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The bistable behaviour displayed by the m.i.-n-p+ switch (designated m.i.s.s.: an acronym for metal-insulator-silicon switch) can be electrically controlled via a third gate terminal. This three-terminal device is named m.i.s.t. for metal-insulator-semiconductor thyristor. The function of the gate control is to strengthen, or weaken, the intrinsic regeneration within the m.i.s.s., by means of majority-carrier injection, minority-carrier injection, or electrostatic control of the n-p+ junction voltage. The previously reported feedback model of the m.i.s.s. device is extended to cover the three-terminal m.i.s.t. Simple closed-form expressions for the gate-control efficiency are derived for the two modes of operation of the m.i.s.t. It is shown that the gate-control efficiency is largest for the avalanche-mode m.i.s.s. with a majority-carrier injecting gate.