Yield of Black Swans

h EXCEPT FOR GETTING your chip to market on time, optimizing yield is perhaps the most important thing we can do to improve IC profitability. We address this problem in several ways: design for manufacturability (DFM) through layout rules, process control, and increasingly clean cleanrooms. In an ideal world, this would solve our yield problems. We know it doesn’t, so we build a diagnostic capability into our chips in order to react and fix yield issues faster. We’ve learned that random defects from particles are no longer the major cause of yield loss, and that systematic factors are the dominant problems in today’s fabrications. I suggest that we should think of these in a way that is exactly opposite from how we usually think of themVrandom defects are actually very deterministic, while systematic problems are random. In ‘‘The Black Swan,’’ Nassim Taleb notes that while many books on probability use casinos as examples of uncertainty and randomness, they are actually terrible instances of these. Large numbers of people betting very small amounts will lose quantities that can easily be predicted. He notes that the real uncertainty facing the casino owner is very differentVwins by high rollers, cheaters, or the unexpected loss of a big and lucrative show. Random particle hits are similar to the small gamblerVwhile you can’t tell what an individual will do, you can set the rules (game or design) to influence the yield. The interesting systematic cases are the things you never expected and thus must react to. These cases are the ones which are truly random. They are the black swans, the things you can’t anticipate by studying and tracking test results and data from instrumenting the process. You might see the black swans sooner by using binoculars (in this case, looking for the warning signs of a process excursion), but you can’t predict them. Let’s look at another place where yield is importantVagriculture. For millennia, crop yields were poor and random, with good weather producing good crop yields, bad weather causing famine, and poor soil management techniques reducing production even in good times. The application of technology and bigger farms in England led to higher yields. If climate, insects, and disease would cooperate we’d have more or less constant and predictable yields. But they don’t, and we have crop yield excursions just like we have silicon yield excursions. Crop yield problems last years or decades, not days or weeks, and finding a new insecticide takes longer than finding a design rule violation, but the problems are fundamentally quite similar. This is why studying yield is so interesting. DFM rules are all very fine, but sometimes obeying the rules is not good enough to avoid problems. Sometimes designs can still achieve high yields while still violating the rules. We write tests for faults that may never occur, and usually design conservatively for improved reliability. We can work hard at predicting yield and designing for yield, but eventually the black swan shows up and we have to fix the unexpected problem (which, happily for our job satisfaction, is never boring). h