We report on optimization of the growth conditions for MgxZn1-xO (x = 0, 0.04, 0.05, 0.12) thin films grown on c-plane Zn-polar ZnO single crystal substrates by using plasma-assisted molecular beam epitaxy (PAMBE). A normal vector to the ZnO substrate surfaces was angled at 0.5 +/- 0.1 degrees off from the [0001] c-axis toward the [1 (1) over bar 00] direction, leading to a stable step-and-terrace structure. A growth temperature (Tg) higher than 800 degrees C led to the ZnO films presenting the first excited state luminescence of A-free excitons in photoluminescence (PL) spectra at 12 K. A Tg higher than 800 degrees C enhanced optical attributes of a MgxZn1-xO film. The longest PL lifetime of fast-decay components reached 3.5 ns in time-resolved PL measurement for an Mg0.12Zn0.88O film grown at 900 degrees C, indicating a concentration of nonradiative recombination centers is substantially eliminated compared to the previously reported PL lifetime of 60 ps for an Mg0.11Zn0.89O film grown by pulsed laser deposition.
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