Formation Of Vacancies In Crystals Research Articles

An extended theory of vacancy formation and its application to ionic conduction in the intrinsic and extrinsic regions

ABSTRACT The theory of the vacancy formation in crystals has been extended by generalising the vacancy formation energy that depends on the number of vacancies resulting from thermal activation. This extension enables to describe the freezing of defect concentrations at lower temperature, while the derived vacancy concentration reduces to the Boltzmann–Arrhenius law at higher temperature. The implications of the low-temperature patterns and its relevance to non-equilibrium process in the defect concentrations have been also touched upon. In addition, based on the approach explored, we further construct a model for the ionic conductivity in the intrinsic and extrinsic regions, which is formulated by focusing on the relation between the number concentration and the mobility of ionic charge carriers. A theoretical background to the continuity (knee) across which the both ionic conductivity patterns are smoothly connected is corroborated by the present work.

Parameters of vacancies’ formation in the carbon-subgroup crystals

The parameters of formation of vacancies in crystals of elements of the carbon subgroup (Cdiam, Si, Ge, α-Sn, Pb) are calculated. The method used takes into account both quantum effects at low temperatures and delocalization of atoms at higher temperatures. It is shown that consideration of atom delocalization brings about an increase in the values of enthalpy and entropy and the volume of the vacancy formation. At low temperatures, the parameters of vacancy formation depend heavily on temperature, with the entropy of vacancy formation becoming negative. In the region of high temperatures, good agreement was obtained with both experimental data and theoretical estimates reported in other publications. The dependence of vacancy-related parameters on temperature in the course of isobaric heating of diamond in the range from 100 to 4500 K is studied. The limits of applicability of the Arrhenius equation with temperature-independent energy of activation process are discussed. It is shown that there is validity of the “compensation rule” (correlation between the entropy and enthalpy of vacancy formation) and of the correlation between the volume and entropy of the vacancy formation within the entire studied temperature range.

The thermodynamic characteristics of formation of vacancies in carbon subgroup element crystals

A method for calculating the parameters of formation of vacancies in crystals formed by spherically symmetrical atoms was developed. Both quantum effects at low temperatures and the possibility of the delocalization of atoms at high temperatures were studied. The parameters of formation of vacancies in carbon subgroup element crystals C-diam, Si, Ge, α-Sn, and Pb were calculated. The inclusion of the delocalization of atoms was shown to increase the enthalpy, entropy, and volume of vacancy formation. At low temperatures, the parameters of vacancy formation were found to depend strongly on the temperature, and the entropy of vacancy formation became negative. At high temperatures, close agreement with experimental data and theoretical estimates reported by other authors was obtained. The temperature dependence of vacancy parameters was studied for diamond heated isobarically from 100 to 4500 K. The applicability scope of the Arrhenius equation with a temperature-independent activation energy is discussed. The validity of the “compensation rule” (correlation between the entropy and enthalpy of vacancy formation) was demonstrated. It was also shown that the volume and entropy of vacancy formation were correlated over the whole temperature range studied.

Atomistic simulation of void nucleation in aluminium lines

Abstract The formation of voids in aluminium interconnects in integrated circuits was studied atomistically with emphasis on nucleation. Input computational cells included different levels of concentrations of vacancies and stresses together with the typically observed structural defects (grain boundaries and dislocations) in metal lines. The input cells were relaxed using Monte Carlo (atom transpose) and static energy minimization (strain relaxation) techniques concurrently. Besides agglomeration of vacancies in unstrained crystals, the formation of vacancies in crystals under tension was found to be a main contributor to void nucleation. Climb and glide of dislocations were observed atomistically during the formation of voids. Compressive stresses in the metal lines, on the other hand, prevented the formation of voids.

Electrostatic energy of vacancy formation in crystals of polar molecules

An exact expression is derived for the electrostatic energy of a crystal of polar polarizable molecules containing an unrelaxed vacancy. The energy exceeds twice the electrostatic binding energy per molecule L by a polarization energy term, when changes in dielectric response due to the vacancy are ignored. The electrostatic energy of a molecule at a crystal surface is estimated from surface and bulk polarization energy measurements. It can be as high as 1.5 L. making the electrostatic energy of vacancy formation significantly less than L. the value for non-polarizable molecules. This may help to explain anomalous results for certain plastic crystals.