  Neutron and $\gamma$-ray irradiation damages to transistors are found to be
non-additive, and this is denoted as the irradiation synergistic effect (ISE).
Its mechanism is not well-understood. The recent defect-based model [ACS Appl.
Electron. Mater. 2, 3783 (2020)] for Silicon bipolar junction transistors (BJT)
achieve quantitative agreement with experiments, but its assumptions on the
defect reactions are unverified. Going beyond the model requires directly
representing the effect of $\gamma$-ray irradiation in first-principles
calculations, which is not feasible previously. In this work, we examine the
defect-based model of the ISE by developing a multiscale method for the
simulation of the $\gamma$-ray irradiation, where the $\gamma$-ray-induced
electronic excitations are treated explicitly in excited-state first-principles
calculations. We find the calculations agree with experiments, and the effect
of the $\gamma$-ray-induced excitation is significantly different from the
effects of defect charge state and temperature. We propose a diffusion-based
qualitative explanation of the mechanism of positive/negative ISE in NPN/PNP
BJTs in the end.
