Example: Semiconductor alloys

The following example is published by J. C. Mikkelsen Jr. &  J. B. Boyce in Physical Review Letters, 49, 1412 (1982) and shows the effect of alloying in the microstructure of InGaAs semiconductors.

The binary semiconductors InAs and GaAs crystallize in the cubic (zincblende) structure shown in Fig. 1. Their ternary compounds of Ga_1-xIn_xAs crystallize also in the zincblende structure. Ideally, the cubic (fcc) sublattice of As anions is displaced by (a/4,a/4, a/4) relative to the cubic cation sublattice. If the Ga and In atoms can be randomly distributed in the cation sublattice, where a is the lattice constant of the cubic unit cell.  the alloy is called random in contrast to the ordered alloys where the In and Ga atoms occupy specific positions in the cation sublattice. For example, in the case of Ga_0.5In_0.5As pure Ga and pure In atomic planes alternate along the (111) axis, i.e. the atomic plane sequence along the (111) axis is: As-Ga-As-In in the case of the ordered alloy while it is As - (Ga,In) - As - (Ga,In) in the case of a random alloy.

According to Vegard's law the cell parameter a for the ternary alloy Ga_1-xIn_xAs is given by the Eq. 1:

Figure 1

(
Equation 1)

where a_InAs=2.623Å and a_GaAs=2.448Å are the unit cell parameters of the parent binary compounds. The unit cell constant of the ternary alloy depends on the composition and takes values between the lattice constants of the binary compounds.  The law of Vegard is verified experimentally by X-ray diffraction (XRD) measurements. The As-cation distance should equal (Ö3/4)a and it should obey Vegard's law. However, EXAFS measurements have demonstrated that this is not true. Instead, as shown in Fig. 2, the Ga-As and In-As distances (blue lines) are not equal and although they increase with the In content, their increase is smaller than-predicted by Vegard's law. Thus, at an atomic scale, the As-cation bondlengths are determined mainly by molecular orbital energies (chemical character) and not by the periodicity of the crystal. However, macroscopically the average crystal lattice and the symmetry are conserved since locally the As-Ga and As-In bonds are shorter and longer, respectively, than the average value predicted by Vegard's law. This example demonstrates that EXAFS provides information that can not be obtained by diffraction measurements since it probes to local microstructure around a specific absorbing atom.

Figure 2


Reference: http://users.auth.gr/~katsiki/ALLOYING.htm