Publisher Summary The chapter presents a study on relations between the concentrations of imperfections in crystalline solids. Many properties of crystalline solids, such as the electronic or ionic conductivity, the color, the luminescence, and the magnetic susceptibility are determined by the presence of imperfections. Generally, six types of primary imperfections are distinguished; namely phonons, electrons and holes, excitons, vacant lattice sites and interstitial atoms or ions, foreign atoms or ions in either interstitial or substitutional positions, and dislocations. In addition atoms of the base crystal may be present at lattice sites normally occupied by other atoms. Five types of primary imperfections—namely, electrons and holes, vacant lattice sites, interstitials, misplaced lattice atoms, and foreign atoms—are discussed in this chapter. The chapter presents a new treatment of these problems by making use of a graphical representation. This treatment, together with the use of a band scheme for the electronic energy levels, greatly facilitates the application of the theory and the deduction of conclusions from it. Apart from a few exceptions, binary nonmetallic compounds of the formula M X will be considered almost exclusively. Here M indicates an element of a more electropositive character (metal) and X an element of a more electronegative character.

Relations between the Concentrations of Imperfections in Crystalline Solids

Solution-processed planar perovskite devices are highly desirable in a wide variety of optoelectronic applications; however, they are prone to hysteresis and current instabilities. Here we report the first perovskite-PCBM hybrid solid with significantly reduced hysteresis and recombination loss achieved in a single step. This new material displays an efficient electrically coupled microstructure: PCBM is homogeneously distributed throughout the film at perovskite grain boundaries. The PCBM passivates the key PbI3(-) antisite defects during the perovskite self-assembly, as revealed by theory and experiment. Photoluminescence transient spectroscopy proves that the PCBM phase promotes electron extraction. We showcase this mixed material in planar solar cells that feature low hysteresis and enhanced photovoltage. Using conductive AFM studies, we reveal the memristive properties of perovskite films. We close by positing that PCBM, by tying up both halide-rich antisites and unincorporated halides, reduces electric field-induced anion migration that may give rise to hysteresis and unstable diode behaviour.

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Perovskite–fullerene hybrid materials suppress hysteresis in planar diodes

Defect-interface interactions

This article reviews the transport of atoms through crystalline solids under the influence of external electric fields, chemical and isotopic concentration gradients and thermal gradients. The main emphasis is on the statistical and thermodynamic description of these phenomena via the theory of mobile lattice imperfections - vacancies and interstitial atoms. In discussing the various phenomena in detail (§ 5) extensive use is made of non-equilibrium thermodynamics as providing a convenient general formalism. Particular attention is given wherever possible to the physical interpretation of the descriptions provided by this formalism. An introductory survey of the properties of vacancies and interstitials in relation to diffusion phenomena is given in § 2. This includes a summary of the various defect models applicable to different solids - metals, ionic solids, semiconductors and insulators. Section 3 deals in greater detail with certain necessary aspects of the statistical thermodynamics of solids containing defects. Section 4 briefly summarizes the basic theory of non-equilibrium thermodynamics, oriented towards matter transport in crystalline solids; attention is drawn to several pitfalls in this approach. Finally, § 5 is the main object of the review; it applies the material developed in §§ 3 and 4. This section deals with (i) isothermal diffusion in metal alloys, including chemical diffusion, and isotopic tracer diffusion, particular attention being given to dilute systems, (ii) electrolytic conductivity, ionic mobility and both solute and solvent diffusion in ionic solids, special attention being given to the relation between these quantities and to a generalized form of the Nernst-Einstein relation, (iii) the Soret effect and thermal diffusion, especially in metals and dilute alloys, and (iv) thermoelectric phenomena in ionic solids. The article does not deal with grain boundary or surface diffusion and does not specifically discuss diffusion-controlled chemical reactions, sintering or creep. Discussions of these aspects of the subject are given in the works listed in the bibliography.

https://iopscience.iop.org/article/10.1088/0034-4885/27/1/305/pdf

Matter transport in solids

A defect model for the grain-boundary barrier has been proposed to explain the phenomena of voltage instability/stability of the ZnO varistor. The key element of the proposed model is the zinc interstitials which are present in the depletion layer as excess zinc, arising from the non-stoichiometric nature of ZnO. Both instability and stability have been described in terms of diffusion of these interstitials in the depletion layer, followed by chemical interactions with defects at the grain-boundary interface. Finally, a large body of experimental data is presented to indirectly validate the proposed defect model.

A Grain-boundary Defect Model for Instability/stability of a ZnO Varistor

It is shown that an electric potential exists between the surface and the bulk of ionic crystals. The potential is expressed in terms of the energies necessary for formation of lattice defects. The distribution of the potential and of lattice defects near the surface is calculated. The difference between the concentration of lattice defects near the surface and that in the bulk leads to a ``surface conduction.'' The magnitude of the potential, the thickness of the space‐charge layer near the surface and the ``surface conduction'' are calculated for NaCl crystals using numerical values, calculated by Mott and Littleton [N. F. Mott and M. J. Littleton, Trans. Faraday Soc. 34, 485 (1938)] for the energies of formation of lattice defects. The effect of charged impurities in the crystals on the surface potential is discussed. The importance of the surface potential on diffusion, photoelectric effect, and photographic effect is mentioned.

Space‐Charge Layer and Distribution of Lattice Defects at the Surface of Ionic Crystals

Injected Light Emission of Silicon Carbide Crystals

Light Emission Produced by Current Injected into a Green Silicon-Carbide Crystal

The calculations of Simpson, on the energy of an electron localized in a crystal at an impurity carrying a single positive charge, have been extended to impurities carrying a multiple positive charge. The thermal and optical activation energies corresponding to the transition of the electron from the $1s$-orbit to the conduction band are derived. The various contributions to the polarization energy of the lattice near the impurity are analyzed in detail, which leads to an expression differing from that used by Simpson. The results are applied to a tentative interpretation of activation energies of SiC crystals as observed by Busch.

Kurt Lehovec

Papers

Space‐Charge Layer and Distribution of Lattice Defects at the Surface of Ionic Crystals

Injected Light Emission of Silicon Carbide Crystals

Light Emission Produced by Current Injected into a Green Silicon-Carbide Crystal

Energy of Trapped Electrons in Ionic Solids

Theory of Electric Breakdown in the High-Temperature Region and Its Relation to Thermionic Emission