Statistical Model and Transistor Size Effect of Hot Carrier Injection for Stability Reinforced SRAM Physically Unclonable Function

Hot carrier injection (HCI) has been strategically leveraged to enhance the stability of SRAM physically unclonable functions (PUFs). Since the effects of HCI are not constant, exhibiting cell-to-cell variability, a comprehensive distribution model is essential to harness HCI effectively. This article presents a statistical distribution model of mismatch after HCI burn-in and examines the impact of transistor size of PUF on the distribution shape, yielding enhanced stability and shorter HCI burn-in time. The proposed mismatch model after HCI burn-in integrates the native distribution with a Poisson distribution for number of captured electrons and a Gamma distribution for the effect of captured electrons. Model calculations based on size effects reveal that over three times reduction in HCI burn-in duration by enhancing the size to quadruple times: a 15-min for quadruple-size transistor SRAM PUF compared to 46-min for single-size PUF. The model is confirmed by the real chip measurement. The PUFs with several sized transistors are fabricated in a 130-nm standard CMOS process. Experimental results show that quadruple-size transistor SRAM PUF reaches 1.82E−09 unstable cell ratio after 18-min HCI burn-in, which align with the model based expectation. Furthermore, robust stability is exhibited even the worst VT corner (0.6V / $-40^{\circ }\mathrm {C}$ ), demonstrating zero bit error (BER<7.81E−08).