The wide-band-gap semiconductors GaN, AlN, and ZnO have properties that make them attractive candidates for fabricating light-emitting diodes, laser diodes, transistors and solar cells. With band gaps in the visible and ultraviolet, these materials and their alloys can emit and absorb in important regions of the electromagnetic spectrum. Despite the promise of these wide-band-gap semiconductors, their electronic conductivity cannot be completely controlled. In this work, we investigate the lack of conductivity control in these materials using first-principles calculations.

We first focus on sources of unintentional n-type conductivity. The sources of such conductivity have long remained unknown, and high concentrations of donors make it more difficult to achieve full control of the conductivity of wide-band-gap semiconductors. We have found that silicon, a common impurity in ZnO, acts as a shallow donor and likely contributes to background n-type conductivity.

Another shortcoming of these materials is that they are difficult, and sometimes impossible, to dope p type. This is a major barrier, since optoelectronic devices require both p-type and n-type material. Group-V impurities, which substitute on the anion site, are commonly thought to be attractive p-type dopants, especially for ZnO. We find these acceptors lead to highly localized, atomic-like states, making them ineffective dopants. Nitrogen, often touted as a promising acceptor in ZnO, is instead found to be an exceedingly deep acceptor that cannot lead to p-type conductivity. Carbon, a common impurity in the nitride semiconductors, exhibits similar behavior. We calculate characteristic optical signals for these acceptors, allowing for experimental verification of our predictions.

Finally, we investigate how defect-trapped holes can limit the effectiveness of cation-site acceptors. We find that Mg, the only p-type dopant for GaN, features a localized hole despite being an effective acceptor. In AlN, Mg is also highly localized, hampering hole conductivity in this material. In ZnO, Group-I acceptors such as Li, also trap holes, making them inefficient dopants, and limiting the prospects for achieving p-type ZnO.

Overall, we find that our results can explain the difficulties in improving the doping efficiency of Mg-doped GaN, and why alternative dopants are not effective. Our results indicate that substitutional acceptors in ZnO are deep defects, and demonstrate why p-type doping of ZnO is currently impossible.