Nanostructures

This chapter describes theoretical concepts and tools used to calculate the electronic structure of materials. We first present ab initio methods which are able to describe the systems in their ground state, in particular those based on the density functional theory. Introducing the concept of quasi-particles, we show that excitations in the systems can be accurately described as excitations of single particles provided that electron—electron interactions are renormalized by the coupling to long-range electronic oscillations, i.e. to plasmons. We then review the main semi-empirical methods used to study the electronic structure of nanostructures.

The electronic structure of bulk semiconductors is characterized by delocalized electronic states and by a quasi continuous spectrum of energies in the conduction and valence bands. In semiconductor nanostructures, when the electrons are confined in small regions of space in the range of a few tens of nanometers or below, the energy spectrum is profoundly affected by the confinement, with in particular:

In this chapter we deal with the dielectric properties of semiconductor nanostructures. The realization of nanodevices usually requires to combine semiconductors with metals, insulators and molecules in a small region of space. The behavior of these systems strongly depends on the complex repartition of the electric field. Many interesting problems are related to dielectric properties: the current—voltage characteristics of a device, the binding energy of a dopant or an exciton, the energy of a carrier in an ultra-small capacitor, the optical properties and many others. Thus, their simulation at the nanometer scale becomes a critical issue for the development of nanotechnologies.

In this Chapter we discuss the different types of calculations which have been performed for the electronic excitations in semiconductor nanostructures. These range from carrier injection (quasi-particle energies, charging effects) to optical excitation and radiative recombination. We start with basic considerations (Sect. 4.1) where confinement effects and self-energy contributions due to surface polarization are formally separated, which will prove useful when analyzing the results of sophisticated calculations. We then treat excitons (Sect. 4.2) in the effective mass approximation (EMA) which, while simple, remains a powerful tool for the interpretation of many data [202]. This is followed by more refined semi-empirical calculations mainly concentrating on evaluations of the exchange splitting (Sect. 4.3). The two following sections (Sects. 4.4 and 4.5) deal with the application of quantitative methods (GW for quasi-particles, Bethe—Salpeter equations for excitons) to the case of silicon nanostructures. The results allow us to discuss the limits of validity of more approximate methods and to derive useful rules. Finally we describe calculations of charging effects and multi-excitonic transitions which can now be described quite satisfactorily (Sect. 4.6).

In this chapter, we deal with the optical properties of nanostructures. In a first part, we start with a general formulation of the optical transition probabilities taking into account specific problems related to the small size of the systems. In a second part, we consider the electron—phonon coupling using macroscopic or microscopic formulations and we analyze its consequences on the optical line-shape. The last two sections are devoted to the description of the optical properties in nanostructures of semiconductors with direct or indirect bandgap.

The main objective of this chapter is to analyze the influence of the quantum confinement on the electronic levels of point defects and impurities, from quantum wells to quantum dots. In the first two parts, we present the general trends for hydrogenic and deep defects. In the next sections, we consider particular situations: dangling bonds, self-trapped excitons and oxygen related defects at the Si-SiO₂ interface.

This chapter deals with the importance of non-radiative processes which can severely limit the luminescence properties of nanocrystals. We give two detailed examples of such processes: multi-phonon capture at surface point defects and Auger recombination of electron—hole pairs. Both are known to play a central role not only for silicon but also III–V and II–VI semiconductor nanocrystals embedded in different types of matrices. As a typical example of surface point defect, we choose the dangling bond for silicon crystallites in a SiO₂ matrix. The reason is that the properties of such defects at the planar Si—SiO₂ interface are well-known. Extrapolation of these results shows that one dangling bond is enough to kill the luminescence of the crystallites. In the second part, we describe a calculation of a phonon assisted Auger recombination process. This turns out to be efficient, in the nanosecond to 10 picosecond range for small crystallites, which is shown to explain several experimental observations on nanostructures. Finally, we concentrate on hot carrier relaxation processes. We first discuss the predicted existence of a phonon bottleneck for small crystallites which is an intrinsic effect limiting their optical properties. We end up this section by reviewing different processes which can overcome this limitation, again based essentially on Auger processes or capture on point defects followed by re-emission.

The research on transport properties of nanoelectronic devices has become a worldwide effort due to the possibility to fabricate structures at the nanometer scale. Metal-Oxyde-Semiconductor transistors with channel lengths as small as 10 nm are now being actively studied both theoretically and experimentally [464]. Remarkable experiments have been performed to measure the current I through single-quantum systems, such as molecules [465–472] or semiconductor quantum dots [249, 473–478]. In these experiments, the molecules or the quantum dots are connected to metallic electrodes under bias φ using scanning tunneling microscopy tips [249, 465, 468, 476], nanometersize electrodes [469, 477] or break junctions [470, 472]. Measurements display features arising from the quantum states of the system and from Coulombic effects (see Chap. 4). Peaks in the conductance dI/dφ characteristics are attributed to resonant tunneling through discrete levels. Also, semiconductor nanocrystals can be assembled to form artificial materials with interesting transport properties [479–481].