How to determine the ionicity factor quantitively ?
From the article of Ali Zaoui
Correlation between the Ionicity Characterand the Charge Density in Semiconductors
Fi + Fc = 1 Fi : ionity factor Fc: Covalence factor
Introduction
One of the problems in defining the ionicity of a bond is the difficulty of transforming a qualitative or verbal concept into a quantitativc, mathematical formula. Every definition involves some assumptions, and who can say which assumptions are more valid than others. However, many detailed calculations exist on both crystal and polyatomic molecules which are simple enough to helpfully make use of some model Hamiltonians or other restrictive assumptions and whose reliability depends on semi-empirical parameters.
Phillips’ [ 11 stimulating assumption concerning the relationship of the macroscopic characteristics of a covalent crystal (dielectric constant, structure) and the microscopic ones (band gap, covalent and atomic charge densities) is based essentially on the isotropic model of a covalent semiconductor, whereas Christensen et al. [2] performed self-consistent calculations but used model potentials which were derived from a realistic GaAs potential where additional external potentials were added to the anion and cation sites. In this way the ionicity was gradually changed, and from the theoretical charge transfers a mapping on the Phillips scale was obtained. These models achieve considerable success in unifying distinct properties. However, in general the ionicities found by Christensen tend to be somewhat larger than those of Phillips. Garcia and Cohen [3] achieved the mapping of the ionicity scale by an unambiguous procedure based on the measure of the asymmetry of the first principle valence charge distribution [4]. As for the Christensen scale, their results were somewhat larger than those of the Phillips scale.
In this paper, following the idea of Garcia and Cohen [3] based on the measure of the asymmetry of the total valence charge density, we have established a new empirical formula for the calculation of the ionicity fi of a specific class of materials. The theory yields a formula with three attractive features. Only the pseudopotential form factors are required as input, the computation ofJ itself is trivial and the accuracy of the results reaches that of ab initio calculations. The latter option is attractive since it allows the consideration of hypothetical structures and the simulation of experimental conditions that are difficult to achieve in the laboratory, e.g. very high pressures.
Results
To achieve a scaling relation for ,fi of ANB8-N compound semiconductors, we have used the pseudopotential method for determining suitable charge densities. In our pseudopotential approach we have adjusted the pseudopotential form factors by a nonlinear least-squares method described elsewhere [5 to 71, in which all the parameters are simultaneously optimized under a definite criterion of minimizing the root-mean-square deviation. Optical, UPS, and XPS data are used [8 to 151. Table 1 gives the adjusted pseudopotential form factors. An important observation for studying fi is that the charge densities are completely different in going from Si to ZnS through GaAs (Fig. 1). Hence, the charge densities are predominantly dependent on f,. Going along a row starting from the homopolar semiconductors, i.e. studying the sequence of IV-IV, 111-V, to 11-VI compounds, the ionicity increases. This well-known trend also follows from the quantitative density calculations.
Correlation between the Ionicity Characterand the Charge Density in Semiconductors
Fi + Fc = 1 Fi : ionity factor Fc: Covalence factor
Introduction
One of the problems in defining the ionicity of a bond is the difficulty of transforming a qualitative or verbal concept into a quantitativc, mathematical formula. Every definition involves some assumptions, and who can say which assumptions are more valid than others. However, many detailed calculations exist on both crystal and polyatomic molecules which are simple enough to helpfully make use of some model Hamiltonians or other restrictive assumptions and whose reliability depends on semi-empirical parameters.
Phillips’ [ 11 stimulating assumption concerning the relationship of the macroscopic characteristics of a covalent crystal (dielectric constant, structure) and the microscopic ones (band gap, covalent and atomic charge densities) is based essentially on the isotropic model of a covalent semiconductor, whereas Christensen et al. [2] performed self-consistent calculations but used model potentials which were derived from a realistic GaAs potential where additional external potentials were added to the anion and cation sites. In this way the ionicity was gradually changed, and from the theoretical charge transfers a mapping on the Phillips scale was obtained. These models achieve considerable success in unifying distinct properties. However, in general the ionicities found by Christensen tend to be somewhat larger than those of Phillips. Garcia and Cohen [3] achieved the mapping of the ionicity scale by an unambiguous procedure based on the measure of the asymmetry of the first principle valence charge distribution [4]. As for the Christensen scale, their results were somewhat larger than those of the Phillips scale.
In this paper, following the idea of Garcia and Cohen [3] based on the measure of the asymmetry of the total valence charge density, we have established a new empirical formula for the calculation of the ionicity fi of a specific class of materials. The theory yields a formula with three attractive features. Only the pseudopotential form factors are required as input, the computation ofJ itself is trivial and the accuracy of the results reaches that of ab initio calculations. The latter option is attractive since it allows the consideration of hypothetical structures and the simulation of experimental conditions that are difficult to achieve in the laboratory, e.g. very high pressures.
Results
To achieve a scaling relation for ,fi of ANB8-N compound semiconductors, we have used the pseudopotential method for determining suitable charge densities. In our pseudopotential approach we have adjusted the pseudopotential form factors by a nonlinear least-squares method described elsewhere [5 to 71, in which all the parameters are simultaneously optimized under a definite criterion of minimizing the root-mean-square deviation. Optical, UPS, and XPS data are used [8 to 151. Table 1 gives the adjusted pseudopotential form factors. An important observation for studying fi is that the charge densities are completely different in going from Si to ZnS through GaAs (Fig. 1). Hence, the charge densities are predominantly dependent on f,. Going along a row starting from the homopolar semiconductors, i.e. studying the sequence of IV-IV, 111-V, to 11-VI compounds, the ionicity increases. This well-known trend also follows from the quantitative density calculations.
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