University of Virginia

The future of microelectronics depends critically on our ability to design and manipulate electronic properties of materials at an atomic scale. Regardless of the specific nature of future devices, we need a `bottom-up' understanding of current flow through ultrasmall systems.
The field effect transistor (FET) forms the key electronic element from a device-engineer's perpective. It describes a prototype switch or an amplifier, and is relevant to electronic and optical circuits, biological processes, as well as fundamental physics of quantum transport. We would like to understand the electronic properties of an FET for various geometries, materials and the underlying physical phenomena.
The FET consists of a resistive semiconducting channel connected to macroscopic source dand drain contacts with a lot of conducting states. A metallic gate is used to modulate the channel resistance by applying a vertical field. A source-gate bias voltage attracts (or repels) electrons into the channel thereby reducing its resistance, whereupon a source-drain bias voltage drives current through the channel. An oxide insulates the channel from the gate, so that current only flows out of the drain without leaking vertically into the gate.
The current tends to have a prominent onset at a threshold voltage as a function fof the gate bias. For varying drain voltages, the current starts off being ohmic (linear with a characteristic resistance or mobility), but saturates at high drain bias. One goal of a device engineer is to keep the current saturated, which becomes difficult as transistors scale down in size.
The first step is to draw an energy level diagram for the channel. Filled states are identified by photoemission experiments, and empty ones by inverse photoemission. A Fermi-Dirac function separates the filled and empty states at the Fermi energy EF, which is determined by the contact work function upto which contacts states (which are closely spaced) are filled by contact electrons.