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Posted Sun Apr 8th, 2012 10:14am Post subject: Moore's Law

In re: _Four and Half Years On_, there's a minor inaccuracy in the way you've described Moore's Law. It doesn't impare the quality of the article at all, and 99% of the people who cite Moore's Law make exactly the same mistake, but the correct version is a bit more interesting.

The actual statement of Moore's Law is that the 'optimal transistor budget' increases by a factor of two roughly every eighteen months. The trouble is that nobody outside the industry knows what 'optimal transistor budget' is. Broadly speaking, it's the most (and least) complicated circuit you can afford to make with a given process.

First of all, we measure circuits in terms of transistors because the transistor is usually the smallest, most common, and most useful thing you can print on a chunk of silicon.

There are two kinds of costs associated with making integrated circuits: the ones associated with processing the whole wafer, and the ones associated with processing the individual circuits (called 'dice') that you get from a wafer. There are also two kinds of errors that turn potential dice into garbage: the ones that happen while you process the wafer, and the ones that happen while you process the dice.

Wafer costs are usually the same for a process, no matter how big your circuit is.. say $100 per wafer. The errors that occur while producing the wafer are usually stated in terms of area.. one per square centimeter, for instance. The best way to get a good wafer yield is to make lots of small, simple dice, because that reduces the amount of silicon that you lose around any given error.

Die costs are usually proportional to the number of dice you have. Say you lose 5% of your dice while breaking the wafer apart, another 5% mounting them in packages, and spend 5c per die to make and test the package. The best way to get a good die yield is to make fewer, larger dice.

When you balance those costs against each other, you come up with a die size that's most cost-effective to make with that process. If you go smaller than that size, you lose money to die errors. If you go larger, you lose money to wafer errors.

Once you know that size, and the number of transistors you can fit into that area, you have your optimal transistor budget.. the best number of transistors to make per die with that process.

Making transistors smaller doesn't necessarily improve your budget. If you pack twice as many transistors into the same area, but lose twice as many dice to errors either in processing the wafer or breaking the wafer into dice, it doesn't improve things much. On the other hand, if you keep your transistors the same size but reduce wafer processing errors so you can make dice 40% larger and still get the same yield, you double your optimal transistor budget.

Historically, transistors have gotten 30% smaller (twice as many per square centimeter) about every 2-3 years, and dice get about 20% larger (50% more transistors per die) at the same rate. The improvements in both directions are what give us Moore's Law.

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Posted Thu Apr 19th, 2012 6:13am Post subject: Moore's Law

Wait, what? There is essentially a fixed cost per wafer on a process, and we can expect an x amount of defects per wafer. So the smaller the die size of the product (within a given TDP or clock range), the higher the overall yield will be. So when you say the best way to get a good die yield is to make fewer, larger die? (and lets not get into calling them dice...) There is a higher chance of a larger die containing multiple errors or defects, thereby making the entire die unusable. Even though modern CPUs/GPUs/etc. use a lot of redundancy to limit single point errors, if a die gets a handful of these defects, no amount of redudancy is going to save it. So, as I understand it, the "optimal" size for a fully working chip is around the 70 mm squared range up to around 120 mm square. This allows good yields overall and a mitigation of multiple defects on a die on a 300 mm wafer.

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Posted Wed Apr 25th, 2012 1:14pm Post subject: Moore's Law

Is this a real debate or are there sock puppets about?

Really? Wow.

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