Who Makes Custom Chips?
toybuilder asks: "I have an idea for a neat consumer product that could benefit greatly from a really simple bare-die chip to reduce cost and size. I took a VLSI and chip design class back in college about 10 years ago, so I know how to design the circuit I want in CMOS. Now, I'm sure there must be fabs for older-generation designs (maybe in China/Taiwan) that I could have such a chip made -- I've seen bare chips in musical greeting cards and in tiny toy gadgets. How do I go about making my chip design into reality if I only want to make a fairly short run (a few *chips* during development, and maybe a 6" wafer's worth of the final design)?"
You want MOSIS. Providing small volume chip fab services (via short ganged-mask wafer runs at flexible mainstream fab houses) for decades now, Mosis is exactly what you want if FPGA and a programmable microcontroller aren't what you really need.
If you want to attempt it, MOSIS does small run fabrication by batching up small runs onto a single wafer and running them through commercial fabs like IBM and TSMC. The prices aren't out of reach.
However, you should remember from the VLSI class you've taken that it may take several runs before getting anything usable. Unless your design has some aspect that makes using a FPGA infeasible, you'd probably be better off with the FPGA. As I recall, a couple of FPGA vendors can also do conversions from FPGAs to hard-wired ASICs if you desire it later.