Quantum Monte Carlo study of Doppler broadening of positron annihilation radiation in semiconductors and insulators

Positron annihilation in solid-state matter can be utilized to detect and identify open-volume defects. The momentum distribution of the annihilation radiation is an important observable in positron-based measurements and can reveal information on the chemical surroundings of the defect sites. In this paper, we present a variational quantum Monte Carlo method for simulation of the momentum densities of annihilating electron-positron pairs in semiconductors and insulators. We study finite-size effects, effects of lattice vibrations, and different levels of trial wave functions. Small simulation cells and simple wave function forms are found to be sufficient for accurate calculations in the simulation of pristine lattices, enabling cheap accumulation of results. We compare calculated predictions of the Doppler broadening of the 511-keV $2\gamma$ annihilation line in aluminium nitride and silicon against experimental data measured from reference samples. Our results achieve better agreement with experiments in these materials than conventional state-of-the-art methods and prove that direct modeling of the electron-positron correlations is important for a supporting theory of positron annihilation spectroscopies.

Figure 1

Unconvoluted Doppler spectra of C (left) and AlN (right) in the [100] and $\mathrm{[}\overline{1}2\overline{1}0]$ directions, respectively. In both materials, the APMD is computed with two different simulation cell sizes (blue, 16-atom cell; violet, 54-atom cell in C and 72-atom cell in AlN) with a SJ wave function and with a SJB wave function in the smaller simulation cell (light blue).

Figure 2

Discrepancy of the calculated Doppler spectra of Si with vibrational corrections in $T=0\mathrm{K}$ (blue) and $\mathrm{T}=300\mathrm{K}$ (violet) against the results from static lattice, calculated as ${\rho }_{\text{vib}}\left(p_L\right)-{\rho }_{\text{stat}}\left(p_L\right)$, where ${\rho }_{\text{stat}}\left(p_L\right)$ and ${\rho }_{\text{vib}}\left(p_L\right)$ are the Doppler spectra of the static and vibrating lattices, respectively. Results along the [100] (left), [110] (middle), and [111] (right) lattice directions are shown.

Figure 3

Low- and high-momentum parts (left and right panels, respectively) of the Si Doppler spectrum along the [110] direction. The data include the experimental benchmark result [44] (black), our VMC data [blue, and violet when the state-independent (SI) core spectrum is used], and, for comparison, DFT-based results calculated by the state-dependent (SD, red) and state-independent (green) models. The core spectrum obtained from these models and used also in QMC is shown separately. In the left panels, the SD core spectrum was added to the QMC valence spectrum; in the right panels, QMC with both core spectra is shown.

Figure 4

Low- and high-momentum parts (left and right panels, respectively) of the AlN Doppler spectrum along the $\mathrm{[}\overline{1}2\overline{1}0]$ direction. The data include the experimental benchmark result [46] (black), our VMC data [blue, and violet when the state-independent (SI) core spectrum is used], and for comparison the DFT-based results calculated by the state-dependent (SD, red) and state-independent (green) models. The core spectrum obtained from these models and used also in QMC is shown separately. In the left panels, the state-dependent core spectrum was added to the QMC valence spectrum; in the right panels, QMC with both core spectra is shown.