Electron Transport: Resonant Tunneling Through Semiconductor Heterojunctions

1. Nanoscale Transistors Encounter Quantum Mechanics

As the scale of solid state electrons continues to shrink, the quantum nature of electrons becomes more apparent due to tunneling effects. As of Intel's introduction of the Dual-Core Itanium 2 in 2006, almost 2 million transistors were able to be placed on a single silicon chip. Current processes for etching transistors allow for features on the order of tens of nanometers. Is tens of nanometers a scale where the quantum nature of electrons becomes important? In other words is the "size" of the electrons on par with the feature size? De Broglie tells us that the wavelength of the electron is

(1)

and if you estimate E~kT, the thermal energy, then you obtain a wavelength of ~20nm. Clearly the quantum aspect of the electrons should be evident on the scale of the transistors. What does a transistor look like? Lets look at the most common type of transistor to be seen on a computer chip, a Metal Oxide Semiconductor Field Effect Transistor or MOSFET.

Figure 1: MOSFET

If the gate voltage is positive with respect to the substrate then a conducting channel forms in the p-type semiconducting region from the source to the drain. This is the on mode for a MOSFET. If the gate voltage is negative then the depletion region is enhanced and no current can flow from source to drain. This is the off mode. A pivotal component of the MOSFET is the oxide layer between the gate and the channel. The oxide layer is a barrier to electron flow from the channel to the gate. Ideally all current should go from source to drain. Any current which flows into the gate is lost work which causes the transistor to waste energy and run hotter than necessary. The scale of the oxide layer is on the same scale as the rest of the semiconductor components, namely tens of nanometers in the highest end devices. We saw in (1) that the electrons have a size roughly the same as the oxide layer which means quantum effects such as tunneling will be important. Notice how hot your processor gets even when it is idling? This is due in part to leakage current from electrons tunneling directly through the insulating barrier. Let us investigate quantum tunneling...