  This paper proposes an event-triggered boundary control for the safe
stabilization of the Stefan PDE system with actuator dynamics. The control law
is designed by applying Zero-Order Hold (ZOH) to the continuous-time safe
stabilizing controller developed in our previous work. The event-triggering
mechanism is then derived so that the imposed safety conditions associated with
high order Control Barrier Function (CBF) are maintained and the stability of
the closed-loop system is ensured. We prove that under the proposed
event-triggering mechanism, the so-called ``Zeno" behavior is always avoided,
by showing the existence of the minimum dwell-time between two triggering
times. The stability of the closed-loop system is proven by employing PDE
backstepping method and Lyapunov analysis. The efficacy of the proposed method
is demonstrated in numerical simulation.
