Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

First-principles calculations for point defects in solids

The Barkhausen effect (BE) in metallic ferromagnetic systems is theoretically investigated by a Langevin description of the stochastic motion of a domain wall in a randomly perturbed medium. BE statistical properties are calculated from approximate analytical solutions of the Fokker–Planck equation associated with the Langevin model, and from computer simulations of domain‐wall motion. It is predicted that the amplitude probability distribution P0(Φ) of the B flux rate Φ should obey the equation P0(Φ)∝Φc−1 exp(−cΦ/〈Φ〉), with c>0. This result implies scaling properties in the intermittent behavior of BE at low magnetization rates, which are described in terms of a fractal structure of fractal dimension D<1. Analytical expressions for the B power spectrum are also derived. Finally, the extension of the theory to the case where many domain walls participate in the magnetization process is discussed.

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Domain-wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I, Theory

Equilibrium vacancies and thermophysical properties of metals

An ac technique is described for measuring low‐frequency resistance fluctuation spectra with improved sensitivity over dc methods achieved by avoiding preamplifier 1/f noise. The technique, easily implemented with decade resistors and a lock‐in amplifier, allows the current noise of low‐resistance (r<10 kΩ) specimens to be measured to frequencies below 1 mHz. Use of a center‐tapped, four‐probe specimen geometry allows discrimination between specimen and contact noise and eliminates noise due to bath temperature variations. The technique is demonstrated in use to determine the dependence of the 1/f noise of Cr films on film area. Measurements with simultaneous direct and alternating currents provide means to study the noise of nonlinear devices and frequency‐dependent conductors.

ac method for measuring low‐frequency resistance fluctuation spectra

Electromigration in thin-film interconnection lines: models, methods and results

Thermal-Equilibrium Properties of Vacancies in Metals through Current-Noise Measurements

A theory of the power spectrum of the Barkhausen noise is presented, accounting for the frequency behaviour of the experimental spectra in the whole range of analysis frequency between 1 Hz and 20kHz, when the magnetizing frequency is kept relatively low (below 0.1 Hz). The theory assumes the existence of a correlation between the number of clustered pulses in a large Barkhausen discontinuity and the time interval from such a discontinuity to the preceding one: the longer this time interval, the larger the number of clustered pulses. An experimental check of the dependence of the noise power spectrum on the magnetizing frequency in rings of Fe−Si 4% is given. It is shown that the theoretical results fit the experimental data without the introduction of any arbitrary constant.

Time-amplitude correlation effect between large Barkhausen discontinuities (in the magnetization noise)

A current noise due to dislocation processes in aluminum film samples has been put in evidence during plastic deformation. Burst‐type dislocation generation and annihilation processes have been observed, showing the discontinuous character of plastic flow and the presence of strong correlation effects on dislocation dynamics. Noise behavior shows a strong enhancement of the dislocation generation and annihilation events with increasing temperature, a fact which accounts for the material softening at high temperature. The stress‐strain behavior of the metal film upon cyclic deformation is obtained from the noise results; in particular it is possible to detect the very beginning of plastic deformation of the metal and the temperature dependence of the elastic limit. The behavior of the dislocation density during cycling can also be obtained. Such a behavior of the dislocation density during cycling can also be obtained. Such a behavior is accounted for by a theoretical model where the competing effects of g...

M. Celasco

Papers

Thermal-Equilibrium Properties of Vacancies in Metals through Current-Noise Measurements

Time-amplitude correlation effect between large Barkhausen discontinuities (in the magnetization noise)

Application of the current noise technique to the investigation on dislocations in metals during plastic deformation

Study of dislocation dynamics in metals through current noise measurements