Experimental and theoretical studies of the thermal equilibrium defect density in undoped a-Si:H are reported. The defect density measured by electron-spin resonance increases with temperature with an activation energy of 0.15–0.2 eV. The equilibration time is activated with an energy of about 1.5 eV, and the shape of the decay follows a stretched exponential, as in doped a-Si:H. The experiments confirm that defect equilibration occurs over a range of temperatures and sample deposition conditions. The relaxation time depends on the growth conditions, and the thermal defects are shown to anneal more slowly than optically induced defects. The temperature dependence of the thermodynamic equilibrium defect density is calculated, based on the weak-bond–dangling-bond conversion model. Four specific defect reactions are analyzed, two of which involve the motion of bonded hydrogen. The defect density is sensitive to the details of the model because of entropy effects. The experimental data agree well with the analysis, but do not conclusively distinguish between the different possible defect reactions because of uncertainties in the parameters of the model. The different annealing rates of thermal and optical defects are accounted for by relating the distributions of hydrogen-bonding energies, the defect-formation energies, and the valence-band-tail states. It is proposed that the time dependence of the relaxation is related to the shape of the valence-band-tail distribution.

• Received 21 February 1989

DOI:https://doi.org/10.1103/PhysRevB.40.6236