Atomic nature of the Si-B4 paramagnetic center assessed by multifrequency electron spin resonance

Abstract

An electron spin resonance (ESR) study has been carried out in the range 4.2--120 K on the trigonal Si-B4 center in annealed $(200--350\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C})$ neutron-irradiated $p$-type Si. Detailed observations reveal a rich $^{29}\text{S}\text{i}$ hyperfine (hf) structure, indicating interaction of the unpaired electron with up to five shells of equivalent Si sites. Optimized consistent computer-assisted fitting of spectra observed at three ESR frequencies point toward a set of 1-2-2-3-3 equivalent Si sites for the five observed shells in decreasing hf splitting, respectively, with the 1-3-3-3-3 set, conforming with the trigonal symmetry of the defect, giving satisfactory results as well. The strongest interaction of the unpaired electron is with one Si atom. Full angular mapping of all five hf doublets enabled inference of the hybrid coefficients, i.e., localization of the unpaired electron and $s\text{\ensuremath{-}}p$ ratio over the different Si sites. Stepping from previous theoretical work, two tri-interstitial models are discussed from where, although lack of theoretical results on the molecular wave-function coefficients prevents definite assignment, the tri-interstitial ${\text{I}}_{3}\text{-I}$ model is advanced as a plausible candidate. An uncommon drastic temperature dependence is observed in which all resolved $^{29}\text{S}\text{i}$ hf doublet splittings collectively and evenly narrow with increasing temperature toward 1/4 of the low-temperature values along a bounded exponential (Boltzmann factor) decay, with activation energy ${E}_{\text{a}}\ensuremath{\approx}0.0041\text{ }\text{eV}$. There is an attendant upward shift in ${g}_{\ensuremath{\parallel}}$. An effect due to thermal dilatation as possible origin is excluded. Instead, it is ascribed to even redistribution (delocalization) of the low-temperature unpaired hybrid by 75% over next-neighboring sites, possibly within a four-defect cluster arrangement.