First a disclaimer
This Stack has been trending towards physics lite for some years now. It's a disappointment. It's true that we need to embrace the basic objectivity expected by Stack Exchange, but it's frustrating how many people think that if something can't be done with today's science, it's somehow magically unbelievable.
Talk about boring.
Gratefully, there are people like yourself who are looking to create engaging fiction that allows me to suspend my disbelief.
Next, what is a "community wiki?"
Answers can be set to be "community wikis." The respondent (in this case, me) loses the ability to earn reputation. But the answer benefits because everyone is able to add to the answer to make it comprehensive! I did this with the Worldbuilding Resources answer.
The goal is that people can add to what I'm about to propose. While I could take the next two or three days to create a fairly comprehensive technology/supply tree for "modern electronics." I don't have that much time to give. That's OK! Because there's a lot of people on this Stack with similar background and skills to my own. They'll understand a piece of the puzzle and change this Wiki to reflect that. It might take a week, but the results will be beneficial not only to you and your RPG, but to others who are looking for (a) a simplified dependency tree for modern technology and (b) insight into the process of building such a tree. That's a win-win-win if I ever heard one!
The Rules!
There must be rules for wikis or people are as likely to unintentionally vandalize the wiki as improve it. Here are the rules for this wiki:
The goal is a simplified dependency tree, not a high-detail "this is everything you need" tree. If we allow too much detail, we need to allow for child care, government taxation, insurance, and a host of other things that are true in Real Life but not useful from the perspective of building a world or a game. Suspension of disbelief is as much about creating a balance between a minimalist framework and necessary detail.
While I have no inherent objection to people moving things around (e.g., between levels) or changing the proposed dependencies, I ask that people really think through any changes they make to what others have injected before them. This is less about "you idiots don't know what your talking about!" than it is, "oh, if you think about it from a minimalist perspective, that shortcut/simplification makes sense." It's more important to add things than to modify things. But, if you sincerely believe climate change will worsen if you don't modify something that came before, OK. Just take the time to think it through.
Finally, please don't guess. If you don't have personal experience in a particular dependency, don't assume that your opinion will outclass what was likely an entry based on personal experience and training. Remember, nobody who participates in a Community Wiki will get reputation. This is about working together to build something bigger than would usually be seen by a single answer on the Stack.
All of the dependencies in the proposed tree are dependent on historical technologies. These are technologies that are no longer relevant or even used. An example might be "steam engines." I'm not sure we could have achieved Electricity without the presence of steam engines or steam technology. But outside of electrical generation, you don't see it today (that I can think of) in the entire "modern electronics" tree. I don't believe historical technologies are "necessary detail," but that is just my opinion.
One last thing: The initial tree I proposed reflects the dependency for modern electronics. There are dependencies listed as level 2 or 3 that people might think should have been level 4 or 5. An example is Magnetism. I assigned it level 2 because the control of magnetism for the purposes of modern electronics is very precise compared to, e.g., a compass. The assignment reflects the importance to modern electronics, not it's historical importance. Remember rule #4. The discovery of magnetism may have led to modern electronics, but its discovery on or before 600 B.C. means absolutely squat to modern integrated circuit design. Including historical dependencies means including all the intervening innovations and IMO that's too detailed for the purposes of this wiki.
Thank you!
Simplified Dependency Tree for Integrated Circuit Manufacturing in 2022
Level 1
Pneumatics: The ability to move gases around and to manipulate pressure. Depends on Machining and Pumps.
Optics: The ability to manipulate photons including generation, focus, and termination. Depends on Machining, Silicon, Abrasives, and Thermology.
Electron Microscopy: The ability to move electrons around and use them both for abrasive purposes (to etch, drill, cut, etc.) and for doping purposes (to ionize). Depends on Machining, Magnetism, Chemistry, and *Optics."
Robotics: The ability to move materials around with strength and precision without direct human interaction. Depends on Machining, Automation, and Magnetism.
Automation: The use of either mechanics or electronics to automate a process with repeatability and precision. Depends on "Machining," "Electricity," "Logic," and "Software."
Software: The use of a structured language to develop instructions for automation (whether using plug arrays, punch cards, magnetics of any kind, or a keyboard). Depends on "Logic."
Level 2
Machining: The ability to manufacture machines. Depends on Hydrology, Electricity, Material Science, and Tools.
Magnetism: The generation and control of magnetism to manipulate electrons, gasses, or solids. Depends on Chemistry, and Electricity.
Electricity: The generation and control of electrons in solids. Depends on Chemistry and Metallurgy.
Silicon: The study of silicon both for glass making and as a semiconductor. Depends on Material Science.
Transportation: The ability to move large quantities of resources, machinery, and goods. Depends on Machining and Chemistry.
Level 3
Material Science: The understanding and practical application of gasses, fluids, and solids. Depends on Chemistry, Metallurgy, and Hydrology.
Chemistry: The understanding of how materials interact. Depends on Metallurgy, Hydrology and Thermology.
Level 4
Tools: The manufacture of tools. From a basic hammer to precision measuring devices. Depends on Metallurgy, Thermology and Logic.
Pumps: The ability to move gasses and liquids around. Depends on Metallurgy, Woodworking and Logic.
Abrasives: The ability to cut, grind and polish solids. Depends on Woodworking, Metallurgy and Logic.
Level 5
Woodworking: The ability to manipulate wood. Depends on Forestry and Logic.
Metallurgy: The ability to manipulate and alloy metal. Depends on Mining and Logic.
Thermology: The ability to create and manipulate heat. Depends on Wodworking and Logic.
Level 6
Mining: The ability to obtain inorganic materials from the Earth. Efficiency depends on Hydrology and Logic.
Forestry: The ability to obtain wood from the Earth. Efficiency depends on Agriculture and Logic.
Agriculture: The ability to obtain organic materials. Efficiency depends on Hydrology and Logic.
Level 7
You'll notice that I ignored anything having to do with money. When you simplify things, money is nothing more than a medium of exchange that allows people to obtain food, recreation, housing, etc. It must exist in a detailed dependency tree because without the concept of "money" (in any form), the ability to organize people to get long-term complicated things done grinds to a halt. However, I don't think things like that are needed when we're talking about what's needed to resurrect modern electronics post-apocalypse. Especially when how many resources and how much knowledge is available post-apocalypse is 100% in the OP's control.
