VLSI Testing Lecture 2: Yield & Quality

1. VLSI Testing Lecture 2: Yield & Quality • Yield and manufacturing cost • Clustered defect yield formula • Defect level • Test data analysis • Example: SEMATECH chip • Summary • Problems to solve Lecture 2 Yield & Quality

2. VLSI 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 wafer Lecture 2 Yield & Quality

3. Clustered VLSI Defects Good chips Faulty chips Defects Wafer Clustered defects (VLSI) Wafer yield = 17/22 = 0.77 Unclustered defects Wafer yield = 12/22 = 0.55 Lecture 2 Yield & Quality

4. Yield 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 ) G(a+x ) (Ad /a) x = ------------- . ---------------------- x ! G (a) (1+Ad /a) a+x where Γ is the gamma function a = 0, p (x ) is a delta function (maximum clustering) a =∞ , p (x ) is Poisson distribution (no clustering) Lecture 2 Yield & Quality

5. Yield Equation Y = Prob ( zero defect on a chip ) = p (0) Y = ( 1 + Ad / a ) - a Example: Ad = 1.0, α = 0.5, Y = 0.58 Y = e - Ad Unclustered defects: α = ∞, Example: Ad = 1.0, α = ∞,Y = 0.37 too pessimistic ! Lecture 2 Yield & Quality

6. Defect 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. Lecture 2 Yield & Quality

7. Determination 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. Lecture 2 Yield & Quality

8. Modified 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 / b) - b Assuming that tests with 100% fault coverage (T =1.0) remove all faulty chips, Y = Y (1) = (1 + Af / b) - b Lecture 2 Yield & Quality

9. Defect Level Y (T ) - Y (1) DL (T ) = ——————— Y (T ) ( b + TAf ) b = 1 – —————— ( b + Af ) b 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. Afand β are determined by test data analysis. Lecture 2 Yield & Quality

10. Example: 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) Lecture 2 Yield & Quality

11. Test Coverage from Fault Simulator Stuck-at fault coverage Vector number Lecture 2 Yield & Quality

12. Measured Chip Fallout Measured chip fallout Vector number Lecture 2 Yield & Quality

13. Model Fitting Chip fallout vs. fault coverage Y (1) = 0.7623 Chip fallout and computed 1 -Y (T ) Measured chip fallout Y (T ) for Af = 2.1 and b = 0.083 Stuck-at fault coverage, T Lecture 2 Yield & Quality

14. Computed DL 237,700 ppm (Y = 76.23%) Defect level in ppm Stuck-at fault coverage (%) Lecture 2 Yield & Quality

15. Summary • 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% Lecture 2 Yield & Quality

16. Problems to Solve • 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. • 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% Lecture 2 Yield & Quality

17. Solution 1 Defect level, DL, is given on Slide 9, as follows: DL = 1 – [(β + Taf)/(β + Af)]β where 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 following result: (1 – DL)1/β = (β + Taf)/(β + Af) or T = [{(β + Af)(1 – DL)1/β– β}/(Af)] × 100 percent Lecture 2 Yield & Quality

18. Solution 2 Defect level, DL, as given on Slide 9, is: DL(T) = 1 – [(β + Taf)/(β + Af)]β Substituting, • Fault density, f = 1.45 faults/sq. cm • Fault clustering parameter, β = 0.11 • Chip area = 1 cm2 • Fault Coverage, T = 95% • We get, • DL(T) = 0.00522 or 5,220 parts per million Lecture 2 Yield & Quality