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NMOS transistor has parastic BJT npn. During snapback, this BJT transistor that conducting the current. So, the snapback current is actually a parasitic BJT current
Some explanations:
Due to high electric field at NMOS drain, electron-hole pairs are generated as a result of avalanche break-down, then parasitic BJT is triggered when source-substrate junction is forward-biased.
I assume you are referring to joule-heating by "J-E heating": the power consumed by Rsub of parasitic BJT.
It perhaps before snapback only BVds affect; while P-sub current cause parastics NPN BE junction conduct, parastics NPN affect. Vce is smaller than BVds.
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