Random-walk model for the saturation of1fnoise amplitudes

The equivalence between multistate trapping and the continuous-time random walk (CTRW) is used to model the excess low-frequency current noise in the presence of an applied voltage. Tunaley's CTRW model for $\frac{1}{f}$ noise gives the noise-power spectrum $P\left(f\right)\mathrm{}$ in terms of the waiting-time distribution $\psi \mathrm{}\left(t\right)\mathrm{}$. This distribution can in turn be expressed in terms of a dimensionless trap concentration $G$ and a probability distribution of release rates $p\left(r\right)\mathrm{}$. The noise-power spectrum is given as an explicit nonlinear functional of ($\frac{G}{1+G}$) and of $p\left(r\right)\mathrm{}$. When $G\ll 1$ we recover the usual linear superposition of Lorentzian spectra. An important feature of the model is the saturation of $P\left(f\right)\mathrm{}$ for large $G$. We consider two possibilities for $p\left(r\right)\mathrm{}$. When $p\left(r\right)\mathrm{}$ is of power-law form we obtain interesting analytic results, but we suggest why this situation does not apply to experiment. When $\ln r$ has a distribution with a broad maximum, we have a generalization of the activation-energy model of Dutta and Horn which seems a likely candidate for a variety of experimental situations. In particular we suggest that $\mathrm{fP}\left(f\right)\mathrm{}$ is a slowly varying function of frequency which is not of power-law form.