An excellent question! A CPU (central processing unit) is complicated piece of machinery that is essentially the hardware that allows your computer to work. While I can't comment too much on the electrical engineering aspects (e.g., circuit design, logic gates), I can give some idea about the materials.

There are actually many materials that go into making a CPU, ranging from the substrate or the interconnects between components; but the main material is silicon. The basic building block of any electrical device is a transistor, and the active material is silicon.

Current computers are based on binary, or 0's and 1's. How this is encoded in the hardware is through high or low voltages. The transistor is essentially the switch that toggles between the 'on'/1/high voltage state or 'off'/0/low voltage state. From that you can build ever more complex devices.

And the material that makes this possible is silicon.

You might ask, well, why silicon? The first reason is because it is a semiconductor. That means at or around room temperature (which is around where all your electronics operate), silicon doesn't conduct electricity. The key is that although it is not naturally conducting, we can easily engineer it to be so.

In fact, to make it conductive, we intentionally put impurities in the material!

It turns out that silicon isn't actually the most optimal material we can use for electronic devices. However, because it is so abundant and cheap, it is hard to out-compete.

Nevertheless, there are a few driving forces that are pushing towards other novel materials. The first is that there are many more specialized applications for which more expensive and better materials have a market. The second has to do with what is known as Moore's law. Named after Gordon Moore, the co-founder of Intel, Moore's law is more of a prediction than a law. It states that the number of transistors in an integrated circuit doubles about every two years. For the past 40 some years, that prediction has held more or less true- every couple of years the components on an integrated circuit get smaller and smaller. However, there is a physical limit to which these components can shrink. We are actually at the point where we're running into sizes where quantum mechanical effects are important (this is on the scale of a few atoms!). Thus, silicon is only sustainable for a few more years, if we are to continue improving the performance of our machines.

We need to find alternate materials with comparable or better performance. Read more here.

This is actually a very active field of research across all kinds of fields- materials science, physics, and even biology!

Hope this helps!
Best,