Mechanism leading to semi-insulating property of carbon-doped GaN: Analysis of donor acceptor ratio and method for its determination

Carbon impurities in GaN form both acceptors and donors. Donor-to-acceptor ratios (DARs) determine the semi-insulating behavior of carbon-doped GaN (GaN:C) layers and are still debated. Two models are discussed; both can theoretically achieve semi-insulating behavior: the dominant acceptor model (DAM, $DAR<1$⁠) and the auto-compensation model (ACM, $DAR=1$⁠). We perform a capacitance–voltage analysis on metal/GaN:C/nGaN (n-doped GaN) structures, exhibiting Fermi-level pinning in GaN:C, 0.7 eV above the valence band maximum. This observation coupled with further interpretation clearly supports the DAM and contradicts the ACM. Furthermore, we reveal a finite depletion width of a transition region in GaN:C next to nGaN, where carbon acceptors drop below the Fermi level becoming fully ionized. Calculation of the potential drop in this region exhibits DAR values of 0.5–0.67 for GaN:C with total carbon concentrations of $1018$ cm$−3$ and $1019$ cm$−3$⁠. Based on those results, we re-evaluate formerly published density functional theory (DFT)-calculated formation energies of point defects in GaN. Unexpectedly, growth in thermodynamic equilibrium with the bulk carbon phase contradicts our experimental analysis. Therefore, we propose the consideration of extreme carbon-rich growth conditions. As bulk carbon and carbon cluster formation are not reported to date, we consider a metastable GaN:C solid solution with the competing carbon bulk phase being kinetically hindered. DFT and experimental results agree, confirming the role of carbon at nitrogen sites as dominant acceptors. Under N-rich conditions, carbon at gallium sites is the dominant donor, whereas additional nitrogen vacancies are generated under Ga-rich conditions.