I don't want to build the integrated circuit myself, I want to send the schematics to an IC factory to build my design and ship it back to me. Is that possible? I have finished prototyping on the FPGA.
So my question is, is there such a thing as sending your IC design to a manufacturer to build it for you?
Sure, but unlike making a PCB this is not a simple thing to do.
First, you don't simply send over your HDL. Fabs require geometry, in GDS format. So that means you have to convert your HDL using some sort of HDL to GDS flow. Not only that, you need to conform to the fab process design rules. You'll most likely want to use standard cell logic, and for this you'll need to get your hands on a process development kit (PDK) that's compatible with the process. But that's just for the logic gates, you'll also likely need to get RAM IP (usually in the form of a RAM generator), PLLs, IO components, etc. Depending on the process, licensing all of this can be expensive. And you'll also have to wire up all of the clock and power connections as well. And you'll want to simulate as much as possible to try to prevent mistakes, and add extra debug logic such as internal JTAG chains so you can test the design. And you'll have to get it packaged, including doing things like placing bond pads on the die that get connected to the package pins.
Yes, the term you are looking for is "shuttle service" or "multi-project wafer".
The general term for a semiconductor company that doesn't make its own chips (most don't!) is "fabless". Plenty of companies service this market e.g. https://efabless.com/ ; they even offer a free-with-conditions service for open source projects. https://efabless.com/open_shuttle_program/2
It's not cheap otherwise.
Yes, you can send your design to an IC manufacturer and they will build it.
But the design is not a schematic, it is the physical layout of every transistor and connection, such as a GDS II file. And it is your responsibility to completely verify that your design works.
Oh, and you need "deep pockets". This is very expensive. There are some services, such as MOSIS, that will build a handful of simple devices for you for a few tens of thousands of dollars.
As other answers have stated, you can send the logic description to a house which will translate it into an IC.
Since you specify that you have checked your logic by an FPGA, you might be interested to know that one of the early FPGA manufacturers used to offer a service. If you realized a design on one of their FPGAs (which used anti-fuse programming, so the FPGAs were one-shot programming), they would take the configuration file and generate a mask which would essentially replicate the pattern of blown anti-fuses, by replacing the fuse elements with a metallized layer, and use this for a short run of "FPGAs" which were essentially pre-programmed. However, there was no possibility of of accidentally over-writing the fuses, since there weren't actually any. The result was an IC which perfectly replicated the behavior of the test FPGA, while not actually being programmable.
