I am a developer of a cheap product and i have no experience in mass production. Device is fully functional and represents a single sided PCB, a microcontroller, a bunch of diodes and a few passive elements. However, MC is kinda overkill and schematic could be done with some simple TTL/CMOS logic and passive elements. I can easily create VHDL or logic equivalent. I can't use standard logic IC's due to size restrictions. It would be best to use a few hundreds of transistors on a custom chip, if that's possible. I saw a ton of devices that are ridiculously cheap and have some circuitry in COB. This one costs 10c shipped, that's 4 times cheaper than a MC in my PCB 
I had no luck finding a suitable manufacturer. I found some MPWs like MOSIS, but that's obviously not what i need. So, is there a way to create about 10k of devices with cheap custom COB?
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1\$\begingroup\$ Some microcontrollers are offered as bare die. (Example) \$\endgroup\$– AndreKRCommented Jul 26, 2018 at 6:21
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1\$\begingroup\$ 1. You can manufacture a custom chip under $50k (no matter how many of the chip you will actually make) at TSMC: tsmc.com/english/dedicatedFoundry/services/cyberShuttle.htm 2. You can assemble Chip-on-Board at JingHongYi: pcbjhy.com/metal-core-pcb/57132185.html \$\endgroup\$– Brian CannardCommented Apr 18, 2020 at 0:19
2 Answers
A custom chip for 10k units is unlikely to be cheap, as the masks will almost certainly cost more than $1k, which means your chip cannot possibly be made for $0.10. The reason the one you've found costs $0.10 is because they sell in a much greater volume (100k-millions), so the cost of masks and setup for a production run is spread over many more units.
That being said, a chip like the Silego GreenPAK might be a good option for you, as it's a small and extremely cheap (the cheapest on mouser is SLG7NT4375 at $0.195 each for 1k) CPLD. Assuming your design fits and doesn't need too much analog functionality, this should work for your use case.
A micro controller isn't necessarily overkill, and may also be pretty cheap. For instance, the lowest cost mcu on digikey is the ATTINY5-MAHR at $0.14 each for 1k. Additionally, if you're willing to navigate the markets in asia, prices can potentially be even lower.
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\$\begingroup\$ How much does it cost to assemble a chip I've already ordered, say, at TSMC onto a "Chip-on-board" - for doing exactly these: placing (and gluing?) the IC, welding the gold wires, and putting a blob of black resin on top? And what are the best suppliers? \$\endgroup\$ Commented Apr 18, 2020 at 0:15
If you can handle a chip cost of about $1, have 16 or fewer I/Os, and can run at 1.2V, then you can use a Lattice ICE40UL640-SWG16ITR. It has 640 logic cells and comes in a 2.5mm x 2.5mm package. You can program it in VHDL.
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1\$\begingroup\$ How is $1 even remotely competitive with low end MCUs? \$\endgroup\$ Commented Jul 26, 2018 at 4:05
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1\$\begingroup\$ It really depends on what you want to do. There are certainly things that you could not do with a $0.14 MCU that you could do with a 640 cell CPLD, and vice versa. \$\endgroup\$– crj11Commented Jul 26, 2018 at 4:08
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\$\begingroup\$ The task has already been prototyped with an MCU... \$\endgroup\$ Commented Jul 26, 2018 at 4:12
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1\$\begingroup\$ I agree that my answer may be more applicable to the general case of low complexity physically small devices, and that it can not beat an ultra cheap MCU in this case. \$\endgroup\$– crj11Commented Jul 26, 2018 at 4:17