Amplitude Dependence of Metastable Defect Formation
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AMPLITUDE DEPENDENCE OF METASTABLE DEFECT FORMATION W. B. JACKSON, C. NEBEL and R. A. STREET Xerox Palo Alto Research Center, Palo Alto, CA 94304 ABSTRACT The kinetics of small changes from thermal equilibrium are measured and simulated for thermally induced metastable changes. We find that only a distribution of rate constants is consistent with the data, and therefore we can eliminate certain types of microscopic models for metastability which depend on a single variable such as the carrier density. INTRODUCTION The microscopic origin of metastability is an important unresolved problem in the study of amorphous materials. An issue of particular recent concern is the origin of the nonexponential kinetics of metastable defect generation and annealing. One proposed cause of nonexponential behavior is the time dependence of factors affecting the rates of creation and annealing. An often considered source of time dependence is the dependence of the generation on carrier density which in turn depends on the time dependent defect density.[1] A second source of nonexponential behavior considered particularly for disorder systems is a distribution of reaction rate constants.[2-4] The total system response is a summation of all the individual rate constants and is therefore not exponential. Unfortunately, for fixed distributions of rate constants, initial conditions, and timetemperature scans, the kinetics of a distribution of rate constants can be written in terms of time varying quantities. Therefore, it has been difficult to distinguish between the two sources of nonexponential behavior in metastability. In this work, we examine thermal quenching metastability in doped materials for small changes from equilibrium both experimentally and using simulations. We find that a distribution of rate constants appears to be necessary to explain these results. We can therefore eliminate several classes of models for metastability. KINETICS OF SMALL CHANGES FROM EQUILIBRIUM Consideration of small changes from equilibrium greatly simplify the analysis of defect kinetics. For example, in the case of a model which depends on the concentration of a single species such as the dopant or carrier concentration, the change in concentrations can quite generally be written as dN(t)fN(t)) (1) dt where fis some general function including the effects of defects on carrier density etc. For small changes about the equilibrium values Neq defined by f(Neq)=O, we can expand fusing Taylor's theorem yielding dA(t) dt
af A(t)=-RA(t) aA
(2)
where A(t)=N(t)-Neq. The time dependence of such a system should therefore be exponential. On the other hand, if f(.) depends explicitly on the time and not through the time dependence of the defect density, then for small changes the time dependence will not be exponential. Alternatively, if there a number of parallel
Mat. Res. Soc. Symp. Proc. Vol. 297. '1993 Materials Research Society
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processes enumerated by a variable such as the barrier energy, E,the time decay of the system is determined by[2] (3) dA(
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