The Extreme Engineering of ASML’s EUV Light Source
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For one, memristors offer a chance of building truly 3d, dense, power efficient structures.
I worked at Intel and I had a lot of interesting discussions on how a 3d processor would look like with memristors. Everyone agreed if it can be made to work we would jump ahead of Moore's law by several orders of magnitude.
Memristors can act as both memory and energy circuitry. Not only that, but they are very simple (and thus can be printed very densely) and yet at the same time can be very easily programmable (just put a little bit more current to change the state). They are persistent -- once programmed can remember the state for very long time (potentially centuries -- depending on the exact process and composition). And because they are just resistors at low currents, they can be red extremely fast and extremely efficiently.
Because of how little energy it uses (it only really uses energy when memristor needs to be programmed), they can be stacked in three dimensions without any limits other than our printing technology.
I meant memory and processing circuitry. Memristors can be used to build logic gates more efficiently than existing transistors.