Determination of Mg composition in MgₓZn₁ˍₓO alloy: Validity of Vegard’s law

Vegard’s law and inductively coupled plasma atomic emission spectrometry were employed to determine the Mg composition in MgₓZn₁ˍₓO layers deposited on 6H–SiC substrates. With the increase of Mg composition in MgₓZn₁ˍₓO 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 MgₓZn₁ˍₓO 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 MgₓZn₁ˍₓO alloy is the subject of locally disordered Mg potential fluctuations and an artifact of the cMgO and aMgO lengths calculated theoretically.This work was supported in part by the Special Postdoctoral Research Fellowship Program, Photodynamics Research Center, The Institute of Physical and Chemical Research RIKEN, Japan