Positron Annihilation Spectroscopy (PAS) & Defect Lab

Positron Annihilation Spectroscopy (PAS) is a non-destructive nuclear characterization technique capable of probing sub-nanometer open-volume defects (monovacancies, divacancies, vacancy clusters, and nanopores) at parts-per-million sensitivity. Positrons (\(e^+\)) implanted into a material thermalize within picoseconds and diffuse through the crystal. Because atomic nuclei have positive charges that repel positrons, missing atoms (vacancies) create localized attractive potential wells. Trapped positrons annihilate with surrounding electrons, emitting two collinear 511 keV gamma rays. By measuring the positron lifetime (PALS) and the Doppler broadening of the 511 keV gamma line (DBAR), the size, chemical identity, and concentration of open-volume defects are quantitatively extracted.

Positron Annihilation Lifetime Spectroscopy (PALS) measures the time difference between the birth gamma ray (e.g., 1.274 MeV from \(^{22}\text{Na}\) decay) and the 511 keV annihilation gamma ray using fast scintillation coincidence detectors. Because local electron density is lower inside an open vacancy, the annihilation rate is reduced and lifetime increases (e.g., 218 ps in bulk Si versus 325 ps for divacancies), directly measuring vacancy size. In contrast, Doppler Broadening of Annihilation Radiation (DBAR) measures the Doppler shift \(\Delta E = c p_L / 2\) of the 511 keV gamma line using high-purity germanium (HPGe) detectors, extracting the longitudinal momentum distribution of the annihilating electrons via the \(S\)-parameter (low-momentum valence electrons) and \(W\)-parameter (high-momentum core electrons).

The \(S\)-parameter (shape parameter) is defined as the central area under the 511 keV annihilation peak (\(|\Delta E| < 0.85\text{ keV}\)) divided by the total peak area, reflecting annihilations with low-momentum valence and conduction electrons. Trapping in open-volume vacancies increases the \(S\)-parameter because the overlap with high-momentum core electrons is reduced. The \(W\)-parameter (wing parameter) is the area in the high-energy tails (\(2.2\text{ keV} < |\Delta E| < 4.5\text{ keV}\)), representing annihilations with tightly bound core electrons. Plotting \(S\) versus \(W\) provides a distinct chemical fingerprint identifying whether the vacancy is surrounded by silicon, oxygen, gallium, or impurity atoms.

In insulating porous materials such as SiOCH ultra-low-k dielectrics, implanted positrons can capture an electron to form a hydrogen-like bound state known as positronium (Ps). Parapositronium (\(p\text{-Ps}\), singlet) annihilates rapidly in 125 ps, while orthopositronium (\(o\text{-Ps}\), triplet) lives for 142 ns in vacuum. Inside mesoporous films, \(o\text{-Ps}\) collides with pore walls and undergoes pick-off annihilation with an electron of opposite spin, shortening its lifetime to 1–50 ns. Using the quantum mechanical Tao-Eldrup model, the pick-off annihilation lifetime directly correlates with the mean pore radius \(R\) (typically 0.5 to 5.0 nm), enabling non-destructive evaluation of pore connectivity, matrix collapse, and plasma etch damage.