If the voltage on the plate is large enough, it attracts the extra electrons more strongly than the positive charge on the phosphorus ions.
Extra electrons thus form a thin layer adjacent to the plate that moves across the gap. This flow "closes" the silicon electrical switch. Current will continue until the positive voltage is removed from the gate electrode.
This voltage-controlled switch is called a MOSFET and is the basis of most integrated circuits (the acronym stands for metal-oxide-semiconductor field effect transistor).
