WARNING: This post contains some spoilers for the anime/manga Dr.Stone.
As I'm watching Dr.Stone, I see Senku and the gang trying to make vacuum tubes for their circuits. The vacuum tube is an ancestor to the transistor. It is quite hard to make and is fragile because glass is used to enclose a vacuum and the metal (Tungsten) inside has to get quite hot. Transistors, however, can be tiny and easy to use. I know enough Physics and Electrical Engineering to know pretty well how transistors work but I'm not sure how they can be made.
The environment and circumstances in the world of Dr. Stone:
- There's a single (genius) scientist from the modern world (everyone in the world got turned into stone and some got unpetrified after some thousands of years)
- They can do metal work and smithing
- They have a water wheel that can generate some electricity
- They also have some batteries
- They're making wires out of gold
- A furnace is available but runs on either manual pumping or on the water wheel
- Many common metals are available
Can they make transistors in such a world? If yes, about how small can the transistors be?