Quantum Transport: Atom to Transistor

The reader may wish to review Section 1.6 before reading this chapter.
Since this chapter is rather long, let me start with a detailed overview, that can also serve as a summary. In Chapter 1, I described a very simple model for current flow, namely a single level ? which communicates with two contacts, labeled the source and the drain. The strength of the coupling to the source (or the drain) was characterized by the rate ? 1/ ? (or ? 2/ ?) at which an electron initially occupying the level would escape into the source (or the drain).
I pointed out that the flow of current is due to the difference in agenda between the source and the drain, each of which is in a state of local equilibrium, but maintained at two different electrochemical potentials and hence with two distinct Fermi functions:
| (9.1.1a) | |
| (9.1.1b) | |
by the applied bias V: 2 ? 1 = ? qV. The source would like the number of electrons occupying the level to be equal to f 1( ?) while the drain would like to see this number be f 2( ?). The actual steady-state number of electrons N lies somewhere between the two and the source keeps pumping in electrons while the drain keeps pulling them out, each hoping to establish equilibrium with itself. In the process, a current flows in the external circuit (Fig.