6.1 Introduction

In this monograph, we began by considering the traditional MOSFET, which has a two-dimensional channel. We then discussed nanowire transistors, which have one-dimensional channels. To conclude, we should consider the possibility of a zero-dimensional channel, which would occur, for example, if we could make a transistor out of a single molecule. Before considering molecular transistors, however, we need to understand how molecules conduct electricity. Conduction in molecules is still an active topic of research, but an understanding is beginning to emerge, and a simple conceptual picture explains a lot [6.1]. This conceptual picture of conduction in molecules can be generalized into a theory for ballistic nanotransistors that applies to transistors with channels of any dimensionality [6.1]. The simple model demonstrates that single molecule transistors are possible, and numerical simulations can be used to identify the challenges quantitatively. Finally, we must address single electron charging. As transistor channels shrink, the number of electrons in the channel decreases. It is possible to have even less than one electron in the channel, because it is spatially extended over the source, channel, and drain. A special kind of transistor known as a single electron transistor can also be realized. In a single electron transistor, only a discrete number of electrons can exist in the channel, and the number can be controlled by the gate voltage. They are not a replacement for the MOSFET, but their unique characteristics are potentially useful in conjunction with CMOS. The "general theory" that we have discussed in...