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InAs nanowires with Al$_x$In$_{1-x}$P or Al$x$In$_{1-x}$As shells were grownon GaAs substrates by the Au-assisted vapour-liquid-solid (VLS) method in a gassource molecular beam epitaxy (GS-MBE) system. Core diameters and shellthicknesses were measured by transmission electron microscopy (TEM). Thesemeasurements were then related to selected area diffraction (SAD) patterns toverify either interface coherency or relaxation through misfit dislocations. Atheoretical strain model is presented to determine the critical shell thicknessfor given core diameters. Zincblende stiffness parameters are transformed totheir wurtzite counterparts via a well known tensor transformation. An energycriterion is then given to determine the shell thickness at which coherency islost and dislocations become favourable.

Critical shell thickness for InAs-Al$_x$In$_{1-x}$As(P) core-shell nanowires