I. Introduction
Gallium oxide , one of the ultra-wide bandgap semiconductors, has attracted considerable attention because of its potential application as a power electronic device. has several polymorphs such as . Among them, is the most stable phase at ambient temperature and pressure and has a bandgap of 4.5 eV [1]. Thus, single-crystalline substrates are available for device applications. There are many reports on Schottky barrier diodes (SBDs) based on thin films grown by homoepitaxial technique [2] [3]. However, the substrate is rather expensive and has low thermal conductivity, which is an obstacle to the power device applications. On the other hand, is one of the metastable phases with a bandgap of 5.6 eV [4]. A thin film of can be heteroepitaxially grown on a sapphire substrate, which is more economical and possesses higher thermal conductivity than substrate, by gas phase synthesis methods such as mist chemical vapor deposition (mist-CVD) [5], halide vapor phase epitaxy (HVPE) [6], and molecular beam epitaxy (MBE) [7]. Among these growth methods, mist-CVD is a low-cost, energy-saving and safe process because of the use of aqueous solution as a precursor and the reaction under atmospheric pressure to form thin films. This suggests that an film grown on a sapphire substrate via mist-CVD process is a promising material for power device applications. Indeed, there are some reports on SBDs based on Sn-doped [8] [9]. Oda et al. demonstrated vertical SBDs with a low on-resistance of 0.1 , which is close to the lowest value obtained for SiC that is also one of the wide bandgap semiconductors [8]. As for the n-type doping of , tetravalent elements such as Si and Ge in addition to Sn are possible. However, SBDs based on Ge-doped have been less reported owing to the lack of effective way to dope with Ge [10].