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AUBURN ELEC 7250 - Lecture2

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VLSI Testing Lecture 2: Yield & QualityVLSI Chip YieldClustered VLSI DefectsYield ParametersYield EquationDefect Level or Reject RatioDetermination of DLModified Yield EquationDefect LevelExample: SEMATECH ChipTest Coverage from Fault SimulatorMeasured Chip FalloutModel FittingComputed DLSummaryProblems to SolveSolution of Problem 1Solution of Problem 2Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 1VLSI Testing Lecture 2: Yield & QualityVLSI Testing Lecture 2: Yield & QualityYield and manufacturing costClustered defect yield formulaDefect levelTest data analysisExample: SEMATECH chipSummaryProblems to solveCopyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 2VLSI Chip YieldVLSI Chip YieldA manufacturing defect is a finite chip area with electrically malfunctioning circuitry caused by errors in the fabrication process.A chip with no manufacturing defect is called a good chip.Fraction (or percentage) of good chips produced in a manufacturing process is called the yield. Yield is denoted by symbol Y.Cost of a chip:Cost of fabricating and testing a wafer———————————————————————Yield x Number of chip sites on the waferCopyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 3Clustered VLSI DefectsClustered VLSI DefectsWaferDefectsFaulty chipsGood chipsUnclustered defectsWafer yield = 12/22 = 0.55Clustered defects (VLSI)Wafer yield = 17/22 = 0.77Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 4Yield ParametersYield ParametersDefect density (d ) = Average number of defects per unit of chip areaChip area (A)Clustering parameter (α)Negative binomial distribution of defects, p (x ) = Prob (number of defects on a chip = x )  (+x ) (Ad /) x= ─────── . ────────── x !  () (1+Ad /) +xwhere Γ is the gamma function= 0, p (x ) is a delta function (maximum clustering)= ∞ , p (x ) is Poisson distribution (no clustering)Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 5Yield EquationYield EquationY = Prob ( zero defect on a chip ) = p (0)Y = ( 1 + Ad /  ) Example: Ad = 1.0, α = 0.5, Y = 0.58Unclustered defects: α = ∞, Y = e - AdExample: Ad = 1.0, α = ∞, Y = 0.37too pessimistic !Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 6Defect Level or Reject RatioDefect Level or Reject RatioDefect level (DL) is the ratio of faulty chips among the chips that pass tests.DL is measured as parts per million (ppm).DL is a measure of the effectiveness of tests.DL is a quantitative measure of the manufactured product quality. For commercial VLSI chips a DL greater than 500 ppm is considered unacceptable.Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 7Determination of DLDetermination of DLFrom field return data: Chips failing in the field are returned to the manufacturer. The number of returned chips normalized to one million chips shipped is the DL.From test data: Fault coverage of tests and chip fallout rate are analyzed. A modified yield model is fitted to the fallout data to estimate the DL.Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 8Modified Yield EquationModified Yield EquationThree parameters:Fault density, f = average number of stuck-at faults per unit chip areaFault clustering parameter, βStuck-at fault coverage, TThe modified yield equation:Y (T ) = (1 + TAf / ) - Assuming that tests with 100% fault coverage(T =1.0) remove all faulty chips,Y = Y (1) = (1 + Af / ) - Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 9Defect LevelDefect Level Y (T ) - Y (1)DL (T ) = ——————— Y (T ) (  + TAf )  = 1 – —————— (  + Af ) Where T is the fault coverage of tests, Af is the average number of faults on the chip of area A, β is the fault clustering parameter. Af and β are determined by test data analysis.Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 10Example: SEMATECH ChipExample: SEMATECH ChipBus interface controller ASIC fabricated and tested at IBM, Burlington, Vermont116,000 equivalent (2-input NAND) gates304-pin package, 249 I/OClock: 40MHz, some parts 50MHz0.8m CMOS, 3.3V, 9.4mm x 8.8mm areaFull scan, 99.79% fault coverageAdvantest 3381 ATE, 18,466 chips tested at 2.5MHz test clockData obtained courtesy of Phil Nigh (IBM)Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 11Test Coverage from Fault SimulatorTest Coverage from Fault SimulatorStuck-at fault coverageVector numberCopyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 12Measured Chip FalloutMeasured Chip FalloutVector numberMeasured chip falloutCopyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 13Model FittingModel FittingY (T ) for Af = 2.1 and  = 0.083Measured chip falloutY (1) = 0.7623Chip fallout and computed 1 -Y (T )Stuck-at fault coverage, TChip fallout vs. fault coverageCopyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 14Computed DLComputed DLStuck-at fault coverage (%)Defect level in ppm237,700 ppm (Y = 76.23%)Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 15SummarySummaryVLSI yield depends on two process parameters, defect density (d ) and clustering parameter (α).Yield drops as chip area increases; low yield means high cost.Fault coverage measures the test quality.Defect level (DL) or reject ratio is a measure of chip quality.DL can be determined by an analysis of test data.For high quality: DL < 500 ppm, fault coverage ~ 99%Problems to SolveProblems to Solve1. Using the expression for defect level on Slide 9, derive test coverage (T) as a function of fault clustering parameter (β), defect level (DL), and average number of faults (Af) on a chip.2. Find the defect level for:Fault density, f = 1.45 faults/sq. cmFault clustering parameter, β = 0.11Chip area = 1 cm2Fault Coverage, T = 95%Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 16Solution of Problem 1Solution of Problem 1Copyright 2001, Agrawal & Bushnell Lecture 2 Yield & Quality 17Defect level, DL, is given on Slide 9, as follows:DL = 1 – [(β + Taf)/(β + Af)]βwhere T is the fault coverage, Af is the average number of faults on a chip of area A, and β is a fault clustering parameter. Further manipulation of this equation leads to the


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