Introduction

The highly anisotropic crystal structures of the layered high Tc superconducting cuprates induce the necessity of using epitaxial films in most devices based on high Tc thin films. Each individual application demands a specific crystallographic orientation of the film as well as a certain combination of substrate, high Tc superconducting film and non-superconducting layer materials. The intention of this chapter is to provide examples of what aspects need to be considered when designing the device and predicting its behavior. The behavior depends on the detailed microstructure of the thin films. The examples are therefore discussed in terms of microstructure and how it can be controlled and manipulated.

As in all epitaxial structures, the interfacial interactions are crucial for the resulting microstructures. The direct interaction between the substrate and a single-layer high Tc thin film is illustrated in the following section. The description is followed by a discussion of different aspects of the use of buffer layers. The text is restricted to high Tc YBa2Cu3O7–x (YBCO), mainly owing to the fact that the vast majority of published data concern this superconductor. However, there are common characteristics of epitaxial film growth between different high Tc superconductors. Results from the YBCO films can thus be used when considering the other high Tc superconducting thin films which is pointed out in Section 14.10.

The mechanical interaction between the different epitaxial layers may result in the formation of misfit dislocations. Nucleation and propagation of cracks can ensue if the mismatch in thermal expansion coefficient is relatively large.

Introduction

The charge carriers in high temperature superconductors are the electron holes confined to the CuO2-plane [9.1, 9.2], and thus, the distribution of charge plays a key role in determining their superconducting properties. Several groups of researchers have calculated the electronic structure of different superconducting oxides [9.3–9.5], and core-level spectroscopic studies are plentiful, both emission spectroscopy, and absorption spectroscopy with incident electrons and incident X-rays. In absorption spectroscopy, attention has focused on the near-edge structure of the K- and L-edge of copper, and, in particular, the Kedge of oxygen which exhibits clear signatures of the electron holes that are responsible for superconductivity [9.6, 9.7]. On the other hand, there have been few experimental studies of the spatial distribution of the electron charge in these superconductors.

In high-temperature superconductors, the density of electron holes is typically considerably less than 1% of the total density of electrons. However, the electron diffraction patterns and images of these superconductors, with their high local concentration of charge, is expected to be strongly influenced by the charge distribution. One reason for this expectation is the large crystal unit cell, resulting in reflections at small angles which are very sensitive to the charge. We realize this from the classical picture of the scattering of fast electrons by an atom. Charged particles interact with the electrostatic potential, and thus, for small scattering angles, which correspond to large impact parameters, the incident particle sees a nucleus that is screened by the electron cloud. Thus, the scattering amplitude is mainly determined by the net charge of the ion at small scattering angles, q.

Introduction

The discovery of cuprates exhibiting superconductivity at relatively high temperatures has opened up new prospects for the application of superconductivity in many areas, in particular in sensor systems and in electronics [13.1, 13.2]. In this respect the superconducting quantum interference device (SQUID) is one of the most attractive developments. Many different designs have been fabricated and studied, and modern SQUIDs on the basis of YBa2Cu3O7 have reached field sensitivity and performance levels not far different from those known for devices produced with classical low temperature superconductors [13.3, 13.4].

The physical properties of cuprate superconductors depend sensitively on the preparation conditions and the resulting microstructure. Owing to the essentially two-dimensional superconductivity and the very small coherence length in the cuprates, grain boundaries in general reduce the critical current density by orders of magnitude compared with the bulk value. Therefore much attention has been paid to the development of techniques for growing high quality epitaxial thin films of superconducting and appropriate non-superconducting materials required for active and passive electronic devices on suitable single-crystalline substrates. The remarkable progress achieved is closely related to both the development of proper materials preparation techniques and high quality materials characterization. In fact, device production requires atomic or close to atomic structural perfection. High-resolution transmission electron microscopy, which developed atomic resolution in many materials during the early 1980s, i.e. shortly before the new materials were discovered, has contributed substantially to the understanding of the structural properties of cuprate superconductors and to their use in electronic devices.

Besides instrumental resolution, two important technical factors are decisive for the enormous potential of high-resolution electron microscopy for superconductivity research.

Introduction

The electron–specimen interaction not only provides information about the atomic structure of the materials, but also gives clues about other physical properties of the materials. The science of extracting this valuable information from smaller and smaller volumes of specimens is called microanalysis and is a very fruitful development of modern electron microscopy. Playing a pivotal role in this science is the scanning transmission electron microscope (STEM) which was introduced mainly to provide point-by-point analysis at high spatial resolution. The advantage of scanning is that it enables each pixel to be associated with a data set which might be a diffraction pattern, an X-ray emission spectrum, or an electron energy loss spectrum. The advantage of transmission is that it prevents the beam broadening which degrades the resolution of images formed by scanning a bulk sample. In this chapter, we will review the physical principles of the various imaging and analytical techniques available in the STEM, and assess their usefulness in connection with the research into high-temperature superconductors (HTSC). In many ways, there is a large overlap between the requirement of HTSC research and other branches of the material sciences. Thus we hope that our review can also serve as a brief introduction to STEM for researchers both inside and outside the HTSC community. For specific examples of the application of the STEM in HTSC, we will refer readers to other chapters in this book and the original papers.

Electron optics of STEM

There are currently two variants of STEM, depending on whether it is specifically designed for scanning microscopy operation or adopted from conventional transmission electron microscopy work.

Introduction

Thin films of the high-temperature superconductor, YBa2Cu3O7, may be synthesized as highly oriented structures having a high degree of homogeneity as compared with bulk processed materials. These thin films exhibit some of the best transport properties of high-temperature superconductors (HTSC), particularly the highest superconducting critical currents as a function of temperature and magnetic field. The microstructure of films of different orientation is composed of arrays of specific crystallographic defects which may include, for example, low-angle grain boundaries, (110) twin boundaries, 90° domain boundaries, other misoriented regions or grains, stacking faults, antiphase boundaries, second phases, etc. The surface and interface structure may vary considerably, a smooth surface being essential for device fabrication. Thin-film synthesis also provides methods for fabricating or isolating localized crystallographic interfaces, such as grain boundaries, for transport studies. Therefore, in addition to their importance for technological applications, HTSC thin films may also serve as model systems for studying fundamental behaviors of these materials. In understanding properties it is essential to characterize the microstructure in as much detail as possible. In this chapter we will discuss the microstructure of YBa2Cu3O7 (YBCO) thin films as characterized by transmission electron microscopy (TEM), with emphasis on the interface structure of films having a-axis and (103) orientation, and of individually fabricated boundaries synthesized using a-axis oriented films.

Grain boundaries

YBa2Cu3O7 (YBCO) thin films are grown in situ by a variety of vapor phase deposition techniques usually with either the c-axis or a(b)-axis normal to the plane of the film [12.1, 12.2]. We will refer to the films by their normal orientation.

Biexcitons and Exciton-Exciton Interactions in Semiconductors

The concept of the excitonic molecule was introduced independently by Moskalenko [1] and Lampert [2]; later, the excitonic molecule was called the biexciton [3]. The biexciton represents the bound state of four Fermi quasiparticles, namely two electrons and two holes. More simply, it can be regarded as a bound state of two excitons.

Besides biexcitons, one can in general talk about “trions” and “quaternions,” which are bound states of any combination of three or four electrons and holes, respectively. A trion always carries charge; a quaternion may or may not have charge, biexcitons being one kind of quaternion. Several different types of trions and quaternions are expected to be stable in semiconductors in both bulk and two-dimensional (2D) structures; later in this chapter we discuss a proposal [4] for superconductivity based on charged quatemionic bound states of electrons and holes.

Since biexcitons are also integer-spin bosons, they are expected to obey the same Bose statistics as excitons, including Bose narrowing of the energy distribution, discussed in Chapter 1. This has been seen in the semiconductor CuCl. We review experiments on Bose effects of biexcitons in CuCl at the end of this chapter.

We have already briefly discussed the exciton-exciton interaction in Subsection 2.1.3 in terms of the estimate of the s-wave-scattering length that goes into models of the weakly interacting Bose gas. As we mentioned there, this interaction is essentially a van der Waals force, but with the additional complications of comparable electron and hole masses and electron-hole exchange. In this section, we treat this interaction in greater detail, since it determines whether excitonic molecules and/or electron-hole liquids (EHLs) can form.

Introduction

As discussed briefly in Chapter 1, the general theory of phase transitions in the electronhole system predicts that in a system with a simple band structure, when annihilation and polariton effects are neglected, there will always be a region of phase space in which BEC of electron-hole pairs occurs. In this chapter we examine some of the more complicated features of the electron-hole phase diagram.

The many-body system of electrons and holes appears deceptively simple. If one neglects the possibility for electron-hole annihilation, one can consider the following apparently simple system: two types of Fermi particles with equal mass and opposite charge, interacting only by means of Coulomb interaction. As we will see in this chapter, however, the phase diagram for this system is extraordinarily complex, and the full theory for the phase diagram is not yet complete. We emphasize that most of these complexities arise solely from the above simple model and not from the other complicated features of solids such as band structure, band-to-band recombination, etc. Therefore much of this theory applies equally well to the case of electron-positron plasma or electron-ion plasma. The similarity of the e-h system to the electron-proton system, for example, suggested the existence of excitonic molecules [1,2] and, moreover, the possibility of a gas-liquid phase transition of exciton and biexciton gas into a Fermi electron-hole liquid (EHL). The EHL is the bound state of a macroscopically large number of electrons and holes [3-6], similar to the many-electron-proton system.

As stressed by Keldysh, however, this similarity is not complete. In a comprehensive and instructive review [7], he pointed out the peculiar properties distinguishing the e-h system from any other, which we summarize here.

Condensate Formation in the Bose Gas

An important question in connection with the experiments aimed at achieving BEC of a weakly interacting Bose gas with a finite lifetime is the time needed for the formation of the condensate. It is not at all evident that the condensation can always take place within the lifetime of the system. For the case of liquid He, the assumption of equilibrium seems satisfied because 4He atoms, which do not decay, undergo roughly 1011 interparticle-scattering events per second, assuming classical hard-sphere scattering. In other boson systems, however, nonequilibrium effects may have a significant effect. For excitons in a semiconductor, the lifetime of the particle may be only a few hundred scattering times. Spin-polarized hydrogen also has a finite lifetime to nonpolarized states [1], and alkali atoms can recombine into molecules [2]. Naively judging from classical behavior, one might assume that hundreds of scattering times may seem more than adequate time to establish equilibrium. The case of Bose condensation is unique, however, since a macroscopic number of particles must enter a single quantum state that by random-scattering processes alone is highly improbable. Therefore we need not assume that the time for Bose condensation is short.

Early experiments with orthoexcitons in CU2O seemed to indicate that the excitons might not have enough time to condense within their lifetime [3]. As discussed in Subsection 1.4.3, the orthoexciton density increased to approach the BEC boundary given in Eq. (1.18) and highly degenerate Bose-Einstein momentum distributions were observed, but a significant condensate fraction did not appear. Instead the gas increased its temperature to accommodate extra particles, reaching temperatures well above the lattice temperature.

Introduction

In this chapter we generalize the theory of the weakly nonideal Bose gas to the case of the interaction of excitons with acoustic or optical phonons, i.e., in the case of interaction with another Bose subsystem, the quasiparticle number of which is not conserved. To simplify the question, we assume that the exciton-phonon interaction leads to only intraband exciton scattering and does not change the total number of excitons in the band. In other words, we consider an isolated exciton band or suppose that the processes of interband scattering are not important because of the symmetries of the exciton and the phonon states and the values of the interaction constants.

The theory of the interaction of condensed excitons with phonons has primary importance in the question of whether excitons will be superfluid. In Chapter 2, we saw that the fact that the excitons are particle-antiparticle pairs does not prevent them from becoming superfluid. At first glance, however, it is not easy to draw an analogy to other Bose condensates such as liquid He. In the case of liquid He, interactions with the external world are limited to the surfaces of the container, while for excitons, the phonon field interpenetrates the same region of space as the exciton gas. The situation is more analogous to the case of a superconductor. Unlike a BCS superconductor, however, in an exciton condensate the lattice phonons have nothing to do with the pairing. We shall see that nevertheless the excitonic condensate remains superfluid in the presence of a phonon field. At the end of this chapter we review recent experiments that may be evidence of excitonic superfluidity.

The Bogoliubov Model of the Weakly Nonideal Bose Gas

In this chapter we review the basic theory of Bose-Einstein condensation (BEC) of excitons. To start, this means we must review the basic theory of BEC of any kind of particle, the theory known as the Bogoliubov model, after the foundational contributions made by N. N. Bogoliubov. This model introduces all the strange things associated with BEC: spontaneous symmetry breaking, off-diagonal long-range order (ODLRO), macroscopic occupation of a single quantum state, etc.

It is often said that physicists who spend years studying quantum mechanics eventually warp their intuition so much that things like ODLRO seem normal. It is well worth stepping back every now and then to think about just how strange a Bose condensate is. First, consider the idea of spontaneous symmetry breaking. Many systems exist in which the underlying physics, expressed in the Hamiltonian, do not favor one state over another. The a priori probability of occupation of the different states by a particle is equal, i.e., symmetric. Nevertheless, in some cases, thermodynamics requires that a macroscopic number of particles must somehow “choose” one of the states preferentially. If they did not, the system would not be in equilibrium, i.e, could not have a definable temperature. If the particles preferentially choose one state, then the underlying symmetry has been broken.

In the context of magnets, the breaking of the symmetry of the magnet (to have all its constituent dipoles lined up one way and not another) is energetically favored, since there are terms in the Hamiltonian that give lower energy for aligned dipoles, e.g., μS1 · S2.

Turbulence and chaos in a semiconductor crystal? These are just some of the intriguing predictions of nonlinear optics with coherent excitons. In this chapter we discuss some aspects of nonlinear coherent optics with the participation of the excitons, photons, and biexcitons. As in many nonlinear systems, these effects arise because of feedback mechanisms, i.e., the light impinging on the system affects the electronic states, which in turn affect the dielectric constant of the medium through which the light passes. These effects are closely related to the phenomena of self-organization [1-8] and optical bistability [7-10] and self-pulsations and the appearance of chaos [2-6]. The cooperative nonlinear coherent processes in optical systems have recently attracted much attention [7-20]. These investigations have stimulated the development of new mathematical methods [21-31] and have opened up possibilities for many new applications. The theoretical and the experimental investigations in these directions give rise to the theory of solitons [32∧2] and lead to the new developments in the optics of ultrashort pulses [43-58].

Ultrafast phenomena such as self-induced transparency and nutation are related to the propagation of solitons and pulse trains, whereas the transient stages of the ultrashort lightpulse penetration in the media are described by area theorems. These coherent ultrafast phenomena typically take place during intervals of time less than the relaxation time, i.e., femtoseconds to picoseconds in typical solids. Collisions and incoherent scattering processes destroy the coherent evolution of the excited particles. But if coherent macroscopic states of the excitons, photons, and biexcitons have been formed because of spontaneous or induced BEC, in this case one can consider their time evolution over intervals of time much greater than the relaxation time.

Introduction. Polaritons and Semiconductor Microcavities

As we have mentioned previously, BEC of excitons or biexcitons and lasing can be seen as two limits of the same theory. Lasing occurs in the case of strong electron-photon coupling (recombination rate fast compared with interparticle-scattering rate) while excitonic BEC occurs in the case of weak electron-photon coupling (recombination rate slow compared with the interparticle-scattering rate.) A laser can be seen as a Bose condensate in which the long-range phase coherence exists in the photon states [1], while in the exciton condensate the coherence exists in the electronic states. This is one of the reasons for some of the confusing debates in the early history of excitonic Bose condensation – in many systems there is not a sharp distinction between an excitonic condensate and supperradiance, i.e., luminescence with enhanced intensity due to stimulated emission [2-4].

In the previous chapters, we have so far considered a laser light source only as a source of excitons by means of quantum transitions. In Chapter 6, the laser radiation was taken into account as a given external factor. This chapter is dedicated to phenomena related to a strong and noticeable exciton-photon interaction, when the light significantly influences the energy spectrum of the high-density excitons [5-9]. As we will see, this leads to many fascinating effects related to instabilities.

A strong exciton-photon interaction implies a strong polariton effect, in which photon and exciton states are mixed (as in Fig. 1.3). When this mixing is strong, it is not obvious how to define the ground state of the system.

Because in many of the experiments discussed in this volume the semiconductor CU2O was used, and because this material is less well known than other semiconductors such as Si and GaAs, we review here some of the basic properties of CU2O.

CU2O is actually one of the earliest semiconductors studied [1], and the proof of the existence of excitons in this crystal [2, 3], which confirmed the theories of Frenkel [4], Wannier [5], and Mott [6], led to an exciting period of expansion in the field of excitonic physics in the late 1950s and early 1960s, during which time many of the optical properties of this intriguing crystal were established [7-19]. (For general reviews, see Refs. 20 and 21.) The same property that makes it an excellent material for nonlinear optical effects, namely, a very large excitonic binding energy (150 meV), makes it a poor electrical conductor even at room temperature. Therefore CU2O has not been studied or fabricated extensively by the electronics industry, and high-quality samples are still not widely available.

Band Structure. Most of the complexities of the band structure of CU2O stem from the d orbitals of the Cu atoms in the valence band. CU2O forms into a cubic lattice with inversion symmetry, which is the Oh symmetry group [22]. In the Oh symmetry, the five 3d orbitals are split by means of the crystal field into a higher threefold degenerate Γ+5 level and a lower twofold degenerate Γ+3level. The lowest conduction band, on the other hand, is formed from the 4s orbitals that have Γ+1 symmetry in the Oh group.

What is an Exciton?

Many people seem to have trouble with the concept of an exciton. Is it “real” in the same sense that a photon or an atom is? Does the motion of an exciton correspond to the transport of anything real in a solid?

Simply put, an exciton is an electron and a hole held together by Coulomb attraction. Of course, for some people the idea of a “hole” is a difficult concept, so this may not help much. Nevertheless, a hole is a “real” particle and so is an exciton.a Modern solid-state theory [1,2] gives equal footing to both free electrons and holes as charge carriers in a solid, exactly analogous to the way that electrons and positrons are both “real” particles, even though a positron can be seen as the absence of an electron in the negative-energy Dirac sea, i.e., a backwards-in-time-moving electron.

All excitons are spatially compact. The strong Coulomb attraction between the negatively charged electron and the positively-charged hole keeps them close together in real space, unlike Cooper pairs, which can have very long correlation lengths because of the weak phonon coupling between them. The sizes of excitons vary from the size of a single atom, e.g., approximately an angstrom up to several hundred angstroms, extending across thousands of lattice sites. Excitons are roughly divided into two categories based on their size. An exciton that is localized to a single lattice site is called a “Frenkel” exciton, after the pioneering work of Frenkel [3] on excitons in molecular crystals. Frenkel excitons appear most commonly in molecular crystals, polymers, and biological molecules, in which they are extremely important for understanding energy transfer.