Ordering in III/V Alloys
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ORDERING IN IIIIV ALLOYS G.B. Stringfellow College of Engineering, University of Utah, Salt Lake City, Utah 84112
ABSTRACT Simple calculations using the delta-lattice-parameter (DLP) model indicate that the enthalpy of mixing is invariably larger than or equal to zero for II/V alloys, and increases with increasing difference in lattice constant for the constituent binary compounds. In terms of the regular solution model this suggests the occurrence of miscibility gaps. Solid phase immiscibility has indeed been observed in a number of systems. Nevertheless, such alloys can be grown by OMVPE, including the highly metastable alloys GaPSb and InPSb. Initially surprising was the occurrence of ordered structures in these same alloys. The regular solution model apparently specifically excludes immiscibility and ordering in the same system. However, when the positive enthalpy of mixing is due to strain energy effects, as in III/V alloys, Hume-Rothery recognized very early that such phenomena should be anticipated. This was later confirmed by detailed first principles calculations. In fact, the tendency for ordering is anticipated to increase as the difference in tetrahedral radii of the elements sharing a common sublattice increases. Thus, it is somewhat surprising that ordering was first observed in the AlGaAs system where Al and Ga have nearly equal sizes. Ordered structures have now been observed in several III/V alloy systems including the ternary systems GaAsSb and GaInP and the quaternaries GaInAsP, GaInAsSb, and AlGaInP. In this paper, ordering in other alloy systems such as GaPSb and InAsSb will be described. Surprisingly, no strong correlation between atomic size difference and the degree of ordering has been observed. Another unexpected observation is that the preferred ordered structure for most ternaries involves ordering along the f Il1 }directions. Both first principles total energy and simple strain energy calculations indicate that such ordered structures are only slightly more stable than the disordered solid solution. Other ordered structures, including Llo, where ordering occurs along the (100) directions, are considerably more stable. Both phenomena must be explained in terms of the surface kinetic processes occurring during epitaxial growth. Such an explanation is supported by the importance of kinetic parameters such as growth rate, temperature, and substrate orientation in determining both the degree of order and the specific ordered structures observed. THERMODYNAMIC BACKGROUND The regular solution model is a semi-quantitative model for the calculation of the free energy of mixing of multicomponent systems. The entropy of mixing is considered to be ideal and the enthalpy of mixing is calculated assuming interactions only between nearest neighbor atom pairs with the atoms residing on a lattice with coordination number Z. For a solution consisting of only A and C atoms, the nearest-neighbor bond energies are designated HAC, HAA, and HCC. The bond energies are commonly thought of as being due to "chem
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