Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)1 ELEC 7770 Advanced VLSI Design Spring 2010 VLSI Yield and Moore’s Law Vishwani D. Agrawal James J. Danaher Professor ECE Department, Auburn University Auburn, AL

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)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.

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)3 Importance of Yield  Cost of a chip = Cost of fabricating and testing a wafer  Yield × Number of chip sites on the wafer

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)4 Clustered VLSI Defects Wafer Defects Faulty chips Good chips Unclustered defects Wafer yield = 12/22 = 0.55 Clustered defects (VLSI) Wafer yield = 17/22 = 0.77

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)5 Yield Parameters  Defect density (d ) = Average number of defects per unit chip area  Chip area (A )  Clustering parameter (  )  Negative binomial distribution of defects, p (x ) = Prob(number of defects on a chip = x ) Γ ( α +x ) (Ad / α ) x = .  x ! Γ ( α ) (1+Ad / α ) α+x where Γ is the gamma function α = 0, p (x ) is a delta function (max. clustering) α = , p (x ) is Poisson distribution (no clustering)

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)6 Yield Equation Y = Prob( zero defect on a chip ) = p (0) Y = ( 1 + Ad / α ) – α Example: Ad = 1.0, α = 0.5, Y = 0.58 Unclustered defects: α = , Y = e – Ad Example: Ad = 1.0, α = , Y = 0.37 too pessimistic !

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)7 Effect of Defect Clustering Yield Ad = 0.5 Clustering Parameter, α e -0.5 = 0.607

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)8 Ranges of Yield Parameters Yield of 1 cm 2 chip Defect density, d in defects per cm Clustering parameter, α Mature process Initial process

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)9 References  Clustered yield model  M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory and Mixed-Signal VLSI Circuits, Springer, 2000, Chapter 3.  C. H. Stapper, “On Yield, Fault Distributions, and Clustering of Particles,” IBM Jour. of Res. and Dev., vol. 30, no. 3, pp , May  The unclustered defect model was first described in paper:  B. T. Murphy, “Cost-Size Optima of Monolithic Integrated Circuits,” Proc. IEEE, vol. 52, no. 12, pp , December  A general reference on clustered distributions:  A. Rogers, Statistical Analysis of Spatial Dispersions, London, United Kingdom: Pion Limited, 1974.

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)10 Gordon E. Moore

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)  “Cramming More Components onto Integrated Circuits,” Electronics, vol. 38, no. 8, April 19,   The complexity for minimum component costs has increased at a rate of roughly a factor of two per year (see graph on next page). Certainly over the short term this rate can be expected to continue, if not to increase. Over the longer term, the rate of increase is a bit more uncertain, although there is no reason to believe it will not remain nearly constant for at least 10 years. That means by 1975, the number of components per integrated circuit for minimum cost will be 65,000. I believe that such a large circuit can be built on a single wafer.

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)12 Moore’s 1965 Graph 1975

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)  “Progress in Digital Integrated Electronics,” IEDM Tech. Digest, 1975, pp  ... the rate of increase of complexity can be expected to change slope in the next few years as shown in Figure 5. The new slope might approximate a doubling every two years, rather than every year, by the end of the decade.

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)14 Figure 5 of Moore’s 1975 Paper 16M 1M 64K 4K Year Components per chip

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)  “Lithography and the Future of Moore’s Law,” Proc. SPIE, vol. 2437, May   By making things smaller, everything gets better simultaneously. There is little need for trade-offs. The speed of our products goes up, the power consumption goes down, system reliability, as we put more of the system on a chip, improves by leaps and bounds, but especially the cost of doing thing electronically drops as a result of the technology. (SPIE – Society of Photonic Instrumentation Engineers)

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)16 Also in the 1995 Paper... I have no idea what will happen beyond 0.18 microns. In fact, I still have trouble believing we are going to be comfortable at 0.18 microns using conventional optical systems. Beyond this level, I do not see any way that conventional optics carries us any further. Of course, some of us said this about the one micron level. This time, however, I think there are fundamental materials issues that will force a different direction. The people at this conference are going to have to come up with something new to keep us on the long term trend.

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)17 Moore’s Law Source: Wikipedia

Spring 10, Jan 13ELEC 7770: Advanced VLSI Design (Agrawal)  Problems with technology:  High power consumption  Power density  Leakage  Process variation – larger as a fraction of feature size  Increased noise sensitivity  Problems with design:  Verification of correctness – logic and timing  Ensuring reliable operation  Testing