This article presents statistical modeling for bitcell mismatch shift with respect to hot carrier injection (HCI) burn-in on a static random access memory (SRAM)-based physically unclonable function (PUF). A compound distribution based on a Poisson distribution and a Gamma distribution is used to model the mismatch shift. The Poisson distribution models the number of injected hot carriers, and the Gamma distribution models the mismatch shift value induced by a certain number of injected hot carriers. This model is evaluated by testing chips fabricated in a 130-nm CMOS process. Experimental results collected from 2-min to 8-min HCI burn-in match the model well. Results also show that the number of injected hot carriers has a linear relation with the burn-in time to the power 0.6.