Donor and acceptor concentrations in degenerate InN

A formalism is presented to determine donor ${\mathrm{(N}}_D)$ and acceptor ${\mathrm{(N}}_A)$ concentrations in wurtzitic InN characterized by degenerate carrier concentration $\mathrm{(n)}$ and mobility (μ). The theory includes scattering not only by charged point defects and impurities, but also by charged threading dislocations, of concentration $N_{\mathrm{dis}}.$ For a 0.45-μm-thick InN layer grown on ${\mathrm{Al}}_2{\mathrm{O}}_3$ by molecular beam epitaxy, having $N_{\mathrm{dis}}{\text{=5×10}}^{10}\hspace{0.17em}{\mathrm{cm}}^{\text{−2}},$ determined by transmission electron microscopy, $\text{n(20\hspace{0.17em}}\mathrm{K}{\text{)=3.5×10}}^{18}\hspace{0.17em}{\mathrm{cm}}^{\text{−3}}$ and $\text{μ(20\hspace{0.17em}}\mathrm{K}\text{)=1055\hspace{0.17em}}{\mathrm{cm}}^2/\mathrm{V} \mathrm{s},$ determined by Hall effect measurements, the fitted values are $N_D{\text{=4.7×10}}^{18}\hspace{0.17em}{\mathrm{cm}}^{\text{−3}}$ and $N_A{\text{=1.2×10}}^{18}\hspace{0.17em}{\mathrm{cm}}^{\text{−3}}.$ The identities of the donors and acceptors are not known, although a comparison of $N_D$ with analytical data, and also with calculations of defect formation energies, suggests that a potential candidate for the dominant donor is H.