Physics of Semiconductor Devices

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Flatband voltage

A MOS capacitor consists of an aluminum layer, an n+ Si layer, an oxide layer, and a p-doped silicon substrate where Na = 20000000000000000 cm-3. The contact between the aluminum and the n+ region is a tunnel contact.

When no voltage is applied between the aluminum layer and the substrate, in which regime is the MOS capacitor?

Should a positive or negative voltage be applied to the gate (with respect to the substrate) to achieve the flatband condition?

Assuming that the Fermi energy of the n+ region is at the conduction band edge, what is the magnitude of the flatband voltage at 300 K?

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If the voltage is increased just past the flatband voltage, in which regime is the MOS capacitor?