Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film

Abstract

Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.

In situ synchrotron x-ray studies of strain and composition evolution during metal-organic chemical vapor deposition of InGaN

“…[6][7][8]11 However, the nature, conditions for existence, and origins of composition inhomogeneity in InGaN are still under debate. 1, 10,12,13 Calculations indicating that equilibrium phase separation should occur in unstrained InGaN alloys 14,15 are often cited to explain composition inhomogeneity, although recent theoretical work 16 suggests that single phase ordered structures may be most stable in epitaxially strained films. Experiments indicate an opposite trend-in unstrained nanowires, singlephase InGaN has been grown across the full composition range, 17 while inhomogeneities are typically found in epitaxially strained films.…”

Prediction of ordering and spontaneous rotation of epitaxial habits in substrate-coherent InGaN and GaAsSb

“…1 is the average of the energies of the constituents each at its own, free-floating bulk lattice constant. This "epitaxial-stabilization" effect leads to a variety of fascinating phenomena, such as the appearance of ordered epitaxial phases without a counterpart in the bulk phase diagram, 2,11 as well as to the enhancement in solubility under epitaxial condition, 9 or the change in the equilibrium alloy composition ͑"lattice latching"͒ relative to bulk growth. 6 Such effect exists when the film thickness is below a critical thickness.…”

Scale bridging description of coherent phase equilibria in the presence of surfaces and interfaces

“…An important example is heteroepitaxal growth in thin films 7 , where stresses can arise due to the mismatch between film and substrate. Cluster expansion methods, which are powerful methods for predicting alloy phase diagrams, have also been applied to epitaxial films 8,9 . However, in general such techniques do not take into account the elastic effects, which are induced by surfaces and interfaces, beyond the nano scale for substitutional solid solutions 10,11 .…”