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As I know the word "chracterization" is normally used for transistors, capacitors, resistors, substrate, dielectric and conductivity for IC and substrate Er, Sigma, tangant delta for PCB and the chracterization is not used for a manufactured system on a board or pcb; in that case "Test" is ussually used!!!
You have to find the operating conditions under which your chip is working. You have your test, you specify the operating voltage range, temperature range and create so called schmoo plots (characteristics where you can see in which areas all your tests passed and where they failed), you perform also parametric test and probably IDDQ test. You can check also your timing for certain paths.
All this gives you enough real data you would need for your data sheet and model.
I hope this help you to specify key words in google, if you start to search there for any additional
information
It is the schmoo plots used by the product engineers.
They will appy functional vectors or ATPG vectors in tester with respect to differnt volatge and temperture, they will plot curve for freq vs volatage .( this plotting is called schmoo ploting).
In this way they will charetrize the chip with respect to different volages .
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