experimental Setup Develop MBIST-solver to implement our heuristics C++ / g++ 4.8.0 User options include min/max # partitions, min/max # memories in a partition, max diameter, power constraint, weight parameters, … MLPart: Memory partitioner CPLEX 12.5.1: ILP solver Testcases: six industrial testcases (from industry partners) TC #M #P DMAX TC1 143 13 3900 TC2 150 11 4500 TC3 124 8 2200 TC4 160 3400 TC5 137 7 3200 TC6 148 12 4100 TC = testcase M = #memories P = #partitions DMAX = maximum diameter w/o BIST [μm]

Industrial solution (TC1) Experimental Results Our solutions Reduce test time by up to 11.57% (Testcase 3) Reduce number of BIST controllers by up to 41.6% (Testcase 6) Reduce maximum diameter by up to 31.7% (Testcase 6) Large Maximum Diameter Smaller Maximum Diameter memories BIST controller Industrial solution (TC1) Test time = 1067 # BISTs = 13 Maximum Diameter = 3900μm Our solution (TC1) Test time = 969 # BISTs = 12 Maximum Diameter = 2100μm

Outline Motivation and Contributions Related Works ILP Formulation Heuristic Flow Experimental Results Conclusions and Future Work

Conclusions and Future Work Three-step heuristic methodology Co-optimization of (1) Memory BIST grouping, (2) test scheduling, and (3) memory BIST logic placement Objective: minimize test time for a given #BIST controllers Handle various serial / parallel testing options in ILP Minimize diameter of BIST groups  less-critical timing, less need for LVT instances in BIST implementation, etc. Future work Integrate these optimizations into ‘production’ PD flow Improve hypergraph weighting, scalability of ILP Improve congestion- and timing-awareness of BIST placement

Thank You!