Thermal and Optical Stretched Exponentials in Defect Kinetics in a-Si:H
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THERMAL AND OPTICAL STRETCHED EXPONENTIALS IN DEFECT KINETICS IN a-Si:H DAVID REDFIELD and RICHARD BUBE Stanford University, Department of Materials Science and Engineering, Stanford, CA 94305
ABSTRACT The dispersive descriptionof defect generation in a-Si:H that leads to stretched-exponential transients is extended by relaxing the assumption that light-inducedprocesses and thermally induced processes have the same dispersive character. This is done by separating the rate equation for the defect density into two parts,one thermal and one optical, each with its own dispersion parameter. The solutions of this new equation - which must be obtained numerically- generally have two distinctparts: there may be a two-part rise or a peak, depending on the relative values of the two stretch parameters. Using thisformulation we have readilysimulated the recently observed peak in relaxation of a previously heavily degradedsolar cell while exposed to a weak light. We find no way to explain other reports in similar two-part experiments that relaxationis faster under weak excitation than without.
INTRODUCTION Since the stretched-exponential (SE) description for light-induced degradation in a-Si:H was proposed 1 - 3 it has been very successful in describing these kinetics for the metastable-defect den7 6 45 sity in homogeneous films, , for the behavior of solar cells, and large photovoltaic modules. Also, this description has been found to include the dependence of solar-cell efficiency on temperature and light intensity, using the same parameter values as for defects. 6 It is generally agreed that properties of such materials should have distributions of values, and the SE represents such a distribution of defect time constants. A physical interpretation of the significance of the SE as a sum of independent simple exponentials was presented at the last MRS symposium on a-Si:H in 1992.8 Nevertheless, there are reasons, both theoretical and experimental, to refine this description, and that is the purpose of this paper. Theoretically, it is desirable to remove the simplifying assumption in Refs. 2,3 that all of the thermal and optical processes share the identical dispersion parameter that represents the distributions. Although we do not know the detailed nature of the conversion events that go into the formation or anneal of the defects, it seems possible that thermally induced processes have different character from those that are induced by carrier recombination (i.e., optically induced). This paper separates thermal and optical processes, and gives each set its own stretch parameter. On the experimental side, there are unusual two-step degradations whose kinetics cannot be explained by any SE alone.9 , 10 In Ref. 10 a peak was reported in the transient response of a solar cell under 1-sun exposure after it had been previously heavily degraded by 50 suns; a peak cannot be generated by a SE. We show here that when the single-dispersion-parameter assumption is relaxed to satisfy theoretical goals, the modified equation can readi
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