Origin of the n-type conductivity of InN: The role of positively charged dislocations

As-grown InN is known to exhibit high unintentional $n$ -type conductivity. Hall measurements from a range of high-quality single-crystalline epitaxially grown InN films reveal a dramatic reduction in the electron density (from low ${10}^{19}$ to low ${10}^{17}{\mathrm{cm}}^{-3}$ ) with increasing film thickness (from $50\text{to}12000\mathrm{nm}$ ). The combination of background donors from impurities and the extreme electron accumulation at InN surfaces is shown to be insufficient to reproduce the measured film thickness dependence of the free-electron density. When positively charged nitrogen vacancies $\left(V_{\mathrm{N}}^{+}\right)$ along dislocations are also included, agreement is obtained between the calculated and experimental thickness dependence of the free-electron concentration.