Room-Temperature Ballistic Nanodevices

One of the most important physical parameters to describe the quality of a piece of semiconductor material is the electron scattering length le. Also referred to as the mean-free path, it stands for the average distance between the randomly distributed scatterers in the material, such as lattice defects, impurities, and phonons. The electron mean-free path is typically a few nanometers (1 nm = 10−9 m) in silicon and about 100–200 nm in high-quality compound semiconductors such as GaAs. The electrical resistance of a semiconductor device is closely associated with the scattering length le. Conventional semiconductor devices are much larger than the electron scattering length. As a result, electrons have to encounter a large number of random scattering events to travel from one device lead to another. In the last two decades, advanced semiconductor technologies have allowed the fabrication of devices that are smaller than the electron scattering length. In such devices, electrons may travel from one electric lead to another without encountering any scattering event from randomly distributed scatterers such as impurities. Instead, the electrons are scattered only at the device boundaries, that is, moving like billiard balls. Such electron transport is referred to as ballistic transport [1–3]. There had been a long debate in history on whether there is any electric resistance in such ballistic electron devices. Some had believed that the absence of scattering means that the resistivity inside the device is zero. Although this is, as will be discussed later, wrong because the concept of resistivity does not hold any longer in the ballistic transport regime, it was realized quite clearly that the electron transport in a ballistic device is very different from the transport in a traditional, macroscopic semiconductor device. Consider a conventional semiconductor device that is much larger than the electron scattering length. Any electric current induced by an applied voltage consists of electrons diffusing in an electric field, as shown in Figure 1. The diffusive transport can be described by Ohm’s law, which states a linear relation between the current and electric field (or applied voltage). However, if we examine the electron transport at the microscopic scale, we would find that every electron is accelerated between two subsequent scattering events by the electric field. As a result, the velocity component of the electron in the opposite direction of the electric field increases constantly until the next scattering event occurs. Since the current carried by the electron is equal to its velocity multiplied by the electron charge e, the current is time dependent, even in the presence of a constant electric field. This is seemingly in contradiction to Ohm’s law. Actually, Ohm’s law is valid at the macroscopic scale because of the existence of the large number of scattering events, which counteract the acceleration effect of the electric field, causing the average velocity of all electrons to be proportional to the strength of the electric field. The above discussion reveals that, at a scale that is smaller than the average distance between impurities or other scatterers, Ohm’s law does not hold, and that new transport properties are expected to arise in these ballistic devices of a dimension smaller than le. A number of new device concepts have been generated based on ballistic electron transport in the last two decades. Among these novel devices are only a few that have been demonstrated to work at room temperature. Quite understandably, being capable of operating at room temperature is an important criterion for practical applications. In this chapter, we review these recent breakthroughs in roomtemperature ballistic devices. The theoretical framework to treat ballistic electron transport, namely, the scattering