Origin of donor compensation in monoclinic (Al$_x$Ga$_{1{\rm -}x})_2$O$_3$ alloys

Abstract

(Al$_x$Ga$_{1{\rm -}x})_2$O$_3$ alloys are frequently used in heterostructures with monoclinic Ga$_2$O$_3$, resulting in a large conduction-band offset, which leads to charge carrier confinement, a property that is desirable for device applications. However, when (Al$_x$Ga$_{1{\rm -}x})_2$O$_3$ alloys are $n$-type doped with Si, the most efficient shallow donor, there is a significant reduction in the number of charge carriers when the Al content of the alloys is greater than 26%, rendering intentional doping ineffective. Here we show that this compensation is due to cation vacancies forming in response to donor doping. We use hybrid density functional theory to study cation vacancies in monoclinic AlGaO$_3$ and monoclinic Al$_2$O$_3$. We find that vacancies prefer to occupy split-vacancy configurations, similar to vacancies in Ga$_2$O$_3$. Furthermore, by comparing the formation energy of the vacancy with the formation energy of Si donors, we show that vacancies are lower in energy than Si donors, independent of the Fermi level, as soon as the alloys contain more than 16% Al. Therefore, cation vacancies will compensate the donor doping, explaining experimental observations.

Figures (3)

• Figure 1: All possible vacancy positions in monoclinic Ga$_2$O$_3$. The vacancy positions are represented by the white spheres and labeled according the coordination of the atom that was removed with I representing a tetrahedrally-coordinated cation and II representing an octahedrally-coordinated cation. The split positions are outlined by dashed boxes and the bare positions by dashed circles. The ia configuration (light violet box) involves both a tetrahedral (I) and octahedral (II) site, while the ib (bright green box) and ic (red box) involve two tetrahedrally-coordinated cations.
• Figure 2: The formation energies for cation vacancy and Si$_\text{I}$ defects in both O-poor [(a)-(c)] and O-rich conditions [(d)-(f)] for monoclinic Al$_2$O$_3$ [(a), (f)], AlGaO$_3$ [(b), (e)], and Ga$_2$O$_3$ [(c), (f)].
• Figure 3: The Fermi level where the formation energy of the lowest energy cation vacancy intersects with the formation energy for the Si donor as a function of alloy composition. The solid lines are linear interpolations. The orange circles are the levels for O-poor conditions and the green squares for O-rich conditions. The black dashed line is the CBM as function of alloy concentration based on the previously determined bowing parameter Peelaers2018.