1/f^γ noise from single-energy-level defects

Several flicker-noise models, such as the island model which ascribes flicker noise to the charge fluctuations of defects, obtain a 1/f^γ spectrum, with γ≃1, from the superimposition of Lorentzian spectra proportional to the relaxation time τ of the process being considered, weighted by the distribution D_τ of τ. Here it is shown, rather, that the Lorentzian power spectral density of the charge fluctuation of single-energy-level defects, characterized by both tunnel and thermally activated emission, is proportional to τ^1+ν, with ν>0. Indeed, this result implies that, in the previous superimposition, the equivalent distribution D_τe∝τ^νD_τ of τ has really to be used instead of D_τ. In relation to the case of D_τ and ν=0, such a change leads to an increase in the weight of the greater τ’s, to a shift of the eventual maxima of D_τ towards the greater values of τ, to a considerable increase in the effective number of defects (with dispersed τ) which are able to generate 1/f^γ noise with γ≃1, and accordingly, to a satisfactory and simple explanation of the ubiquity and existence of flicker noise down to however low frequency f, as is found experimentally. In particular, for thermally activated emission for which we have ν=1, the new model, as compared with the previous ones characterized by ν=0, leads to a much smaller value of the activation energy obtained by means of 1/f^γ noise measurements. A new general method for computing the local frequency exponent γ(f) of the spectrum is also described. The theoretical results obtained from the new approach closely agree with the experimental findings concerning metal-film and thick-film resistors.