1/f Fluctuations due to Second-Order Reactions

Abstract

This paper presents a new 1/f fluctuation model in which a 1/f power spectrum with a wide frequency range is obtained, without artificial assumptions such as a uniform distribution of traps in oxide layers. Second-order reactions produce transient waves inversely proportional to the elapsed time soon after they begin. The transient waves can be broken into square pulses, which are superposed at random. A 1/f power spectrum is then obtained regardless of the initial value and the rate constant of the reaction. The validity of the model is confirmed by numerical simulations, in which 1/f power spectra are observed over a wide frequency range compared with the sampling range.