This book is intended to provide an introduction to the physics and applications of soft x-rays and extreme ultraviolet (EUV) radiation. These short wavelengths are located within the electromagnetic spectrum between the ultraviolet, which we commonly associate with sunburn, and harder x-rays, which we often associate with medical and dental imaging. The soft x-ray/EUV region of the spectrum has been slow to develop because of the myriad atomic resonances and concomitant short absorption lengths in all materials, typically of order one micrometer or less. This spectral region, however, offers great opportunities for both science and technology. Here the wavelengths are considerably shorter than visible or ultraviolet radiation, thus permitting one to see smaller features in microscopy, and to write finer patterns in lithography. Furthermore, optical techniques such as high spatial resolution lenses and high reflectivity mirrors have been developed that enable these applications to a degree not possible at still shorter wavelengths. Photon energies in the soft x-ray/EUV spectral region are well matched to primary resonances of essentially all elements. While this leads to very short absorption lengths, typically one micrometer or less, it provides a very accurate means for elemental and chemical speciation, which is essential, for instance, in the surface and environmental sciences. Interestingly, water is relatively transparent in the spectral region below the oxygen absorption edge, providing a natural contrast mechanism for imaging carbon-containing material in the spectral window extending from 284 to 543 eV. This provides interesting new opportunities for both the life and the environmental sciences.

A lot of features connected with absorption and emission of light in nanocrystals can be understood in terms of the quantum confinement approach. In this approach, a nanocrystal is considered as a three-dimensional potential box in which photon absorption and emission result either in a creation or in an annihilation of some elementary excitations in an electron subsystem. These excitations are described in terms of quasiparticles known for bulk crystals, that is, electrons, holes, and excitons.

This chapter is meant to remind readers of some principal results from elementary quantum mechanics and to provide an elementary introduction to solid state physics, which is essential for the following chapters. We then depart from elementary “particle-in-a-box” problems and consider the properties of an electron in a periodic potential. In the next step, we introduce the concepts of effective mass and quasiparticles as elementary excitations of a many-body system. Finally, we give an idea of the low-dimensional structures that constitute, undoubtedly, one of the major fields of research in modern condensed-matter physics.

A few problems from elementary quantum mechanics

Particle in a potential well

To restate some basic properties of quantum particles that are necessary to consider electrons in a crystal, we start with a particle in a one-dimensional potential well (Fig. 1.1).

Semiconductor nanocrystals can be fabricated using a number of technologies, differing in the environment in which nanocrystals appear, growth conditions, size range, and size distribution, as well as physical and chemical stability and reliability. Nanocrystals can be developed in inorganic glasses and crystals, in liquid solutions and polymers, or on a crystalline surface. In this chapter we provide a brief overview of these techniques and give a synopsis of nanocrystals developed by various techniques.

Nanocrystals in inorganic matrices

Glass matrices: diffusion-controlled growth

Fabrication of nanocrystals embedded in a glass matrix by means of diffusion-controlled growth is based on commercial technologies developed for fabrication of color cut-off filters and photochromic glasses. Color cut-off filters produced by Corning (United States), Schott (Germany), Rubin (Russia), and Hoya (Japan) are just glasses containing nanometer-size crystallites of mixed II-VI compounds (CdSxSe1−x). Empirical methods of diffusion-controlled growth of semiconductor nanocrystals in a glass matrix have been known for decades or even centuries (in the case of color stained glasses). Commercial photochromic glasses developed in recent years contain nanocrystals of I-VII compounds (e.g., CuCl, CuBr, AgBr). Typically, silicate or borosilicate matrices are used with the absorption onset near 4 eV (about 300 nm), thus providing optical transmission of the semiconductor inclusions to be studied over the whole visible range.

Growth of crystallites results from the phase transition in a supersaturated viscous solution.

In quasi-zero-dimensional structures under optical excitation there are, along with reversible processes that decay over the recombination time of electron-hole pairs, processes that result in a persistent change in the optical properties. These processes are controlled by the integral dose of the absorbed radiation rather than radiation intensity. Numerous examples of similar behavior can be found in photophysics and photochemistry of molecular structures. Similar to molecular structures, semiconductor nanocrystals embedded in a matrix or precipitated in a solution exhibit a variety of guest-host effects. Some of the phenomena related to the photo-induced modifications in absorption and/or emission features will be the subject of the present chapter. The main attention will be given to laser annealing, photodarkening, persistent spectral hole-burning, and photochemical reactions resulting in permanent spectral hole-burning. Finally, we consider the intercrystallite migration of carriers and its effect on luminescence kinetics.

Laser annealing, photodarkening, and photodegradation

Semiconductor-doped glasses exposed to prolonged illumination by laser light of a wavelength corresponding to resonant absorption by nanocrystals were found to exhibit systematically a number of photo-induced modifications. These include, first of all, a sharp decrease in the intrinsic edge luminescence versus impurity and defect related emission. Second, the lifetime of electron-hole pairs decreases by several orders of magnitude and reaches 10−11 s. Finally, additional structureless absorption with a coefficient on the order of 1 cm−1 appears in a wide spectral interval. The initial properties of the samples can sometimes be restored by heating to temperatures of 400–500°C.

We consider an ideal nanocrystal to be a bit of a crystal with a spherical or cubic shape, the so-called quantum dot. Such species do not exist in nature. Nevertheless, it has been very helpful for the physics of nanocrystals to use these simplified models to trace the basic effects arising from three-dimensional spatial confinement. An extension of the effective mass approximation towards spatially confined structures leads to a particle-in-a-box problem and provides a way to calculate the properties of nanocrystals that are not possible to analyze in other way because of the very large number of atoms involved. This approach fostered the systematic experiments that have determined the major advances in nanocrystal physics. At smaller sizes it converges with the results of the quantum-chemical approach, in which the given number of atoms in the nanocrystal is accounted for explicitly rather than the size.

In this chapter we consider systematically the properties of electron-hole pair states resulting from the effective-mass consideration. We see that an elementary excitation in the electron subsystem of a nanocrystal can be classified as exciton with an extension “exciton in a quantum dot.” Afterwards, a survey of quantum-chemical techniques along with the selected examples for semiconductor clusters will be given. Finally, the distinctive size ranges will be outlined to specify the steps of the evolution of properties and of the applicability of the different approaches and concepts to the mesoscopic structures confined in all three dimensions.

In this chapter we consider the optical processes in nanocrystals that can be interpreted in terms of creation and annihilation of a single electron-hole pair within a crystallite. Size-dependent absorption and emission spectra and their fine structures, as well as size-dependent radiative lifetimes, will be discussed for nanocrystals of II-VI, I-VII compounds and, where possible, for nanocrystals of III-V compounds and of group IV elements. Nontrivial aspects of excitonphonon interactions that manifest themselves in homogeneous linewidths and/or intraband relaxation processes will be outlined. Challenging experiments providing the optical information relevant to a single nanocrystal will be discussed as well. Most of these results have become possible because of a number of the spectrally and spatially selective techniques described in Chapter 4. An influence of a microcavity on spontaneous emission of nanocrystals, the competitive recombination mechanisms, and the electric field induced effects will be analyzed as well.

Size-dependent absorption spectra. Inhomogeneous broadening and homogeneous linewidths

Experimental evidence for quantum-size effects in real nanocrystals

In the early 1980s A. I. Ekimov and A. A. Onushchenko (Ekimov and Onushchenko 1982; Ekimov and Onushchenko 1984) and L. Brus with coworkers (Brus 1983; Rossetti, Nakahara, and Brus 1983) published pioneering articles in which size-dependent absorption spectra of semiconductor nanocrystals resulting from quantum confinement were demonstrated for the first time. During the same period S. V Gaponenko et al. reported on inhomogeneous broadening of the optical absorption spectra of glasses doped with semiconductor nanocrystals (Gaponenko, Zimin, and Nikeenko 1984).

The advances in physics and the technology of semiconductor nanocrystals that were summarized in Chapters 2–7 provide comprehensive knowledge on the optical and electronic properties of nanocrystals and make it possible to create novel mesoscopic materials with desirable parameters by means of stoichiometry and size control. In these chapters the intrinsic properties of nanocrystals were discussed, implying the absence of any cooperative effect on the properties of a given nanocrystal ensemble. In recent years significant progress has been made in moving from randomized nanocrystals towards spatially organized structures like nanocrystal superlattices, quantum dot solids, and photonic crystals. The principal results obtained in the field will be reviewed in this chapter.

Superlattices of nanocrystals: quantum dot solids

There are several ways to develop a nanocrystal superlattice, that is, a structure consisting of identical nanocrystals with regular spatial arrangement. The first is to use zeolites, which form a skeleton with regular displacement of extremely small cages, the size of a cage being typically about 1 nm. A number of clusters such as CdnSm and ZnnSm can be embedded in these cages, the cluster size distribution and geometry being controlled by the topology of the three-dimensional host surface (Wang et al. 1989; Stucky and MacDougall 1990; Bogomolov and Pavlova 1995 and references therein). Using various zeolites as frameworks for semiconductor clusters makes possible the study of regular three-dimensional cluster lattices with variable intercluster spacing.

Because of inevitable size distribution, shape variations, different concentration of impurities and defects, and fluctuations of local environment and charge distribution, every ensemble of nanocrystals dispersed in some solid or liquid medium possesses inhomogeneously broadened absorption and emission spectra. Therefore, a number of properties inherent in molecular and atomic inhomogeneously broadened spectra can be a priori foreseen for nanocrystals. These include spectral hole-burning, fluorescence line narrowing under selective excitation, and decay time distribution. At the same time, spectrally selective techniques developed for inhomogeneously broadened molecular and atomic structures have been successfully applied to nanocrystals providing evaluation of individual parameters smeared as a result of inhomogeneous broadening. This chapter gives a brief overview of specific phenomena inherent in all spectrally inhomogeneous media and a survey of the relevant experimental techniques including nonlinear pump-and-probe spectroscopy, fluorescence excitation spectroscopy, and single molecule spectroscopy.

Population-induced optical nonlinearity and spectral hole-burning

Every real system consisting of particles with discrete energy levels exhibits absorption saturation under intense optical excitation. The only example of a nonsaturable system is an ensemble of ideal harmonic oscillators that possess an infinite number of equally spaced energy levels, optical transitions allowed only for a couple of neighboring levels, and the probability of optical transitions being proportional to the level number (Stepanov and Gribkovskii 1963).