Overview of Nanoelectronic Devices <s> A. Islands, Potential Wells, and Quantum Effects <s> Much of our understanding of electron transport in solids is based on the semiclassical picture that views electrons as particles obeying Newtonian mechanics in an external field and occasionally scattered by phonons and impurities. Quantum effects such as size quantization and tunneling, however, cannot be understood within this conceptual framework. <s> BIB001 </s> Overview of Nanoelectronic Devices <s> A. Islands, Potential Wells, and Quantum Effects <s> Abstract A coherent overview of the exciting field and challenging areas of research in mesoscopic physics and nanoelectronics is given. The unifying role of the S -matrix theory or “ input-quantum process-output ” language of quantum mechanics in the formulation of quantum transport in mesoscopic physics and nanoelectronics is clarified, with time-independent S -matrix theory applied to mesoscopic systems and double-time-axis time-dependent S -matrix thoory, coupled with the lattice Weyl-Wigner formulation of quantum dynamics of electrons in solids, applied to the highly nonlinear, far-from-equilibrium and high-speed nanoelectronic devices. At steady state and near equilibrium, the two independent formulations yield equivalent results. The technological impact of the many-body quantum distribution-function (QDF) (typified by the Wigner distribution function) approach is demonstrated by a complete transition from the level of basic nonlinear quantum transport physics to an engineering computer-aided design tool for integrated circuits (ICs). This is done in the derivation of the equivalent circuit model for resonant tunneling devices which incorporates the quantum inductance. In this review, emphasis is given to major developments in quantum transport, computational nanoelectronics, new device concepts, and novel transport physical phenomena found in small structures, with potential device and IC applications and deemed most likely to have a significant impact on the future developments of nanoelectronics. <s> BIB002 </s> Overview of Nanoelectronic Devices <s> A. Islands, Potential Wells, and Quantum Effects <s> Waves and particles. The Schrodinger equation. Tunnelling. The harmonic oscillator. Basis functions, operators, and quantum dynamics. Stationary perturbation theory. Time-dependent perturbation theory. Motion in centrally symmetric potentials. Electrons and anti-symmetry. Solutions to selected problems Index. <s> BIB003
The smallest dimension of the island in a solid-state nanoelectronic device ranges from approximately 5-100 nm. The island may consist of a small region or layer different from the surrounding material. Otherwise, edges of the island may be defined by electric fields from small electrodes patterned in the shape of the desired island boundary. Often, the island is embedded between two narrow walls of some other material, or an insulating oxide of the island material, or an insulating defect zone in the substrate. In any case, therefore, the island is surrounded by potential energy barriers, which impede the movement of electrons in and out of the island region. This is illustrated in Fig. 2 , in which the energy barriers arise from walls of a different material. Within the island, mobile electrons will tend to form a puddle that usually is much smaller than the dimensions of the island. The puddle is surrounded by a depletion region that forms (for example) because electrons in the puddle are repelled from surface charges that collect on the boundaries of the island. Thus, the physical features that form the island may have to be fabricated many times the size of the useful region for electron confinement  . This is one factor that works against the miniaturization of such quantum-effect and single-electron solid-state devices. (Despite the fact that the depletion region confines mobile electrons to only a portion of the island, we shall not make a distinction in our terminology between the shape and size of the island and those of the potential well for electrons on the island.) Two essential quantum mechanical effects are exhibited by electrons confined to nanometer-scale islands between closely spaced potential energy barriers BIB002 ,  , BIB003 , BIB001 . First, quantum mechanics restricts each electron's energy to one of a finite number of one-electron energy levels (quantum states with discrete, "quantized" energies). The smaller the distance between the barriers (i.e., the smaller the island), the more widely spaced in energy are the levels for the electrons in the potential well between the barriers. In Fig. 2 , the symbol is used to represent the energy spacing between two energy levels in such a potential well. Second, if the potential barriers are thin enough (approximately 5-10 nm or less, depending on the height of the barriers), electrons occupying energy levels lower than the height of the barrier have a finite probability of "tunneling" through the barrier to get on or off the island. However, for an electron of a given energy to tunnel through a barrier, there must be an empty state with that same energy waiting on the other side. These two effects, energy quantization and tunneling, strongly influence the flow of electrons through a nanoelectronic device. When a bias voltage is applied across the island, it induces mobile electrons in the conduction band of the source region to attempt to move through the potential well in the island region to get to the region of lower potential in the drain region. The only way for electrons to pass through the device is to tunnel on to and off of the island through the two high potential barriers that define the island and separate it from the source and the drain.. But tunneling can occur and charge can flow toward the drain only if there is an unoccupied quantum energy level in the well at an energy that matches one of the occupied energy levels in the source band. (In extended systems, such as the bulk metals or semiconductors in the source and drain, the allowed energy levels for electrons are so closely spaced that they form bands over a range energies, in contrast to the discrete energy levels in a single atom or in a nanometer-scale potential well. As shown schematically in Fig. 2 , the electrons occupying the source conduction band range continuously in energy from that of the lowest energy level in the band at the "band edge" to the level of the highest energy conduction electrons at the "Fermi level"). As is also shown in Fig. 2 , a similar energy band contains the conduction electrons on the drain, and usually there are many available unoccupied one-electron quantum states at energies above this band, as well. So, once an electron is able to tunnel from the source to the island under a bias, it is usually free to complete its passage through the device by tunneling once again from the well onto the drain.