Electrical conductivity tensor of β−Ga2O3 analyzed by van der Pauw measurements: Inherent anisotropy, off-diagonal element, and the impact of grain boundaries

Abstract

The semiconducting oxide β-Gallium Oxide (β-Ga 2 O 3 ) possesses a monoclinic unit cell whose low symmetry generally leads to anisotropic physical properties. For example, its electrical conductivity is generally described by a polar symmetrical tensor of second rank consisting of four independent components. Using van der Pauw measurements in a well-defined square geometry on differently-oriented high-quality bulk samples and the comparison to finite element simulations we precisely determine the ratio of all elements of the β-Ga 2 O 3 3-dimensional electrical conductivity tensor. Despite the structural anisotropy a nearly isotropic conductivity at and above room temperature was found with the principal conductivities deviating from each other by less than 6 % and the off-diagonal element being ≈ 3 % of the diagonal ones. Analysis of the temperature dependence of the anisotropy and mobility of differently doped samples allows us to compare the anisotropy for dominant phonon-scattering to that for dominant ionized-impurity scattering. For both scattering mechanisms, the conductivites along the a and b-direction agree within 2 %. In contrast, the conductivity along c-direction amounts to 0.96× and up to 1.12× that along the b-direction for phonon and ionized impurity scattering, respectively. The determined transport anisotropies are larger than the theoretically predicted effective mass anisotropy, suggesting slightly anisotropic scattering mechanisms. We demonstrate that significantly higher anisotropies can be caused by oriented extended structural defects in the form of low-angle grain boundaries for which we determined energy barriers of multiple 10 meV.

Influence of Polymorphism on the Electronic Structure of Ga2O3

“…The large number of structural phases and the strong anisotropy of β-Ga 2 O 3 present difficulties for theoretical approaches. Nevertheless, previous theoretical work carried out on Ga 2 O 3 polymorphs focuses on various properties, for example, optical response, electron transport, electronic structure, and X-ray absorption spectra, calculated at different levels of computational expense and accuracy. − Experimental studies predominantly consider material growth and optical properties with more extensive information available for the β-phase. ,− Very few studies to date combine theory and experiment, thus leaving some doubt over the accuracy of calculations and uncertainty in the understanding and interpretation of experimental data. ,,− Overall, little information is available for the polymorphs of Ga 2 O 3 and studies considering a set or subset of the polymorphs are extremely rare. However, comparative studies of the polymorphs are invaluable for discerning trends between the different structures and advancing our understanding of the material.…”

Temperature-Dependent Anisotropic Refractive Index in β-Ga2O3: Application in Interferometric Thermometers

“…Even though the behaviour reported in [ 11 ] as a function of temperature could be extrapolated for higher temperatures, it is not straightforward that this would be a good approaching fact since it has already been reported that other properties of β-Ga 2 O 3 do not show the same behaviour at temperatures below room temperature and at higher temperatures. For example, the electrical conductivity shows a much sharper change at temperatures below 300 K than above [ 20 ]. The trend is the same but the rate of variation is quite different.…”

Silane‐Mediated Expansion of Domains in Si‐Doped κ‐Ga2O3 Epitaxy and its Impact on the In‐Plane Electronic Conduction

“…In particular, the data reported in this work quantitatively show an at least (lower estimate due to series resistances, see Figure 7) one order of magnitude higher in‐plane resistivity (i.e., charge carriers crossing domain interfaces) than out‐of‐plane resistivity (i.e., charge carriers flowing along the vertically oriented domains), in line with previously reported qualitative experimental data. [ 30 ] In this framework it is important to stress out that theoretical [ 50,57 ] and experimental [ 29 ] works on κ‐Ga 2 O 3 as well as the comparison among similarly structurally anisotropic oxides (e.g., β‐Ga 2 O 3 [ 58 ] and SnO 2 [ 59 ] ) exclude the possibility that the extent of this highlighted (lower bound) anisotropy could be possibly related to the pure orthorhombic structure of Ga 2 O 3 . The measurements here reported have been performed on nominally undoped samples ($\[{\Phi _{{\rm{Si}}{{\rm{H}}_4}}} = \;0\]$, maximum domain dimension around 20 nm, see Figure 3) deposited on GaN templates; this has been done to avoid the presence of SiO x precipitates (confined in the first 200–300 nm close to the substrate interface in layers deposited with $${\Phi _{{\rm{Si}}{{\rm{H}}_4}}}$$, see Figure 4) that could potentially interfere in the out‐of‐plane R measurements.…”