Bond-lengths of the atomic nearest-neighbor and next-nearest-neighbor in A1−xBxC1−yDy III–V solid solutions

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Abstract

On the basis of the FDUC model and the hypothesis of the constant covalent radii, the expressions of the atomic nearest-neighbor and the next-nearest-neighbor bond-lengths were derived for A1−xBxC1−yDy III–V quaternary solid solutions. This set of bond-length expressions predicts the averaged bond-lengths and bond angles at any concentration (x, y) for the III–V pseudobinary and quaternary solid solutions, which are only dependent on the lattice parameters and the concentrations of the pure end compounds. When x=0, 1 or y=0, 1, A1−xBxC1−yDy III–V quaternary solid solutions degenerate into the relative pseudobinary solid solutions, in which the nearest-neighbor and the next-nearest-neighbor bond-lengths agree well with the experimental results. Further discussion and comparison with other theoretical models are also given in this paper.

Introduction

III–V compounds are important semiconductor materials with wide application in industry. The properties and function of semiconductor devices are mainly determined by the atomic arrangements and distributions in the semiconductor materials. Therefore, building the atomic structure model to describe the nearest-neighbor and the next-nearest-neighbor bond-lengths is very important, in not only semiconductor materials preparation and applications, but also fundamental research. There are some theoretical studies [1], [2], [3], [4], [5], [6], [7], [8], [9] on the local atomic structural models of III–V pseudobinary solid solutions. However, these theoretical works cannot predict the change of bond-lengths with composition in the quaternary solid solutions. As far as we know, there are no experimental measurements available for the local atomic structures in A1−xBxC1−yDy III–V quaternary solid solutions. Cai and Thorpe (CT) [10] gave an analytical solution for the quaternary A1−xBxC1−yDy solid solutions. Their bond-lengths are not only dependent on the concentration (x, y), but also dependent on two “topological rigidity parameters a** and b**” which themselves depend on the ratio β/α and on the topology of the lattice. Here α and β are the force constants. In this paper, on the basis of the FDUC model [11], a set of more convenient and succinct expressions of the nearest-neighbor and the next-nearest-neighbor bond-lengths of A1−xBxC1−yDy III–V quaternary solid solutions are derived.

Section snippets

A1−xBxC III–V pseudobinary solid solutions

First, we give trivially the FDUC model and the bond-length expressions [11] of A1−xBxC pseudobinary solid solutions. Most of the III–V compounds belong to Zincblende-type structures. The space group is F43m. In the FDUC model, A1−xBxC solid solutions were supposed to consist of five distorted unit cells. That is, all the crystallographic sites on the surfaces of each unit cell are occupied by atom C, but the four crystallographic sites in the interior of each unit cell are occupied by n

A1−xBxC1−yDy III–V quaternary solid solutions

From the concentration point of view, the A1−xBxC1−yDy III–V quaternary solid solutions can be approximately considered as a mixture of A1−xBxC and A1−xBxD solid solutions. Their occupancies are 1 − y and y, respectively. On the other hand, they can be also considered as a mixture of AC1−yDy and BC1−yDy with the occupancies of 1 − x and x, respectively. The experimental studies [12], [13] demonstrated that the nearest-neighbor and the next-nearest-neighbor bond-lengths changes with concentration

Discussion

The expressions of the nearest-neighbor and the next-nearest-neighbor bond-lengths were given in Section 3 for A1−xBxC1−yDy III–V quaternary solid solutions. On the basis of the bond-length expressions of III–V pseudobinary solid solutions, we only made one assumption of constant covalent radii (see Eq. (10)). In fact, this assumption is not necessary. In a more general case, a cross-term 3(aAC−aAD+aBD−aBC)xy/16 or 2(aAC−aAD+aBD−aBC)xy/8 will be, respectively, added to the bond-length

Conclusions

On the basis of the FDUC model and the hypothesis of constant covalent radii, we obtained the nearest-neighbor and the next-nearest-neighbor bond-length expressions in A1−xBxC1−yDy III–V quaternary solid solutions. These succinct bond-length expressions predict the nearest-neighbor and the next-nearest-neighbor bond-lengths as well as the averaged bond angles at arbitrary concentrations (x, y) for all III–V pseudobinary and quaternary solid solutions. By comparison, we found the topological

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