The muon spin response to intermittent hyperfine interaction: modelling the high-temperatureelectrical activity of hydrogen in silicon

Abstract

At temperatures above 600 K in silicon, unlike at lower temperatures, the partitioning ofmuonium between its neutral paramagnetic states and its charged or electronicallydiamagnetic states corresponds closely to thermodynamic equilibrium. The individualcharge states are short lived, with many cycles of carrier capture and release occurringwithin the muon lifetime. The resultant intermittent hyperfine interaction depolarizes themuons strongly, with longitudinal and transverse relaxation rates remaining distinct up toabout 700 K but becoming equal at still higher temperatures. Data up to 900 K arepresented and interpreted. The muon spin rotation spectrum in transverse magnetic fields,although collapsed to a single broad line in this charge exchange regime, is shiftedsubstantially from the muon Larmor frequency, the shift being non-linear in field andonly in small part due to electron polarization. A new density matrix treatmentshows how all three observables can be accounted for with a consistent set oftransition rates. These in turn may be interpreted in terms of effective donor andacceptor energy levels appropriate to this high-temperature regime, confirmingnegative-U behaviour and providing the first estimate, for muonium, of this elusive parameter. Attemperatures where passivation complexes are dissociated, these findings provide a guideto, and microscopic models for, the electrical activity of hydrogen.