No firmware, as it is an ASIC miner. If you want to look at how these things work, there's a good chance the individual cores run a version close to this FPGA implementation, but of course at higher clock rates and there are 64 of these in the chip:

https://github.com/kramble/FPGA-Litecoin-Miner

The 'controller' is just a USB to Serial interface to the ASIC, nothing to see there