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This chapter discusses the excitons in organic-based nanostructures. In particular, two-dimensional Frenkel-Wannier-Mott (FWM) excitons in hybrid organic-inorganic nanostructures (quantum wells, quantum wires, quantum dots) are considered. Linear and nonlinear optical response of hybrid FWM excitons is calculated. Based on the fast energy transfer, new concept for light-emitting devices is proposed. Exciton energy transfer from organics to semiconductor nanocrystals and its possible application to carrier multiplication in quantum dots is mentioned. Finally, FWM excitons and polaritons in a hybrid microcavity containing crystalline organic layer and a resonant inorganic QW, are considered. First experiments demonstrating properties of hybrid structures are mentioned.

This chapter first considers the basic principles of molecular beam epitaxy (MBE) of III-V materials. It describes a typical MBE system and its components with special attention to the reflection high-energy electron diffraction system for in-situ monitoring of a growth surface. Metal organic chemical vapour deposition (MOCVD), chemical reactions in MOCVD process and typical reactor scheme are then described. The chapter also describes different methods of in situ formation of one- or zero-dimensional quantum size objects, including formation of quantum wires on a V-grooved substrate, quantum wires and dots on high-index surfaces, and selective epitaxial growth of low-dimensional structures. Special attention is paid to a method of quantum dot formation in Stranski–Krastanow growth mode.

This chapter contrasts the results of Chapter 10 with the theory of ballistic transport through quantum point contacts. It discusses the experimental observation of conductance quantization based on the ideal quantum wire model, the adiabatic approximation, and in the nonadiabatic case. As a result, Landauer's view on the conductance is conveyed relating conductance to transmission. The transmission is worked out in the saddle point approximation of quantum point contacts. Interaction effects are briefly discussed.

Unlike all of the previous chapters, this one is devoted to low-dimensional semiconductor structures (quantum wells, quantum wires and quantum dots-nanocrystals). Basic classification of these structures is outlined and densities of electronic states are described. A detailed theoretical treatment of electronic states and exciton effects in quantum wells, both with infinite and finite barriers, is presented in effective-mass approximation. Strong and weak quantum confinement limits are discussed. Selection rules for optical transitions in quantum wells are outlined and optical absorption and emission spectra are compared. Specificity of exciton behaviour is stressed. Quantum dots with spherically symmetric potential are described in strong and weak quantum confinement regime. Salient luminescence features of quantum dots are summarized and illustrated via typical examples. Briefly mentioned are other interesting luminescence-related phenomena: phonon bottleneck, excitons indirect in real space, enhancement of nano-luminescence by metal nanoparticles and exciton multiplication.

This chapter discusses the fundamental upper limit that quantum mechanics places on the thermal conductance of nanoscale width, suspended dielectric wires, known as the Landauer formula for the thermal conductance. A derivation of the Landauer thermal conductance formula is first given by solving for the phononic energy current flowing down an elastically isotropic suspended wire joining two heat reservoirs with slightly different temperatures. An overview is then given of the various experimental attempts to measure the Landauer thermal conductance, beginning with pioneering work of Wybourne and coworkers in the early eighties, and culminating in the first successful measurement by Schwab and coworkers in 2000. The conclusion briefly discusses further possible experimental directions and also discusses the universal, i.e. materials and particle statistics independent, nature of the Landauer thermal conductance.

Stimulated emission and lasing can be achieved easily in a number of semiconductor nanostructures. This chapter gives an overview of a series of physical mechanisms that were found experimentally to give rise to positive optical gain in quantum wells, quantum wires and nanocrystals. In quantum wells, these are radiative recombination of localized excitons, LO-phonon assisted exciton recombination and electron–hole plasma luminescence. In quantum wires the data are rather scarce; localized excitons and electron–hole plasma appears to be involved in lasing. Separately treated are the cases of nanocrystals dispersed randomly in a matrix and that of heterostructures with ordered quantum dots (grown by Stranski–Krastanow method). Exciton and biexciton mechanisms of optical gain in quantum dots are analyzed. The crucial competing role of Auger recombination is expressed via the filling factor. Prospects of random lasing in semiconductor nanostructures are outlined.

This chapter discusses the principal optical processes in quantum wires (QWRs) and boxes (QBs). Topics covered include interband absorption in QWRs, excitonic absorption in 1D, zero-dimensional systems, absorption and gain in 0D systems, and excitons in quantum dots and nanocrystals. Exercises are provided at the end of the chapter.

This chapter considers the interaction of phonons with one- and zero-dimensional (1-D and 0-D) carrier systems in quantum wires and dots. Wires and dots are discussed in separate sections: each starting with a brief review of how the structures are formed, and then going on to consider their basic physical properties. The theory of emission and absorption of bulk (3-D) phonons by electrons in 1-D and 0-D is considered. The chapter explains how the requirements of energy and momentum conservation leads to the ‘phonon bottleneck’, i.e. a reduction in the carrier-phonon scattering rates as the dimensionality is reduced. Each section ends with a review of experimental measurements of carrier-phonon interactions. The focus is on phonon measurements using the techniques of heat pulses and phonoconductivity. The chapter concludes with a discussion of the outstanding issues, e.g. the carrier relaxation processes in quantum dots.

This chapter discusses the effects of disorder in fermionic systems, including Anderson localization. There are important differences for the disorder effects between the one-dimensional world, where localization occurs because electrons bump back and forth between impurities, and the higher dimensional world, where Anderson's localization is a rather subtle interference mechanism. The discussion looks at one-dimensional electrons subject to weak and dense impurities, in which the disorder can be replaced by its Gaussian limit. The application of disordered systems to quantum wires, one of the ultimate weapons to study individual one-dimensional systems, is considered.

While the physics of low-dimensional structures mainly involves their electronic properties, an understanding of the interaction between the electrons and holes and the phonons present within and around the confined layers is frequently needed if this physics is to be understood in detail. This introductory chapter gives examples of this and outlines the experimental methods that have been used to study the electron-phonon interactions. These include both optical and transport techniques and also techniques that involve the use of phonons as probes: phonon techniques. Phonons interact much more strongly with electrons than photons of the same frequency since their momenta are usually much closer to those of the confined electrons, and phonon techniques have been used to obtain information ranging from the confinement widths to the dispersion curve of quasiparticles in the fractional quantum Hall state.

Low-dimensional structures consisting of semiconductor heterostructures of thickness down to a very few atomic monolayers were grown ideally by MBE and resulted in a surge of interest in MBE itself. Short period superlattices, doping superlattices, quantum wells, wires and dots and two-dimensional electron gases (2DEGs) all proved of significance from scientific and commercial viewpoints. Superlattices and quantum wells showed negative electrical resistance, doping superlattices provided tuneable energy gaps, and quantum wells, quantum wires and quantum dots were characterised by confined energy states which offered photon energies tuneable by varying their dimensions. They also demonstrated increasingly sharp density of state functions, of interest for semiconductor lasers. 2DEGs showed very high electron mobilities by minimising ionised impurity scattering. The 2D localisation in 2DEGs resulted in discovery of the quantum Hall effect and fractional quantum Hall effect.

This chapter discusses the roles of phonon-assisted tunnelling and, to a lesser extent, phonon scattering, in two related types of low-dimensional semiconducting structures: resonant tunnelling devices and superlattices (phonon-assisted tunnelling effects in quantum dots are discussed in Chapter 4). Phonon-assisted tunnelling describes the process in which electron or hole tunnelling is accompanied by the emission or absorption of a phonon. Phonon-assisted tunnelling by longitudinal optic phonons gives rise to satellite lines in the I(V) characteristic of the device. However, phonon-assisted tunnelling by acoustic phonons can only be seen as a change in I(V) produced by a change in the phonon occupation number, such as that resulting from an incident heat pulse. The chapter also includes brief descriptions of work on coherent phonon generation from superlattices, on the effect of surface acoustic waves on single electron transport in quantum wires, and on the role of phonon-assisted tunnelling in quantum cascade lasers.

This chapter presents typical band structures for superlattices and quantum wells computed using the methods described in Chapter 9. It identifies important features of the conduction and valence subbands and minibands, their dispersions, optical matrix elements, and characteristic dependences on the materials, thicknesses, and compositions. The changes that occur when the energy gap becomes very small are also discussed. To complete the picture, it considers how the band structure of wurtzite materials differs from their zinc-blende counterparts, as well as the band structure of quantum wires and dots that feature multidimensional confinement.

In this chapter we consider light coupling to elementary semiconductor crystal excitations—excitons—and discuss the optical properties of mixed light–matter quasiparticles named exciton-polaritons, which play a decisive role in optical spectra of microcavities. Our considerations are based on the classical Maxwell equations coupled to the material relation accounting for the quantum properties of excitons.

Nanostructures in which the electrons are confined in two directions and unconfined in the third are known as quantum wires. Theories of electron confinement and phonon spectrum in quantum wires have focused on two simple geometries: wires with rectangular cross section and wires with circular cross section. This chapter covers: scalar and vector potentials in cylindrical coordinates; ionic displacement components for longitudinally polarized modes, and for transversely polarized modes, and for interface modes; hybrid LO modes; energy normalization; acoustic stresses and strains; particle displacements for LA, TA1, and TA2 modes; and free surface.

This chapter covers: t effect of confinement in nanostructures: in the single heterostructure, in the quantum well, in the quantum wire, and in the quantum dot. There is also discussion of the scattering rate.