Thin films of ZnO and Mg<sub>x</sub>Zn<sub>1-x</sub>O were epitaxially grown on Zn-polar ZnO substrates by plasma assisted
molecular beam epitaxy. The miscut of c-plane ZnO substrates toward the [1-100] axis direction leads to a flat substrate
surface with straight step edges. The growth mode of epitaxial ZnO films significantly depended on the growth
temperature, and a substrate temperature over 800°C was needed for flat film surfaces with monolayer-height steps.
Photoluminescence (PL) peak originating from the n = 2 state of A-free excitons was observed at 12 K for the ZnO films
grown under stoichiometric and O-rich growth conditions. Mg<sub>x</sub>Zn<sub>1-x</sub>O films were also fabricated under Zn-rich
conditions. The film surface exhibited a step-and-terrace structure. The effective PL lifetime of Mg<sub>0.08</sub>Zn<sub>0.92</sub>O film was as
long as 1.9 ns, which is the highest value ever reported, presumably due to a high purity level of the film.
We have used molecular beam epitaxy (MBE) to deposit gallium (Ga) doped ZnO (ZnO:Ga) films. The as-deposited ZnO:Ga films have worked as ohmic contacts for the p-type GaN layers without any kinds of post annealing process. The as-deposited ZnO:Ga films on <i>a</i>-plane sapphire substrates have resistivities of 2-4×10<sup>-4</sup> Ωcm, and over 80 % transparency in the near-UV and visible wavelength regions. The brightness of InGaN light-emitting diodes (LEDs) with ZnO:Ga <i>p</i>-contacts has doubled compared to LEDs with conventional Ni/Au semi-transparent p-contacts when measuring the brightness from right above the device surfaces. In addition, using MBE, we have grown homoepitaxial polar ZnO films on (000+1)-plane (+c-plane) ZnO substrates, and also grown non-polar ZnO films on (1-100)-plane (<i>m</i>-plane) and (11-20)-plane (<i>a</i>-plane) ZnO substrates. Growth temperatures have not affected nitrogen-doping levels for +c-axis oriented (Zn-polar) nitrogen doped ZnO (ZnO:N) films. The phenomena were quite different from that for (000-1)-axis (-<i>c</i>-axis) oriented (oxygen-polar) growth, where nitrogen concentrations in ZnO decrease with increasing growth temperatures. We have observed <i>c</i>-axis direction growth for both of <i>m</i>-axis and <i>a</i>-axis oriented films. Oxygen-rich growth conditions flatten surfaces for both <i>m</i>-axis and <i>a</i>-axis oriented films, and the surfaces of <i>m</i>-axis oriented ZnO films flatten with increasing growth temperatures. Nitrogen concentrations in <i>m</i>-axis oriented ZnO:N films have been independent on growth temperatures.