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Typically a chip is packaged to protect it and to make it easier to handle. Is it possible to look at exposed chip (see images here https://electronics.stackexchange.com/questions/56649/what-is-a-die-package) under microscope and know the components and the circuit involved?

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No.

A experienced chip designer can make some educated guesses, but can't know for sure. A highly regular array will be some memory, for example. Larger structures near pin pads will be the output drivers.

You can't tell the dopant levels just by looking, and there are many layers to modern chips. You can only see the top interconnect layer directly. That will obscure other layers.

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  • $\begingroup$ Then you can grind off the top layer with an extremely fine equipment and try analyzing the next. Soviets did this, reverse-engineering American chips. But with current transistor densities, this is absolutely pointless: developing the chip from scratch would be cheaper. $\endgroup$
    – SF.
    Mar 8 '17 at 12:06

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