TABLE OF CONTENTS In Chapter 1 I stated that the full quantum transport model required us to generalize each of the parameters from the one-level model into its corresponding matrix version. Foremost among these parameters is the Hamiltonian matrix [ H] representing the energy levels and we are almost done with this aspect. This chapter could be viewed as a transitional one where we discuss an equilibrium problem that can be handled using [ H] alone, without knowledge of other parameters like broadening that we will discuss here.
The problem we will discuss is the following. How does the electron density inside the device change as a function of the gate voltage V G, assuming that the source and the drain are held at the same potential (drain voltage V D = 0, see Fig. 7.1)? Strictly speaking this too is a non-equilibrium problem since the gate contact is not in equilibrium with the source and drain contacts (which are in equilibrium with each other). However, the insulator isolates the channel from the gate and lets it remain essentially in equilibrium with the source and drain contacts, which have the same electrochemical potential 1 = 2 ? . The density matrix (whose diagonal elements in a real-space representation give us the electron density n( 
)) is given by
| (7.1) |  |
and can be evaluated simply from [ H] without detailed knowledge of the coupling to the source and drain. I am assuming...
