Quantum Transport

In conventional electronic devices such as field-effect transistors (FETs) or diodes, the size of the device is usually quite large, so that the wave nature of the electron or its discrete charge do not influence the behavior of the device. Furthermore, all individual components of these devices are of a size much larger than an individual atom. However, with the continuous shrinking of integrated circuits, novel effects will arise at the nanoscale: Contemporary FETs are already now approaching the length scales in which some of the transistor’s parts are scaled down to atomic dimensions. For example, the width of the channel of a state-of-the art FET is only about 35 nm (Figure 1) and the thickness of the gate insulator is only few atoms thick (inset to Figure 1). The outlook what a commercial FET might look like is already in a development stage nowadays. For example Singh et al. could show that by process techniques that are also used in industry, working silicon nanowires FETs with channels composed only of a 3 nm silicon nanowire can be fabricated (Figure 2a). At low temperatures, they were able to see significant fluctuations in the current flowing through the transistor (Figure 2b) as a function of the gatesource voltage. These fluctuations are due to single-electron charging effects, as will be explained in the remainder of this chapter. Before we come to the description of phenomena in electric transport that only appear when electrons are confined to small dimension, we will discuss the basics of the conventional FET, as it is the basis for many of the phenomena described in the following. Figure 1: Scanning electron microscopy (SEM) image of a contemporary field-effect transistor (FET). (Inset) Transmission electron microscopy (TEM) image of a gate insulator (source: Intel).