Identifying vacancy complexes in compound semiconductors with positron annihilation spectroscopy: A case study of InN

We present a comprehensive study of vacancy and vacancy-impurity complexes in InN combining positron annihilation spectroscopy and ab initio calculations. Positron densities and annihilation characteristics of common vacancy-type defects are calculated using density functional theory, and the feasibility of their experimental detection and distinction with positron annihilation methods is discussed. The computational results are compared to positron lifetime and conventional as well as coincidence Doppler broadening measurements of several representative InN samples. The particular dominant vacancy-type positron traps are identified and their characteristic positron lifetimes, Doppler ratio curves, and line-shape parameters determined. We find that indium vacancies ($V_{\text{In}}$) and their complexes with nitrogen vacancies ($V_{\text{N}}$) or impurities act as efficient positron traps, inducing distinct changes in the annihilation parameters compared to the InN lattice. Neutral or positively charged $V_{\text{N}}$ and pure $V_{\text{N}}$ complexes, on the other hand, do not trap positrons. The predominantly introduced positron trap in irradiated InN is identified as the isolated $V_{\text{In}}$, while in as-grown InN layers $V_{\text{In}}$ do not occur isolated but complexed with one or more $V_{\text{N}}$. The number of $V_{\text{N}}$ per $V_{\text{In}}$ in these complexes is found to increase from the near-surface region toward the layer-substrate interface.

Figure 1

Isosurface plot of the calculated positron density (transparent sphere) in the relaxed lattice structure of the (a) InN lattice and (b) 4$V_{\text{N}}$, (c) $V_{\text{In}}$, and (d) 2$V_{\text{In}}$ defects. Light gray (silver) and dark gray (green) balls indicate N and In ions, respectively.

Figure 2

Calculated momentum density of annihilating $e$-$p$ pairs in the delocalized state of the InN lattice and trapped at the $V_{\text{In}}$, respectively. Trends in the spectra are indicated with respect to the InN lattice.

Figure 3

Ratio curves of the calculated momentum densities of annihilating $e$-$p$ pairs in selected vacancy complexes in InN. All spectra are convoluted with a Gaussian of 0.53 a.u. FWHM (except $V_{\text{In}}^{0.66\text{a.u.}}$, $\text{FWHM}=0.66$ a.u.) and divided by the momentum density spectrum of the InN lattice.

Figure 4

$SW$ plot of conventional line-shape parameters $S$ and $W$ for the calculated momentum distributions of annihilating $e$-$p$ pairs trapped at different vacancy-type defects in InN.

Figure 5

As-measured (open symbols) and extrapolated (closed symbols) line-shape parameters from conventional Doppler broadening measurements of different samples (see text for as-measured, and Table for extrapolated values). Extrapolated points have been calculated using trapping fractions determined in positron lifetime measurements. For samples I and II, line-shape parameters for the near-surface (“layer”) and near-interface region are given separately.

Figure 6

Experimental coincidence Doppler spectra of the investigated samples in the layer (a), (b) and interface (c) region. The data has been divided by a suitable reference spectrum for the InN lattice. Computational ratio curves are shown for comparison.