Determination of Mg composition in $MgxZn1−xO$ alloy: Validity of Vegard’s law Available to Purchase

Vegard’s law and inductively coupled plasma atomic emission spectrometry were employed to determine the Mg composition in $MgxZn1−xO$ layers deposited on 6H–SiC substrates. With the increase of Mg composition in $MgxZn1−xO$ layers, the $c$-axis length decreased by $5.2048−0.072x$⁠, while the $a$-axis length increased to $3.2491+0.047x$⁠. The lattice constants estimated by Vegard’s law and a theoretical model exhibited an uncertainty of $∼3%$ that has been attributed to the $∼2%$ lattice misfit in the $MgO∕ZnO$ materials system. Localized exciton peaks of $MgxZn1−xO$ alloy in photoluminescence (PL) measurements disappeared completely, while the neutral donor-acceptor pair and 1-longitudinal optical-phonon energies decreased rapidly with the increase of Mg composition. These PL data do not comply with Vegard’s law. The asymmetric behavior in the $MgxZn1−xO$ alloy is the subject of locally disordered Mg potential fluctuations and an artifact of the $cMgO$ and $aMgO$ lengths calculated theoretically.