Method of manufacturing a metal-oxide-semiconductor field-effect transistor (MOSFET) having low off-state capacitance

A semiconductor device comprising:

• a first contact on a first side of a gate;
• a second contact on a second side of the gate;
• a first dielectric material, between the first contact and the second contact, comprising a first portion adjacent to the first contact and a second portion adjacent to the second contact;
• a second dielectric material between the first portion of the first dielectric material and the second portion of the first dielectric material, the second dielectric material being over the gate,
• wherein a dielectric constant of the first dielectric material is greater than a dielectric constant of the second dielectric material;
• and
• a liner layer that is over the first contact and the second contact.

A semiconductor device, comprising:

• a source and a drain that are each on a gate;
• an air gap over the gate between a first contact, over the source, and a second contact over the drain;
• a dielectric material in a region between the air gap and the first contact and a region between the air gap and the second contact;
• and
• a liner layer that is over the first contact and the second contact and that is under the air gap.