Power switch units for microelectronic devices are disclosed. In one aspect, a microelectronic device may include a functional circuit, and a power switch unit to switch power to the functional circuit on and off. The power switch unit may include a large number of transistors coupled together. The transistors may include predominantly positive-channel, insulated gate field effect transistors, which have a gate dielectric that includes a high dielectric constant material. Power switch units having such transistors may tend to have low power consumption. In an aspect, an overdrive voltage may be applied to the gates of such transistors to further reduce power consumption. Methods of overdriving such transistors and systems including such power switch units are also disclosed.