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what's the purpose of going so thin
It's not thin; is't small.
3nm equates to the smallest feature size in that particular technology.
It could be 3nm wide wires or anything else. Without context 7nm, 5nm, 3nm means nothing.
Intel 10nm is more dense in transistors per millimeter square than TSMC 7nm.
Also the number of layers metal in a technology also matters.
Smaller geometry normally translates into lower power and a faster chips.
 
Intel : we barely move to 7nm
N in Nnm is just a moniker. It has nothing to do with actual device/process sizes (not since Intel came up with FinFET). If Intel wanted to, they could name their next process 0.5nm and be ahead of TSMC. It's just a nature of foundry business that they have to introduce new process every year. The new process always has some improvements but they are not necessarily related to smaller sizes. However, historically the process names were always determined by device sizes so the companies continue using this convention.
 
So, in theory, we should be at the end of the road for silicon by the end of the decade? Or will we be able to stack these layers a lot more now? Still will mean a power consumption increase along with more heat the more we stack these silicon layers.

Isn’t graphene supposed to take over next? I think it’s going to be a really long time until we can miniaturize quantum computers unless we have some major breakthroughs in physics so that’s probably off the table for the next thing.

What if it just becomes physically impossible to make faster processors in the coming years? What if it just plateaus for decades? At least if that’s the case software should get a lot better, lol. But what if we don’t end up needing faster processors for most things outside of things like ML, science and medicine? Who is ever going to need better than 16K video (likely edited to 8K in post)? Why even make a camera with more than 150MP resolution for most users, including most professionals? Might we reach a point where we’re content with our technology’s ability to do what we need? I know that given historic context such a thing sounds foolish, but there are limits that must be hit eventually and specifically when it comes to video and photos there are limits on human perception that are already being hit. It’s an interesting thing to contemplate.
 
How can you even measure something that is 3nm? How can you build it?

You build it by carefully controlling where radiation (UV light, typically) hits photoresist. You typically do that by creating a mask that only allows the light to pass through holes in the mask. The mask can be much bigger, and then the light is focussed using lenses to the smaller size of the chip.

As for measuring, there are lots of ways, depending on what you are measuring. Transmission or scanning electron microscopy allows you to directly see the structures. Or you can measure the electrical behavior of the structure and from that infer it’s dimensions.
 
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Intel should have bought TSMC a long time ago, problem solved. Then they could stuff sofas, coffee tables, refrigerators and anything else they wanted into a room.
Not necessarily. Yahoo could have bought Google, but that doesn’t mean Google under Yahoo would be what it is today.
 
Everything is not for sale in the world of business.
The FTC, SEC, and others might disagree with what is for sale.
There are hostile takeovers, but everything is not for sale.

Everything is for sale.

A government agency may hold it up but it's still for sale.
 
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