Role of carbon and hydrogen in limiting n -type doping of monoclinic ( Al x Ga 1 – x ) 2 O 3
In this study, we use hybrid density functional calculations to assess n -type doping in monoclinic ( Al x Ga 1 – x ) 2 O 3 alloys. We focus on silicon, the most promising donor dopant, and study the structural properties, formation energies, and charge-state transition levels of its various configurations. We also explore the impact of carbon and hydrogen, which are common impurities in metal-organic chemical vapor deposition (MOCVD). In Ga 2 O 3 , Si Ga is an effective shallow donor, but in Al 2 O 3 Si Al acts as a DX center with a ( + / – ) transition level in the band gap. Interstitial hydrogen acts as a shallow donor in Ga 2 O 3 but behaves as a compensating acceptor in n -type Al 2 O 3 . Interpolation indicates that Si is an effective donor in ( Al x Ga 1 – x ) 2 O 3 up to 70% Al, but it can be compensated by hydrogen already at 1% Al. We also assess the diffusivity of hydrogen and study complex formation. Si cation – H complexes have relatively low binding energies. Substitutional carbon on a cation site acts as a shallow donor in Ga 2 O 3 , but can be stable in a negative charge state in ( Al x Ga 1 – x ) 2 O 3 when x > 5 % . Substitutional carbon on an oxygen site ( C O ) always acts as an acceptor in n -type ( Al x Ga 1 – x ) 2 O 3 , but will incorporate only under relatively oxygen-poor conditions. C O – H complexes can actually incorporate more easily, explaining observations of carbon-related compensation in Ga 2 O 3 grown by MOCVD. We also investigate C cation – H complexes, finding they have high binding energies and act as compensating acceptors when x > 56 % ; otherwise the hydrogen just passivates the unintentional carbon donors. C-H complex formation explains why MOCVD-grown Ga 2 O 3 can exhibit record-low free-carrier concentrations, in spite of the unavoidable incorporation of carbon. Our study highlights that, while Si is in principle a suitable shallow donor in ( Al x Ga 1 – x ) 2 O 3 alloys up to high Al compositions, control of unintentional impurities is essential to avoid compensation.