Evolution in Time of Radiation Defects Induced by Negative Pions and Muons in Crystals with a Diamond Structure

Abstract

Evolution in time of radiation defects induced by negatively-charged pions and muons in crystals with diamond structures is considered. Negative pions and muons are captured by the nucleus and ionize an appropriate host atom, forming a positively-charged radiation defect in a lattice. As a result of an evolution in time, this radiation defect transforms into the acceptor center. An analysis of the full evolution process is considered for the first time. Formation of this acceptor center can be divided into three stages. At the first stage, the radiation defect interacts with a radiation trace and captures electrons. The radiation defect is neutralized completely in Si and Ge for a short time t ≤ 10 −11 s, but in diamond, the complete neutralization time is very large t ≥ 10 −6 s. At the second stage, broken chemical bonds of the radiation defect are restored. In Si and Ge, this process takes place for the neutral radiation defect, but in diamond, it goes for a positively-charged state. The characteristic time of this stage is t < 10 −8 s for Si and Ge and t < 10 −11 s for diamond. After the chemical bonds' restoration, the positively-charged, but chemically-bound radiation defect in diamond is quickly neutralized because of the electron density redistribution. The neutralization process is characterized by the lattice relaxation time. At the third stage, a neutral chemically-bound radiation defect captures an additional electron to saturate all chemical bonds and forms an ionized acceptor center. The existence of a sufficiently big electric dipolar moment leads to the electron capture. Qualitative estimates for the time of this process were obtained for diamond, silicon and germanium crystals. It was sown that this time is the shortest for diamond (≤10 −8 s) and the longest for silicon (≤10 −7 s)

Formation of chemically bound positively charged radiation defect induced by negative muon in diamond crystals

“…Calculations of a radiation transition rate of the neutral defect in the chemically bound state in the "main" crystals with a diamondtype structure (C, Si and Ge) in the assumption of a fast neutralization, were carried out in [21]. However, in accordance with conclusions in [22], the obtained results appear to be correct only for silicon and germanium, while for diamond it is necessary to consider the formation process of a chemically bound positively charged defect.…”

“…To confirm the suggestion on a fast neutralization of a radiation defect, calculations of electron capture by a charged radiation defect, formed by a negative muon in silicon and diamond crystals [21,22], were performed. The calculations in [22] have shown that the kinetics of electron capture by a positively charged radiation defect in silicon and diamond is essentially different.…”

“…(3) and (5). Therefore, contrary to calculations performed for neutral defects in Si and Ge [21], it is necessary to calculate matrix elements only for singlet states. Accordingly, a radiation transition in dipole approximation for triplet-states (with a maximum spin value of the ( μ B) + defect) is forbidden.…”

“…As shown, a neutralization process of a positively charged center ( μ B) + chemically bound to lattice, is determined by the lattice relaxation time. A neutralization process for radiation defects induced by a negative muon in other crystals with a diamond-type structure (silicon and germanium) was considered in [21], where there were obtained estimates of the rate of a neutral center ( μ A) 0 formation (A is a host atom of the lattice) as a result of a radiative transition. Calculation of a thermalization rate of the radiation defect and formation of an acceptor center will be considered in the next work.…”

The Many Facets of Diamond Crystals

“…In addition, this question is also important for the process of ion implantation, which is frequently used to modify diamond properties [60]. Yury Belousov in his contribution reports in-depth theoretical calculations of the time evolution of radiation defects induced by negative pions and muons in diamond, silicon, and germanium [61]. Radiation damage of diamond by these particles is not commonly considered, but since they are the products of the interaction of high-energy protons with a target, the corresponding radiation defects may be important for the relevant applications.…”