Samples of synthetic fused silica have been implanted at room temperature with silicon ions of energy 1.5 MeV. Fluences ranged from 1011 to 1013 cm−2. Samples were probed using variable‐energy positron annihilation spectroscopy. The Doppler‐broadening S parameter corresponding to the implanted region decreased with increasing fluence and saturated at a fluence of 1013 cm−2. It is shown that the decrease in the S parameter is due to the suppression of positronium (Ps) which is formed in the preimplanted material, due to the competing process of implantation‐induced trapping of positrons. In order to satisfactorily model the positron data it was necessary to account for positron trapping due to defects created by both electronic and nuclear stopping of the implanted ions. Annealing of the 1013 cm−2 sample resulted in measurable recovery of the preimplanted S parameter spectrum at 350 °C and complete recovery to the preimplanted condition at 600 °C. Volume compaction was also observed afterimplantation. Upon annealing, the compaction was seen to decrease by 75%.
We have studied optical changes induced by ArF (6.4 eV/193 nm) excimer laser light illumination of high purity SiO2 implanted with Si2+ (5 MeV) at a fluence of 1015 ions/cm2. Optical absorption was measured from 3 eV (400 nm) to 8 eV (155 nm) and showed evidence of several well-defined absorption bands. A correlation in the bleaching behavior appears to exist between the so-called D band (located at 7.15 eV) and the well-known B2α band which is attributed to oxygen vacancies. Changes in the refractive index as a function of ArF illumination were measured and found to be in good quantitative agreement with a Kramers-Kronig analysis of the optical absorption data.
Let φ be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number such that if the ratio of the number of clauses over the number of variables of φ strictly exceeds κ, then φ is almost certainly unsatisfiable. By a well known and more or less straightforward argument, it can be shown that κ 3.