In Coop 8 you considered an important kind of transistor called a MOSFET1 . The figure below shows a transmission electron micrograph of a MOSFET, but for the purposes of this question, let's approximate the transistor as two parallel, square charged plates of length L and separated by a distance d << L. The top plate has a uniform charge density +σ and the bottom plate has a uniform charge density -σ. The current flowing between the plates is negligibly small. (If you are already familiar with the concept of dielectric constant, assume that κ = 1 in the oxide. If you are not familiar with it, you need not be concerned.)
(a) Calculate the electric field between the two plates and not near the edges. Use any approximation justified by d << L.
(b) The breakdown field is the maximum electric field that can be established inside a transistor before it fails. In a typical transistor, d = 1.0 nm and L = 35 nm. If the breakdown field is typically 5 × 108 N/C, what is the maximum charge that one can put onto either plate of the transistor?
(c) What is the maximum voltage between a point on the top plate and a point on the bottom plate before breakdown occurs?
(d) At this maximum voltage, what minimum amount of work would you have to do to move a single electron from the top plate to the bottom plate?